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Credit: A. Ijjas
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In footnotes or endnotes please cite AIP interviews like this:
Interview of Paul Steinhardt by David Zierler on June 4, June 18, June 30, and July 8, 2020,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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In this interview, Paul Steinhardt, the Albert Einstein Professor in Science at Princeton, recounts his childhood in Miami and his undergraduate experience at Caltech, where he became interested in theoretical physics and where Feynman played a key influence on his development. He surveys where physics is stuck and compares similar challenges that both string theory and inflation are facing, and he explains his reasons for going to Harvard for his graduate work. Steinhardt describes being a student of Sidney Coleman’s and his focus on gauge theories. He discusses his postgraduate work at IBM Research and as a Junior Fellow at Harvard, and he explains the opportunity that led to his faculty appointment at the University of Pennsylvania. Steinhardt describes his increasing interest in cosmology and the influence of Alan Guth. He explains his dual interest in condensed matter physics and where he saw commonality with his cosmological research. Steinhardt conveys the importance of his collaboration with Dov Levine and he explains why he thinks the notion of a multiverse is nonscientific but not necessarily impossible. He explains his focus on quasicrystals for a time at the exclusion of cosmology, and the circumstances leading to his decision to join the faculty at Princeton which was a central point for research on the cosmic wave background. Steinhardt discusses his work on dark energy and the cosmological constant and his related interactions with Michael Turner. He describes his efforts to link the mystery of the Big Bang with the physics that can be understood after the beginning of the universe, and why the notion of the universe having a clear beginning is problematic. Steinhardt describes his frustration with string theorists who are working on abstract rather than existential research problems, and he surveys the technological advances that could make some of the intractable puzzles in cosmology testable, including the bouncing model of cosmology. He relates an epic story of mineral mining in pursuit of earthly quasicrystals, and at the end of the interview, Steinhardt describes his search for good puzzles as the common thread that connects all of his research.
This is David Zierler, oral historian for the American Institute of Physics. It's June 4th, 2020. It is my great pleasure to be here today with Professor Paul Steinhardt. Paul, thank you so much for being with me.
Thanks, David. Thanks for inviting me.
Terrific. OK. So, to start, please tell me your title and institutional affiliation.
I am the Albert Einstein Professor in Science at Princeton University. I am on the faculty of the Department of Physics, and also of the Department of Astrophysical Sciences.
When were you named to the Einstein chair?
In 2001. I succeeded my colleague Jim Peebles.
So let's go right back to the beginning. Tell me a little bit about your family background, your parents.
My parents were both from New York City, one from the Bronx, one from Brooklyn. They were both lawyers. My father, Charles Steinhardt, was drafted in World War II and fought in the Asian theater. He was drafted just before he finished his law degree, came back, finished his law degree.
My mother, Helen, and my father originally met in law school. They reconnected once he got back from the war, and got married. They set up a law practice together in Manhattan for a while, and then my father decided to join the Air Force and become a Judge Advocate in the Air Force. I was born shortly after that decision in Washington, D.C.
Oh, so your family was in Washington, D.C. by the time you were born?
Yes, briefly. Yes. I think he was there to get briefed on his new position in the Air Force.
What service did your father serve in during the war?
He was in Burma and China during World War II, in the Army.
OK. All right. So your parents were both lawyers and they practiced together for a time?
They had practiced together for a time, and then, when my father went into the Air Force, my mother decided to give up practice for a while and raise four kids, including me.
So, two parents as lawyers, did you have to fight against the tide of becoming a lawyer yourself?
Not at all. In fact, my father was the main inspiration for my going into science, inadvertently. He was a great storyteller, and he used to tell me wonderful bedtime stories. And I guess he ran out of material at some point and began to tell me stories about scientists making discoveries.
And they were always very dramatic stories. They were especially dramatic when it came to the moment of discovery, discovering something new. And that notion just somehow resonated with me -- the idea of discovering something that no one ever knew before, and that idea that you can be the only person on the planet to know that, whatever that was, I don't know, just resonated with me. It's what drew me to science. So, besides the usual juvenile things one's interested in doing, like becoming a cowboy or something like that, science was definitely it for me from the very beginning, some kind of science.
And this attraction towards discovering something new clearly resonates in terms of the fields of research you've been involved with for sure.
Yes. So I would say that, as you probably experience from talking to various scientists, some scientists are driven by a particular set of questions.
And others are more like me. You're looking for a good puzzle, that if you solve that puzzle, answer that question, you'll be excited to discover the solution. You're looking for any such opportunities, no matter the subject, rather than focused on any particular topic. I'm definitely a scientist of the second type.
So it's fair to say that that serves as an explanation for how, in one career, you could be as interested in the big bang as you are in quasicrystals?
I think so. And, in fact, as a kid, I was always interested in all the areas of science. I created a lab in our garage. I'd make experiments, or do various activities and pretend I was a scientist of one sort or another. I also collected rocks and leaves.
Unfortunately, a tragic event occurred when I was around 9, which is my father passed away due to Hodgkin's disease. And that changed my life—up to that point we had been moving every three years. We'd been in Paris, France, we had been in Rome, New York, and St. Louis, and that's where he became ill. We moved to Miami, Florida after he passed away. So I grew up the rest of the time, until college, in South Florida.
Oh, so you were only born in D.C., you didn't really spend much of your childhood there?
I'd say probably a few weeks. I'm not even sure. It's probably measured in weeks.
Because I think that once my father had finished his training, he was immediately transferred. And I may not have quite the history right. I think he was briefly in Alabama. His first long assignment was in Paris, France; and then Rome, Italy; New York, and then St. Louis, Missouri.
How did your mother cope with being a widow with young kids?
It was pretty tough. It was a big challenge. She did not want to practice law again after that, because I think she just viewed it as too close to her relationship with my father. She chose to move us to Miami, because she thought it was the easiest place to raise kids.
By this time, there were four of us. I was number two of four. And she tried various jobs until she finally settled on becoming a junior high school math teacher, which she did very well and was very successful at. But it was a challenge. And, fortunately, her mother, my grandmother, and grandfather came to live with us, and that helped a lot, but still very—
Did your mom remarry?
Mm-hmm. So your formative years were spent in Miami?
Did you go to public school there?
All the way through 12th grade?
Yes, only public school.
And so, at what point did you start to exhibit excellence in math and science? Was that early on or did that come later?
It was pretty early on. I mean, moving around a lot at the beginning, because I was changing every three years, I was experiencing different schools and school districts. But, by the time I moved to Miami, pretty fast I was excelling in math, and I was given an opportunity to do some math research in fourth grade. So that was kind of my first experience trying to do research, doing real research and actually trying to do something novel. And, in trying to do that, I would write to scientists and try to get advice on things.
The main project I was working on had to do with prime numbers and sequences of prime numbers that can be related by algebraic equations. And it was stimulated by an article I read in Scientific American by Stanislaw Ulam. I didn't know who he was or what he had accomplished.
But I wrote to him and he wrote back to me.
That was really inspiring. In fact, I was always reading about scientists and then trying to picture myself in that world -- what it would be like to do that kind of science or this kind of science.
Did you find yourself outpacing your teachers in terms of what they were able to teach you?
Well, fortunately, I was living in Dade County, Florida, which is a big county, a big school district, and also very progressive.
So the great thing was—I had truly excellent teachers, and they also had resource teachers who were there to help the more advanced, more gifted students in elementary school. By the time I got to middle school, the NSF had started some special program for advanced mathematics training of young students. And I had a chance to take part. There was a special program in math, and a special program in science. In the math program, you started off going to— I think in 7th or 8th grade -- I started taking calculus at the local junior college in parallel to whatever math I was doing in regular school. So the program had you doubling the amount of math you took each year from that point onward.
As for the science program— this was an NSF research program, so there had to be a control group as well as an active group. Unfortunately, in the science program I was assigned to the control group, which means I wasn't in the program. [laugh]
So I didn't get to participate in that until pretty late when they decided to let the control people also get involved in the program. And that's where I took my first physics course.
Uh-huh. Was that love at first sight for you when you took that first physics course?
It was not. I was convinced that I was going to be in biology, in medical research.
Probably influenced by my father's passing away.
And the math was kind of something on the side I just enjoyed doing. I didn't think of it as something central to what I was doing. The physics course I had was a brief course. It was a great teacher, and very dynamic. But the problem with physics is that, when you learn it at that level, you typically have no contact with what's going on at the frontier of physics.
You learn F = ma, you're learning 300-year-old physics. Whereas, when you were taking biology or chemistry, you were learning something that was more modern. I was also working during the summers in various biological and medical labs around Miami as part of various summer programs and research opportunities. So there, you could get right to the frontier of research -- whereas in physics, the frontier was very remote.
And then, when I took the advanced placement physics course in high school, I happened to have an awful teacher, probably one of my worst science teachers, so I had no taste for physics when I graduated high school. I was pretty sure I was going to do biology, and math was kind of there in the background. But I never thought of myself as a mathematician. I just thought it was something I was good at.
What kinds of colleges did you apply to besides Caltech?
I applied to many. [laugh] So I had no confidence in how things were going to work out. But I definitely wanted to get a good opportunity. So I probably applied to about a dozen schools or something like that.
Some in the South, which I definitely did not want to go to, but if that were my last resort, that's what I would have to do. I was pretty convinced that I wanted to go to Princeton at the time. And I had never heard of Caltech, but my bad physics teacher insisted that I apply to Caltech, because he knew about it.
He thought it would be a good idea.
So the names like Gell-Mann and Feynman, they meant nothing to you as an 18 year old?
They really didn't. I knew a few names, because I'd also occasionally go to physics conferences at the University of Miami. I lived about a half mile from the University of Miami, so I would go there, and I'd attend them. Paul Dirac would come, and there'd be a few other names which I knew. But it was not what I thought I was going to do in life, so it was more out of curiosity. I was interested in all of science. Some great people were coming, and I wanted to see what they were thinking about. I didn't absorb very much, but I just got a sense of the atmosphere.
This same physics teacher that encouraged you to apply to Caltech, was he the same terrible teacher for AP physics?
He insisted that I apply.
[laugh] So he did you one big favor.
Yeah, he did me a big favor. So this often happens, right? You think it's all bad. No, it's not all bad. Something good could happen. This was also the turbulent year of 1969, 1970.
So there were issues like, “Are you going to be drafted? Is your university going to close?” And things like that.
Now, you were on the young side of that, in terms of the Vietnam draft, but that was something that you had to deal with?
Yeah. So my draft year would've been a few years later, but it still would've been the middle of my college years.
And during that time, the question of whether you would get a student deferment or not, was not clear. It was a crazy time politically, unlike the present time, which is perfectly calm and sane. [laugh]
Right. [laugh] Right.
So it wasn't quite as crazy as the present, but almost as crazy as the present.
Yeah. So, Paul, you were not thinking of physics departments specifically when you were applying to school?
Not at all. Not at all. In those days, Caltech was doing something which no other school was doing at that time. They would send a Caltech professor and a student to your hometown to interview you and your teachers. I was really impressed by that -- that I was actually talking to someone at an advanced level. So I started looking more and more closely Caltech.
I was also getting more and more concerned about how life was going to be during this Vietnam era at Princeton and Harvard, because they were in the process of closing during that time due to protests. And as I learned more about Caltech, I got more and more interested in it and realized, “Oh, it's a much more special place than I imagined.” I just hadn't ever known about it, living in Florida. I just hadn't been thinking about the West Coast at all as a place I was likely to go.
Did you consider Berkeley and Stanford also?
Yes. I applied to all those places. But going to Berkeley instead of Princeton and Harvard wasn't going to make the political unrest on campus better. [laugh]
And Stanford -- I didn't know too much about Stanford, either, because I was more East Coast oriented at the time. But, as I began to learn more about Caltech, I became increasingly interested in it. I discovered something interesting years later. I had a favorite science book when I was a little kid which had a chapter on each of the sciences, and it was very nicely written. It was, of course, for kids, but, at the same time, it was written at a pretty high level describing what was going on at the frontiers in each of the fields of science it described. And I didn't realize it, until I looked back at it years later, that the book was from Caltech. It was all about science being done at Caltech.
So somehow it was programmed in my mind, without my knowing it, that I was destined to go there. But I certainly didn't know that at the time I made the choice. I actually thought it was a bit of a risky choice for me, but I went there thinking I was going to do biology with a backup of math.
So you got there and then what happened? At what point did you switch over?
Oh, it took about two weeks.
[laugh] That's fast.
Everyone has to take physics, and, in fact, one of the reasons why I went to Caltech was that I had some strange notion that maybe physics isn't as bad as it seemed from my terrible high school class. If I chose to go to Princeton or Harvard -- with my broad interests, not just science interests -- I could imagine filling up my schedule and avoid taking physics. So I thought one of the advantages of Caltech is that I would have no choice. I would have to take physics.
And within the first two weeks I encountered a number of well-known scientists. Tommy Lauritsen, an inspiring teacher, was the lecturer for my first physics course. I became aware of Richard Feynman and Murray Gell-Mann. And Caltech was using the Feynman Lectures in Physics as the course text.
Which was just completely mind blowing. The book doesn't tell you how to do anything, and yet you have to figure out how to solve the difficult problems that you are assigned.
Yeah. Can you describe that? How did that work? How did that course work with the Feynman Lectures?
Sort of like you might guess, which is you throw it at the students, who have to read, reread, and reread the chapter again – until they can nearly recite every line. The in-class lectures cover some of the material, but not enough to enable you to solve problems in the problem book; at least not enough for me. Hidden in the Feynman Lectures, though, are ideas that should help you solve the individual problems, without explaining at all how to solve any specific problem.
So at the beginning of the week, you'd start working on reading and starting to do the homework as best you could. It would take you 'til the very last moment of that week to finish the problem set. And you just did that week after week after week. And through that process, it just felt like your mind was continuously being expanded. You came to appreciate that physics is about how to go from a description of something, some phenomena that you're describing, to equations, to solving the equations, to interpreting that in terms of what it means in terms of the phenomena.
And, in some ways, the Feynman Lecture approach forced you to go through that process. Feynman’s lectures described some general principles with examples of some physical phenomena. But unlike other physics texts, it doesn't tell you how to solve problems that involve those principles. You had to figure out how the general principles and the specific problems you were assigned were related, and what the principles imply for physical phenomena. It was a great way of preparing the mind to do physics, I think.
So, Paul, that's a wonderful explanation from a teaching perspective. But, I'm curious, one of the things that you said earlier that struck a chord with me was, you were turned off in high school because you were learning things that felt ancient, right?
Newtonian physics, 300 years—I mean, the things that were going on in the 1960’s just at Caltech would turn that assumption on its head in terms of all of the—the discovery of the charm quark, for example, what B.J. Bjorken—
Oh, that's right.
Right? So was it also impressed upon you that physics was also like a hot-off-the-press, lots of new discoveries are happening in the here and now, as well?
Yes. So you'd read about the people who were teaching you, and you'd discover the fact that you're being taught by people who were actually on the frontline of those discoveries..
Some of them weren't the best lecturers, but it didn't make a difference. The fact that they were working on the experiments or proposing the ideas made it clear that they were committed heart and soul to science they were teaching. That's what made the difference. The idea that it was something that's happening right now, and the discoveries that were being made right now, by the very people who were introducing me to the subject. I quickly started attending colloquia every week, and that also exposed me to “What's going on right now?”
And you could also observe the interaction, the intense interaction, among the faculty and graduate students. You could see all that happening. So this was not something remote hundreds of years ago, it's something happening right now. That was transformative, too.
Now, in terms of your skillset, coming in with the idea of math and biology, that would suggest to me that there's a sort of 50/50 split in terms of when you would settle on theory or experimental physics.
So, I'm curious, between the more abstract, like on the math side, and the more hands-on with the experimental—so I'm curious at what point in your undergraduate career that you started to define yourself in terms of being a theoretical physicist?
That's a good question. So having decided after a few weeks to become a physicist, I had no idea what the possibilities were.
So I decided to be very systematic about studying various possibilities. I used my summers, as well as the regular academic year, to pursue research opportunities. I especially used the summers to explore different areas of physics, with the idea that I would then make a choice at the end of that process.
So what were some of your summer projects?
So, the first summer, I arranged a reading course on general relativity, because that seemed to be an important subject. By the end of my second year, I decided I wanted to try a high-energy experiment. So I spent the summer of 1972 at Fermilab—
—working on a Caltech experiment, the neutrino experiment there.
Was that a good experience at Fermilab?
It was a very good experience. I had the chance to work with Frank Sciulli and Barry Barish, from whom I learned a lot, as well as students and engineers at Fermilab. That experience taught me that's exactly what I didn’t want to do. [laugh]
Not experimental physics in general, but high-energy experiment. I didn’t like the scale of it. I didn’t like the fact that I didn't have control of it, that it was too massive, too big. I was working on one little piece, or a few little pieces of a giant thing. When I was a kid, I would have a lab and I would control everything —I'd have to prepare the material, do the experiment, write the notes. I'd have to do everything. So the idea that somehow I'm a small cog in a big machine, that didn't suit me psychologically.
So Caltech and Fermilab had a joint venture going with his project?
It was a Caltech experiment at Fermilab. Fermilab was just getting started.
In fact, the accelerator itself was working, but it was not yet sending beams to the experiments. Frank Sciulli and Barry Barish had a neutrino experiment there, Experiment 21, which was designed to study weak interaction physics and look for tests of, not quite W’s and Z’s yet, but tests of the then-existing standard model of weak interactions. But the neutrino beam that our experiment depended on had not yet started. There were giant scintillators that were there to capture interactions after a neutrino would strike a target. I did some work on the target, and some work on the giant scintillators. But I didn't stick with the experiment—I just spent one summer doing that.
And it was a great experience to be at Fermilab, especially at that early time, to see all the different projects under construction and to get a hands-on experience. I had a small little piece I had to design from scratch. So it was all good experiences to have. I think it's really important for a theorist to have that opportunity. First of all, I love experiments. I love doing experiments. If I have the opportunity to do them, I try to do them, even today. Experimental work comes back into my life from time to time—like the quasicrystal work we’ll be talking about.
But I was getting more and more of a sense that there is a split personality between theorists and experimentalists in the sense that, if I'm an experimentalist, I think my job is to be completely skeptical of anything theorists would tell me. And my job would be to show that they're wrong. I would have to have that kind of aggressive attitude. Ignore what they say. I'm supposed to be the eyes and ears. And they're probably wrong.
On the other hand, if you're a theorist, I think you have to go through different stages, but an important stage at the beginning is to be a complete booster of your idea. You can't get it off the ground at least unless you have some thought, some belief that it has a chance of making it. So what I felt in that experimental experience—and a later one, which we haven't gotten to yet—that, in both cases, my strong impression was that I would be too much of a booster of the idea to be a good experimentalist.
So, although I still get involved in experiments when I can, I always make sure there's the right kind of experimentalist working with me so that I don't let my my biases get in the way of the results. But I was just beginning to struggle with that idea during my Fermilab experience. I decided that high energy physics experiment is the wrong scale for me, but maybe I would find some other kind of experimental physics that was a better fit.
But over time, I came to realize that, no, I don't have the right personality for that, either. I want to be more on the idea-creating side of physics, and for that I have to be a booster, at least at the beginning. I have to be a little bit biased to get ideas off the ground, and then rely on experiments to correct my biases.
Who were some of the professors at Caltech you became close with?
Well, obviously, Frank Sciulli and Barry Barish, with Barry through senior year. I also worked with Professor Andy Ingersoll on an early model to explain the red spot on Jupiter. But by far, the most influential mentor was Dick Feynman.
I had a number of experiences with him. Midway through my sophomore year, my roommate Dave Glackin and I arranged to have Feynman teach a course we invented, called "Physics X." We pitched him the idea, and he agreed. But it was not a real course with academic credit – it was completely off the books. Physics X was an informal, voluntary meeting with Feynman that occurred once a week. He would come into the lecture hall, and you'd have a chance to ask him a question about anything – anything other than a homework problem -- and he would respond. The “course” continued the whole time I was there, and continued for several years afterwards. And that experience was extremely important for me, because before then I only knew Feynman, from a distance, as being a particle theorist. But the fact that you could ask him really about anything was the striking thing—
He didn't particularly want you to ask him about particle physics. He insisted that you ask him about some phenomenon, something you really wanted to understand. And then you could watch him think through the topic, and struggle to explain it.
Often it would've been something he knew about, but the great times were when it was something he didn’t know about, or hadn't really thought about. You could see right in front of your eyes how he would struggle with it. And the fact that he was just as curious, just as engaged, no matter the topic -- it just sent a message to me that all science is interesting; there's no science which is more interesting than others, especially if you're discovery oriented. Anything you discover that is something new is just as good as anything else, in some sense. It's not that you have to choose to be this kind of physicist, or that kind of physicist.
That's what influenced my thinking more than anything. In becoming a physicist, I didn’t have to make an absolute choice of specialty. I have to make a choice of what I'll first study, but I don't have to commit myself that that's the only thing I'll ever study.
And, to fast-forward—
I just need to choose something that will teach me a lot, give me a lot of tools, and then I will have the confidence to do anything.
And to fast-forward, to look at the remarkable diversity of the research endeavors that you've been involved with, clearly what you learned from Feynman was formative.
Absolutely. Yeah, absolutely. And then, in addition to Physics X, I did some research projects with Feynman, as well, and they ranged from something that you might think is mundane to things that were more formal, but they were all pursued with equal enthusiasm and were all equally fun. And that's the other thing he taught me. He made physics so much fun.
Because of that, even when you were struggling, struggling was OK. Feeling bad was OK too when things weren't working out. The fun was knowing that when you stick with a problem and you keep pounding away, sometimes something good happens or you discover you're on the wrong track – either way you learn something new. It's one of those two things.
Was your sense that Feynman was unique given both his stature and his accessibility to undergraduates? Generally, you would think that somebody at that level—
Yeah. He was definitely a standout figure on campus. I think that anyone that was an undergraduate during those years was influenced by him, in one way or another. He gave frequent public lectures that everyone would attend. His attitudes about science generally were also highly influential—you might call it his "philosophy of science," the way science works. That was also really influential to me.
And a lot of debates we're having these days in cosmology I think would benefit from people going back and listening to what he was telling us, how he would approach science. He wasn't the only person saying those things. He was often drawing ideas from philosophers of science, like Karl Popper and others.
But he was an active scientist. He was putting those ideas into action, which is different than someone talking from a distance about how science should generally work. Now, these ideas have come to be how I as a scientist think as I'm approaching a problem. How I need to be self-critical at the same time that I’m trying to promote an idea. How do you prevent yourself from fooling yourself? How do you make sure that you're doing science, and not some other kind of activity? Science is a very particular kind of activity, but sometimes, especially, again, if we're talking about cosmology, sometimes it borders into what sometimes people call "metaphysics" -- ideas not susceptible to scientific testability.
And you need to be really aware when you've crossed the line from science to metaphysics. Not that there's anything wrong with the second activity, but you really have to know which you are doing. Whereas, I think, nowadays, that line is more often being blurred.
You mean, even in the hard sciences, those lines are getting blurred? Is that what you're saying?
Yes. Especially in the last 20 or 30 years.
If you look at what are the leading ideas that have been around since the 1980’s, you might talk about string theory, or you might talk about inflationary cosmology. Those are two ideas that many people have believed and pursued for all those decades. But you should ask yourself, “What is the experimental evidence for them? Do these theories really explain experiments or observations, or don't they? Do they allow many possibilities? Are they so flexible that many experimental outcomes would fit, or maybe even any outcome would fit?”
I think you would find that these leading ideas run into this kind of trouble. They have evolved over the years to become theories in where there is no way of testing them empirically. They're impervious to falsifiability. Some people describe this as a good feature, because the theories cannot be wrong. But from a scientific point of view, this is a very serious problem.
They're impervious because of the current technological capacity to create experiments to prove or disprove them?
No. No, that's a standard situation that occurs in science that only delays when the falsifiability test can actually be performed. The theories I am referring to have evolved to the point where any empirical outcome, whether made today or in the future, can be made to fit. All outcomes – any outcomes -- are equally preferred.
So let's say inflation, for example. Inflation was supposed to explain why the entire universe is smooth and flat, and why it has certain fluctuations in energy density that observers can detect using the microwave background, which can account for the formation of galaxies. In other words, why everywhere in the universe has the very special characteristics we observe, rather than something else.
What we've learned is that inflation fails to do any of this --and I guess I was one of the first to point out that it does not work as originally claimed.
First of all, once inflation starts -- if it starts -- it's eternal. That is, at any given time, most of space is continuing to inflate and is nothing like what we observe. Constantly spinning off from the inflating spacetime are patches of spacetime that stop inflating, but the cosmological properties in those patches are not the same. In fact, they span all conceivable, physically-allowed outcomes. This situation has come to be called the “multiverse,” though that term makes the situation more scientifically attractive than it really is. So we might be in one patch in the multiverse, which has some particular set of properties. If you could go to another patch of the multiverse, it would have different properties. And, in fact, any combination of properties that's physically allowed by the fundamental laws will occur and will occur an infinite number of times.
And there's no way of saying which one’s more probable. Everything is possible, nothing is preferred. Such is the nature of the multiverse, which is a very nice name for saying what I would call theoretical disaster.
Just imagine -- your theory was supposed to explain why things are this way and not that way, or more probably this way than that way. Instead, what you find is – your theory predicts that all are equally possible. So some of the proponents would say “Great, no experiment can possibly disprove our theory now. We can learn about our patch of the multiverse, our particular environment, but we can never disprove this idea.” And I would say, “Well, this is disaster, because your theory now fails the fundamental criterion of what makes a theory scientific -- it's now unfalsifiable -- impervious to any experimental test.” Now, all this has been clouded by the way people talk about the subject.
Because what they say is, “Before we understood that inflation produces a multiverse, we thought inflation predicted the same properties everywhere in space, such as spatial flatness and a nearly scale-invariant spectrum of density fluctuations, and some of those predictions were later verified.” So they credit inflation with explaining those results.
But it's not important how we originally thought inflation works. You now know the theory doesn’t actually work like that. It actually produces a multiverse in which almost nowhere in the universe has the properties that were originally thought to have been predicted. So today you shouldn’t give inflation credit for predictions that we now know it really does not make. In other words, we should not ignore the fact that our thinking about inflation has developed and our original impressions were wrong.
We began thinking the theory worked one way. We thought it was dominated by classical laws of evolution with a little bit of quantum mechanics mixed in to make small perturbations. And so, from that perspective, it looked like, yes, inflation does powerfully smooth and flatten the universe. And that's what you'll read a lot in textbooks.
But what we actually learned a few years later, is that those quantum effects actually take over. What we originally thought is that the quantum fluctuations were always small compared to the classical effects. But gravity can amplify quantum effects. So rare fluctuations that you would say would be rare and unlikely, but that might keep inflation going, become huge compared to the regions that you thought were typical. That is how the simple classical universe that we originally thought inflation produces --and that makes definite predictions --turns into the multiverse that was not anticipated and that makes no predictions.
You are forced to flip your thinking—instead of classical physics dominating, quantum physics takes over, because it gets enhanced by gravity and then you are forced to flip your ideas of what's typical in the universe, and what's not typical in the universe. So what's typical in an inflationary universe is spacetime that is inflating. And then there are rare regions, which are a set of measure zero, that will have ended inflation, but, because quantum physics has been dominating all this time, their properties depend on the particular history of quantum fluctuations that occurred earlier in that given region.
But quantum physics is inherently random, so the properties in that region will be random. And by producing an infinite number of such regions in an eternally inflating universe, you end up spanning all possibilities. And that's how you end up taking away all the predictive and explanatory power of the original inflationary hypothesis that assumed classical physics only. So the common impression of inflation is based on the original misunderstanding of how inflation plus quantum mechanics come together.
Mm-hmm. And so, to bring this back to Feynman—
—the way that Feynman taught you how to think was that there were certain boundaries that you had to place on yourself to know where exactly the science ended?
Right. He had a series of lectures on science at Cornell in which he talks about how to avoid fooling yourself. And what you have to avoid are theories which are so flexible that, after you make an observation, you say, “Oh, yeah, I know how to fix the theory to explain that. I turn this knob, I turn that knob.” And then another observation, “You turn this knob and that knob.” And the multiverse is kind of the ultimate limit where all the knobs have been turned. So everything is possible and therefore nothing you measure or any combination of things you measure can be inconsistent. But that means the theory also has no power, because the point of a theory is to powerfully explain something. Why it is this way, but not that way. If it says the outcome could've been anything and excludes nothing, it adds nothing to our understanding.
That's not progress. Inflation theory taken this trajectory over time, beginning from the 1980’s to the present, and this is its present state of affairs.
Right, right. In terms of developing that historical narrative, I've heard it said many times that theoretical particle physics has been sort of stuck in a rut since the late 1970’s and the early 1980’s. And so, I'm curious if you see a connection between the rise of these impossible theories in the 1980’s and the decline of theoretical particle physics in the late 1970’s?
I think they're definitely related. In the 1980’s, we thought we were in really good shape in terms of particle physics. I was a graduate student in the 1970’s and a postdoc up to 1981. We thought we were doing well on the cosmology front—we thought inflation was going to explain everything—and we thought we were doing well on the particle physics front. There was going to be some kind of grand unification, and grand unification would probably demand some extra symmetry, like supersymmetry, to enforce it.
And then, supersymmetry led to superstrings. And it looked like, “OK, we now have all the building block ideas we need to explain everything.” And both those two major thrusts, inflation and string theory, have dominated up to the present, but getting into increasing trouble as we've understood more about them. The theoretical community continues to bet heavily on them, but the result has been that there's been relatively little progress in either case in explaining why things are the way they are. Because what we've really discovered, is that each of them breaks down in one way or the other.
Inflation -- I would say we're 99.9% confident that inflation has this problem I've described of quantum runaway and multiverse. I say that, because even the proponents of inflation would claim it. They may not call it a problem, but they agree that inflation produces a multiverse. We don't disagree on that. We just disagree on whether it's a good thing or a bad thing.
For string theory, it's unclear, because we might not have the right mathematical tools to understand it yet, and then our conclusions about what it gives us may not be correct. But according to some, based on the present understanding, it has a similar problem as inflation. It doesn't produce a single type of particle physics. It produces a nearly infinite variety, like the multiverse – an exponential number -- of different possibilities called a landscape of possibilities. And if that landscape picture is correct, it actually has the same sort of problem that inflation does, which is that it gives too many possible outcomes. And so, like inflation, it's not really telling us why things are one way versus another way. According to the landscape picture, the properties of particles and fields we find in our observable universe would only be characteristic of a particular valley in an energy landscape, and would be different in a different valley.
So you say, “Well, how do I know that other valley exists? Can I go test?” “No, you can't. Sorry. You can only test things in your valley.” “Well, how do I know that the other valley is even out there somewhere?” “Well, because our theory says it has to be there.” OK. “But then you have to rely on faith that the picture is true?”
In other words, I think both theories require that we must first assume they are true, based on the appeal of symmetry and mathematics, say, and then claim success because, among the nearly infinite number of different possible outcomes is the one we observe.
Which is fundamentally unscientific, you're saying?
Yes, that's right. It's a different mode of thinking. And even some people would say they recognize that, “Yes, we're using symmetry and beauty and mathematics to guide us. That's why we think this idea is right or that idea is right.” OK. I think you're allowed to use any tool, any trick in the book you want to figure out a good theory, but, at the end of the day, you'd better have a good theory.
And a good theory should be powerfully explanatory and explain why things are this way and not that way, and there ought to be things you can measure -- if not today, but that you can conceivably measure someday -- that would tell you whether the theory passes or fails depending on how the measurements come out.
If you are allowing theories that allow a nearly infinite number of outcomes, the theory is not falsifiable as a matter of principle. Then, as I was saying before, you're doing a different activity
Shelly Glashow, I spoke to him yesterday. He talked about his campaign to make some university faculties string free, which I found pretty funny. [laugh]
Yeah. I think, in this, we are both concerned that theorists were swept away by mathematical power and beauty. On the particle physics side, it seemed promising to imagine that, “Oh, use some powerful mathematical ideas, extra dimensions, strings, membranes, supersymmetry, really powerful bits of mathematics, and that's sufficient to guide us.” And, well, in the history of science, an approach based purely on mathematical beauty doesn't have the best track record. It’s not impossible that it will work, but that approach doesn't have the best track record.
Science tends to be more nitty-gritty. You need experiment, theory, experiment, theory, testing, skepticism. You need that grinding process to really make progress.
Did you have a senior thesis at Caltech?
I did have a senior thesis. I was doing some more work on weak interactions with Barry Barish for my senior research. And I was also doing two projects with Feynman, one of which, as I said, it sounded kind of silly. It had to do with understanding how Super Balls work, when you bounce them around and they make all kinds of funny angles and rebounds and the like. Although it might sound juvenile, it was a fun project which even surprised Feynman as to how it worked. That was one of my nice experiences to show him that something he was convinced was impossible was actually quite possible.
[laugh] What was possible? What'd you show him?
Well, the idea of the project, was to construct a matrix which -- given the initial velocity and spin of the Super Ball—would tell you if it hit a wall at a certain angle how it would come off. And then, once you knew that, you could compute the outcome of a sequence of bounces. You could predict where the Super Ball would bounce, just by multiplying different matrices. What I was explaining to him, is how you could bounce the ball in a corner, the ball in the corner would come back at you at nearly the same angle, not quite, but nearly the same angle.
And, as he thought about it, Feynman said, "Well, if that were true, you could just drop the ball straight down and you're telling me it would go off at a sharp angle." I said, “I hadn't tried that, but, yes, I think that's true.” And I drew a Super Ball out of my pocket, and we tried it and, sure enough, it did just what the matrix said it should do.
And it was an important experience, because I had made enough mistakes in front of Feynman by this point, and when you made a mistake in front of Feynman, his language was—he was, in a gentle way, a rough guy -- you know, he'd say, "Oh, that was stupid!" And you'd think to yourself, "OK. I know I'm stupid."
I wonder, Paul, if you had a cultural affinity with him as a New Yorker and your parents as New Yorkers?
It must be. I think that was definitely part of it. So I didn't mind the “insult” as much as others who I knew had a similar experience. But then, when he made this mistake and he looked at me, he said, "Oh, I'm so stupid!" I realized, oh, OK, stupid is a word—
Right. Goes both ways.
It was his aggressive way of getting you or himself to think harder. You're not trying to insult someone by calling them stupid. You're saying “You're not thinking clearly enough. Be honest. You have made a mistake.” And the little sting helps you remember that mistake. So for me, it was all a very positive experience that gave me the toughness needed for research.
The other project I worked on with him was more formal. It had to do with learning about solitary waves. That was a fairly recent idea at the time, which led to ideas about solitons and other ideas that have since become very popular. Feynman was very skeptical that you could take two nonlinear waves and pass them through one another without altering either one.
I had just learned how to solve partial differential equations on a computer working with Andy Ingersoll on a project to understand the Jupiter red spot, so I knew how to simulate the collision of these solitary waves on a computer. And, sure enough, again, although we were both skeptical, the mathematicians who had claimed it was true actually knew what they were doing. It was, again, an experience that together we learned something to be true that we had originally been skeptical about. It also gave me a strong first experience with solving partial differential equations on a computer , which has also been an important tool in various projects that I work on.
So, Paul, I have to ask, given the close relationships that you developed with these giants at Caltech, did you have to resist the urge of just staying on as a graduate student with them? I mean, graduate students in other places would've dreamed to have this kind of access, and here you are as an undergraduate doing this kind of work. Did you think that maybe it was the best idea to just stay where you were?
Well, fortunately, Caltech didn’t give me that opportunity. They really encouraged students to go elsewhere, which I think is a smart thing.
So, when the time came, I spent a lot of time thinking about what would be a good place. The summer after my junior year, in 1973, I was doing theoretical condensed matter physics. I was studying the property of glassy solids, developing the first computer models of amorphous silicon with Richard Alben and Denis Weiare at Yale. It was a summer NSF program. So I had a taste of that. I was already invited, based on that experience, to go to IBM the following summer to work on an experiment with Marc Brodsky, a solid state or condensed matter experiment, which I ended up doing.
But, by this point, I had decided particle theory was something that I was going to choose for graduate school, because I felt it taught a student the most advanced tools that a theorist would need. And so, I began to think about where would be the best place to go.
You asked about Caltech. Of course, that would've been an obvious place. But, as I began to read about the current ideas in particle physics, I saw that there were groups at Princeton and Harvard that were exploring new ideas in quantum field theory called gauge theories. Now, at Caltech at the time, Feynman was involved in parton models. And on the West Coast, there was a lot of interest in S-matrix theory. And the notion that quantum field theory, which had been in the doldrums for the period of the 1960’s, might be coming back in the form of gauge theories was not accepted very well on the Caltech campus, at least as far as I could tell from my undergraduate perspective.
But I thought that the attempt was very interesting. So I decided I would go to Harvard where they were exploring those ideas, because I thought it was interesting. I remember being told, I won't name names, by one of my advisors —and it's not Feynman—that, "If you're going to go to Harvard, make sure you learn something real before you study those gauge theories."
But, within a month or so of arriving at Harvard, the J/psi particle was discovered. And then that started what seemed like an infinite seminar at Harvard, which went continuously for several months, led by people like Steven Weinberg, Sheldon Glashow, Howard Georgi, and a whole array of people who had been working on gauge theories. And I felt really lucky to be at that sort of epicenter at that time. That was a transformative experience.
What was so exciting about gauge theory?
The unification idea.
The idea of broken symmetry and unification. Two things that seemed to be different and unrelated -- like with electromagnetic and weak interactions -- could be unified in this way. And you could even test this idea. And that it was also related to the quark structure. It tied everything together in a way that seemed to have promise towards some kind of ultimate unified theory. I was intrigued by that idea, as many people are who enter the field. It just seemed much more hopeful than the approaches that I was familiar with that were being pursued at Caltech.
I should be careful. Obviously, there were people at Caltech who were also pursuing gauge theories, Gell-Mann for example —but, as an undergraduate student, I was not as aware of those things. But I was aware that the West Coast was less heavily involved in it. So I decided to go to Princeton or Harvard, and I ended up going to Harvard.
And was there a particular professor at Harvard you had your mind set on working with?
I originally thought I was going to try to work with Weinberg. And certainly it was great that he was there when I was at Harvard. But one of the other things I wanted to do at that time was make sure I got to choose the problems I worked on. Weinberg was more of “I'm going to suggest something to you to work on.” And one of the advantages of having Sidney Coleman as an advisor, I learned after I arrived, was that he never suggested anything. It was up to you to figure out what you wanted to pursue, and work it out.
And, although I could see that it was frustrating for some students, it was exactly what I wanted. I wanted someone that if I chose something, if I worked on it and got stuck, he's smart enough to get me unstuck. But he wasn't going to tell me what problem to work on. So, after about a year or so, I decided that was a better choice for me.
Mm-hmm. What were your impressions in terms of generally the way physics was done at Harvard versus the way physics was done at Caltech?
Well, two very different views, because one's an undergraduate view and one's a graduate student view.
So, if I were a graduate student at Caltech, I'd have been much more aware of other activities, like Gell-Mann's activities. I'm not aware that he did much with undergraduates when I was there.
Also, as an undergraduate at Caltech, I would interact with a broad spectrum of people in physics. Nuclear physicists -- there weren't really condensed matter physicists at the time at Caltech, but I had the summer experience at Yale. A little bit of astrophysics, a little bit of general relativity. I was taking seven courses a term and doing research, just running from one subject or activity to the other.
Suddenly, as a graduate student without so many courses, I had time to develop depth in particle physics, while continuing to explore other areas. Each week I would attend at least one seminar outside my field, which I thought was an important thing to do so I did not become too narrow scientifically.
Another aspect of Caltech, was that it was also a very narrowing experience, in terms of being a purely technical place. I had had a very classical education going into Caltech. In fact, I almost transferred from Caltech after the first year, because I just thought it was too narrowing. We couldn't talk politics. We couldn't talk philosophy. The students were just very, very narrow when I was there.
But instead of transferring, I decided to invert my education. Which meant that, when I got to Harvard, I started taking courses outside of science. I took philosophy and logic and art history and music history. I took what would be the distribution requirements an undergraduate might take, but as a graduate student, when I could be more relaxed and selective. So for me Harvard was just a very different experience.
What was Coleman working on in those years?
He was working mostly on gauge theories. A particular project, which I followed closely, was how you could retranslate a theory of fermions coupled to gauge fields in 1+1 dimensions into a theory of bosons, so called "bosonization,” which allowed you to make precise predictions about its properties. Sidney had me read drafts of his paper on the subject. I learned a lot from those.
He was also giving, at the same time, his famous Erice Lectures during summers, which were about everything having to do with gauge field theories. A few years later, he began to work on the idea of bubble nucleation with Frank De Luccia, who was my roommate, so I was following that, as well, even though, at the time, I didn't foresee that it was going to relate to anything I was doing.
To be honest, I was first more influenced by Sidney's abstract work in gauge theories in 1+1 dimensions, a more abstract subject. I thought it would be nice to understand the 1+1 dimensional gauge theories and work my way up as a way of just learning the subject. In the summer, after my first year at Harvard, I went to the Erice Summer School in Sicily—mainly because Sidney was giving his Erice Lectures there, but also to hear lectures by others. I was struck by the series of talks that Ken Wilson gave on lattice gauge theories.
It was very early days for lattice gauge theories. Wilson had this brilliant idea of how you could apply ideas that worked for studying critical phenomena for exploring gauge field theories using a of lattice formulation which made it possible to describe interactions in the limit of strongly-coupled theories. I came back from Erice with what I thought would be a nice idea for a project. Sidney had shown how, using the Fermi description of this 1+1 theory, you get a certain spectrum of particles. And when you bosonize and take the strong coupling limit, you get a different spectrum. If Wilson is right, then, “I should be able to find some analog behavior if I formulate a lattice gauge theory version? How would lattice theory reflect the difference that Sidney had worked out analytically?” And so, eventually, I did come to understand how that works. There's a kind of phase transition that happens on the lattice where it behaves in the weak-coupling limit like an Ising model, and in the strong-coupling limit like a Heisenberg model.
Now I should explain, the only reason why I'm mentioning that project is because that ended up being my thesis -- inadvertently. I thought it was just a little exercise to get myself started. But when I completed it and presented it to Sidney, he said, "Great! That's your thesis." I hadn't even been there for three years, so I said, "Wait, wait, wait, wait. I'm not ready to go out in the cold, cruel world." So I did stay for another year and finished up the project, and started doing other things.
So, Paul, that's actually what I wanted to ask you about, because to just sort of foreshadow to, again, this idea of your fearless research agenda in terms of the number of areas that you felt comfortable working in. Did you feel right off the bat that, even the very concept of a single dissertation topic was a limiting kind of endeavor for you and it would be difficult, if not him saying just, like, do this? And maybe he recognized that in you and realized that he might've had to focus you because, one of the things you have to do in graduate school is to get the dissertation done.
Yeah. It could well be. At the time, it just seemed a little frightening. [laugh]
You mean frightening what? In terms of actually settling on a topic or what?
No, no, no. I was eager for that. It felt frightening that he thought I was ready to go to the next stage.
I had thought about this lattice gauge theory problem. I had executed it. So I felt good about having learned enough to do that. But as a postdoc, you have to be able to do that as your regular business. You should be able to continue to do that over and over.
And I didn't have any immediate problems in mind of what I would work on, based on my one experience. I certainly didn't work on that problem because I wanted to specialize and work lattice gauge theories. I just thought that was an interesting puzzle to understand how a lattice gauge theory could capture what looked so different in Sidney’s formal approach. I had gone after a puzzle, but it wasn't a puzzle that had a natural follow-on, as far as I was concerned. So I just didn’t feel completely prepared to make that transition yet to postdoc. But I think often students feel that way so... [laugh]
What do you see as your primary contribution with your dissertation?
Oh, I don't think it was a major piece of work—it's not so memorable, even to me. It was showing that, in fact, the lattice gauge theory was able to capture the rather surprising analytical properties that Sidney had found. I liked that I was was able to resolve the puzzle in an interesting way by essentially having a phase transition in the spin degrees of freedom on the lattice. I just thought that was a neat idea.
Also, by this time, I had had a number of experiences in condensed matter physics, so I liked lattice gauge theory, because it connects to a lot of condensed matter problems. I just enjoyed the way the problem worked out, because it was surprising to me. I couldn't see the solution coming until I worked it out, so I enjoyed that surprising aspect to it. I'm not sure it had any significant impact. Occasionally, people write to me about it, but, on the whole, I thought it was just —as I said, like a little project for me, and not something I would've thought of as a dissertation.
Who was on your committee?
It was Sidney Coleman, Steve Weinberg, and Howard Georgi.
And, when you finished, what were your options? What do you think would be the most productive next step for you in terms of developing your career?
Well, fortunately, Sidney had nominated me as a Junior Fellow for the Harvard Society of Fellows, and they accepted me. What I thought was exciting about that, was that I had complete freedom to do whatever I wanted. I was not tied to any group. I thought the graduate experience was important to teach you how to do research, and how to get expert enough that you can actually produce something new. I mean, it was a very important experience, a formative experience in that way. But it was also very narrowing. I was ready to try to do other things.
So, in fact, in 1978 -- the summer after finishing graduate school and before I began as a postdoc -- I returned to IBM Watson Research Labs in Yorktown Heights, New York. I had been there in the summer after my senior year to work with Marc Brodsky on a condensed matter experiment. He brought me there for the summer to work with him to make and characterize the first junctions comprised of amorphous and crystalline solids -- as a possible electronic diode-like component. That had reaffirmed my notion that I don't have the right psychology to be an experimentalist.
But, in the process, I'd also met people there that were interested in doing continuing work on computer simulations of glassy and amorphous solids loosely related to what I had done at Yale in the summer after my junior year. And, in particular, how you cool from a liquid to a glass, or to an amorphous solid, which, even today, is not a completely understood subject. So I was invited back by that group, led by Praveen Chaudhari. He invited me to come and develop molecular dynamic simulations of supercooled liquids and glasses, and to study their defect and elastic properties. So I spent the summer after my PhD at IBM’s Watson Laboratory — which began a series of visits to IBM over the next decade or so.
Now, I've often heard it said of Bell Labs that when newly minted PhD physicists went to work at a place like Bell Labs they were certainly not turning their backs on academia, that it was just one of the best places to do basic research. Was that your sense with IBM, as well, that university opportunities were very much on the horizon for you?
Yeah. I hadn't even thought about going to IBM as a long-term prospect, because I like university life -- I like the diversity of it. I like teaching, I like running into a variety of people. But the Watson lab was still a very stimulating place to visit and spend summers —just great people. For the question I was interested in, which Praveen had introduced me to, it was the place that had the right resources and the people with the right interests. It just fit some of the research that I wanted to do.
Also, I liked the idea of breaking up my time during research in high energy physics with the condensed matter physics. Just because I just found it more stimulating. I feel that I can be fresher when I'm working on a subject after I've stepped away from it for a while. If you have two completely different directions you want to go, or maybe three different, you can constantly switch from one to the other. I never have to be stuck in a situation where I feel forced to keep going in a straight line in my research.
Just stop, do work on something else that's bubbling up, and that you've been quietly investing a little time in at the same time.
Did you start to pursue professional collaborations during your time at IBM in terms of people that you considered peers that you were working with?
Yes. I mean, I was working with Praveen Choudhari, who was, himself, nominally an experimentalist—
—but a brilliant thinker who was full of original theoretical ideas. We often had far-ranging discussions that would lead to new directions for theoretical research. I'd go off and see how far I could get and meet with him regularly to get his insights.
He was also a very wise person. If I needed advice or consultation on how to handle professional decisions -- and sometimes even personal decisions—he was just a very calm, mature person with a broad, peaceful outlook on life. Just a great person to know. Continuing to work with him, more than anything else, is what kept me going back to IBM.
Were you publishing a lot and going to conferences during your IBM years?
Yes. I was only working at IBM during the summers.
But, yes, I was publishing papers and going to conferences in both high energy physics and condensed matter physics. These were two parallel lives.
So, even beginning at that point, there are people that knew me from that life, and then other people who knew me from particle physics life, and others who know me from the cosmology life later on. But they don't necessarily know about each other. But I find that very stimulating, too.
And then, how did the opportunity at Penn come together? Were you recruited?
Yes. I was applying for jobs after the Junior Fellowship. By this time, I had already begun my first works on cosmology, so I'd never done cosmology before. I'd never taken a cosmology course. A year earlier, I had gone to a talk by a young Alan Guth introducing inflationary cosmology at Harvard. And I often described it as the most exciting and the most depressing talk I ever went to. It was exciting, because he began describing the basics of big bang cosmology and I thought, “Oooh, that’s great science that I don’t know anything about.” Then he talked about the problems of big bang cosmology, and I thought, “Oh, it has these really big puzzles, the flatness and smoothness problems.”
Then he described a possible solution, inflation. “Oh! And what drives inflation? It’s some kind of phase transition? I am already fascinated by phase transitions from my experiences in condensed matter physics.” And then, at the last five minutes of the talk, Alan explained how it fails, it hopelessly fails. Once inflation starts, it can never stop, and he never was able to recover a universe that looked anything like what we observe. End of talk.
And I thought, “Oh no!” I just sat there. I just sat there, like, mentally exhausted. He took me on this whole long exciting path and then crashed. The idea just can't be failing on this ground. There must be a way around it.
Now, had you studiously avoided cosmology throughout your education, or how was this sort of the first time you had come into contact with these ideas?
Well, yeah. I think maybe it stemmed from Caltech attitudes, at least the ones as an undergraduate that you heard, that cosmology was one of these fuzzy subjects with lots of room for speculation, but not much data to decide which idea was right.
And, because I was busy doing other things, I was barely aware of the 1964 cosmic microwave background discovery, even though it was described in Feynman's book. But it still seemed like a subject that not many people were working on. On nuclear synthesis, yes, but not like early universe cosmology, not that kind of thing. But it just seemed very, very speculative. And, yeah, I was just busy doing other things.
And did Guth convince you that either it was speculative, but that was OK, or that it wasn't as speculative as you would've thought?
He convinced me it wasn't as speculative as I thought.
So what did Guth convey about that that convinced you of that, that it wasn't so speculative?
Well, because all the ingredients he was putting together seemed pretty solid.
So there's some general relativity, there's some grand unified field theories, and the idea of symmetry breaking in phase transitions. I had no experience with cosmology, a little with general relativity, as I described. Of course, grand unified theories were very much related to gauge theories which I understood, and symmetry breaking and those kinds of concepts. But then the idea that a first order phase transition could have such a dramatic cosmological effect to cause the universe to just totally change its structure and accelerate was just—I hadn't even imagined such a thing.
And if that's possible, who knows—since I have interest in condensed matter physics, maybe there are other condensed matter physics effects that can do interesting things in cosmology. And inflation is just the beginning of a series of new possibilities. But I think, at the moment, after Alan’s talk, I was thinking, “Oh, he's probably only tried one idea, only a first order phase transition. Maybe I'll take a few weeks off and see if I can find something better.” So I thought I would take a little detour for a few weeks into cosmology, not realizing that it would last the next, what, 40 years.
[laugh] But, with that thought in mind -- that maybe I can come up with something clever that he missed. And that's what I started doing. I started to spend the next few weeks going over what he had said. And the nice thing about the subject is it doesn't take that long to get to the frontier. If you want to know about the whole history of cosmology and everything that has been learned astrophysically, whatever, yes, it takes a study. But if you want to get into the frontier and say, “I want to ask about this particular question, smoothing and flattening, and how can you end transitions?” There wasn't much work on it, so you could get to the frontier very, very quickly.
That's true of a lot of the things I work on, I always find something of that nature. You get into the field, and, of course, there are experts who have been in that field for decades, and the subject has been going for hundreds of years. But if you have a particular question which is at the frontier, there's actually relatively little knowledge you need to know to work on your problem. And then you can backfill what you need, if you find you're making success. Then you can backfill and determine what you needed to know and didn't know.
So why was that the case in the early 1980’s, that the prerequisites, so to speak, were so few and far between for cosmology? What does that tell us generally about the field and about, perhaps, some of the technological limitations up to that point?
Well, I don't think it's just true for cosmology. As I said, a lot of the things I work on, I kind of jump into the middle. And you can jump into the middle, because of what I said. Because if you have a particular question, if you have an angle of attack, you have a question that you're asking that other people are not —you're questioning an assumption and you have an angle of attack that other people haven't thought of. You can use that angle of attack to dive to the middle of your subject, pull together the basics that you need. Because for that particular question you're asking, you don't need to know everything about the subject. You need to know enough about the particulars of that aspect. And then, if that turns out to be fruitful, you kind of backfill over time, as you become more and more expert. You don't have to start off as an expert. You can decide if there’s something promising there first.
I describe it to my students like there are two ways of doing research. One is you decide -- there's definitely oil here. I’m just going to dig and dig and dig—just stay there and dig and dig and dig until I hit oil. But, of course, that may never happen. And the other approach is you dig shallow oil wells all over the place, and then you wait and see which one strikes oil, then you go there. Meanwhile, you don't stop. You just continue to dig other oil wells in other places while that's happening. So, when that first finally goes—you have success there, and a little bit later maybe the next one goes. And so, it's more that approach.
So I was diving into this for a few weeks, I thought, and seeing if I could come up with some clever ideas. This idea of putting together particle physics and cosmology—there had been bits and pieces of it going back at least as far as Andrei Sakharov in the early days, thinking about how do you produce a matter-antimatter asymmetry. Also very primal ideas about how quantum fluctuations might seed structure in the universe, conceptual ideas.
Had you thought much about black holes up until this point?
No. And actually—I've done relatively little work on black holes up to this point.
Might be in my future but not up to the present time, just because I'm interested in larger scales and time evolution.
And so, by the 1970’s, there was a confluence of ideas. The big bang theory had become now pretty much established relative to steady state, so you didn't have to debate that. There was some early evidence of dark matter. There was the proposal that maybe neutrinos have mass, and that they might be the source of dark matter. The monopole problem had been identified by John Preskill, who was a fellow grad student when I was at Harvard. There was just this realization that there seemed to be these connections between what we were doing in quantum field theory, and that gauge theories might have these connections to cosmology.
There was relatively little work done at the time, and then there was this explosion that occurred. Inflation helped create this explosion of work, so the momentum was building up, and then I think that the inflationary idea, that you could do so much to change the universe with relatively little. I mean, “A field rolling down a potential, really? And gravity, that's it?” You could do so much. So it just made it very easy entry into the subject if you were from the particle physics side. I think if you were from the more traditional cosmology side, it may have been a bit intimidating.
There was a slew of particle physics trained people who came into cosmology at that time, myself included. And driven by that—driven, I think, by Alan and then the work that Andy Albrecht and I did, and Andrei Linde did, suddenly the subject became very, very promising. The particle physicists came in and changed the field to being more particle physics oriented and connected. And that meant there was a tremendous advantage to come from the particle physics side, rather than the traditional astrophysics cosmology side, because you had tools which the other side didn't have.
What were those tools?
The tools of quantum field theory, finite temperature field theory. The gravity part was relatively simple, so you didn't need that part. And you are dealing with an epoch before there are any planets, stars, or galaxies – before there was any significant structure at all. The universe appeared to consist of an almost perfectly uniform distribution of hot gas – matter and radiation – spread across the entire universe. What could be simpler than that? The entire universe is characterized by temperature and nothing else, or so it seemed. And, yet, there were big puzzles to be solved – like how that gas came to be, and what created the slight deviations from uniformity -- which the traditional cosmologists knew existed but had no clue how to solve.
So it just seemed just the right time to bring in this new generation of people coming from a different direction.
Right. And so, Paul, when you say about, "You can get right to the frontier relatively quickly"—
—from your vantagepoint, what were those most fundamental questions that you knew, not from decades of work in cosmology yourself, but just innately as a scientist, as a physicist, what were those fundamental questions that struck you immediately as these are the things that I want to spend my time on?
What were the puzzles, you mean?
Well, I started off with the ones that Guth had identified in his talk, which were simply the smoothness and flatness and absence of monopoles. I hadn't realized, just because I hadn't thought about cosmology before, that that's a puzzle coming out of the big bang. “Why would you expect it to be smooth? It could be, but you wouldn't expect it to be. I mean, it could be an infinite number of possibilities. It's like the multiverse. An infinite number of possibilities, why this very special choice?” And I hadn't appreciated at that time the role of the Hubble horizon, or the limited horizon. The fact that we're only really observing—because I hadn't studied cosmology—that we only really see a limited patch of the universe. “So how do you get it so smooth on such a large patch of space? and yet it's a finite amount of space? How do you manage that?”
So it seemed to me, after I heard Alan's talk, that he had this idea of inflation, something about condensed matter ideas fixing problems, but it didn't seem to be that it had to be that solution. So I first began looking for different solutions that would allow the inflation to occur, but also allow it to end.
That's what I was hoping to do by using maybe ideas in condensed matter physics that—since Alan had first used the simplest idea, the first order of transition -- maybe there were other ideas which would get around the roadblock he had encountered. So that's what I thought I might spend a few weeks trying to do, see if I could come up with an alternative to a simple first order transition that would save Alan’s idea.
What happened in those few weeks? What did it tell you about your prospects going forward?
So I had a first idea -- which was an interesting idea, but it's not an idea we use today -- which had to do with actually using the monopoles to help seed the phase transition. So what Alan was thinking about, is what we would call homogeneous nucleation. You begin with a smooth universe, and then quantum produce bubbles -- Coleman-De Luccia bubbles -- that would expand, converting from false to true phase, or from metastable to stable phase.
Alan’s problem was he couldn't get them to coalesce, as would occur in the laboratory, because gravity got in the way. It stretched the space between the bubbles so they couldn't come together. So he ended up with a very inhomogeneous universe in the end. But, in phase transitions—some transitions are first order, some are second order. Second order wouldn't have worked in this case, because it wouldn't have produced the entropy at the end that you needed. But then there were other ideas I knew about in condensed matter physics called inhomogeneous nucleation.
So, in fact, when we try to supercool water, one of the challenges is, if there are any impurities in the water, they'll seed crystallites and help complete the phase transition, and ultimately complete the phase transition at much higher temperatures than if it were truly pure water.
So I thought, “Oh, OK. What would be good impurities?” Well, monopoles are actually themselves little defects, in a gauge field. They're like topological defects. So, OK, maybe they could act like impurities and speed up the end of the phase transition. So I spent a lot of time thinking about—working out the details of how they might source such a transition. This made for an interesting study in quantum field theory. It helped me get my job at Penn, because that's what I spoke about when I visited there to interview. But I wasn’t in love with this idea.
So it's like I was describing at the beginning. You go through this period of boostering, and then, after a point, you have to turn around and look back and say, “OK, now, do I really like this idea?” So at some point I went away from that. And then, shortly before I left for Penn, I began working on another kind of phase transition called spinodal decomposition, which was not even well known among condensed matter physicists. It was not taught. Maybe now it is, but at the time it was not taught in the common literature, but I had run into it in reading about phase transitions.
Unlike Guth's version of inflation, where you supercool and you have a barrier in the way -- in this situation, when you supercool, what'll happen is that, at some point, the barrier will go away. And then there's nothing to stop the system from going continuously from false to true phase. That sounded good. That sounded like, “We could begin in the false phase, supercool, have our expansion, and then, if the barrier goes away as we continue to cool, we can just smoothly roll away from false to true phase.” And this was the seeds of now the idea of what eventually came to be slow roll inflation, the paper that Andy Albrecht and I ended up writing about a few months later. So I was working on that. The idea was seeded then. I thought that would be one of the first things I wanted to work on when I got to Penn.
Paul, when you're talking about the inflationary model and we use terms like flat and smooth, I immediately think about when Einstein talked about the frustrations of using language, words, to describe these concepts. So can you just talk a little bit about, what does smooth even mean in this context? What is smooth? How do we use smooth to understand—
Yes. Smooth is easy. Flat is hard.
OK. So let's start with smooth.
So smooth—if the universe were perfectly smooth everywhere, it would have the same temperature and concentration of matter and energy everywhere. Now, obviously, that's not true about our universe. Not even in the rooms that we're speaking are things smooth. But, if we look at the average properties of the universe and looking at different directions in the universe, and, in particular, if we look at the—nowadays we'd say looking at the microwave background radiation -- we'd find that, if you get to large enough distances, when the light comes from a time when the universe was much younger, you'll find the beginnings were an incredibly smooth distribution.
We didn't know it at the time, because we couldn't measure it, but now we can quantify it and say it's smooth to one part in 10,000. So that's smoother than the surface of the table that you probably have in front of you. If you run your finger along there, somehow the universe on cosmic scales began with a smoother distribution than that. Everything we observed comes from that incredibly simple beginning.
Now, if you're coming out of a big bang, some quantum process, so totally out of control, violent process, you expect a huge amount of turbulence and very turbulent distributions in matter and energy. And if you simply expanded from that point onward, it would just become more and more concentrated and turbulent and rough, because gravity tends to do that once you have the inhomogeneities. So the only way you can explain the smoothness is to have made it smooth at, or just after, the big bang to begin with, or maybe before the big bang. Didn't have that idea at the time, but you had to have some process to do that which would take it from a typical distribution --high entropy, very random distribution -- to something very special, nearly identical in different regions of space. So that's the smoothness problem, homogeneity problem.
The flatness problem is actually a little bit more subtle. It's often described in a way which is too simplistic, such as “Why is the curvature of space small when the laws of physics, according to general relativity, make it more probable that the universe is curved like a sphere or hyperboloid, rather than flat like a plane and obeying the laws of Euclidian geometry?” That's the way it's often described. It's actually more subtle than that. Because what we really mean when we say, "flat" -- and this is important when we talk about things like contracting models ---
--it's important to know that what we really mean by flat is not that it's necessarily flat, but that spatial curvature isn’t important cosmologically. That is to say, its contribution to the expansion of the universe is small compared to other contributions. It may be large in terms of absolute numbers, but if other contributions are larger, it has no cosmological effect.
And that might not seem like a big distinction right now, but if we get to talking about why contracting models work much better than expanding models in smoothing the universe, that's important to bear in mind. Because normally, if you think about something contracting, people have in mind a balloon. In fact, it's often used, and it's a bad analogy, but they often say, “Oh, in the expanding case or inflation case -- obviously it's like blowing up a balloon, it's going to become flatter and flatter if you imagine were standing on top of it.” I could show you right off, if you really believe that picture, you don't need inflation because the universe is expanding by an exponential in the original big bang model without inflation. So why wasn't that expansion already enough to make it flat?
There's something missing in that analogy. It's not how flat it is, it's how flat it is compared to how far you can see. And that's set by your horizon. So, if you just have slow expansion, like in the original big bang model, it turns out the horizon grows so fast compared to the expansion rate that, even though it's expanding and becoming flatter, you're seeing more of it, so that the curvature becomes more apparent. That is, if you have a universe which only has matter and radiation, no inflation, what happens? If you begin only seeing a small piece of the universe, that piece might appear flat.
But over time, as you more and more of the universe because light has had a chance to travel a longer distance, any curvature should become more and more apparent. So cosmologically the universe is said to be becoming more and more curved. In inflation, you still have expansion, but the horizon, the part you can see, is not growing. If you can only see that one part, it appears to be flatter. The universe is said to be flattening.
So that's the cosmic sense in which it's flatter and flatter. In a contracting universe, we can have in slow contraction a situation analogous to a situation where the balloon is contracting very slowly but the horizon is contracting very fast. So, even though the balloon is getting more curved as it slowly shrinks, the fraction you're seeing of it is rapidly becoming smaller. So, once again, cosmically from that limited viewpoint, the universe looks flat. And that's all we measure cosmologically. We don't measure the actual curvature. We measure its contribution to what we see within our horizon. And so that's sufficient to solve the flatness problem. Wisdom that I didn’t know at the time but learned much more recently.
So, to get back on this concept of working very comfortably within the realm of science and being able to measure things—
—what were some of the most compelling experiments that convinced you that these very heady concepts were, in fact, the province of science and not speculation or metaphysics?
Well, the first thing is you could test it. So it's a collection of pieces of ideas. There's the general relativity. “Do we trust Einstein gravity back to that time? How far back can we trust it?” Well, it seemed like at the time we could trust it all the way back to at least nucleosynthesis periods, at least to the one second mark. Of course, we're extrapolating back further back in time -- to within a fraction of a second. And we know if we could really go back to when the energy density in the universe exceeds the Planck density, it's going to be different. But it seemed like inflation didn't need to get to those very high densities.
So although it's an extrapolation, it wasn't a crazy extrapolation to say “OK, given that goes back to one second or well below Planck density, I'll buy the Einstein gravity part of the story for now. The grand unified theory is also part of the story.” Of course, it was a popular idea at the time. So you could ask how well that was doing at the time. At the time there was a lot of enthusiasm that this idea was going to work in one form or another. And Harvard was a real center for this research. So it seemed hopeful. It seemed electroweak unification was in good shape. So why not grand unification?
Inflation would also support the idea there had to be dark matter, in the sense that, to be cosmically flat, you needed to have the total energy density equal to the critical density. So in addition to ordinary matter, which we knew could only be a few percent of critical based on nucleosynthesis -- we knew we needed to have another energy component in there. Dark matter seemed like the obvious candidate. People thought, at the time, that neutrinos were an obvious candidate. There were even some early experiments that claimed to measure neutrino masses that were in the right range to account for the dark matter density. Sounded like everything was fitting together. General relativity, grand unified theories, proton decay was supposed to be relevant. Those experiments were ongoing. The neutrino experiments measuring masses. Just seemed like everything was fitting together beautifully.
Of course, it was a mirage. [laugh] The neutrino story went away, proton decay went away. We haven't seen it yet, et cetera. And our notion of grand unified theories might still be—it's not clear how that's going to go with string theory and all that. But it seemed like there was just a confluence of ideas, all happening, and we were going to wrap up everything in just a short period of time. String theory came along and added to that sort of optimism during that period within the next few years. So I'm sort of covering a period of 1980 to 1985.
So different things happening, coming in and out. But it just seemed like there was a lot of optimism. Yahoo! We're gonna put together our astrophysicists and our cosmologists and our relativists and our particle physicists, and we're gonna all work this out together. It's gonna be done. It's gonna be really exciting.
So, Paul, I think that's a great place, in terms of a narrative break, in terms of we're gonna start for round two on your time at Penn, and then we'll end on this optimistic note about this all coming together, and we'll see what happens. So I think now's a good place. I'll cut the recording here.
This is David Zierler, oral historian for the American Institute of Physics. It is June 18th, 2020. I'm delighted to be back with Professor Paul Steinhardt of Princeton for round two of our discussion. Paul, thanks so much for joining me again today.
Thanks, David. Thanks for having me back.
To start, we're going to take it back a little bit, back in the narrative, before you joined Penn. Tell me a little bit about when you got involved in condensed matter physics, and who some of the key people were that got you interested in this field.
This starts with my undergraduate days at Caltech, when I decided that I was going to choose physics. I didn't know what area of physics to choose from, so I decided to spend different summers and different research experiences during the year exploring different areas. And after my junior year, I applied to an NSF-supported program at Yale University, which would give me exposure to condensed matter physics, which I had no exposure to up to that point.
And did somebody tell you at Caltech, “Paul, this is a blind spot for you. Condensed matter is pretty exciting. You should look into this?” Or this was pretty much on your own?
Just pretty much on my own. Again, I think influenced by Feynman. The main message I got from Feynman was that all physics was interesting; it was just a matter of finding a good problem. So I thought, “OK, so I should learn other areas to look for good problems.” And I was accepted to the program, and I worked mainly with Richard Alben, who was a professor there at the time.
And what was his work on, at the time? Richard’s?
He was working on amorphous silicon. Silicon as a crystal makes a beautiful tetrahedral diamond network that is extremely well understood. But when you form silicon from liquid rapidly, it forms an amorphous phase, a glassy phase, which was not well understood at the time, in 1973. And even today, we continue to debate about the precise arrangement of atoms, the ideal arrangement of atoms in amorphous silicon.
And this lack of understanding is primarily due to what? Instrumentation? Theory?
A combination of things. If you make amorphous silicon, and I make amorphous silicon, depending on how we each make it, the arrangement of atoms might be somewhat different. Are you interested in what happens if you make it very rapidly, or if you make it as cool as possible? Cool it as slowly as possible, but so that it still remains amorphous. But then you have to watch out—if you cool it too slowly, it will form a crystal. So there’s a question of what is—sometimes what people call the ideal glass, or the ideal structure. The optimal structure that could form without forming a crystal. And that’s somewhat of an experimental question, but also a theoretical question that theorists still debate about. “And is there a phase transition from liquid to glass, analogous to what we have in going from liquid to crystal? Or is glass a frozen liquid?” Which would be a naïve point of view. And all these subjects continue to be debated. One of the problems is that you don’t even know exactly where the atoms might sit.
So when I arrived at Yale, the topic that Richard suggested to me was to try to produce a computer model of amorphous silicon. So this is the 1970’s. It was early days. And there didn't exist, at that time, any kind of computer model. When people would model it, they would actually take tetrahedral plastic units and stick them together and to try to form a structure that would remind them of some image they had in their minds of what amorphous silicon might look like. But plastic doesn't have the same forces between it that real silicon atoms do.
So, my job was to make a physical model, then roughly measure the coordinates, then take those coordinates, put them on the computer, and relax it under the real forces we think silicon bonds with. So it was the first, if you like, realistic computer model. And then we could calculate all kinds of things about it—its elastic properties, its electronic properties.
And so a whole series of papers emerged from that little beginning —I forget whether it was three or four papers—on different aspects of it. Working mainly with Richard, but Michael Thorpe and Denis Weiare were also there at the time. All three of them left a few years later, but they were all there at the time, and it was a lot of fun. Very intense summer, but a lot of fun working with them.
And at the end of that summer, everyone in the program had to give a talk. And they invited people from IBM, in particular Marc Brodsky, who was then at IBM, to come and listen to the talks. Then, at the end, he made me an offer to go to IBM the next summer to work on an experimental project. So after my senior year – the summer of 1974, between Caltech and Harvard -- I spent the summer at IBM Research in Yorktown Heights, New York, working with Marc in the lab. We were trying to make junctions between amorphous silicon and crystalline silicon -- novel electronic elements. And while I was there, I met Praveen Chaudhari, who was an experimentalist but with a strong theoretical bent, who later became Director of IBM Research, and then became Director of Brookhaven National Lab.
Paul, this research during the summer, this was pure basic science? Was IBM interested in some practical commercial applications of this research?
Well, I think it was eventually going to be practical. I would call this pure research. The first junctions—these would be alternative diodes or semiconductor junctions, not between crystal and crystal, or p- and n-doped, but between amorphous and crystal -- to see if they had interesting electronic properties. So that’s how I first met Praveen, and we talked a little bit about amorphous metals. Amorphous silicon has covalent bonds, amorphous metals have metallic bonds. So metallic bonds are modeled by central force potentials.
And then I went to Harvard, and spent the next four years working on particle physics. I was always worried that graduate school would narrow me too much, so I purposely chose that summer after my PhD to try to do something different, and decided to go back to IBM. It was 1978. I talked to Praveen, and he said, “OK, why don’t you come work on this idea of modeling now, making computer models of amorphous metals?” The idea was to begin with the liquid phase, and simulate cooling it to form a glass. And then, again, we had a whole series of things we wanted to study about that glassy or amorphous metal phase. Again, its mechanical properties, its defect properties. We had a whole program of ideas that we worked on over that summer, and for the next few summers.
By that time, I had a foothold in condensed matter physics. And as a graduate student, I should say, I would often attend the condensed matter seminars anyway, just because I tried to attend seminars from different fields. And so it was just one of those subjects that I was just keeping track of—it’s one of those schizophrenic things I was doing on the side, while trying to work mainly on my particle physics, particle theory PhD. But it turned out to be very influential.
This is a theme that we'll return to, because as we discussed last time, one of the things that’s so unique about your research agenda is how incredibly diverse it is. So even if, as an undergraduate, you thought it would be interesting to spend a summer on condensed matter, as you just said, entering Harvard, you were very self-conscious to work against becoming narrowly focused, right?
And so my question is, that’s sort of usually how the system works. The dissertation is supposed to be narrowly focused, right?
So I'm curious, sort of—again, in terms of is this mostly about your intellectual ambition even as a young man? Are there particular people—I know you mentioned Feynman who said, you know, all of physics is interesting. Which is wonderful as a thing to say, but not necessarily as a way to lead one’s scholarly life. So I'm curious, did you always plan to keep your hands in multiple fields in physics? Did you want to identify yourself professionally in that realm, as you were sort of maturing in the field, even from the beginning of your graduate work?
Of course you ask me to remember what I was thinking [laugh] long ago. I think partly it was my personality, that I was broadly curious. I never felt there was one particular type of problem that motivated me. It was almost more of finding really good problems to work on. And then especially in the experiences that we're about to talk about as a postdoc, this going from one subject to the other, going back and forth, using one to inspire the other and vice versa, I just found it rapidly very rewarding and very refreshing. So what I found, for example, as I started my postdoc as a Junior Fellow at Harvard—going straight ahead with what I had done for my thesis was just grinding. Whereas if I was looking at other things, I just found, I don’t know, it was very refreshing, and I could be more creative.
So within that first year, two important things happened. One was Alan Guth's talk on inflation that we discussed. It introduced me to cosmology. Another was a series of talks I heard from David Mermin from Cornell. He was talking about topological defects in crystals and other kinds forms of matter. The combination immediately led me to an idea for a research project in cosmology. As I mentioned, after Guth's talk, I was deeply disappointed that his great idea failed. It failed because once inflation starts, once the phase transition starts and the universe is in a false vacuum phase where it triggers inflation, there is an energy barrier that prevents most of spacetime from escaping fast enough to end.
Having heard the talk by Mermin about topological defects, I had an idea about how to solve Guth's problem. One of Guth's goals, in fact his original motivation, was to get rid of magnetic monopoles, which are, in fact, a type of topological defect formed by the fields that make up the vacuum. Guth's idea was to inflate them away, spread them out so fast that none would be visible today. I had the idea that the monopoles could be useful in ending the phase transition. Since they will be produced anyway, why not put them to good use? Maybe they could do something which I called "dissociate." You see, monopoles are like a vortex in a superfluid. The vortex has an outside and an inside, separated by an wall of energy. The interior of the vortex is normal fluid. In a similar way, a monopole in a false vacuum phase has an inside and an outside separated by a wall of energy, and the inside contains a true vacuum phase.
So, to escape from the false vacuum, instead of relying on very rare quantum fluctuation that generate bubbles of true vacuum that expand, which does not happen often enough or expand rapidly enough to take the universe from the false to the true vacuum phase, my idea was that to use the monopoles that were already abundant when inflation started. Because their interiors already contained true vacuum phase within their energy wall, it was possibly to arrange the energetics so that the wall would simply expand, the monopoles would dissociate, and the expanding monopole walls would complete the conversion of false vacuum to true without any bubble nucleation. So that was the idea I explored.
And then -- this was just my way of thinking about thing -- I switched to thinking, "Well, is there a condensed matter example where something analogous would occur that I could study?" I naturally thought about vortices in a superfluid, the example that had originally inspired me. However, for the simplest superfluid, superfluid helium-3, the conditions turn out not to be right. I discovered, through reading, that the conditions would be right in a superfluid mixture of helium-3 and helium-4. As I read more about this superfluid mixture, I learned that it undergoes a different kind of first order transition, a so-called spinodal transition. Unlike Guth's case, the energy barrier between the false and true phases disappears as the temperature changes. And that's how I got the idea for what became known as a slow-roll phase transition for inflation.
So it was very much this back-and-forth thinking. At one moment, I'm pursuing a question in cosmology; that inspires a question about an analogue in condensed matter physics; from which I learn about a different kind of phase transition; that inspires a new idea in cosmology. By the time I was leaving Harvard, I was getting excited about this new idea of applying this spinodal transition concept in cosmology, instead of the monopole idea, about which I was not so confident. The new idea seemed a lot more promising to me.
Given this mindset and these ambitions, I want to ask a question about your relationship with Sid Coleman. So a dissertation advisor’s job is to oversee a dissertation and to get that student to move on, right?
And given that you're sort of all over the place, in a very good way, did he have to sort of manage you and focus you to get you to just do something? Pick one thing to move on? Did you sort of keep that private, because you realized you needed to do something and move on, and Sid Coleman was your means to do that? Did your share these ideas with him? How did all of that work out?
That’s a good question. First of all, the reason why I really liked having Sidney as an advisor is that he didn't guide me at all. He didn't believe in that. I think it was not his philosophy. And that’s what I liked about it. I didn't want someone to tell me what to do. I wanted someone who, if I got stuck, could tell me how to get unstuck. And that, Sidney was great for. So there were various times when I got stuck on a problem in the quantum field theory area, and it was really useful to talk to him. But in between—he never called. You had to go in to meet with him. He would never contact you.
And in terms of the condensed matter stuff, I don’t think we ever discussed it. It was just something else I was doing. Even as a kid, I was doing research projects, beginning from a little kid, onward. Based on my summers at Yale and IBM, I felt that by the time I went to Harvard, I already had lots of research experience. That’s why I didn't want someone who was going to tell me what to do. I wanted to see if I could come up with good problems. And I thought the best way to do that, was just to practice coming up with ideas and seeing, “How do you find good choices? How do you make bad choices?” So I didn't particularly want to be monitored by anyone.
In terms of keeping your focus, because that’s the name of the game to just finish the dissertation, you were pretty able to do that on your own?
Yes. And as I think we discussed last time, it was kind of an accidental thesis. [laugh] It was a question I had come up with and that I had pursued and worked out. And again, I got stuck at various points, but Sidney was very useful in getting me unstuck, and in some cases putting me in contact with people who had some advice that was very helpful. But it was pretty much an independent project, a solo project, and I was sole author on the paper. It was not something I was doing in collaboration with anybody.
So that’s just the way I was working at the time. And I was still trying to figure out—since it was an accidental thesis, and finished a little bit sooner than I expected, I thought I was now ready to work on a really big problem. But no -- I was already a PhD. That’s when I kind of got a little bit worried. I did want to spread my wings and try other things, and just look at “What are the best places to find good problems?” And so I was doing some of that, which was a risk—it’s not what people generally do at that stage. I was keenly aware that there were other people who were progressing very rapidly by just keeping their narrow focus, and just going straight ahead. I was conscious of that, and just accepted the risk. I gambled that over time, I’d be a much happier scientist if I just took my approach, which was try lots of different things, and lots of different areas, and enjoy learning, and then one stimulates the other.
And the example I just gave you was an example of that. It was not like I planned that. I couldn't have possibly planned that. I couldn't have planned on seeing Guth’s talk. I couldn't have planned on thinking about monopoles. I couldn't have thought about this helium-3 connection, and then the connection back. But it happened, and it happened repeatedly over time. We'll talk about another example in a bit. When the approach keeps working,well, at some point you say, “OK, fine. I go with that.”
I wonder in terms of taking that risk if at least subconsciously you were thinking, you know, “This worked for Feynman. Feynman took risks. He was involved in all kinds of things. And look who Feynman was.” I wonder if you were thinking that this was—
I would never, ever compare myself to Feynman. [laugh]
Not that you would compare yourself, particularly at that stage of your career.
So I never—no. What I mean is, if I were as talented as he, of course I could do that. No, I was taking more risk, because I had more ordinary talent. [laugh] So I knew that, too. So I wasn’t foolish, in that sense. So I just felt that if I was doing science, I should really enjoy it. And if I didn't enjoy it, I could do something else. I wasn’t sure if my career was going to be successful. It took several more years before I thought I would actually be successful, or even be able to get a permanent job. But I just said, “If I can’t do it my way, I'll just go do something else. I'll figure out something else I can do.” So I just knowingly took the risk. And at various times, it was painful. Especially when it came to job searching. But it worked out in the end.
In terms of that job search, is now a good transition to the beginning of your time at Penn?
No, we have to go back one more thing. So I gave the example of the IBM work and how that stimulated interest in defects, and how that then connected to cosmology. But it took another direction, too. Completely different direction. So at this time, this was around the time when Kosterlitz and Thouless -- who later, in 2016, won the Nobel Prize in Physics -- were doing their seminal work on the XY model, and phase transitions in the XY model. And the idea of those phase transitions is that they would occur through the production of pairs of topological defects. So there’s the topological defects appearing again, which was capturing my attention.
And at Harvard, David Nelson and Bert Halperin were working on a theory of two-dimensional melting. So if you have a crystal, which was a hexagonal crystal, and it melts, you might think as you raise the temperature it goes straight from crystal to liquid. But their hypothesis was “No, that’s not what happens. It goes to an intermediate phase in which topological defects form, spread out, and that takes you to an intermediate phase called a hexatic phase.”
And then around that time, in 1980, David Nelson and a student, John Toner, whom I knew well, were working on yet another idea, this time in three dimensions. “Maybe a cubic crystal does something analogous, and instead of going from cubic crystal to liquid, it goes from cubic to cubatic,” which is what they called it, “to liquid. And if that were true, it would be great if there were computer simulations that would illustrate that.”
Well, I had my hands on the world’s largest molecular dynamics computer simulations of liquids—going from liquid to solid. So David Nelson and I had a conversation about that. We could use my simulations to test their hypothesis.
The idea of a cubatic phase—or hexatic phase, for that matter—is the atoms are randomly oriented, arranged, like you might think in a liquid. But if you look more closely at the bonds between them, they on average align along certain preferential directions. So in two dimensions, it would be along the directions of a hexagon. In three dimensions, the hypothesis was it would be along the edges of a cube. So even though the atoms are disordered, the bonds are orientationally ordered. They have average orientations which align in certain directions on average. So I could potentially test that in my simulations.
Now, there was a bit of a barrier to cross, which was, “What’s the right way to measure whether there is this alignment or not alignment?” And so what David and I invented was what we called an order parameter, something which you could average over all the bonds, and it would tell you “If you get a large signal, you have this order, and if you don’t get a large signal, you don’t have this order.”
And then, the way we invented it, was not just to look for cubatic. It turned out to be straightforward to generalize the order parameter method to check for all possible symmetries, not just cubic. That way we could show—if cubatic really showed up, it should get a strong signal. And all the other symmetries should show up as a low signal. Well, now having invented that idea, we apply it in our program, and on our simulations, and cubatic does not show up. But strangely enough, something else does show up.
What does that tell you, that cubatic doesn't show up?
It says it’s wrong. The idea was wrong. You don’t find bonds aligning, on average, along the edges of a cube. So it meant their theory was inconsistent with what we were finding in the simulations. But something else did show up as a strong signal, and that turned out to be icosahedratic -- the forbidden icosahedral symmetry. Something with the symmetry of an icosahedron, which is one of the Platonic solids, with 20 identical triangles. It’s like the Dungeons and Dragons dice that you might have seen, which has 20 sides.
I'm a nerd. I know those dice. [laugh]
They make them in all the different shapes, which are very relevant here. But among them is the icosahedron. Now, that was interesting, because it was unexpected, at first. On the other hand, it was known that if you put together just a few atoms, they like to form icosahedra, with one in the middle and 12 around the outside. It’s also famously known, for hundreds of years, that you can’t make a crystal with the symmetry of an icosahedron.
What our simulation showed, to be more precise, is: “If I begin in one place and compare the bonds as I go out, they tend to align along the icosahedron -- but if you go out far enough, they kind of lose track.” So this was consistent with the centuries-old rule of crystallography that says you cannot have an icosahedral crystal. Because if it were an icosahedral crystal, the alignment would have been icosahedral all the way out to infinity. But instead, this was kind of “icosahedral-like” up to a fairly large distance, about ten atomic spacings—much larger than you'd expect—and then it would kind of peter out, in our simulations. But it was still absolutely surprising that it would occur at all.
And it led to two research projects, one of which David took in one direction, and I took in another. David wanted to see if he could predict and explain why it only went out so far and stopped, and he developed a whole theory to explain that over the next few years. And at this point I was on my way to Penn, and I had a different idea, a crazier idea. “Maybe you could actually make the icosahedral order go out to infinity. Maybe the simulations are actually on the edge of doing that; we just didn't manage to capture it in our simulations?” That was a crazy idea, because it violated the laws of crystallography that had been around for hundreds of years.
And when you say to infinity, what does that mean practically?
As far as an Avogadro’s number of atoms. So not hundreds, not thousands, but Avogadro’s number. As big as you make a typical sample in the laboratory. So that was considered impossible at the time. One of the first things you would have read in a solid state physics textbook at that time, in the first few pages, is “Matter can form certain kinds of forms, and there’s certain symmetries it can’t possibly form. For example, it can’t form an atomic arrangement with this icosahedral symmetry.” You'd find that in elementary textbooks at that time.
And as crazy as it was, what compelled you to keep at this?
I mean, just the intellectual satisfaction of overturning fundamental assumptions?
Of course, yeah. [laugh] That’s a big plus. Well, partly, I felt it was kind of an—again, these were not articulated ideas—but I think the feeling was “Well, I might fail, but if I fail, I still have an interesting question. Which is the maximum distance you could possibly make it icosahedral, and what stops you ?” And if nothing -- then you win big. Then you've really discovered something remarkably new, a form of matter that people thought was impossible before, a new phase of matter.
So you're expecting the first, but you know, maybe the second isn’t impossible. Because already what we found was very surprising. Although it was kind of a marginal result, because it wasn’t infinite, it was enough of a tease to say, “Oh, we've come a lot farther than we thought with this icosahedral symmetry.” Without intending to. Just by putting atoms in a computer with a certain force, and they just condensed into that, without our having made any special effort? It was kind of a teaser. “So, why not? Why not try? Why not take a go after it?” was my thinking.
So yeah, so by the time I left Harvard, I had kind of these two seed ideas, one which I definitely was really gung-ho about, the cosmology one. And this other one, this crazy idea about forbidden symmetries, was something—“Hmm, if I have time, I might put some time into that.” It wasn’t quite clear how that was going to get started. I wasn’t clear how to start that.
So the first question with Penn is, faculty hires are often made thinking about what role the new hire—where that person would fit in the faculty. Right?
So was that baked into your hire—an appreciation that you were not going to fit a traditional, relatively narrow mold, in terms of your research agenda and interests? Was that appreciated at the time?
Very much so. It’s actually why I went to Penn. So I mentioned the disadvantages starting your career going in many directions at the same time. I certainly felt that on the job circuit. I was officially a particle physicist, but I was beginning to make forays into cosmology. Nowadays, that would seem very ordinary, but at that time, that was considered kind of “iffy.” Particle physicists were just beginning to move into that direction. And then I was doing this other stuff in condensed matter physics.
So in most places I applied to, either I didn't get interviewed, or if I did get interviewed, there was always some moment where I felt like I was being put against a wall, when they said, “OK now, which one of those things are you going to do, actually?” And my answer was, “Well, actually, all of them.” [laugh] I mean, I knew that was the wrong answer. I knew that wasn’t what they wanted to hear. But almost always the response was, “Oh, thank you very much,” and that was the end of that.
Paul, I'm curious about who you considered peers among this very rarified group of people who were officially particle physicists, but had interests in cosmology. And how you said that at the time, in the early 1980’s, this was a very forward way of thinking, as opposed to today, it’s sort of more normative. Who were some of the people who were, along with you, pioneers in making these connections?
There are giants like Andrei Sakharov and Steven Weinberg, who would spend some of their time thinking about cosmology, and wrote about it. But it was not their main focus at the time. It was a small bit of what they did. With the advent of gauge theories, we had the idea with grand unification, we could suddenly go to temperatures and densities beyond what you could get in the laboratory. But they implied that there would be phase transitions that occurred, fractions of an instant after the big bang, that could have substantive effects, such as producing monopoles.
John Preskill, who was a grad student at the same time I was there, for example, pointed out that would create a problem. You'd overproduce these monopoles. That ended up inspiring Guth and Henry Tye to think about how to solve that problem, and Guth eventually to introduce the idea of inflation. I'm summarizing people who were close to me, sort of influencing me directly. But you could go around the world, and there would be a spotty set of people in Japan, in Europe, in Russia, who were also beginning to take the relationship between quantum field theory and the early universe more seriously, and the role of phase transitions more seriously in the early universe.
So that sphere was growing, but the particle physics community, as a whole, was more focused on accelerator physics. And even in the early years, I would say for the first—I'm not going to be precise about this -- but at least for the first five to ten years, when I was an assistant professor and applying for a grant to the DOE and I was working in cosmology—that’s what I was applying to get support for. It was always, “Well, we can kind of slip this in. We'll try to quietly slip this into the DOE.” Because it was not part of their mission. This was considered like you're doing something a little bit on the outside of what we actually do. Nowadays, of course, it’s a core of what they do. It’s one of their primary areas. But at the time, it was definitely considered “iffy,” if that’s what you were working on. And you always had to show, “Oh, but this will help us understand something about accelerator physics in some way.”
Now you mean “iffy” as a multidisciplinary issue. You don’t mean “iffy” in terms of people who would identify themselves primarily as cosmologists.
I was really moving into cosmology, and what we would call today particle cosmology. And if you were doing that, the DOE felt it had certain missions that it was supposed to support, and cosmology was not officially within their mission, as they viewed it at that time.
To the extent that these are semantics—
But there were very wise directors, managers, at the DOE, and they knew to look the other way. They were smart enough to look the other way. And there were really wonderful people there. And this also applies to my work in condensed matter physics. They also looked the other way when I would work on condensed matter physics. They said, “If you continue to do only this for ten years, and you're going off in some direction far from particle physics long term, we can talk, but otherwise just go do your work.” Which would not be as true today.
Right. So as a matter of semantics, in terms of developing cosmology as its own distinct field, obviously those are important distinctions, but for the purpose of putting your best foot forward in a grant application, would it have been better to say you were doing astrophysics, or you were interested in astronomy? Was the concept of cosmology sort of too far out there to be effective in these—?
It would have been the same problem with astrophysics and astronomy. So, I was supposed to say particle physics. If you want to do astrophysics and astronomy, you should go to the NSF. So it was a common thing between the agencies, where they've kind of parsed out which agency is most responsible for certain fields. And then things happen, like fields merge, or new fields come into being, where for a while there’s often years of—it’s difficult to go forward in that subject, grant-wise. And then there’s some acceptance and relaxation again. So at that time, cosmology was considered beyond the edge of what they did, although there were increasingly more people, young people my age, coming into that field.
Were you amenable, or at least were the people making these decisions—were they amenable to the idea that cosmology actually had important things to teach particle physicists? That it was a two-way street?
I think they did. I think they got it. But I think that the instructions they were getting from their higher-ups, or from committees that were supposed to decide where DOE money was supposed to go—they're always worried the core of the field, as they see it, is not getting enough money. So if you're spending money over here, on the side; that’s money not being spent in the core. So there’s always that kind of tension.
And wise directors know how to manage it, and there were really wise directors at the time. P.K. Williams was our DOE program manager. And it was always great to talk to him. He was always very calming, He was very good at looking the other way, [laugh] and just saying, “You're doing great work. Just do it, and we'll worry about it later.” So I don’t know how he was working on the inside. I think it’s more programmed these days, more directed, more stovepiped. That’s definitely the feeling one gets. Where you have to say more precisely, “I'm doing exactly this kind of particle physics, when I do this project. This kind of particle physics and not that kind.” And I'm parsing my time—"So much of my time is on this type, and that type.”
Cosmology is now part of the core, so you don’t have that problem. But if you're doing anything that’s not quite fitting into certain categories, again that causes funding problems, more so now than then. I think they used to give managers more leeway, and they had good managers who showed good wisdom.
I want to ask about your overall experience at Penn, but focused on your initial years there and your impression on whether they were going to make good on this assurance that you did not want to be pigeonholed. In fact, it was a gamble. You went to Penn because you thought that they would allow you to do whatever you wanted to do.
Did it play out pretty well, as you had hoped?
Yes, very much so. I immediately started working in cosmology. The day I arrived, already there were two prospective students sitting at my door who wanted to work with me on cosmology.
Now, was the astronomy and physics program, were they merged at that point? Were they separate?
No, no. At that time, physics was a separate department from astronomy. There was a rather small and aged astronomy department. The people were approaching retirement, and the university was beginning to think about what to do with them, but basically they were being left—
They were not regenerating.
They were not really regenerating. They had one person there that was younger, who left.
Was there talk about merging the departments during your time there?
Yes, eventually. I actually led the effort, but that was ten years later. At that point, they were really thinking of closing the department. I helped lead a group that said, “No, no, that’s not what you should be doing. This is a very exciting field, but it belongs as part of physics, and that’s a better way of growing a new modern astrophysics effort.” By that time, everyone in the old astronomy department had left, and I helped bring on the first few people that now form the core of the astrophysics part of the department, to help get that started. That was a long effort, but I think it’s very successful.
So day one at Penn, item number one on the research agenda is cosmology.
Yes. Because there, I had a formed idea of what I wanted to do. And one of the two students was Andreas Albrecht, and I assigned him this spinodal problem that I wanted to work on, to try to make some computer models. That is, to try to make some computer simulations of what would happen to the field as it rolled down the potential away from the false vacuum and towards the true vacuum. “What would be the right physics to describe it? And how would it affect the inflation? Could we have our inflation and gracefully exit at the same time? And smoothly exit at the same time?”
And the other project was given to another bright student, Lars Jensen, and his job was to work on the superfluid helium problem and see if we could observe vortex dissociation in that problem. So it was cosmology inspired, but it was more condensed matter. But then he later worked on other important problems that were more cosmology.
So the project with Andy went pretty swiftly. Within a few months, we had identified what I thought was the right physics. It looked like we could get what we wanted, which was you could supercool into this false vacuum phase. As you supercooled enough, for a very special kind of gauge theory, which I'll describe in a second, the barrier would disappear, and something that would be the analog of spinodal decomposition in the helium problem could occur where the field would simply escape from the false vacuum phase and slowly roll down a plateau, an energy plateau, towards a true vacuum phase. And while it was on this high-energy plateau, that energy would drive inflation, and then when it went downhill, inflation would end. And so you could have the inflation, the smoothing, the flattening that you thought you wanted, but you could also have what came to be called the graceful exit, the smooth exit from inflation—what Guth had not been able to get. In fact, Guth and Erick Weinberg had written a paper around that time explicitly explaining how graceful exit was impossible. What Andy and I had found was a loophole they had missed.
And the particular example of gauge theory we were thinking of, was one that connects to Coleman again. It’s a paper which Sidney Coleman and Erick Weinberg had worked on when Erick was a grad student at Harvard -- a special gauge theory with a massless Higgs at tree level, which then gets a mass when quantum corrections are included. It’s called the Coleman-Weinberg model. And that example turned out to be right in the middle of a small range of theories that underwent spinodal decomposition and that would do what we wanted, allow inflation, but also allow inflation to end.
What are the big research questions that this line of work is looking to answer, fundamentally?
Like what Alan Guth was trying to do, he was trying to ask: “Could a phase transition in the early universe account for how you could come out of the big bang with some random initial conditions and end up with conditions where the universe was at a smooth distribution of matter and energy?” And also the geometry of the universe -- instead of being distorted and warped and curved, like it was possible coming out of the big bang, would instead be geometrically flat, like obeying the laws of Euclidian geometry.
So that’s what Alan was trying to do, but failed. He started, but failed, to get back to a universe that looks like ours. Here, the idea was you could have your inflation, you'd smooth and flatten it, but it could only last so long, because eventually this field would roll off the plateau, roll off the high-energy plateau to lower energy, and then you'd have ordinary expansion. You wouldn't have inflationary expansion. And then the energy that was stored in this field, well, the thought at the time was—we hadn’t yet worked that out—could be converted into ordinary matter and radiation that would make the stars and galaxies we observe. So it was trying to take the notion that Alan began with, but complete the picture.
Were you following what was going on at NASA with projects like COBE? Was this interesting to you? Would it be helpful in developing your ideas?
Not at the time. Shortly thereafter. [laugh] But at the time, in these first months at Penn -- so I'm describing the fall of my first year of Penn, which would have been 1981-- we were just trying to see if this idea worked at all. And there was a worrisome part to it, which held me up, and would have held me up for longer, which was: Well, I've already kind of implied that this did not occur for its typical phase transition. You needed a rather special fine-tuned phase transition. So it bothered me that we had a fine-tuning problem that we were trying to explain. “How did the universe begin with remarkably smooth and flat conditions?” We were trying to explain how that could occur through some mechanism, but our mechanism itself had a tuned knob in the middle of it. And so, I was struggling with Andy—we were trying to see on the computer, how much could we push the parameters. “Maybe it’s more robust than we thought?” So that delayed us for quite a while, for a number of months.
And just to take this arc of the story to a certain point -- over winter vacation, we received a preprint from Andrei Linde, who was working in the then Soviet Union, in which he had a good fraction of this idea himself, independently, working with a similar kind of model, Coleman- Weinberg. There were some important differences. He hadn’t gotten the gravity story right. He hadn’t realized that gravity helps you slow this field down. It produces a frictional effect called Hubble redshift, or Hubble damping. And it didn't seem to mind him that it required tuning, and all that.
But it put us in an awkward position, because we had now a pretty large package of work completed. I came back from Christmas vacation. And a few days after the New Year, we had a visitor to Penn, Mike Turner. And I hadn’t been talking about this much to anybody, by the way. Occasionally at lunch, I’d mention something, but I don’t think people were particularly following it. But at this particular occasion, Mike Turner from the University of Chicago had come to give a talk.
Do you know what year this would have been?
This would have been the first few days of January, 1982. And he said, “Oh, there was this interesting paper by”—he was talking at lunch—"by Andrei Linde.” And I said, “Oh, I know all about it.” And I got up and explained what we had done. I explained what was different about our idea, et cetera, et cetera, et cetera. And afterwards, my colleague, Gino Segrè, senior colleague, who was at the time the leader of the particle physics group—he took me aside and he said, “What do you plan to do?” And I said, “I don’t know. I feel like I've been scooped for the most part.” He said, “No you have to stop everything you're doing right now, and you have to write a paper.” Which is what we did.
That was good advice from Gino?
That was great advice from Gino, yeah.
In what way did you feel like you had been scooped?
Oh, well, because Linde didn't have the phase transition idea. He didn't have the gravity effect of Hubble damping, which turns out to be really important for reasons I'll explain. But he just had the idea that there could be a field slowly rolling down a potential. That’s essentially what he had. That was essentially his whole paper. So he still had a piece of the idea.
And I don’t know, at the time, I was kind of naïve about what was the appropriate thing to do. Nowadays, I think I know [laugh] what was—I’d probably give the advice Gino gave me to a younger person. Partly it was maybe being Sidney’s student. Sidney tended to work on problems that he had complete control over, and there was nothing to compete with it. I thought, well, OK, somehow I had—I don’t know, I just felt—I thought—I felt unsure of what to do. And so it was important to have Gino’s advice.
And what was so important about writing this paper at that time, as Gino suggested you did?
Well, because otherwise, if we hadn’t written it, or we had written it months later, then to be honest, we wouldn't have gotten credit for having come up with this idea independently. So by immediately dropping everything and just showing everything we had done—and if you looked at the two papers, you could see there’s a lot of differences between them—it was clear that it was independent. So we weren’t trying to take credit from Linde, but we were trying to say, “OK, we've done something independent. And then if you're interested, you'll find that there’s some aspects in here which are missing there, but which may turn out to be important.” And did turn out to be important. So it was mainly for that reason. Otherwise, we would have just had put all that energy in, and it would have gone to naught.
Andrei called it “new inflation,” and we called it “the spinodal transition idea.” Andy and I also introduced the idea that gravity provides a kind of friction that slows the field down and helps inflation. This is called slow-roll inflation. So we each introduced some new terminology in the field.
Your career—just to say—your research interests make the narrative of the career—it’s actually tricky just to sort of keep things going forward, because we go back, and there’s all of these interconnections, so—[laugh]
I have the same problem. [laugh]
When does Dov Levine enter the picture?
It seems strange in retrospect. So in October—going back to the fall of 1981 when I started at Penn -- I was invited to give a physics colloquium, and I decided, because I wanted to make a point, not to talk about cosmology or particle physics, but to talk about the work I had been doing in condensed matter physics.
This is a way to remind everybody that this is still on the table for you.
Yeah. And that it was, in my view, an exciting project, even though it might not have quite the same pizzazz.
Was Penn strong in condensed matter?
Yes. Penn has historically been always strong in condensed matter, and it has always been one of the greatest strengths of the physics department, more than particle physics for sure. So, yeah, so this was also kind of daring on several [laugh] counts. But I had a good story to tell, and it was very successful. I basically talked about the stuff I had done with David Nelson on the glasses, that I was describing to you. But at the end of the talk, when I talked about this icosahedral order, I said something which I thought would get me into big trouble – which was “Although we only showed this icosahedral order extends to a certain degree, we were only using examples of single type atoms. It’s conceivable that, if you had two or more types of atoms, that you might be able to extend this icosahedral order much further, in fact maybe even to infinity, and if so, that would be something that would violate the laws of crystallography.” That was kind of the climax to the talk.
The talk was well received. I got questions about lots of things. But no one commented on the crazy idea at the end. In fact, I think I called it a crazy idea or something like that. A crazy idea. But in the audience was this young student, Dov Levine, and he came to me a few days afterwards, made an appointment with me, and said he wanted to work on that. This is what he’d like to work on. I said, “No, you didn't listen to me. I said this was a crazy idea.” [laugh]
“This is probably not going to work.” Because we really had no idea where to start. How would you start to construct such a thing? But he insisted that he really, really wanted to do it. I said, “OK. Well, let’s try something.” We didn't know where we were headed towards—but that’s the work that eventually led to quasicrystals.
I began by saying, “OK, what we're going to do is something analogous to what I did back when I was at Yale. We're going to start to make models of icosahedra, and then icosahedra of icosahedra, and try to see how far we can go and keep the icosahedral going, and see where we're forced to stop.” So that’s what we started off doing. We started with Styrofoam balls and pipe cleaners and trying to build things, and then measuring the coordinates roughly, and then relaxing them now under metallic forces, rather than the way I was doing it before with silicon.
What were some of Dov’s talents? What did he bring to the project?
Fearlessness was the most important one. [laugh]
Good humor, because this was really a ridiculous thing to try to do. I should say that his interest before that point had been general relativity. So he could have easily come to ask me to do cosmology, but instead he asked me to do this crazy thing. So I think courage, foolhardiness [laugh], a good sense of humor, is what he had to bring at the beginning. And willingness to — well, start on this crazy project, where you're doing science with Styrofoam balls [laugh] and pipe cleaners. So it’s kind of a silly thing that you're doing. But it was a means to an end.
So in the meantime—yeah, so it’s a little hard to explain the chronology, right? Because early in 1981, certainly this inflation thing is exploding. Because once I wrote that paper, and with Andrei’s paper, suddenly everyone was interested in inflation. Because they could now see how they could make workable models. It was like the beginning of a phase transition.
At the same time, Dov’s showing up in my office every now and then, and we're trying to do something crazy with our pipe cleaners and our models, and trying to see how we could build bigger and bigger icosahedral models. So I’d say for the first year or so—yeah, I guess the first year, full year, back to October 1982—not much happened on that. Except for failures. Except we saw, as we tried to build out our models, it was getting harder and harder. In fact, when I had the feeling when—almost had a proof that it was impossible to continue the icosahedral symmetry any further —we almost wrote a paper saying, “Ah, see? You can’t do it. And here’s the limitations.” But we didn't [laugh] do that. Now I'm trying to figure out which part of the story to pick up —so let’s say that takes us to fall 1982, for what’s going to become the quasicrystals.
Are you calling it quasicrystals before 1983?
1983 is when we first began to give it a name. We first called it crystalloids, and then later quasicrystals, as we came to understand it better. But at this point, we're just trying to see how icosahedral you can make something, what the limits are. Meanwhile, Nelson has an argument that says there’s a limit to how far you can go, at least for identical atoms. So he’s working on that point of view. So right now, we're not talking. It’s friendly – it was just because I'm at Penn and he’s at Harvard. I'm doing my thing, and he’s doing his thing -- we're not really communicating on a regular basis, Nelson and us. So that’s fall 1981. Meanwhile, this inflation thing happened.
Now, there were several things that bothered me about the slow-roll inflation idea as soon as we published it. The first, as I mentioned, was the fine-tuning. And secondly, there was no model for how you can reheat the universe. And so that’s something that Mike Turner and I, after he visited Penn, began to discuss, since I had showed him our idea. Eventually he and Frank Wilczek, along with Andy and me, wrote the first detailed paper to be written on how you can reheat the universe at the end of inflation. Sort of a detailed model. The field would roll off a plateau, oscillate around the bottom of the potential, the oscillations would excite degrees of freedom, matter, and radiation degrees of freedom, and that’s how you would convert the energy in the field to matter and radiation. Resolving that issue was pretty straightforward.
And then the third thing that bothered me, was that we had maybe succeeded too much. Inflation may have made the universe too smooth. Through slow-roll, not just smoothed it, but super smoothed it to the point where there would not even be galaxies or stars. That's the way it seemed at that moment.
And what is the distinction between smooth and super smooth?
Oh, I just meant it was so smooth, there was essentially no perturbation in the distribution of matter and energy. Glassy smooth, as opposed to smooth but with small bumps in it. And that’s a problem, because now you had a different problem. Not “How did the universe become smooth?” but, “How did you get the small degree of lumpiness in the early universe?” Because a real early universe had lumps and smoothness. Lumps on small scales, but when you average over large enough scales, it looks rather smooth. So you have to figure out how you're going to—where’s the lumpiness is going to come from? And, well, the only prospect for that, the only thing around, was quantum physics, because we had included the classical laws.
So this led to the question, “What would the quantum fluctuations do to this field as it rolled down the hill? Could they possibly be important? Could they provide some needed unsmoothing?” That was high risk stuff, because, you could find that the quantum fluctuations did nothing—the universe would still remain glassy smooth. You might find instead, though, that quantum effects drove the universe into a state with large fluctuations in energy and mass that were inconsistent with what we see. And there was no theoretical scheme for calculating how quantum fluctuations of a field in a gravitational general relativistic background would evolve with time in such a way that you could predict what the fluctuations might be left when inflation was over. So Mike and I decided to attack that problem as well.
Is Mike talking about dark energy at this point, or that’s still too early in the game?
Way too early, yeah. That’s not until 1998. So we're just thinking about inflation, and how you could get the seeds that eventually you're going to see in the microwave background, and form the seeds for galaxies. That was the idea. And what was known on the cosmology side of that was relatively little. There were speculations going back to Edward Harrison -- now they call it the Harrison-Zel’dovich-Peebles spectrum -- who had a guess as to what the fluctuations had to be to explain the universe we observe, the distribution of galaxies we observe. It was a kind of hand-wavy reasoning. Very hand-wavy, not really mathematics behind it.
And so we knew that if we couldn't get something close to that, we were going to be in trouble. But we had no idea how to calculate the result —we had to figure out how to put general relativity and quantum physics together to do this calculation. Not quantum gravity, but quantum physics of the field, and then classical background described by general relativity. And then we had some conversations -- I was telling Alan Guth about the work Mike and I were doing at one point, and he got interested in that problem, and he and So-Young Pi began to work on this; I think Mike had some conversation with Stephen Hawking, and Stephen Hawking began working on this.
And just around this time—no, I think it was a few months earlier—Stephen Hawking had sent a letter of invitation to me and to others about a meeting he wanted to have that summer, the summer of 1982, the Nuffield Workshop, in which he was bringing together people who were working on cosmology and particle physics generally. And all these groups that were working on this idea ended up meeting there. That wasn’t planned when he sent the invitation, but that’s what ended up being a real focus of that meeting in the summer of 1982.
So there was pressure to try to solve this problem before we got there. Now, this problem--if you produce perturbations in the universe, how that evolved --was a notorious problem of general relativity. Because of the nature of general relativity.
The problem, roughly speaking, is like this: Suppose we're both describing the same universe. We're allowed in general relativity to choose our space and time coordinates differently. It shouldn't change the outcome, the physical outcome, but it changes the way you do the calculation. So, let’s imagine that in your calculation, you think the surfaces of space, of constant time, are surfaces in which the energy density is smoothly distributed. Suppose I don’t choose my slicing that way. I choose my slicing, which is wavy, compared to yours.
And you can do this within the theory? It still works?
Same model, same theory. But we don’t know a priori which is the better time slicing. You might say, on principle, that either slice should give you the right answer. In fact, either should give you the right answer. However, in general relativity, a subtlety which is underappreciated, is that it’s important how you formulate your problem as to whether you can get a definite answer. So if you choose coordinates badly, slicing badly, you can be deceived. So in my case, where I chose the wavy one, I think the system has large perturbations in the energy. In yours, it looks like it has perfectly smooth energy. Now, I haven't told you anything else about the problem. So if I asked you which one is right, you can’t answer the question. Because that would depend upon the rest of the setup. I slice one way, I found one answer; you found another answer. But obviously, at most one of those can be true. And maybe they're both not true. Maybe both of us reached our conclusions because of artifacts of the way we chose the slicing.
This is called, in general relativity, the gauge problem. And this had plagued the subject of perturbations in cosmology for decades going back to the 1940’s. How do you choose it in a way—how do you separate out a real perturbation or a real lump of stuff that’s going to condense and form a galaxy, versus a pseudo one, because you happened to choose some funny slicing?
And it turned out, just by coincidence around 1980, Jim Bardeen at the University of Washington, who is a famous relativist, had found a way of cracking this problem. He had shown that if you choose certain appropriate variables, they're so-called “gauge invariant.” They don’t depend upon your slicing. And Mike knew about that, and so we quickly engaged Jim to join our team. So our team was Jim Bardeen, me, and Mike. And we pursued developing his idea and applying it to inflation. So Jim didn't have an application at first. Now he had an application. And of course he didn't include the quantum fluctuations in the field. He didn't have that idea in there. So we had to ask,“How do you take the quantum fluctuations of the field, add it to Jim Bardeen’s gauge invariant formulation to make a prediction?” But we were convinced this was the only way to get a reliable answer.
So when we got to Nuffield, that’s what we were working on. We were still in the midst of completing our calculation using a gauge invariant approach. And then Alan’s group was using an approach which is not gauge invariant, as was the case with Hawking and with Alexei Starobinsky. So we were the only ones that were actually doing a formulation that you could trust. The other ones were using—I don’t know the right word to use—I'll say non-rigorous methods, I guess is the best way to describe it. Which was scary because you could get the wrong answer many ways using a non-rigorous method and getting the right result was so important in this case.
Were you vocal about this impression about the ways that the other research was being conducted?
In a friendly way, yeah. So this meeting was very intense—this was in Cambridge University, UK. It was a very intense few weeks. We were all racing, because each group is hoping to get a definitive answer. We're hoping they're going to agree with one another. And in the end, they did. There were changes in the answers in between, but by the end, all groups got the same answer. Although I would say that if I had had only the other three methods, I wouldn't have trusted it. [laugh]
Not because of me. No. Because now, I have enough experience—there are many ways of getting the answer wrong. [laugh] I can guarantee there’s many ways. And in fact, there are definitely flaws in their methods, too.
So you mean that the groups came to the same answer collaboratively or independently?
I would say semi-independently. So we were talking to one another. You know, “How’s yours going? What did you get?” And different groups gave talks at different times in the meeting. We spoke last. And we were the slowest. If you use heuristic methods, it’s back of the envelope, approximate methods -- you can get to an answer more quickly than if you're actually solving the full [laugh] equations of motion. So if you look at our paper, it’s quite substantial, and theirs are kind of like thin little papers. Because they're kind of guessing that a certain method will work without knowing that it will work. And if you know the history of the subject, and know how many times people got the answer wrong—or since—you'd understand that it was important that there existed a trustworthy calculation. Without the trustworthy method, you should have been suspicious. You'd be rightfully suspicious. But it was friendly in the end.
And the conclusion was that -- if you took the models that people were first thinking of, like Andy Albrecht and Andrei Linde – they failed. They produced density fluctuations that were much too large. They had the right, what we call, spectral shape. You could make it so they were nearly scale-invariant -- which was consistent with the Harrison-Zel’dovich-Peebles speculation -- of what you needed. And that was miraculous, because no one had any other way at the time of making a nearly scale invariant spectrum of perturbations.
So this was the first time there was an idea for doing it. And it happened to come up by accident from this calculation, that you could do it. We didn't force it. I should emphasize, though, it didn't have to be scale-invariant, but it could be. You could choose the model so that it could be. And that got everyone super excited, because that meant inflation had given you something that it had never been designed to do. It was designed to make the universe smooth and flat. There was no mention that it was supposed to make the fluctuations that seed the galaxies. And that it would make predictions for the cosmic microwave background.
This was a satisfying collaboration for you?
Yes. I learned a tremendous amount. I mean, one thing I loved about the whole project, all the projects but especially that one, is how much I had to learn in order to do it. And some of it you're inventing, and some of it you're learning from past work.
Right. Because it sounds like the field is really maturing in real time, at this moment.
Yeah. This was a seminal moment in the history of modern cosmology, when inflation real hit home with the astrophysics community. Everyone got very excited. Because it was explaining the fluctuations, the seeds for galaxies. It was also predicting that the universe has to be flat. That means that we should be able to test that the universe is flat. That means there should be dark matter, and there should be lots of dark matter.” No one’s thinking about dark energy at the time. There should be 95% dark matter and 5% ordinary matter.
So there was all that to go for it. And there was lots of work for astrophysicists, lots of work for microwave background research, lots of work for particle physics, and people began to immediately want to make models of inflation. There was still this problem of the fine-tuning, though. In fact, the fine-tuning got worse.
I should have mentioned something important about the end of the Nuffield meeting. Our group not only presented our results that showed that you could produce fluctuations, that they'd be nearly scale invariant, and that the amplitude would be far too big. But we also showed for the first time that one could construct models -- if you allowed more fine-tuning -- where the amplitude didn't have to be too big, where we could have the just right value. So the amplitude was a problem, but it was a solvable problem -- at the expense of tuning. Worse fine-tuning than we had before, but still a finite amount.
So what happened immediately afterwards, as I said, everyone got excited about this idea. The whole world of physics and cosmology, I think, got excited about this idea. Inflation was giving us something we didn't expect—so many targets for future observations. And then the theoretical side of the question is, “Could you figure out some way to get around this fine-tuning?” Because it was thought at the time that that would help complete the theoretical side of the story. So everything was super optimistic at the time.
However, there was one other thing, which in my Nuffield talk, at the end, I also mentioned -- which turned out to be the seed of a much, much bigger problem. I presented the first example of how inflation could be eternal. How you thought inflation ended by the field slow-rolling, but it might not ever end. Space would divide into patches with different properties. And that idea, when I wrote about it in the conference proceedings, was sort of the beginning of the idea of an eternal inflation that leads to a multiverse, which is the first big huge crack in the inflationary paradigm. But it was not recognized as such at the time. Not even by me. I thought I was identifying a feature of the theory -- not highlighting a fatal flaw that would eventually come to be known by the community and that remains with us today.
So, that was the Nuffield meeting, in brief.
What’s next after that? Do you go back to the work with Dov Levine?
So, everything’s going gangbusters, right? [laugh] Inflation is going gangbusters, especially with Mike Turner. Having identified a first example of a model that wouldn't produce too large of a perturbation amplitude, we produced a paper within a year or so explaining a general scheme for producing lots of models. How you can choose lots of possible candidate fields for the inflaton, the hypothetical field that would be driving this inflation. And it gave a prescription for how to construct an inflation model with it. So it was sort of just blowing out that whole part of the subject, expanding it out.
And then with Dov, as I said, in fall—and I may not get these dates exactly right, but around that time—we're getting kind of to the point we think we have arrived at an answer, “You know, this isn’t going to work.” And one day, Dov brings in something, a picture to me, of something that he had heard about at a general relativity conference, that Sir Roger Penrose had been working on. And it was called a Penrose tiling.
And the Penrose tiling is a tiling which, if you look at its tiles at first, you might at first think you see, “Oh, I think I see five-fold symmetry in there.” Which we knew was exactly the kind of thing—which is forbidden crystallographically -- which would be the two-dimensional analog of the icosahedron, which is also forbidden crystallographically. However, seeing a picture of a piece of the tiling proves you nothing. [laugh] What were its properties, actually? How would you classify it?
So this was part of a Scientific American article that was published—I think it was on the cover of Scientific American. Martin Gardner was the person who was responsible for that article. But it only explained that it was a non-periodic tiling. What Penrose had been trying to do was solve a recreational mathematics problem, which had been around for some time. “Can I find a set of tiles which can only tile a plane non-periodically, and not periodically?”
Back in the 1960’s, it was believed proven that that such a thing was impossible. Then, sometime in the early 1960’s, it was shown that that proof depended on a lemma, an assumption, which had a loophole. Then, a counterexample was constructed. And I don’t have all the names in front of me. But a counterexample was discovered with, I think, like 20,000 different tiles. Shapes. And then over the years, people found simpler examples of it.
And Penrose’s contribution, which I think was more pencil and paper and just the way he thinks, was to reduce the number, I think, first to ten -- then to six --then to two. And so the tiling we were looking at was a two-tile tiling. But all we knew about it, was that it was non-periodic. And even though it had five-fold stars in it—how do you know what you've got?
So I said, “OK, let’s see what this is, and let’s see if we can produce an icosahedral analog of it.” If it turns out to be what we think it is, which is just a really long-range five-fold symmetry, then maybe there’s something analogous in the icosahedral case. But we can only do that, if we first of all understand: what is the story here? what are the symmetries? it’s not periodic, but what is the darn thing?”
And so we turned our attention to the Penrose tiling. And over time, over the next year or so, what we discovered was that the secret of it was that it was not simply that it was `not periodic,’ but that it was something else. It was quasi periodic. So “quasi” here doesn't mean “sort of.” Quasiperiodic has a precise technical meeting. It means it could be described by a sum of periodicities, where the ratio of the periods is an irrational number. Like you could have points which are separated by one unit -- one unit -- one unit -- one unit. And then you could have another set of points which are square root of two units -- square root of two -- square root of two -- square root of two. And if you tried to put them on top of one another – to superimpose them because their periods are disharmonic, in disharmony—it’s like a disharmony in space—then the pattern would never exactly repeat. Yet, it could be dissected into two pieces, each of which is very simple, which repeat.
So if you say something is non-periodic, you might think “random.” I mean, that’s what you would have thought at the time. But the Penrose tiling is definitely not random. It’s decomposable into these two repeating frequencies. And then it suggested, and that's what we quickly showed, was that’s how you get around the crystallographic theorems.” Because they begin with certain assumptions, and the first assumption they begin with is periodicity. If I assume periodicity, a single repeating element, a single node that repeats over and over, then you have strict laws as to what symmetries are allowed. Those are how the laws of crystallography arise. And the way to crack that was to say, “I relax my rules. I allow myself two periods. Or three periods, or four periods. And I can now suddenly get other symmetries.” In fact, we showed you could get any symmetry that was forbidden before. So before, let’s say in two dimensions, if you insisted on a single period, you would have said there were only five possibilities. You can have the symmetry of a rectangle, a square, a triangle, a hexagon, or a parallelogram. Now suddenly, when you allow two or more periods, you find you were missing an infinite number of additional possibilities. So we weren’t just wrong before; we were wrong by an infinite number of new possibilities.
[laugh] You were really wrong. [laugh]
Really wrong! Really wrong. And of course, then the question was, “Could you build something analogous in three dimensions with icosahedral?” So just making a pattern was not enough for us. Because I can make a pattern, but how does that connect me to atoms and molecules when making real, three dimensional material? Well, without thinking about real atoms and real materials, you could at least ask, “Is there something that would force the tiles to be in this configuration?”
And the thing that Penrose had shown was not only did his tiles produce this non-periodic pattern—that wasn’t the novelty—but he could decorate them in certain ways such that the only way they would fit would be in his pattern. It would be like the way you would do with puzzle pieces but with only two types of pieces, each with knobs and holes. You could produce them in such a way that they would only fit together non-periodically, Penrose showed. Ah! Now you can imagine there’s some kind of energetics between atoms and molecules that might mimic those joining rules, that would force them to be non-periodic. And our goals was to see if we could we lift Penrose’s idea into three dimensions and icosahedral symmetry. It’s not too hard to figure out what shape the tiles would be, the analogs, but could we find rules that would force them to go together in that way?
And although that would sound like something straightforward, it turns out that three dimensions is much, much, much, much, much harder than two dimensions. And we took a lot of different tacks on that, before we finally found something that would work. So now we had the idea that quasiperiodic crystals, or quasicrystals, not only were possible arrangements, but they were possible forced arrangements. And so now, it seemed plausible that you could find matter in which the atoms and molecules might form analogous arrangements. It doesn't tell you that directly, but it says that in principle, there’s no mathematical blockage to doing that.
Now the time was probably sometime late 1982, early 1983. I should say that just because you have an idea, doesn't mean you can find a material. In fact, that was the criticism we were getting. When we’d show this result to people—“Oh, that’s really interesting, but you're never going to find any material that actually behaves this way.” So it made it clear that if we were going to go the next step, we were going to have to actually find a real material to behave this way, that formed the quasiperiodic structure with icosahedral symmetry that we had constructed mathematically. In the interim, we tried to at least make a patent for a toy or for the model itself. I felt bad because all this time has passed and we had published nothing on the subject.
Why? Was it unpublishable? What was the problem in terms of publishing?
Mainly the one I just mentioned—that if we had tried to submit it, the main response would have been, “You're telling us there’s all these possibilities, but come on. We've never seen anything like that. And it looks pretty complicated, so if it’s complicated, probably nature’s not going to do it, so you're probably not going to be able to form matter like that in the laboratory either—so it’s not really interesting.” And I wasn’t satisfied with that. I thought we should go the extra mile. Since I knew of no competition in this subject, I thought, “Let’s try to go the extra mile and see if we can actually find a material.” Again, the inflation story is weaving in and out of this chronology. So, only a certain amount of time is available. But I committed myself to going to IBM in fall of 1984, precisely to try to convince some people there to try to make artificial or real materials that would match the theory—to work with real materials scientists, who would help us find a real material that would be a quasicrystal.
Was IBM the best place, or you had contacts there? Why IBM?
I had been going there regularly, ever since those early summers. I had gone there many summers, and I also had two specific groups in mind. There was a crystal growing and classification group there, that was quite active. And there was another group there that worked on colloids. So I thought, “Maybe if you're not lucky to find it with the first group, you might be able to find some sort of colloidal system in which the colloidal particles would arrange themselves this way.” I was also working on the theory of colloids and how they interact, to see if we could produce forced interactions that would mimic the joining rules we had for the quasicrystal tiles. So that was the purpose of going to IBM in the fall of 1984.
How did that work out?
Well, before we do that, let’s just finish 1983. And 1983, I just want to mention again, that’s when this idea was finally published from the Nuffield Workshop that said that inflation not only starts, but it might be eternal. And around that time, Alex Vilenkin at Tufts showed that the conclusion was much more general than that. The same quantum fluctuations that we thought were doing wonders for us would also produce occasionally, rarely, regions where they would keep inflation going. And even though it was rare in the sense that it would happen rarely with time—those regions, when they formed, would keep inflating at such a huge rate they’d soon occupy most of the universe. So you had to invert your picture of the universe now. It was not a universe which had inflated and then stopped inflating everywhere. It was a universe in which these quantum fluctuations always made sure there were regions that kept inflating. Now the regions that stopped inflating were now an infinitesimal minority of spacetime, of space. Now most of the universe at any time, including today, was inflating. And then furthermore, those regions which did stop inflating—well, depending upon these rare quantum fluctuations, they would have different properties. They weren’t all the same.
So it’s not as if you could say, “I don’t care. Although there’s lots of regions that are still inflating, every region that has stopped inflating looks like us.’’ If that had been the case, it would still seem like victory -- an explanation why the universe is the way it is -- since every non-inflating region would be predicted to have the same properties. But that’s not the right story. What happens instead, is that these patches that stopped inflating could have any conceivable set of properties, with different patches having arbitrarily different properties from another. They don’t have to be flat. They don’t have to be homogeneous. They don’t have to have a scale-invariant spectrum of fluctuations. What was found is that the patches would span every conceivable possible combination of properties. And this is what, in nice terminology, is called the multiverse, since there are no universal properties the patches have in common.
Isn’t the problem that this is essentially untestable?
Yes. But it’s not just untestable now – it’s that no test can ever suffice. That’s why it is a fatal flaw. It’s death to the model, if you can’t avoid that problem. At least I would have said so. [laugh] I did say so. But at the time, people thought they had some ideas to get around it. And then every time they thought they had—now I'm going to go ahead, just to take you up to the present on that issue—various times, people thought they had a way around it, including Alex Vilenkin. Some sort of selection rule that would naturally explain why we're more probable than anything else. And then others would study that and show, “No, no, that doesn't work. It actually predicts something else to be more probable.” Then someone would suggest more selection rules might work, but the process repeated. Always a flaw was found. And that continued up until fairly recently. In fact, Alex, I think, continues to try to follow that program. But I think most people have abandoned that program. Because if you have to keep applying more and more rules, more selection rules, which come out of the blue—you just say, “I'm going to make a new rule for how we select which is more probable”—and the new rules keep giving you the wrong answer, it’s telling you that your outcome is always going to depend on your selection rule. And there’s nothing a priori to tell you which selection rule is better.
So more recently, I think especially since BICEP2, since 2014, the attitude has been, “Oh, we just must live with the fact that we live in an inherently unpredictable universe.” And then you say, “But hold it. Why must I accept that point of view?” “Oh, because inflation explains why the universe is the way it is.” “But hold it. You just said that inflation doesn't produce a universe that’s smooth and flat. It produces some patches which are, but also infinitely many which are not. So why should I believe inflation in the first place, if it didn't do what it was supposed to do? It failed to do what it was supposed to do.” At which point, people get mad and leave. [laugh] Some people get frustrated and say, “Ah, well, you're just not getting it. You're asking for too much.”
We have to change our views about what science can do and what it can’t do. And clearly because inflation works so well, we have to accept its consequence, which is it predicts all possibilities and is untestable.” Which makes you wonder why they think it works so well. But that’s actually the way the logic goes in such discussions.
I want to ask you about stubbornness, and how stubbornness applies to these kinds of things. So as you're wrestling with such fundamental concepts, where really almost anything goes, what are the bedrock concepts or laws in physics that you refuse to let go of, that won’t allow you to consider things where you say, “If I accept this, then it all goes out the window”? How are you anchored as you're sort of trying to wrap your head around all of these issues?
Well, we have just come across one of those no-cross lines. [laugh] I mean, we're always struggling in science with issues of testability. But what makes science science, is that you can test the ideas empirically. And there has to be some conceivable way of falsifying. Doesn't mean you have to have the technology today, but there have to be measurements, which are, in principle, doable. That is, for which you know there’s no law of physics that forbids you from doing them. And the test must be such that, if your idea fails that test, you have to discard or amend the model. And that if you amend the model to make it now match some new observation -- you better have enough testable predictions in the amended theory left so you can still test the model. There can’t be a case where every time you make an observation, you say, “Oops, I'll add this knob to fix it.”
And you can’t claim victory if your model is infinitely flexible. So I think that’s an important bedrock idea that separates science from other modes of human thinking. I don’t begrudge other modes of human thinking, but I think it’s really important to draw the line between science and thoughts that are not science, such as other forms of imaginative thinking.
Would you go far as to say, then, that because the multiverse is untestable, it can’t exist? I mean, models are approximations of reality, but they're also limited by our capacities to understand reality. Maybe that’s as much a philosophical question as a scientific question, but just because we don’t have a good model for the multiverse, is that enough for you to be confident that the multiverse can’t be true?
It says it’s not a scientific idea. So it’s beyond the realm of science. You can imagine there are dinosaurs out there—giant dinosaurs the size of galaxies -- out behind the horizon you cannot see. And I can make a model where, say, because of dark energy, you'll never get to see them. Does that mean that’s impossible? No, it’s not impossible. But it’s not scientific. It’s useless. In other words, things are not just true or false. They can be true, or false, or useless in a scientific sense. And that would be a useless idea, because you cannot test its truth or falsity, therefore there’s no sure observable consequence to it. So it’s not a useful scientific idea.
The only reason to pursue such an idea is because you're in love with it; you happen to like that imaginative idea. That’s fine. That’s thinking beyond science. People do that all the time. Many of our modes of human thinking are not scientific. That’s fine. You're allowed to do that. But within the realm of science, you're not allowed to do that. And so I would say, it’s not scientific. And as a scientist, I would challenge you to prove to me that there exists no other possibility. You cannot claim you've exhausted all the other possibilities, as some occasionally do in this field.
By the way, in the case of inflation, the multiverse was not a planned property, right? It was discovered after the idea was first introduced and made popular without knowing that it leads to a multiverse. And then many say, “But I'm going to stick with the idea, anyway.” They want to claim victory because we measure the universe to smooth. They say, “See? That’s proof of inflation. Just what was originally predicted.” Oh, but we only thought that was prediction before we knew about quantum fluctuations during inflation leading to a multiverse.
In a multiverse, the observable universe didn’t have to be that way. It could have any amount of non-smoothness. And then they say, “But I'm going to claim victory for the observation of flatness. And I'm going to claim victory for seeing the scale-invariant perturbations.” Even though those were also thought to be predictions only before we learned of the multiverse. In a multiverse, the observable universe does not have to have those properties. But then some say, “Anything else that disagrees with observations, I'm going to ascribe to the randomness of the multiverse.” Then, that is not a scientifically useful way of thinking.
So would you align yourself with people like Shelly Glashow and his campaign to keep Harvard “string-free,” as he likes to say? Where do you fit in, in those debates?
Well, that’s a related debate, in the sense that—
But that’s the criticism of string theory, right? That ultimately, what they're doing is they're asserting things that are not testable.
[pause] So, just to make sure we're talking about the same thing—so string theory was supposed to give a unique theory of everything, just like inflation was supposed to give a unique description of cosmology. Now, I should say a key difference is that with inflation, we knew a lot about the physics underlying it. So the fact that it produces a multiverse is not disputed by any side. Whether you're pro or con inflation, everybody agrees it produces a multiverse. Just one side says that’s a fatal flaw, and the other side says, “Tough luck, you have to live with it. That’s the only idea we're willing to consider.” That’s the nature of that dispute.
String theory is a little bit different. It’s a subject which is still evolving. It appears to me to have gotten into trouble right now but that may be temporary. There are many beautiful aspects to string theory and it might recover. The real problem comes when you try to include dark energy with string theory, because string theory includes supersymmetry, and supersymmetry is very resistant to having vacua with positive energy density, cosmological constants.
In the early 2000’s—and I think this is where you're getting to—in the early 2000’s, there was a group, KKLT—Kachru, Kallosh, Linde, and Trivedi—who said, “We have figured out how to make a string theory model which will allow dark energy.” It involves a very complicated plumbing exercise in which you have to take your extra dimensions, fold them up in a certain way, wrap certain fluxes around them, put in certain anti-branes in a certain configuration with branes, and then we add some other magic dust, and OK, seems now that we suddenly have, in this plumbing construction, a solution.
Unfortunately because it’s a plumbing solution, you don’t get one. You get nearly an infinite number—10 to the 500, or maybe ten to the 5000, or even more vacuum states with positive cosmological constant, et cetera. And this is what’s called the energy landscape.
The problem with this energy landscape idea is a little bit like that of the multiverse. Every valley in this landscape will have associated with it different physical properties. And so what we observe would just be an accident of living in one possible vacuum as opposed to another, which reminds you a little bit of multiverse. Worse than that, “How is it that all those vacua came to be occupied? I mean, because ours is just one out of so many.” They say, “Oh, we'll lean over and we'll reach out to a multiverse for the answer to that question. We'll say inflation occurred. And with inflation, it produced a multiverse. And included in the multiverse is not just that some regions are flat and some regions are not, some homogeneous and some not -- some rely on one value, and some rely on another value, et cetera. We will also imagine that different regions will end up in different vacuum states depending on quantum fluctuations and chance.’’ That would explain how the region of space we observe ended up in its particular vacuum state.
So they merged the failure of the landscape – a controversial and unsettled idea in current string theory thinking -- with the failure of the multiverse – an established fatal flaw of the inflationary theory. So this has led to a strange relationship between the landscape idea and inflation. The flaw of one relates to the flaw of the other, and then they together claim victory of sorts. Even though you might be even more dissatisfied now. Because now you can’t explain anything, not even the particle masses, as coming out of the theory. Everything, all the properties, are just an accident of what arose in our particular part of the multiverse. And if we were someplace else, we’d have different particle masses and different forces and different cosmological properties. Now, a twist that has happened in that story in the last few years, which I'm also involved in, has been what you might call an anti-landscape idea, coming out of string theory, called the swampland. I don’t know if you're familiar with that.
So you might think after claiming that there’s ten to the 500 of these vacua, that they could have showed you one, at that time, that for sure exists. Just one, out of the ten to the 500 that they could prove existed mathematically. But they couldn't. Because there were parts of the mathematics which they said they didn't have control over, but they assume that will work out. It was a new idea and we should give them time to complete the analysis. Fair enough. But now, twenty years later, after they told us that we must believe in this landscape, that it’s a fundamental aspect of string theory, you might ask, “How many of these vacua are now proven?” The answer is—the same. Zero!
And this has led to another group within string theory, led Hirosi Ooguri and Cumrum Vafa, called the swampland. Which says, “You know what? Maybe the reason why you're not finding them is because they're not there.” And instead, there’s actually certain rules about what’s allowed and disallowed. And what’s disallowed, is to have all those vacua. In fact, you can’t have any such vacua, not even one. To have not even one means you cannot have a cosmological constant. Instead, the dark energy has to be some kind of evolving form of dark energy, which means we are not living in a stable vacuum today; our vacuum state – our universe – is really unstable, just slowly evolving.
There’s a pretty strong argument behind this new swampland line of reasoning, and I have worked with Cumrun Vafa and his collaborators on this. And coincidentally, that connects very nicely to ideas that are alternatives to inflationary cosmology, which is thinking about a bouncing cosmology. But that’s getting us a few decades ahead of where you and are in this interview. It all ties in. So all these different threads keep tying in. So my own work keeps going from one to the other, because I'm trying to look for ways of solving a problem.
Now I think—where are we? We're in the mid 1980’s?
We are in the mid 1980’s, yeah. About 1983, 1984. That’s right. The fall of 1984, where condensed matter will take up our next little portion, I think. The quasicrystal breakthrough, yeah.
Is that a good stopping point for today?
OK, perfect. So I will end the recording here.
This is David Zierler, oral historian for the American Institute of Physics. It is June 30th, 2020. It is my great pleasure to be back with Professor Paul Steinhardt of Princeton. Paul, thank you so much for joining me for round three of our talk.
Thanks, David. You have enormous patience! [laugh]
[laugh] All right, so where we're picking up today from last week is, we are now getting to get into the aspect of your career in the mid 1980’s where you start to deal with condensed matter physics in a more sustained manner. So my first question: This is obviously something that was on your radar prior to the 1980’s, but why in the mid 1980’s does it become a more focused part of your overall agenda?
Yeah, it’s something I had been thinking about for some time, but two things happened before Fall 1984. One is I felt that I had produced a lot of the results in cosmology, on inflation, that were seminal to getting the subject started. We had found the first examples where you could gracefully exit from a first-order phase transition using this spinodal idea that we discussed. Then, we looked at reheating the universe afterwards. Then, we had looked at the perturbations. And then, I had also found the first examples of what we call eternal inflation and this multiverse problem.
And with Mike Turner, I had worked on making lots and lots of variations. In fact, we wrote a paper called “Prescription for New Inflation,” which essentially gave people a sort of formulaic way of making as many models as they wanted of the type. And that’s what people were doing. They were running away doing that kind of thing. And that was a good time to take a break.
But it wasn’t so much that thought as, there had been this other thing going on in the background with Dov Levine for the previous years, and it had reached a point where I felt it was worth taking a gamble, to give it a push. So to drop cosmology for a while—I thought for a few months; turned out to be more or less for a few years—to see if we could push this idea forward. What we had originally been looking for, is if there’s some way of getting icosahedral order to extend over much somewhat larger distances than computer simulations of rapidly cooling liquids suggested is possible. Instead, we found we could even get the icosahedral symmetry to extend to infinite distances. In the process, we discovered, through the Penrose tilings, that there was an actual symmetry involved, this quasiperiodicity, this quasiperiodic translational order. And that meant this was a new phase of matter, if it existed.
At that point, it was only a mathematical idea. If you could find real matter that would behave this way, it would really represent a new form of matter. And that idea was just really, well, a real charge for me to think about. I have to say that to some degree I was influenced, when I was a kid, when I read Kurt Vonnegut’s book Cat’s Cradle. What the story is about, in general, is not a particularly pleasant subject. A scientist in the story discovers a new form of ice, ice-9, which is a new form of matter that hadn’t been known before. And it ends up destroying the world [laugh] which is the bad part of the story. But it just brought the idea to my mind, that in fact, even then, that what we believe to be true is based on our experience. But our experience may be limited, especially limited to what we find in nature. And maybe there’s something—maybe there’s a form of matter that really is a form of matter that we haven't seen before, given our limited experience on Earth and our limited experience in only looking at certain forms of matter up to this point.
So, when the idea Dov and I were working on suddenly led to this idea of a quasicrystal and, “Well, maybe this would be a new phase of matter.” I thought somehow that was worth taking time out. So I took a risk. I was about to take my first leave as a professor at Penn.
You were tenured at this point?
I had just gotten tenured, yeah. I had just gotten tenure the year before.
Had that given you a little bit of breathing room in terms of being somewhat adventurous in your next project, or that really wasn’t a factor as far as you were concerned?
Wasn’t a factor at all, to be honest. [laugh] I have to say it was rather pleasant, the way it worked out, because usually when you go up for tenure—I know from having seen many people go through it, it’s a nerve-wracking experience. You're not sure what’s going to happen. You know, it takes months. In my case, what Penn did, is not inform me at all that this was going on. Just one day, the department chair, Ralph Amado, knocked on my door and said, “Guess what? You have tenure.” “Oh, really!” [laugh] “OK!”
So I didn't have to go through all those torturous plans. So going on leave to IBM was really a scientific decision, that it was worth a risk. And it was very high-risk at that time to take even a semester off from cosmology and miss out on developments. I decided to go to IBM for the first half of that year. And as a backup plan, I went to the Institute for Advanced Study for the second half of that year. So I could go either way, in the second half, depending on how the first half worked out.
Now, Paul, to set the stage, when you hit pause on cosmology, are there certain technical or technological limitations that you're aware of, where you're saying to yourself, “Until x is built, we've pushed this as far as we could, so why don’t we just put this on pause for the time being and then come back to it?” Were any of those considerations part of your thought process in this?
Not really. It’s more a style I was developing, which has now become a style which is even more extreme in this way. Which is, I feel like I'm planting seeds for projects all along. And some of the plants have grown and reached maturity. They can get by with a little less attention for a while. And some of them are just beginning to bloom, and just taking off. They can need lots more attention. So the idea is when that happens, you just switch direction and focus more on whatever is blooming, whatever is the most exciting. Then, you just keep planting more seeds in the background, and then maybe they'll come to fruition.
So that’s what makes this story we're talking about, how I work, how I personally work, rather complicated. Because if we were going to say what I was doing in a given day, you might find that in a given day, it’s not really true that I wasn’t thinking about cosmology. It’s that I had no brilliant ideas about cosmology. This idea about quasicrystals looked more promising to me. More room for new ideas. Or at least enough so, that I was going to take this semester off.
I went to IBM, because first of all, I was familiar with people there. I knew two groups there that I was going to try to convince to help me look for a real quasicrystal. One of them was led by George Onoda. He worked on colloids. So, essentially beads in fluid which have electromagnetic charges. The beads can form crystalline arrays. That’s what are normally studied in them. But I had some thoughts that we might be able to make something that would mimic our system, and that would be a quasicrystal. So that would be a kind of an artificial quasicrystal. And then, there was a big group there that worked on crystal classification. So they had some automated or semi-automated system, that you could bring any material to them, and they'd classify its symmetries. And this was a big operation there, a sort of materials operation there.
So I arrived in, I guess, late August or September; I don’t remember—of 1984. And the first month or so, George was willing to work with me, and we started some effort—it never took off—with the colloids. Although a few years later, we would work together on a different project that was pretty exciting. But at the time, I could not get the crystallographers to work on this subject at all. Just like I had had experience up to that point with many other people to whom I had presented the quasicrystal idea, this seemed pretty far out, in terms of actually getting something to work. And unless I could prescribe for them—you know, combine elements A, B and C and that would make a quasicrystal—they weren’t going to disrupt their program, their machine that was running forward successfully.
In what way did you envision crystallography and the expertise of crystallographers to be useful to what you were after?
What we were working on was a very mathematically abstract idea based on tilings, based on patterns. What I hoped that the crystallographers would do is help me identify likely combinations of atoms that might, for one reason or another, form this state. To begin with, it would have to be combinations of atoms that liked to form units with icosahedral symmetry, and then you might begin from there. So I was looking for advice from them. IBM also had the crystal growing group -- they could have grown it, and then, they could have tested it. I had the vision of having some iterative procedure like that, that they might be willing to take part in.
I should say, for those who aren’t familiar with it, it’s actually—except for the simplest cases, it’s actually very difficult to predict what kind of atomic arrangement will occur if I mix x percent of atom A, y percent of atom B, and z percent of atom C. Because our tools, our theoretical tools for predicting what’s going to happen, are not just not accurate enough, and will probably never be strong enough to make reliable predictions in most cases.
And that’s just because you can make so many different configurations, once you have three or more types of atoms involved. There’s so many different configurations possible, which have energies which are only slightly different from one another. Determining which is the energetically favored arrangement, the one with lowest energy overall, depends on knowing the precise atomic forces to an accuracy that we really can’t hope to know. So this is more of an art or a hunt-and-peck form of science. Some combination of intuition—I mean, there are brilliant new materials makers who have some combination of intuition, rules of thumb, experience, that leads them successfully to do this kind of thing. I was hoping to run into somebody like that. But in general, it’s kind of a tedious, risky process, just like I was trying to do on the theoretical end.
I was just getting settled in. On October 10th, it turned out that David Nelson was visiting from Harvard University. We actually hadn’t talked since I had left Harvard, just because we were both busy, doing our own things. He had gone on from our work together to try to describe why, when you had all atoms of the same type, you couldn't extend the icosahedral symmetry more than a certain amount. Whereas Dov and I were pursuing this other direction of thinking, “Let’s imagine that there are two or more atoms. Maybe you can extend it.”
David had been publishing. We had not been publishing. So he didn't really know anything that we were doing. But he knew I was just interested in the general subject of icosahedral symmetry. He was coming to give a colloquium at IBM that day, and he made an appointment to see me. Because he knew I was there on leave.
And I was excited, because by this time, Dov and I had gotten to the point where we were actually calculating diffraction patterns that you'd expect for an icosahedral quasicrystal. Making plots that would look like a real diffraction image, with spots of different sizes, depending on their intensity. We had shown that they had to be perfectly point-like “Bragg peaks.” But because of the quasiperiodicity, it was unlike a crystal. Whereas for a crystal, the diffraction peaks are spaced out with equal intervals and an empty space in between – here, in a quasicrystal diffraction pattern, because of the quasiperiodicity, there are peaks between peaks between peaks between peaks, all the way down. So it’s kind of a fractal diffraction pattern, in a certain way. But as you go from bright peak to peaks between bright peaks, they get less and less intense. So in reality, if you were looking at it by eye, your eye would pick out the brightest ones. Or, similarly in electron diffraction or X-ray diffraction, with a finite resolution, you detect a certain finite number of them.
But there were certain characteristic features that would allow you to recognize the pattern [snaps fingers] like that. It’s not hard to recognize a quasicrystal pattern. Quasicrystal or near quasicrystal, it’s an instantaneous thing. It has a forbidden symmetry, like five-fold symmetry, or ten-fold symmetry. The pattern actually has to have an even-fold symmetry. It has to have ten-fold symmetry, which is a five-fold symmetric pattern, or you could have fourteen-fold symmetry.
By this time, we had shown you could have had all the forbidden symmetries—all the symmetries we thought were forbidden in nature, based on the crystallography of the past 200 years -- we had shown that all of them are possible, if you allow quasiperiodicity. But we focused on the icosahedral case, because that was the case that had motivated us in the first place, and which we thought was best physically motivated.
So I was really excited to show David that, because he knew nothing of what we had done since 1981. But when he came into the room, he said, “Oh, I have something to show you.” I said, “Oh, I have something I want to show you!” And so we sort of waited each other out for a minute to see who would go first —“No, you should go first.” “No, you should go first.” We settled on his going first. So he brought out of his case—he said, “Well, I want to show you an interesting paper that I got, a preprint. It’s by this group.”
Dan Shechtman , Denis Gratias, John Cahn, and Ilan Blech were the four authors. And David just gave it to me to take a look at. At first I was kind of petrified, because it was about discovering something with icosahedral symmetry. And I thought, “We've been scooped. Someone has gotten there before us.” And in fact, they were showing in the article that they had made this material. They had synthesized a material, in this case an alloy mixture of aluminum and manganese. They had taken its electron diffraction pattern, and they had found that it had a particular axis – with a beautiful ten-fold symmetry, is what they were saying.
I was just reading the abstract at first, not looking into the paper yet. And it sounded an awful lot like what we had. As I began to read the introduction, I realized, what they were really saying is they had found something which had a symmetry which was supposed to be impossible. It was pretty clear that they really didn't have a theory to explain it. So I began to tense like this, you know? “What was this paper?” And I should have said, I had Dov come for this meeting with David, as well, because I wanted him to be there to present our results. So I'm just looking at the paper alone, and then I turn the page, and on that page—they have the diffraction pattern. And the diffraction pattern looks just like the thing Dov and I had computed with even higher resolution.
And [pause] I can’t say exactly what happened at that point. My memory is that I just sat silent for a moment. Because I realized that this was it. That I was the first person to realize that someone had discovered a quasicrystal. And that was a moment—you know, that’s the kind of moment you really want to savor for a long time. But there were two other people in the room, so I could not savor it forever.
But I think I did take a conscious moment out to say, “OK.” And then I just very calmly got up, and I walked over to my desk, and I picked a piece of paper up, which was one of the things I was going to show David. It was our computation of what the diffraction pattern should look like, an actual image of what it should look like. And I just held it out, along with the diffraction pattern in the preprint, to him and Dov. And Dov said, “Oh my god!” And David was a little bit quiet. I think I said something like, “This is what I was planning to show you.” The two patterns were a match. And so Dov and I were quite excited. [laugh]
The other team’s paper did refer to the work that David and I had done as an example of something that could be icosahedral, up to a certain degree. The group was at what was then called the National Bureau of Standards, now called NIST. I think their idea was that they had found something akin to what David and I had found on the computer - a phase which had icosahedral orientational order, but was disordered translationally. But that could not give peaks of the sharpness that they were observing in their electron diffraction pattern. So it was pretty clearly not that. It had to be what Dov and I had described – a phase which has icosahedral orientational order and is ordered translationally, as well, following a quasiperiodic ordering.
So Dov and I, in some probably sort of excited gibberish, tried to explain to David [laugh] what we had been doing, and what we had found. Which was great, and David was supportive. He had to go off, of course, and spend the rest of his day to visit others at IBM. But Dov and I immediately called colleagues at Penn, told them what we were finding. And people responded rapidly, which is an interesting cultural difference between condensed matter and cosmology. Cosmology -- you have an idea today, you might have an experiment ten years from now. With condensed matter -- this kind of thing could be reproduced in a matter of days. So already, in a matter of days, people at Penn, such as Paul Heiney and Takeshi Egami, and I imagine many places elsewhere around the world, were already reproducing this material. It wasn’t hard to make. And it probably had been made many times before, but everyone was so biased about it being impossible to find in nature, or to make in the laboratory, that it probably had been misinterpreted.
In fact, that’s part of the story of the discovery at NBS, by Dan Shechtman et al. Now, I'm interpreting a story that I have by second and third hand, since I was not there. But my understanding is that there was a project, not unlike the IBM crystal classification project, but in this case, specifically for aluminum alloys, to make all kinds of aluminum transition metal alloys, and characterize their crystal structure. Aluminum alloys are very important in all kinds of industries, and so having a complete catalog of all possible aluminum alloys is something that the metallurgy community does.
Shechtman was there as a visitor from Israel, and his role was to do the electron microscopy -- to do the characterization, to look at diffraction patterns for the aluminum alloy samples. And he had noticed this funny example. They had brought to him, among their examples, this aluminum-manganese alloy, and he had noticed that it had rings of ten-fold symmetry in its diffraction pattern. And he got very excited about it because he knew that was supposed to be impossible. But when he showed it to people, they did not get very excited about it. Because, A, they knew that was impossible, and B, there was some obvious other explanation it could be, which is what’s called a multiply-twinned crystal.
You can try to grow an ordinary crystal and when it grows, it might grow as a single crystal, but sometimes it grows as a twinned crystal. That is to say, it grows with a certain orientation of rows in one piece of it, and then suddenly flips, mirror flips, and forms another orientation. And so now it’s two crystals joined along an interface. Furthermore, this can happen multiple times. And there are examples of materials which form multiply-twinned crystals, that is to say, crystals which have many of these joined crystal grains, and they form around a center. Gold, for example, can do this. And it will form what appears at first to be icosahedral symmetry. If you look at it, it will look at first as if you have an icosahedral solid.
Now, when you do diffraction on that material, if you narrow that beam enough, you'll hit just one of those crystals twins, and then you'll see, “Oh, a simple crystal appears.” And then when you pan back and the beam hits the whole agglomeration, the pattern might have an icosahedral symmetry, but, in fact, the real underlying structure doesn't. It’s an agglomeration of crystals in a particular geometric arrangement. That’s different than a quasicrystal. Wherever you aim the beam within a quasicrystal, it’s going to always display the same symmetry. It will always show the icosahedral symmetry.
So in fact, the colleagues, as I understand it, at NBS, including John Cahn, said to Dan, “This is probably not worth your time...” And in fact, this is probably why it had been missed before, because everyone’s thinking, “This is impossible, so it’s not worth my time to do this next tedious experiment. What I should do is prepare samples and try to go around, poke around, with a narrow beam, and then I'll see that I get a crystal, and then I'll say, ‘I have a multiply twinned crystal. So people have seen that hundreds of times. It’s not going to be anything noteworthy.’”
And now, I think the story diverges, according to what I get from different people. At one point, Shechtman did do this experiment, did go back to Israel, but apparently it did not get communicated back to John Cahn at NBS. Cahn was a leading theorist and an important influence—a profoundly important condensed matter physicist, and the person who had brought Shechtman to NBS in the first place. He’d have to pass judgment on the results, if it was going to be submitted for publication. But Shechtman did not come back until two years later, in 1984, showed him that he had in fact done those experiments that showed the aluminum alloy is not a multiple twin, and showed him a theory that Ilan Blech had proposed to explain it. It was not a quasicrystal theory; it was something else I'll describe in a moment. And Shechtman showed him a paper that he and Blech had tried to submit that got rejected.
Again— one of those people should tell the story so one can be sure. But out of that discussion, they finally decide to write a paper which gave only the experimental result, without presenting a theoretical explanation. My understanding from John was that he never liked the so-called theory, so he kept that out of the paper and just presented the experimental discovery. And that was the preprint David had brought to IBM and that we were looking at.
I contacted them at NBS. John Cahn came up with Denis Gratias, one of the other coauthors, to IBM. And we met for an afternoon to talk about what each team had found. I should say this was very much like the story of the work I did with Andy Albrecht on inflation, where the moment that you have the realization that this is real, you drop everything. You must write a paper. You must get it submitted, whatever you had.
So I should step back and say something about that. Dov and I did that, before contacting the group at NBS. I thought we had to be very careful, because whereas I had complete confidence that our theoretical idea was mathematically sound, it was still early days to be sure about the experiment. I couldn't swear about the experiment. So the way we wrote the paper is, “Here’s a proposal for a new state of matter. It involves changing from periodicity to quasiperiodicity. It opens up new possibilities for symmetries, including icosahedral symmetry.” Went through our construction of how you can construct something in three dimensions which not only has icosahedral symmetry, but like the Penrose tile, is forced to have that symmetry. So that means, in principle, there could be atoms and molecules with forces like that that would explain why this quasicrystal could actually form.
And then at the end we said, “Oh, and there’s this paper that claims to have found something with icosahedral symmetry. And this looks like a promising candidate for a quasicrystal, for what could be a real quasicrystal found in the laboratory.” We pointed out some qualitative comparisons between their diffraction pattern and ours. It could only be qualitative, because whereas we could compute things exactly, their experimental patterns were really at that point just images. They weren’t quantitative enough that one could say for sure how perfectly sharp the diffraction peaks were, for example.
I mention that, because there has always been confusion. This is, again, a community which is represented in several disciplines. There are mathematicians. There are chemists. There are metallurgists. There are condensed matter physicists. There’s a variety of different subfields which don’t normally talk to one another, which intersect here. But a certain community had the impression that we were being unfair in our article, in the sense that we were presenting it as if we had already had this idea. Which was true. We already did have that idea.
Yeah. Right. You did have the idea. So what was the problem?
We did have the idea. And there were people -- certainly plenty of people in physics -- who knew about it. But, those in the metallurgical and chemistry communities didn't know that. And they thought that we had kind of pushed the Shechtman paper to the bottom of the article—instead of beginning with, “These guys discovered this alloys and now we're going to propose to explain it.” We didn't do that, because I wasn’t sure they had discovered a quasicrystal yet, at the time. And I thought I idea was important even if the alloy did not turn out to be one. And we'll see in a moment there were good reasons to be skeptical. So some people from that community felt we had somehow tried to steal their thunder, whereas what we were really trying to do was sort of place ourselves in the right position relative to what they had done, which is, “Here’s our idea. It might be related to Shechtman’s alloy. But let’s wait and see. We'll see what the true story turns out to be.”
OK, so having said a few words about that, let me get back to meeting with John Cahn. That was actually an interesting conversation for a reason you wouldn't have expected. It turns out that John Cahn had worked on many important things in the history of condensed matter physics. He was, by then, an elder statesman in the field. But among his contributions was work he had done on spinodal decomposition in metals. So this kind of phase transition which can proceed without having an energy barrier, the same idea that I had worked on that inspired the idea for inflation.
So when he came, he said, “Oh, I see that you also work on cosmology. I've heard that there is some interest in spinodal decomposition in cosmology. Do you know anything about it?” And that was funny, because he was talking to [laugh] exactly the person responsible. So our conversation sort of began from there. That was the fun part. But then it went on to the business of comparing notes, and seeing where we stood. The metallurgy community, including John, was mainly interested in the issue of where the atoms lie in these materials. That continues to be a theme, even to today, in the field; not a completely solved problem—to me, that was less interesting. The interesting question to me is why they form. “Why do materials sometimes do this, rather than something else?”
So things get very compact at this stage. Several things are happening. One is we're submitting our paper. It gets accepted. It appears a month after the Shechtman paper, in PRL. So suddenly, there’s both the experiment and the theory. In the meantime, we're rushing ahead to think, “OK, if there’s really this new state of matter, what are its physical properties that will distinguish it from conventional crystals?”
But isn’t that the first question? How do you know? Wouldn't you first have to realize what distinct properties there are, and then that would—?
Besides diffraction, I should have said. So diffraction I think of just a measure of the geometric arrangement.
OK, I see.
So yes, that is a property. Sorry. But the way I always think about the quasicrystal problem is, “I don’t allow you to do diffraction. I put a sample in a box, black box. You're not allowed to see what it is. What could you do to it that would tell you what it is, and that it’s not a crystal?” That’s kind of the conceptual test. And that’s still early days. I mean, I'm still not really able to give a sharp answer to that question. I can give fuzzy answers to that question, but not sharp answers to that question. But that’s what I was more interested in.
So when I reported back to Penn that there was this discovery, everyone got excited. Penn has a very strong condensed matter group. The experimental group, Paul Heiney and his group in particular, could easily make this material. They used X-ray diffraction, which is more precise than electron. At the same time, Tom Lubensky was there. I had talked to him occasionally about the ideas before. He’s a very wonderful physicist with broad interests. But he got especially interested in this now. He thought the best thing to do next, was to work on the elastic properties—elasticity and defect properties, because that’s the next thing you want to understand about a material. He was expert on that subject, so he tutored me. I got a really sort of crash course in condensed matter physics and how to do these calculations, what’s the modern way to do those kinds of calculations.
And he and my students and postdocs began a series of papers that extended over the next few years on just that topic to show what are the distinctive elastic properties of quasicrystals, how defects in them are qualitatively different than the kinds of defects you can form in crystals, et cetera, et cetera. So that was going on at the same time. That was starting at the same time, the same period between, I would say October 10th and the end of the year.
And another thing—call it foreshadowing of things that will happen in the future—well, probably this goes back to my days of ice -9. Just for fun, I wanted to know, “Is it possible that these have already been discovered in nature?” And so I took some trips to local museums, contacted the American Museum of Natural History—which I was close by; I could go there—also the Smithsonian, and did a sort of first scan to see if there was anything that had been misclassified? [laugh] You know?
As in, it’s almost too good to be true? Is this really uncharted territory you're working in?
Yeah. But also, “Could it be that mineralogists have missed for years that these have existed?” So that’s the flip side. Not that they would have recognized that they had something icosahedral. That would have been news. But that they had misclassified something. They had assumed it was multiply-twinned. Because, as I say, that’s what people would normally have assumed. We have evidence from the literature that probably this phase was discovered at least as early as 1933, but mischaracterized, just for the reasons I said. People, unless they did the right experiments, would have trouble distinguishing it from multiply-twinned crystals.
By that time, 1984, the technology has improved, you can distinguish much more easily. But mineralogists might not have done those tests. So they might have misclassified it. I had no success, but I kept that idea in my mind. It planted the seed in my mind that at some point, I wanted to go back and ask that question. “If quasicrystals turn out to be real, is it really true that it was first made in the laboratory in 1982, published in 1984. Is it that story? Or, is it maybe that they could also form naturally, that they existed thousands of years ago, or millions of years ago, and we just didn't know?” Just an oversight on our part.
So it got nowhere, but I stored that idea—there were too many things that had to be done immediately to oursue. So beginning 1985, the story of quascrystals began to hit the scientific community—this was a big splash in the field. A new form of matter discovered. The quasicrystal idea was put forward alongside Schechtman’s discovery in the laboratory. But shortly thereafter, there began quite a controversy among different factions about whether this quasicrystal picture was correct.
Who were the lead antagonists? Who was mainly criticizing these calculations?
They were not criticizing the calculations. They were proposing an alternative explanation that could fit the data just as well.
So one idea, which was pioneered or led, essentially alone by Linus Pauling, a significant figure, was that what had been found was simply a multiply-twinned crystal after all. We just had not been clever enough to identify the twin units within the material because, in his picture, although it was made of crystallites, the atomic arrangements within the crystallites were very nearly icosahedral. And so then, when you put them together in a twin, it would produce a pattern that looked a lot like the material reported by the NBS group.
Now, in principle, one can easily distinguish between those possibilities, as I said -- between a quasicrystal and a multiply-twinned crystal. You narrow your beam and move it around until it only strikes one of these crystallites, and then the diffraction pattern should resolve into a crystal pattern. Pauling's model was quite complicated, though, and the atoms were arranged so that the crystal diffraction pattern differed by only a little bit from the quasicrystal one. You had to have very accurate measurements of the Bragg peak positions, in order to distinguish the two.
Now, by this time, other groups—especially Paul Heiney’s group at Penn—had shown through the X-ray diffraction that if these were quasicrystals, they were certainly not perfect quasicrystals. The peaks were not quite in the positions that our theory predicted. There was a systematic shift between the measured peak positions, compared to the predictions for a perfect quasicrystal. And they were not truly Bragg peak, they were not truly point-like. They had finite widths. Now, from a quasicrystal point of view, you could say “If the quasicrystal picture is correct, there’s an obvious explanation, which is that the way this material was made was through what’s called rapid quench, spin melting or rapid quench, where you take a liquid mixture of your aluminum manganese, you splat quench; you throw it onto a spinning wheel, which produces a ribbon of the material. And that wheel is so cold it freezes it almost immediately.” Which means the atoms are not going to have a chance to relax into an ideal configuration.
So our idea, which was supported by the elasticity theory that we had been working out with Tom Lubensky, was that if you cooled a quasicrystal very quickly from the liquid this way, it would naturally form certain defects. These defects, known as phason strains, in the quasicrystal were predicted to be much slower to relax than in the corresponding crystal. That explained why they would not relax away, compared to the rapidly relaxing phonon defects that crystals form if the samples are made by rapid cooling. They move at much slower speeds. And then, if you assume that that’s what happened, you could calculate how that would distort the diffraction pattern. And that well explained the diffraction pattern that the NBS group had found and the deviations from the ideal quasicrystal prediction that Paul Heiney had reported. But it didn't uniquely explain it. There’s some arguments about the precise model Linus Pauling used, but in principle, there’s no reason why that multiple-twin picture couldn't produce a similar pattern.
And then there was a third picture which was being developed, which became rapidly popular over the next few years, which is called the icosahedral glass model. It’s actually very similar, or maybe just a simple extension of the idea that Shechtman and Ilan Blech had had. The idea there, is that you really didn't have something that was a quasicrystal; you had something that made icosahedral units. And when these icosahedral units packed together, they packed together with a common orientation or alignment. So the units were randomly distributed like in a glass. If you think of them as like the beads, they were randomly distributed. Although their interior had icosahedral symmetry, they were randomly distributed, not quasiperiodically distributed. And that arrangement also could produce a pattern that could explain the Shechtman, et al pattern and Paul Heiney’s results. And that was the model that Blech and Shechtman had originally tried to publish, but hadn’t succeeded in publishing. Later on, they did publish it, but they hadn’t published the theory when they had first gone back to Cahn, in 1984.
There’s a problem with the Shechtman-Blech and icosahedral glass pictures, though. If you try to pack icosahedra randomly that way, try to do that to your Dungeons and Dragons dice in a box, say, you will find that there are spaces between the icosahedra, because icosahedra don’t form crystals. They are unable to pack together regularly like cubes. And if this is your concept for explaining a material, you have to ask, “What would go in those spaces?” Nature doesn't allow spaces in materials like that. It costs a lot of energy, compared to rearranging the atoms altogether. So in considering this model, you had to hypothesize that somehow some atoms managed to get into those space and fill them, and do so without distorting the icosahedra.
That's a lot to assume, especially that the extra atoms would not affect the diffraction pattern. But, nevertheless, this competing idea began to get a lot of attention because it just seemed to be a simpler, in certain communities’ minds, than the quasicrystal idea. In fact, there was a fundamental problem with the quasicrystal idea, which goes back to the Penrose tiles, and was brought up more and more strongly over the next few years as a counterargument to the quasicrystal picture. Let me back up and explain something. If a quasicrystal is rapidly cooled, it will have some defects in it. The same is true for a crystal. In either case, the defects would cause effects on the diffraction pattern similar to what Heiney had found for Shechtman’s alloy. The classic way of clarifying that defects are the cause, is by annealing the sample -- heating it for long enough that the defects anneal out -- then you'd get a perfect pattern. In the case of the Shechtman’s sample, annealing would result in a pattern that would clearly point to which theory was right, since they predicted different outcomes. Unfortunately. you could not do that for Shechtman’s aluminum manganese sample. The reason is, it was not really a stable phase. It was a metastable phase. So if you tried to heat it and anneal it, it would crystallize. So you could never do any better than cool it rapidly and make this ambiguous state, which could be explained in different ways.
And I'm sure some people would disagree with me, but I would say it remains ambiguous to this day. We really don’t know what the Shechtman sample is. You can describe it as a quasicrystal. You can describe it as an icosahedral glass. You can even explain it using Linus Pauling’s idea, some version of that, as far as I can tell, equally well. But you can’t distinguish, because there’s no test I know of that could distinguish it, and there hasn’t been one done to date.
Going back to the big picture – there was, at the time, this question of principle—why the quasicrystal was an especially a bad idea. And it went back to the Penrose tiles. So I said that for these Penrose tiles, there were rules that can force you to form that tiling. In other words, Penrose didn't just find tiles which could make a quasiperiodic pattern. He found tilings which could only fit together in a way that’s quasiperiodic, by including puzzle piece like joinings, with various knobs and holes in the two tile shapes. So, if I gave you a pile of them and said, “Fill your table with them, without making any spaces,” you would know that there definitely exists a solution. Much like when you take the puzzle pieces out of a box. If it’s an honest company, you know there’s a solution.
But no one says the solution is easy, that it’s easy to find. And in fact, it seems intuitively clear that if I have a structure, like a Penrose tile or a quasicrystal, which is quasiperiodic, one of its properties is that no two points in it, no two tiles in it, are exactly identical in terms of their surroundings. Maybe in their most local surroundings, they're identical, but if I go out far enough, no two are exactly the same. Every one of them, in some sense, is in some sort of distinguishable position relative to all the others.
Now, for a crystal, if you imagine a crystal—atoms attaching to a crystal—so you have a crystallite growing, an atom attaches here and here and here and here, to that boundary site of the the crystal or another. You know because of the repetitiveness of a crystal, the atom will know to sit in the right place just by its local environment, on one part or another part of the surface, without having to know about the others. If I gave you square tiles and said, “Fill you table with them,” you could do that in a matter of seconds or minutes, depending upon how many tiles I gave you. But if I gave you Penrose tiles, my bet is you couldn't do it. You would find that you made mistakes. And you'd have to go back and take out a bunch of stuff and start again, take back the stuff and start again. So the anti-quasicrystal argument at the time was that, in fact, that this problem is a fundamental property of any structure that’s quasicrystalline. You can’t, through any local decision or local force, cause atoms to arrange themselves in the right position. Somehow they'd have to know about the atoms arbitrarily far away, and there aren’t any plausible forces in nature that would allow that kind of long-range interaction. Nothing realistic that would cause it.
Paul, how can you be sure that there are no forces in nature that would do that?
That’s a good question. I should say that we do not know of any that are, essentially because they get screened by all the atoms in between. So when I say arbitrarily far, you're trying to build something which has an Avogadro’s number of atoms. If you said, “Build ten, or a hundred,” OK, you could imagine a force stretching that far. But if there’s a new phase of matter, you should be able to grow it nearly perfectly to macroscopic size. But it seemed from the Penrose tile experience that there is some some mathematical restriction that says you can’t grow a perfect quasicrystal beyond a certain size because you're forced to make so many of these errors along the way?” That was kind of the conceptual argument. It’s a subtle thing.
And even Penrose was very much in line with that. He had written a paper that claimed that there is no rule for deciding what kind of tile to add to an edge if you try to construct a Penrose tiling by adding one tile at a time. That is, if I have put together a finite cluster of tiles into a Penrose pattern, and I tell you, “OK, now add a tile to this edge,” you have to make a decision, “Do I add a fat or a skinny tile to this edge?” You want to make the decision such that you don’t make a mistake. So that you can continue to add tiles without introducing any defects. But you're not allowed to use information about the rest of the tiling. You're allowed to use a finite amount of information about the tilings close to where you have to add a tile, but you're not allowed to use more than that local information. And Penose had shown that you can’t make a decision that reliably will avoid errors.
So the argument was that this quasicrystal is some kind of ideal mathematical ideal, but with an atomic arrangement that could not grow naturally from a liquid, or be made by any ordinary means we know of in nature because it could not be achieved through atom by atom growth without creating lots of defects. Whereas crystals can grow atom by atom without making many defects. And the same would be true if randomly adding icosahedron by icosahedron, in the icosahedral glass model. But in the laboratory, it didn't seem like there was anything special about the way Shechtman's sample had grown by splat quenching, compared to a crystal. So this advantage lent strength to this icosahedral glass model, compared to the quasicrytal picture. Not many people were adherents of Linus Pauling’s idea. I think maybe only Linus. Very few. But the icosahedral glass idea was gaining more and more strength for the first few years.
So, what happened next? So, I may not get my years right, but I think it’s summer of 1987, so now it’s a few years later. So we've written a lot of papers on elastic properties. We've done as much as we can to try to make the case for the quasicrystal picture versus the others. But at least I feel we keep coming up against this issue, this growth issue. It’s one thing to say in principle they could form this way; it’s another thing to say, “How would you actually imagine atoms forming such a thing?” When there seems to be this fundamental limitation, that you can’t add too many without making errors.
So summer of 1987, I went to IBM Research, again to take time out to focus on this issue and talk to people there. A good summer research opportunity. George Onoda, whom I had tried to work with on colloids, came up to me one day at lunch, and he said, “I've been thinking about this issue about the Penrose tiles, and the fact that you can’t grow the tiling out very far.” He said, “So I just tried an experiment. I cut out a bunch of those tiles, and I tried to see if I could fill the table without making a mistake. Yeah, it’s very, very difficult and I didn’t get very far. But, I discovered if I added one or two additional rules, local rules, rules about neighbors of the tile that I'm adding, I could go it a lot farther than with Penrose’s rules alone.”
David DiVincenzo, whom I had known since he was a graduate student at Penn, was also there at lunch as well. We decided we’d gather around the table after lunch and have coffee. George had cut out a bunch of these tiles of paper. So this was like going back to the old days, when Dov and I were doing Styrofoam balls and pipe cleaners. George brought out a box with bunch of these tiles. And at first, he tried to grow them using only the rules Penrose established. So with Penrose, you put down a fat tile. We'll choose this edge. We'll add something there. Choose another edge of cluster that now had two tiles. Add something there. And after repeating this a few ties, then we’d run into an error.
And then George said, “Yeah, but if you study that error, notice that it only occurs if there’s this certain arrangement of tiles that caused the problem.. So make a rule that when you see that arrangement, you don’t a the same tile as we just did. So let’s suppose you add a fat tile there, and it forces a mistake. Let’s make this an additional rule to Penrose’s.
So we added that rule, and we could grow the tiling out a little but farther than before. But not very far. Next error. So then we stood there and we looked at the tiling, and George said, “Oh, but hold it. Once again, it looks like we had a choice at this point, which could have been fat or skinny. But what gave us the wrong choice was yet another kind of local arrangement that we should forbid. If we forbid it, we would not have made the wrong choice there. We would have been able to go farther.” So we wrote down Penrose rules. Then we wrote down Onoda’s first rule. Then we wrote down the next rule. And we tried this for a while, getting stuck, adding a rule, going farther, and we kept on getting farther and farther in growing are tiling until we finally filled the table.
And that was remarkable. None of us had been so successful before in avoiding errors. But of course, we had this huge list of rules to follow now [laugh]. This long laundry list of rules. But as I began to look at the laundry list, I realized, actually, you can summarize it in a very simple way. If you think about Penrose’s rules, Penrose’s rules were essentially reduced to rules about the way two tiles are allowed to share an edge. They're allowed to share one way, but if you flip the tile, you're not allowed to share the other way. And that wasn’t strong enough to force things. It was actually a pretty weak rule, if you want to grow a tiling one by one. If you look at our laundry list, they can all be understood as instead of restricting the way things can join to an edge, they're restricting the way things can join around a vertex. They're telling you, “Look not just at your edge that you adding to — in fact, don’t worry about that edge. Worry about the tiles joining around the vertices to which you are joining.”
There’s only eight types of vertices that can occur in a Penrose tiling. And the rule reduced to, “If you have more than one choice that agrees with the list of eight, don’t add to it all. Randomly choose another vertex on the boundary to add to. If you only have one choice, add that one. We called that a forced site. ” So in other words, it’s still local. It’s still just looking at tiles around the vertex. One didn't have to look at the other side of the tiling. But by only adding tiles when the vertex was forced —that would guarantee that you never made a mistake. Or at least it looked like that, on the table.
Later on, Josh Socolar, my student, joined in this project, and we tried to see if we could prove this rigorously—that you could not ever make a mistake. Josh has amazing geometrical intuition and mathematical insights, and has gone on to make many novel contributions to the field. We continue to collaborate as well. In this case, Josh discovered that actually—and I won’t go into too much detail on this -- but what we actually showed is if you followed our rules that we had up to that point, which had been successful to growing out to the size of table, we would still make a mistake, but only once every ten to the 72 tiles. Much more than Avogadro’s number. And that furthermore, we could even do better than that. If we began with a certain topological defect that we had discovered, you could actually go out to infinity, with just one defect in the entire tiling. Which meant, essentially, with rules not so dissimilar from the way that crystals grow, local rules, you could actually grow out to infinity. And there was no mathematical principle that said you couldn't, and that you couldn't grow a quasicrystal as quickly as you would grow a crystal.
So in fact, Penrose’s proof was irrelevant, because Penrose had assumed that when you choose an edge, you must add a fat or a skinny. Whereas our rule is slightly different. If I choose a certain vertex, I have a choice of adding nothing or something, and I only should add when there’s something forced. And that difference is crucial. It enables you to avoid making errors. It's a subtle, surprising thing, not something you would guess offhand - something we found semi-empirically. I should mention that it took nearly thirty years for Josh and I, along with a bright undergraduate of his, Connor Hann, to get around to prove the same kind of local growth rules exist for quasicrystals in three dimensions for icosahedral symmetry.
Paul, how did you know not to be bound by Penrose’s rule?
That was easy. I didn't know about Penrose’s rule. [laugh] I mean, I didn't know about his statement about undecidability of the tiling, at the time. In fact—I'm getting slightly ahead of the story. The way I discovered it was when we submitted our paper. So our paper specified the rules. By now, we had a rigorous mathematical proof of how it would work and all that. It was rejected by PRL, by two referees, and both referees said, “This can’t possibly be true, because everyone knows you can’t do this for Penrose tiles. You can’t force it. In fact, there’s just an undecidability theorem, due to Penrose.”
That’s how I discovered it. They said it was not possible. It led to a bit of embarrassment. I wrote back to the editor and said, “But hold it. These people are rejecting this on the grounds of what people believed before our paper. But that’s what makes our paper in PRL interesting! Of relevance. Because we're proving it is possible! You can’t reject a paper because it shows something new just because, up to that point, it was believed not to be true.”
It’s also, if I might add, it’s also science, right? You're showing new discovery. [laugh]
Yeah, they found nothing wrong with the argument. They were just saying it had to be impossible, because Penrose said it was impossible. That was essentially the essence of it. And the editor said, “Even if you're right, here’s the problem. You already have two negative reviews, and the only way that you're going to be accepted is if I write to three people, and three of them say it is accepted.” And I said, “Well, no, I want to appeal this. This isn’t right. We're saying one plus one is two -- and then there’s two other referees that say, no, no, one plus one is three. This is mathematics.”
Paul, this also suggests the grip that PRL holds in the dissemination of knowledge within the physics community. Obviously your inclination here is not simply to go to another journal. You want this in PRL and you're willing to fight for it, so that it does get in PRL.
Partly that, and partly—this was wrong.
It’s not my first encounter with PRL where I think they've done something wrong. But for this one, I thought this was terribly wrong. So I made a list of 100 people and I wrote to the editor-in-chief, or the board involved, and I said, “You can go to any one of those people—I have not talked to any of them about what we've done. You can show them our paper. And if they reject the paper, I'll accept that it’s rejected.”
If any one of them rejects the paper?
I said, “You can go to as many, or any one of them. that you want.” Now, I don’t know if they actually did it, but I do know the paper was accepted.
[laugh] Because I said, “You can’t reject a paper when it’s based on math. Not only are we proving it, we have computer simulations. We're showing you with a computer we're growing these tilings. We have a tiling program that will actually follow this algorithm, and tiles out as far as you like. So you can’t tell me that it’s not possible.”
When was the paper published, Paul?
It was published in 1988. Now right around this time—1987, in Japan—an experimental group led by An-Pang Tsai at Tohoku University discovered an important new quasicrystal. And this one -- which was a mixture of aluminum, iron, and copper -- produces an icosahedral phase, but did not have to be grown by splat quenching. It could be grown very slowly.
And that was An-Pang Tsai’s point—to show that you could grow something that was essentially in thermal equilibrium, over a long period of time, and was a stable phase. And this one, when you looked at its spots, they were point-like, to within the resolution of the instrument, unlike Shechtman’s material. And when you checked the alignment of the points, they were spot on where they were supposed to be. This is what I would call the first bonified quasicrystal. You know, unmistakable quasicrystal.
And it blew out the icosahedral glass model immediately. Because the whole point of the glass model was to explain why these peaks had to have finite widths, and this immediately killed that picture. So the leaders of that picture at the time were Peter Stephens and Al Goldman, and they graciously conceded. “When we see this data, it’s over.” With Pauling, it was a little bit different. He was skeptical and still felt he could make his idea work. But to be fair to Linus, he wasn’t well informed about the quality of the new material when he said that.
In the meantime, we replicated the new material at Penn. And Paul Heiney and his student, Peter Bancel, did a lot of studies, diffraction studies, to study its perfection. We invited Linus to come to Penn, where he spent, I don’t remember exactly, a day or two. And we prepared to spend as much time with him as he wanted, to study the data for that sample, and see if we could convince him otherwise.
I really enjoyed meeting Linus. I hadn’t met him before. Of course, he’s legendary. And although he started off very skeptical, he was also very gracious about it, and very serious about it. He was really impressed by Peter's data. He conceded that the kind of model that he had before didn't work. He felt, though, that if he took his twin crystals and now made the unit cells, the repeating units, much, much bigger by a factor of ten or more, he could now fit the data. Of course, this now meant he was making a really complex model, a really ugly model, in order to explain them. Of course you can take that model and always extend it to such a degree that it could fit any data to any finite resolution. But at some point, you have to admit the quasicrystal picture is simpler, explains everything, and now you're making a very elaborate model which doesn't really explain much.
He graciously agreed—he said he wanted to write a paper in PNAS about his new unit cell model, but he would like us to write an accompanying article. And he wanted those two papers to appear together in PNAS, which they did. I would interpret that as him saying, “I still like my multiple twin picture. I agree the quasicrystal picture explains the overall symmetries better. I think mine explains the local arrangement of atoms better.”
So in terms of your objectives in inviting him to Penn, mission accomplished, essentially.
Yeah, I felt so. And we continued to communicate over the years. And I remember in his last year, he was even then writing to me. He had been trying to understand the quasicrystal picture better all along, and he finally got this idea that one way of viewing quasicrystals—which I explained to him at the time—is as projections from higher dimensional crystal patterns. And he was asking me about that. He wanted to understand how that worked. So he was clearly moving in that direction. And then he passed away.
I enjoyed that exchange quite a bit. I think it’s been somewhat misinterpreted in the history, because he was stubborn in a certain way, but—how should I put it? Linus was stubborn in a certain way, but I actually felt he had actually basically conceded the story, even though he had not conveyed it explicitly in words, it was expressed by his actions. So I didn't feel he was being ridiculously stubborn. I just felt he was moving slowly.
And I had no problem with him —he was perfectly happy to talk. It was perfectly friendly. And we roamed from other topics. We talked about a lot of other things, like cosmology, and other things he was interested in. So for me, it was a very positive experience. I think for the metallurgists, and especially people like Shechtman, they seemed to be very frightened of him. He was a strong opponent, and kind of a roadblock in their way, because the rest of the chemists were not accepting the idea, because he was in their way. I don’t know. I think that was just probably my view, or a physicist’s view, versus a chemist’s view, or a metallurgist’s view. But my experience with Linus was positive.
There’s so many things we could mention. Another bright student, Kevin Ingersent, did a beautiful theoretical calculation showing that quasicrystals can form faceted shapes that are impossible for crystals, some of which have been seen in the laboratory.
I also want to just be fair—you're asking me about my personal history in this. So I should say, going back to 1985, after our paper appeared and was first beginning to get splashy, another development that happened is several other theorists came out with other pictures which are quasicrystal pictures, but viewing them a different way.
And not using the term quasicrystal, I assume?
Yes. Yeah. So all trying to explain the same thing, using what I would say is the same picture. It took a while for everyone to agree that that was the same picture; it was the same picture, but in a different mathematical language.
So, for example, we had come up with the idea, thinking about tilings, how you put them together. Others had the idea of this projection from higher dimensions. You begin with a higher dimensional crystal lattice, you project the certain subset of points on a plane, which is oriented in a certain angle according to certain rules; that can also produce a Penrose tiling. So it’s producing the exact same thing, but from a different mathematical procedure. Not by putting together units three dimensions in a certain pattern, but in this way.
We had also studied another way of putting them together according to what are called Ammann lines, after the amateur mathematician Robert Ammann, who invented them.
We also we discovered that there had been a mathematician Nicolaas deBruijn with an ingenious multigrid idea; another group was using something called a projection method. Mathematically oriented people don’t publish in the condensed matter literature, you know, they publish in other journals that we're not familiar with. But over time, people are writing to you, and you're discovering, “Oh, someone had this idea, someone had that idea, which also had many of the seed elements we had discovered.” I wouldn't say they had all the elements that Dov and I had, but they had some really important ones. So like most discoveries, there’s usually some parts which are pre-, and then some parts which are immediately post-, all of which are important. That’s really how things develop. Science is seldom pioneered by a single group on their own.
And Paul, what do you think accounts for this critical mass of discovery around these tightly focused issues at this time?
More or less chance. Once it was clear that there really existed this material that seemed to challenge conventional rules of crystallography, clever people thought of different ways of obtaining what turns out to be the same thing.
We talked about three different ideas, genuinely different ideas—Pauling’s, icosahedral glass, quasicrystal. But within the quasicrystal picture, you could obtain the same structure from many different techniques. And if you understood deeply enough, you’d say, “Oh, that’s just different ways of describing the same thing.” But it may not be apparent to everyone in the field that that’s the case. It may take a while to learn that. I've had silly debates with people who said, “Oh, I like the projection model better than yours.” You can like the projection approach for obtaining the mdoel; but the result is no different than our model. You understand, we're producing the exact same thing. You had to explain that to them.
There’s another picture based on some nice work on Penrose tiles by a pure mathematician named Nicolaas de Bruijn whom I mentioned already —again, we didn't know about his work at the time; I wish we had—it led to our thinking of another way of generating tilings, which we call a topological dual method. Basically you make a set of lines, and let’s say you want to make something with five-fold symmetry; you make a set of parallel lines along five different directions, and then there’s a rule for transforming each intersection of those lines into a tiling. Sort of a topological transformation. And then, so if you want seven-fold symmetry, do the same thing with seven sets of lines. You want something with 143-fold symmetry? You can do that as well. So it’s actually the fastest computational method for generating tiles of any symmetry you want. So that was another view of them.
That picture was important because it revealed something the projection pictures made less obvious, which is one of the things that makes quasicrystals a much more subtle subject and much more difficult subject than crystals. If I am trying to describe the atomic structure of a crystal, say, suppose it has cubic symmetry, you know that one way I can understand the structure is from its diffraction pattern. The pattern will consist of points, Bragg peaks, arranged in a pattern with cubic symmetry. I can then think of the crystals as being composed of units, or unit cells, which are cubes. And then the only uncertainty left is where do the atoms sit in each cube. Because once I determine the arrangement in one cube, I've determined the arrangmeent in the rest of the cubes. And from that, I've determined the entire structure.
So that’s the principle of going from diffraction to working out where the atoms are. Find the symmetry. Given the symmetry, there’s a unique Bravais lattice which has that symmetry, which you can choose to have as your basis working out the structure. And the only uncertainty remains where the atoms are within the unit cell of the Bravais lattice. And from the diffraction pattern, which is like a Fourier transform, you can deconvolve it into the Fourier transform of the lattice, which you know—the cubic lattice, say —and the Fourier transform of where the atoms are in the unit cell. And so you can separate in the diffraction pattern the symmetry knowledge from the atomic decoration knowledge, and therefore decipher the entire structure. This is the method used for DNA back in the 1950’s, for example. It underlies the beautiful subject of crystallography.
That totally fails for quasicrystals. And it fails for several reasons. The first is—if I tell you the symmetry— say I want to analyze a sample with ten-fold symmetry, I'm just naming that as an example—there isn’t a single lattice which has ten-fold symmetry; there’s a continuous infinity of lattices, with the same symmetry, made of the same tiles, just with different sets of arrangements.
So I mentioned that Penrose’s tiling pattern has eight different kinds of vertices in them. These others would have different numbers of vertices in them, and they would be different arrangements. So they would be physically distinguishable from the first. But there’s a continuous infinity of them. And then, in addition, it’s not true mathematically—even if I let you choose one of them -- let you assume the structure is an atomic decoration of a particular tiling, you cannot determine the atomic decoration. The diffraction pattern does not deconvolve into a product of the lattice Fourier transform and the Fourier transform of the atomic decoration as it does for a crystal.
And so determining where the atoms sit in the quasicrystal has been one of the prime puzzles. At present, there is no simple systematic method. People do a couple of things when they write papers. First of all, they arbitrarily choose a particular lattice, usually based on a projection idea. As far as I can tell, there’s no physical motivation for that. That’s just what they do. And then the second thing, is for this deconvolving problem, they also use atomic imaging. So they know where some of the atoms are, and then combine the two to try to figure out where the rest of them are.
Even now—I'm not sure there’s an example of a quasicrystal in which the atoms are entirely agreed to, at the 100% level. In other words, you have individuals who might claim they've figured it out, but I don’t think there’s any that are fully accepted. I think people often say, “We know where 95% of the atoms are for sure, but there’s some uncertainty about the 5%.” So you don’t know, from the data, “Is that 5% because of some chemical disorder in there?” Or maybe I made a mistake in using that particular lattice. Had I chosen the other lattice, I might have gotten them all to fit well.
So in a sense, it’s a fundamental puzzle. It makes finding where all the atoms are, if that’s your goal—not my favorite goal—but if that’s your goal, it makes it fundamentally difficult. But with the Tsai discovery, the question, “Do quasicrystals exist?” was a settled issue. We now understood theoretically that there was no roadblock to growing perfect quasicrystals, and we had evidence experimentally. Because Tsai didn't find just one. He began to find more and more of these highly perfect quasicrystals. And then other groups began to find them, as well. So that essentially settled the issue, “Does this new phase really exist?” So I’d say somewhere around 1989 or so, or 1990, that was more or less settled.
And Paul, are we talking about a class of materials, or a material, a quasicrystal?
Each one is an example. So Shechtman’s material was alumnium-6-manganese, six parts aluminum, one part manganese. That one, I would say we don’t know yet. We may never know because of its fundamental instability. It can’t be annealed. Tsai’s was a particular mixture of aluminum, iron, and copper. And then each of these is particular examples. So as I said, finding new materials is somewhat an issue of hunt-and-peck, and luck and intuition. If I had visited Tsai in 1984 [laugh] instead of IBM, he might have decided to spend his time trying to look for these things. He might have found them earlier. It’s just the way it works when you're talking about looking for new materials. Does that answer your question? I wasn’t sure.
Yeah. So this was a gamble that paid off quite nicely for you, to take this pause on cosmology. [laugh]
I learned so much. Yeah. And I love subjects like this, these kinds of digressions, because you learn so much along the way. I got to work with a lot of great people, both experimentalists and theorists. I like experiment. I don’t do the experiments myself, but I definitely like getting into the room where the experiment is being done. I like to see it being done. I like to look at the data. I'm very much of that nature. I like to be close to where the observations are. And I got to do that more and more, as years went on.
And have you remained interested in quasicrystal developments since the mid 1980’s, late 1980’s?
So around this time, there was another kind of little flip, where I decided I wanted to take a look what was going on in cosmology again. The curious thing I find when I make these flips is that—you know, you've taken some time off. You figure, “I must have missed lots of important things.” You come back and usually there’s not a lot [of important things. [laugh] So it was not as hard as you might think to catch up. I'm saying that especially for young people who might think about being a schizophrenic in their science. It’s actually not so hard to catch up very quickly and get to the front again.
I was hoping by that time, that people would come up with good models of inflation that would get around its problems -- the fact that you had to fine-tune parameters in order to get inflation. You had to fine-tune them a lot more in order to avoid getting quantum fluctuations with too big an amplitude compared to observations.
And then this multiverse problem, which was kind of on the back burner in my mind. On that one, people had claimed that they had solved that problem. They had found ways of explaining how, in the multiverse, you could explain why we would be more likely than others. Claimed it. But others had made counterclaims. And then counter-counterclaims. So in fact, it was the beginning to be increasingly worrisome, which we'll come back to later. But that wasn’t my immediate interest. I wanted to see if I could find models that would be better. I had a colleague, Burt Ovrut, at Penn—we were particularly interested in supersymmetry and supergravity models that might be relevant for inflation, and we did some nice work together that I like.
But before I say more, I did want to say one other thing about funding agencies. When I came to Penn, I was funded as a particle physicist by the Department of Energy. And, as I mentioned, at the time, that was already considered a little bit questionable by the Department of Energy hierarchy, because I was not really doing accelerator physics; I was doing cosmology. But they let me get by with it. And I think I mentioned, especially P.K. Williams, our monitor, was knowingly looking the other way [laugh] and encouraging me. “Just go do good work.”
When it came to this quasicrystal work, and I could tell after a year that it was going to dominate for a period, I went to him and I said, “Do you think I have to drop out of DOE and start applying to NSF or other granting agencies to do this work on quasicrystals?” And what he said was, “Eh, no, don’t do that. Just keep working. If it turns out you do this for a lot of years, and you're never going to come back to cosmology or particle physics, we can talk about it. But don’t disrupt what you're doing. Just go ahead and do it.” That was really a wonderful thing.
Finding funding in condensed matter physics is not easy, especially when I wasn’t brought up in the field. And I thought that way of running the Department of Energy, where you are told, “You may have come in labeled as a particle physicist, but if you're doing good science, just go ahead and do it, because that’s good for us in general” was a great attitude.
And I mention it, because it was really important for my development, and unfortunately I don’t think that would be the response today. I think the attitude is much more about stovepiping, and much more that you have to fit —you have to divide your research, even, into little categories, explain how each fits into different categories of DOE missions. And I don’t think that’s the best policy. I would say that if that had happened to me at this formative stage, I probably wouldn't have gotten nearly as much work done. I don’t know what I would have done. Probably I would have had to look for funding, and that would have been disruptive.
Were you ever concerned, Paul—in your emphasis of having the breadth, that in any given research project, that you did sacrifice some amount of depth?
[pause] Yes and no. I wouldn't say concerned. I don’t think I was concerned. Again, I was developing more confidence in this way of working. My personal best contribution to science was to identify what I thought was the most exciting question at the moment, and move to whatever that is. As long as I felt it was exciting, pursue it. In the meantime, planting these seeds of other ideas, and when one of them becomes exciting, switching over.
I'm not working in isolation. I'm working in a scientific community. So if digging down deep in depth and staying in one place and working on something was an important thing to do at the time, there are plenty of people who will do that. There are plenty of people who are still working on, “Where are the atoms in quasicrystals?” at the present time, and have made important contributions. But I would not have been a good contributor to that subject. It didn't interest me as much as the issues we discussed, and there are plenty of other people who could have done it.
So, I don’t worry about the depth part, because I think other people pick it up. I think I try to figure out what I do best, which is, I’d say, inventing an idea, and then checking it out. And being willing to look into any kind of problem and constantly going to talks in many subjects, and always trying to think of interesting directions independent of subject matter. So I just found that worked better for me, and that’s what I should be trying to do—optimize my own approach.
So having survived the job search back in [laugh] in the early eighties, I decided, “I'm just going to do that. I'm just going to give that way of working a try.” And then I kept on getting positive reinforcement. Picking up Dov as a student, which you might say was crazy to do when the cosmology was first beginning to pick up, wasn’t crazy. It was actually a good thing. That was the seeding, and it paid off. And similarly, I was beginning to seed ideas thinking about the ideas in cosmology. And so when I was ready to turn to that, I could give that a fresh look. Switching from one subject to the next. And that has continued to the present.
Paul, did you return to inflation after quasicrystals? Was that sort of a natural place for you to come back to?
Well, I had wanted to—yeah. Because I had some new ideas, other than the spinodal idea, for how you could complete the phase transition. So I wanted to work on that. There was another mechanism, which I worked out my student Daile La, but I'm not going to go into, because it didn't solve the big problems I wanted to solve. It showed there was another way of solving the graceful exit problem while still having an energy barrier, going back to Guth’s idea and another counterexample to the no-go claim of Guth and Erick Weinberg. Another way of getting around the barrier problem. So I was interested in pursuing that for a bit.
But then something happened in in May of 1992.There were actually two things that were happening. One, I was beginning to work more on cosmology, and two, we wanted to build a new astrophysics group within our Department of Physics at Penn. So we had been, up to this point, a separate Department of Physics and a Department of Astronomy. The Department of Astronomy had collapsed to a large degree. They had a few people left, who were near retirement. The University was going to close the Department. I led a group that said, “No, no, don’t close it up. Don’t get rid of it. Join it with physics, and we will build a new modern astrophysics group.”
So I was working hard on that. And in the process, I was talking to a number of people that work on the microwave background. Because there was more and more activity in trying to look for fluctuations in the microwave background, which if they were there, could eventually, sometime in the far future, I thought, relate to the work I had done with Jim Bardeen and Michael Turner on fluctuations.
Did you consult on COBE at all?
No. Wasn’t involved in COBE at all. I was involved around that time with trying to recruit George Smoot to Penn. And so I knew him. So we were having discussions. I had talked to lots of people at Princeton. I was trying to learn how to recruit. You know, “What would be good areas to recruit in?” And they were telling me this was a good area to recruit in. And George, -- he invited me to come to the COBE announcement in May 1992 in D.C. And what I thought I was going to hear, was that they had discovered some fluctuations in density. Just that they were going to report a number—“The fluctuations in density are one part in ten to the four, and we observed those.” Because we had been waiting for the microwave background measurements to find such fluctuations. Our understanding of the theory was that they should exist at some scale, because there had to be seeds to make the galaxies. If something had smoothed and flattened the universe, there had to be some seeds to make the galaxies, and they should be at more or less that value.
The experiments—some people were getting quite scared, because as the measurements improved, they kept not finding any fluctuation. The universe looked perfectly smooth, down to a level that was uncomfortable, if you had the idea that the universe was composed of dark matter and ordinary matter and was flat. So I thought, “Oh, COBE is going to tell us, ‘Oh, we have now finally detected fluctuations’” —that they have finally gotten sensitive enough they managed to measure a little bit of fluctuation. But what blew me away was they showed much more than that. They showed the first example of a power spectrum. They showed the mean square fluctuations in temperature as a function of angular scale or as a function of multipole moment. A plot, which is now the iconic plot you see in papers and books on the microwave background, which measures where the temperature fluctuations, as you compare temperatures on average on different angular scales.
So the idea is, I make a map of the microwave background radiation across the sky, and I measure the temperature in this direction and this direction, which are separated by a certain angle. I take the products of those two, and then I repeat that for every pair of points which is separated by the same angle, and I get a number. I plot that on a plot, then I repeat it again for a different angle, and a different angle, and a different angle. So this is called the power spectrum. And the COBE team had made this plot of the first 20 multipoles—today this plot extends out to thousands of multiples—but already the first 20 multipoles showing that it was consistent with having a scale-invariant spectrum of fluctuations. Which was what we were saying is possible back in the Bardeen, Steinhardt, and Turner paper in 1983, based on careful computation, and which was consistent with the guess of Harrison-Zel’dovich-Peebles.
I had thought when I published that paper with Bardeen and Turner that it might take 50 years before we’d see data like this; but this was already starting in 1992.
And so my attention turned entirely to the subject of the microwave background for the next few years. Because I immediately recognized that what they had done was naïve. They had fit the data to a perfectly scale-invariant spectrum, which is not what inflation actually produces. That is only an approximation and soon the data was going to be accurate enough to detect the differences between the real prediction and a perfectly scale-invariant spectrum. And they had done that, compared to perfectly scale-invariant, because somehow astronomers had gotten the impression, from probably reading some of the papers—not ours, but early papers on the subject—that that’s what inflation predicted. Whereas our paper—Bardeen-Steinhardt-Turner—carefully pointed out the prediction is that it’s only nearly scale-invariant. There should be a tilt, a small but measurable difference from perfectly scale-invariant. So they had left off tilt. In fact, they didn't even know how to include tilt in their calculation. In fact, I remember going to a meeting at Princeton a few months later, in which I said, “You've left off the tilt. If you're going to test inflation, you've got to include the tilt part of it.” And the first reaction I got from some was, “Oh, you're just trying to be obtuse. You're trying to add a parameter to complicate things.” “No, no, this is a deviation from a perfectly scale-invariant spectrum that is inherent to all inflation models. It's not right to leave this effect out.”
I had a really wonderful postdoc, Rick Davis, who was at Princeton, and he and I immediately worked together to try to write codes that would allow you to predict the cosmic microwave background spectrum on all angular scales. That famous curve that you see with bumps and the like. There had been pioneering work done on this by Dick Bond and George Efstathiou, who had sort of given a prescription of how you would do the calculation. They had actually made such a code themselves, but it was too slow as to be useful. So our goal was to make it, number one. Make it fast enough, number two. But also to include an element they didn't include, eventually, which was the gravitational wave contribution. Because inflation also doesn't just produce scalar fluctuations, density fluctuations; it also produces tensor or gravitational wave fluctuations.
With regard to gravitational wave, Paul, were you following what Rai Weiss was doing at MIT at this time?
No, because these wouldn't be relevant to LIGO. These would have to be waves you would see using the microwave background. The microwave background is measuring temperature fluctuations. Those fluctuations can be due to one of several reasons. It could be due to fluctuations in density. Or it could be that spacetime itself is distorted. That’s what we mean by a gravitational wave. And the temperature fluctuations could be a combination of the two. Inflation naturally predicts it should be a combination of the two. The way inflation produces these fluctuations is beginning from quantum fluctuations of the metric, of the gravitational metric. And then it stretches those fluctuations during inflation to scales much larger than the Hubble radius. And then later, after inflation ends, the Hubble radius grows and catches up with them again, and they come back inside the Hubble radius. That is, the Hubble radius grows larger than their wavelength.
But quantum fluctuations of the metric have various components to them. There are some that we call scalar, that behave as scalars, in terms of symmetry. They correspond to fluctuations in the curvature of space from place to place. There are also some fluctuations that behave as tensors. These produce fluctuations in the shear of space from place to place and they later generate gravitational waves that propagate through space. And since you're fluctuating the metric, and quantum physics doesn’t know that humans divide it into this scalar and tensor, it creates them both, and it creates them both with the same amplitude, more or less. And so that should have been a lot of the power in the microwave background—ultimately, a measurable amount in the microwave background should be due to these so called tensor modes, or gravitational wave modes.
Now, what happens when the horizon catches up to one of these modes—if it’s a curvature fluctuation, it’s like a fluctuation in density; it tends to draw more and more matter in towards the high-density regions, and away from the low-density regions, eventually condensing to form non-linear structure, to form the seeds of galaxies and stars, et cetera. Gravitational waves behave entirely differently. They simply get redshifted away due to the expansion of the universe. So in other words, whereas the curvature fluctuations become stronger and stronger as you wait longer and longer in time—so if you look on smaller wavelengths, which have been inside the Hubble radius for some time, the curvature fluctuations are going to become non-linear structures, which are easy to observe. The gravitational waves have simply been petering out, redshifting away, so they're harder and harder to detect as you get to smaller scales.
LIGO is a much smaller scale than the scale of the observable universe. So by the time you get to LIGO scales, they're way down below the LIGO sensitivity. So you might be able to capture them someday—people are talking about 50 years from now, or something like that—future generation space-based gravitational wave detectors might be able to detect them. But not current detectors. The first place to look for them would be in the microwave background. And that’s what we wanted to know—how would you know that they're there?
And this is to say that current detectors are, what? They're not sensitive enough?
Not sensitive enough. And, there’s foregrounds, which are in the way. Events that produce gravitational waves are all over the universe, like black holes colliding, which creates a much stronger signal, and you can’t pick this inflationary contribution up in the background. So you can’t work on LIGO scales. You need to work on scales where you either know the background sources very well, or there aren’t any such foregrounds in that frequency range. And, we're not there yet. That’s not where the technology is at the present time. Maybe someday. So we first were interested in the power spectrum. What does the tensor contribution look like? What does the scalar contribution look like? They behave differently as a function of angular scale. So we could say, based on the data—we already had a limit—there couldn’t be too much tensor contributions based on the COBE data. All we could detect was scalar. But it was early days. The codes, worked out with Rick Davis, were able to provide the methodology for how you would distinguish scalar and tensor that way.
Then we looked also at polarization of the microwave background, because other groups had talked about these tensor modes back in the 1980’s and had pointed out that not only do they produce temperature fluctuations, but they produce a different polarization of the microwave background radiation. When the photons scatter off electrons and then head towards the Earth, on the last scattering surface, they would polarize that light differently than the scalar fluctuations.
So we did some of the first power spectrum calculations relevant to polarization. These were the seeds for ideas that people picked up on in the next few years that led to the idea of B-modes, and detection method we use today. We sort of worked on that for a number of years, I guess maybe 1991, ‘92, ‘93, ‘94. I wanted to really understand this technology well. My view was that if I understood the data better, I could understand how to interpret it better, and then I could look for hints of unexpected phenomena.
Chronologically now, we are getting up to the point at which you switch over to Princeton.
Not quite yet. Over the next few years, I would say what I was continuing to do was more perfection of ideas that we talked about, both on the quasicrystal side and on the cosmology side. Let me talk about 1994 and 1995, though, and then maybe we can close there. Because that was a very different kind of thing.
In 1994, I was invited to organize one of these workshops at Kavli, what is now called the Kavli Institute in Santa Barbara. I was one of the co-organizers. One of the participants in the program who gave a talk early in the worshop was Jerry Ostriker from Princeton. I had maybe said ten words to Jerry up to this point in time, so I didn't really know him well. He was more distant to me at the time. Now, we're very, very close colleagues.
But at the beginning of his talk, he talked about problems he saw with the conventional view that the universe was composed of dark matter and ordinary matter only. From his point of view, there were a number of hints that there had to be something else. And that something else he was thinking of, was a cosmological constant.
Now I remember going to a meeting—I think it was a few years earlier—shortly after the COBE results came out. It was at Berkeley. And one of the peculiar things about the COBE results is if you took them seriously, and you assumed there was nothing messed up with their measurements, it didn't fit well what was then the model favored by cosmologists at the time with 95% dark matter and 5% matter. The data seemed to call for something else. Something was missing. There didn't seem to be enough matter in the universe to make that picture fit. By matter, I mean dark matter. There was growing evidence that there wasn’t enough, and that was the beginning of Jerry’s talk.
And then also COBE—It didn't have the right amplitude you'd expect if the universe was 95/5. It seemed again to suggest some additional form of energy. I mean, if you did the microwave background calculations like I had, the amplitude would fit better if, in addition to ordinary and dark matter, there was either curvature—the universe was spatially curved as in an open universe—or if there is a cosmological constant.
At the end of the conference, the organizers decided to have a vote. “What do you think the story is?” they asked the audience. They sometimes do that as a joke. At least I view it as a joke. At the end of the conference , We had to fill out a ballot—A, the universe is composed of a 95/5 ratio of dark matter to ordinary; B, the universe is open, so it also has curvature; or C, the universe has a cosmological constant in addition to dark matter and ordinary matter. And as I recall it—they didn't tell who voted which way; the results reported were anonymous—the claim is that only two people voted for cosmological constant. I knew one of them—me. I didn't know who the other one was.
I later learned it was Jerry. [laugh]
Jerry probably thought it was weird when I came up to him after his talk because he knew his suggestion was unpopular. But I immediately felt a resonance—that if this was true, we should be able to do a lot better quantitative job of combining different datasets. In his talk, Jerry was sort of vaguely saying, “Look at this piece of data. Then look at that piece of data. Then look at this other piece of data.” I said, “You know, we can take these different pieces of data, and actually put them on top of one another.” And we can show that even though each type of measurement had its own systematic errors, we can determine whether, given the errors, the measurements combine to point us towards one kind of cosmology or another.
Now, that approach of combining different types of data with different types of errors is used all the time now in cosmology. At that time, that idea was considered strange. But we did that. And we found that remarkably, the only way to get the different kinds of data to match together on the matter side, was if the matter concentration was only around 30% of the energy of the universe. That is to say dark matter plus ordinary matter with 25/5 ratio. Secondly, even though it was early days for microwave background, there were enough data points on that power spectrum curve—or you didn't even need points; you just needed limits—that you could conclude that there had to be some form of energy in addition to matter. It was not consistent with curvature. It could only be consistent with the data if the universe were flat, and the additional component was some form of dark energy.
Why did it have to be dark energy?
You are adding more data as you go along and you're narrowing the choices. Something’s missing, and you have to try to fit different choice of what it can be to the data.
And this assumes that dark energy is a single thing, not just a class of stuff that we don’t understand?
So when I say dark energy, it means something that would be causing the acceleration of the universe. So how do you distinguish, let’s say, whether it’s empty space, curvature, or some form of energy that causes acceleration? You use the fact that the concentration of each would change at different rates as the universe expanded.
So if the universe has curvature, you know that every time the universe expands by a factor of two, that curvature decreases by a factor of four. Whereas for dark energy, let’s say it’s a cosmological constant, the universe expands by a two, but the dark energy doesn't change at all. So that means that, although the data is saying today it could be one or the other, if we go back in time, they would have been changing in different ways. Their contribution to the total energy of the universe, would be different, because going back in time, their concentrations extrapolate differently. One of them becomes irrelevant almost immediately. That’s the dark energy. So even by a redshift of a half, or one, it’s already irrelevant, cosmologically tiny.
Curvature would be important going back much further in time. Now, why is that important? Because, anything you add to the universe that’s not matter, like curvature or dark energy, stops the formation of structure in the universe. You can show that from general relativity. So, if it were curvature, that structure would have stopped growing a long while ago, because the curvature would still be non-negligible back then. The dark energy was irrelevant until very recently, so it would have had hardly any effect on the growth of structure at earlier stages in the universe.
And recently means what, Paul? What are we talking about when you say “recently”?
Cosmically [laugh] dark energy took over about four and a half billion years ago, about the time that our Milky Way formed. Curvature, if that were to account for the missing piece, would have taken over much earlier. And that means growth of structure would have stopped much earlier.
Much earlier as in much closer to the big bang?
Much closer to the big bang, right, that’s what I mean. Which means you have two histories. One, the structure stopped growing early on. And two, it has been growing until very recently, cosmically speaking, when the dark energy took over—relatively recently, four and a half billion years ago. And those differences in growth lead to two measurably different predictions for the microwave background.
And then the second difference is, one involves changing the spatial curvature, and the other one doesn't change the spatial curvature. If dark energy is the missing component, the universe is flat. That means if you have measured the positions of the peaks of the microwave background, the peaks should lie where you'd expect for a flat universe, but with a different height than you'd expect if it were all dark matter because of the difference in structure growth. But the peaks should be at the right place, at the right angular scales.
If the universe were open, you'd have two effects. One is the peak should be in a different place, because the universe is now curved. It’s open. That changes light paths in such a way that these peaks appear at different angular scales, number one. And number two, curvature should greatly amplify the peaks because of its effect on the structure growth. Today we could easily see from the data that it’s obviously not the second case. The data is overwhelmingly clear. But at the time, the data wasn’t yet there. But there were enough experiments that, where there should have been a huge peak if the universe were open, there were actually limits saying there is no peak there. So from that, you could distinguish, it had to be the dark energy idea—it had to be a flat universe with dark energy, and not an open universe with curvature.
So that broke the degeneracy, if you like, so that the whole philosophy of this paper was by combining data sets in different ways, you could constrain parameters, you could check out models, until it finally got down to these two finalists, and the microwave background, the argument I gave, you just broke that degeneracy. So we wrote a paper in 1995 which says, “Observational case for a low-density universe, low matter density universe, with a non-zero cosmological constant.” And we said what it should be. It should be about 70/25/5, the ratio of dark energy to dark matter to ordinary matter.
Which, at the time, people didn't take very seriously. In fact, at the time, there was some early preliminary work from one of the supernova groups which claimed that there couldn't be a cosmological constant. It was early days. It was based on seven supernova. Three years later, of course, we know what happened. Two supernova groups, including this one, published data that came to the opposite conclusion. They came to the conclusion that the ratio of dark energy to matter in the universe is equal to 70/30.
Right. Exactly 70/30.
Yeah. There’s error bars on these results, but I could look back at that paper and be pretty happy that the ratios today are still within the error bars we published. When we produced our results, because it involved this idea of combining datasets in ways that people were just not comfortable with, in the field, it was never really accepted. Readers could not follow the reasoning at the time.
On the other hand, when the supernova results came out, that kind of blew people away because it was simple. Only one data set needed, though the bottom line was remarkably close to what Jerry and I had published three years earlier.
The experience got me started on the issue of dark energy, giving me a three-year head start over everybody else on the issue of dark energy. And I realized that what Jerry and I could really say from what he had shown, is there has to be something that causes the universe to accelerate, but it doesn't say it has to be a cosmological constant. It could be a form of dark energy whose density varies with time. So that got me working on the idea of time-varying dark energy, what we called quintessence.
And so at the same time the supernova results were coming out claiming to discover a cosmological constant, my group was publishing a paper saying we don’t know that dark energy has to be a cosmological constant; there are various reasons why you might think it might not be; and it could also be time-varying. And there were ways of testing that, using the microwave background, we claimed, and using measurements of growth of structure. So that was 1998. And that’s the year that I moved to Princeton. So that takes us up to Princeton, as you wished.
Let’s end, Paul, with just a few questions about this career transition for you. Obviously you feel tremendous loyalty to Penn. You're quite happy at Penn. And you probably realize, at this point, that that pivotal bet that you made at the beginning of your professional career, that this would be the kind of department that would allow you to fly in every direction you wanted to fly in, of course had paid off quite well, right?
So I can only assume that it must have been a difficult decision for you to make the switch to Princeton.
[pause] Yes and no. Yes, mainly because I had a lot of friends there that I had worked with for years; they were important to me. No, because I could see that microwave background was going to be the power tool in this field. And I felt it was important, if I was going to play a role on the cosmology side, to be very close to the data.
Also, I had been working hard up to this point to build our astrophysics group. It had taken a lot of energy out of me. It wasn’t an easy thing to do at Penn. There were a lot of doubts expressed about whether it was going to work or not. It had finally kind of taken seed, and it was a good time to let go of it. To say, “OK, I've helped to launch it. Now I should back off. Because my goal is that they should become self-sustaining.” Which they did, very, very well. Very successfully.
So your goal, Paul, in merging these departments was not necessarily to lead the merge that you had created. That was not one of the things that you were looking to accomplish?
No, I never wanted to do that. I wanted to seed it, and then have it take off on its own. That was really my vision throughout.
And when you talk about being closer to the data, what does that mean exactly with the microwaves?
So after COBE, it was clear what was going to happen next. We were going to need better maps of the CMB. And there were the two proposals that came out shortly after COBE results came out. One became known as WMAP, a U.S. effort, with a large contingent at Princeton. Among the people who started it were David Wilkinson and Lyman Page, and I knew them both well by this point, through all of the work I had done on the microwave background. And we had recruited a really bright young experimentalist, a researcher in their group at Princeton, to join our faculty at Penn -- Mark Devlin, who was building detectors. So I had used their help to help build that part of the Penn group.
But I was very aware of the fact that Princeton’s a place that had really high standards, really high quality work in this area. I also have to say, as a theorist, it’s important for me to identify experimentalists I really trust, who have really high standards. And this was the right group. And I knew they would be doing this experiment, and I wanted to be close to it.
So substantively this was in fact an easy decision for you.
Scientifically, yes. At the time, I thought the quasicrystal work was going to fade away. I was very wrong about that, but that was my impression at the time. So it seemed timely to focus on the cosmic microwave background.
As a theorist, I can’t do an experiment. But what I can do, as a theorist, is try to come up with a competing idea, and see if I think that competing idea does better than the existing idea. One of the problems with inflation, was that the only competing idea for a long time was using the idea of cosmic strings to make structure. It didn't really explain the smoothness and flatness. And that idea, with COBE, was killed. So I was always trying to think about a new approach.
I was beginning to get increasingly itchy about problems with inflation. So in summer of 1999, just after I went to Princeton, I organized, with Neil Turok, a meeting in Cambridge University at the Newton Institute. And that meeting was where I began to think about a new approach, which is the idea of a bouncing cosmology, which continues to grow and grow and grow, year by year, especially over the last few years. So yeah, that was another thing that happened the summer before going to Princeton.
And were you recruited to Princeton?
Who was the driving force behind that? Do you know?
I think Jerry was. Well, it’s a little complicated at Princeton. Physics and Astrophysics are two separate departments. And my understanding is that there have been periods when they've been friendly, and periods when they've not been friendly. [laugh] But they were going through a friendly period, and they've continued to be friendly since I've been there. So I did not experience any of the unfriendliness. But I think Jerry sometimes tells me—it was always a delicate thing, how to bring it up. He had met me at Santa Barbara. The project we had worked on really excited him, and it really is very exciting. We essentially discovered dark energy before everybody else. My impression is that he, maybe working with Jim Peebles, because Jim’s a good friend of his—he probably convinced him to give me a look. I was invited to give a colloquium on the work that Jerry and I had done, and on this idea that dark energy could be time-varying, which is something Jim was also interested in. So I didn't think of it as recruiting at the time; I just thought I was telling them about work we were doing. But this was probably all preliminary checking me out, I'm guessing now. I wasn’t thinking about that at the time. But at one point, the department chair, Stew Smith, called me and said, “Would you be interested in coming if we made you an offer?” I said, “Probably so.” [laugh]
And I wonder if the thought ever occurred to you, maybe you would be looking to merge the departments at Princeton the way you did at Penn, or was it a totally different situation?
No, there would be no reason to do that. They're both powerful, strong departments. So at Penn, the problem was astronomy was going to disappear. That would have been a disaster. So there were two options—rebuild the department, but that would be harder than just merging the two.
Was the Institute a draw for you, also?
Not so much. The thing that drew me was I’d have really strong colleagues in cosmology. I had one or two colleagues at Penn who had interest in cosmology, but not who were at the level of a Jim Peebles or a David Wilkinson or a Jerry Ostriker. And of course there were many others that were at Princeton in other fields whom I knew well. So suddenly, I’d be moving to a center where there would be real giants. And that qualitatively changes things.
So when I was at Penn, I was mostly isolated in what I was doing. I would have to travel all the time to go out to seek information. Which is not a bad thing to do, but I had to go to conferences. I had to travel, often to Princeton, to go to meetings, to go to talks, to go to lunches. Suddenly, I'm in the center. Now, I don’t have to move at all. [laugh] It’s more the opposite. I'm being flooded with information.
But you're defining the center in terms of cosmology. Condensed matter physics at this point is sort of taking a back seat in terms of what’s motivating you.
So I thought. Yes. Didn't turn out to be the case. How my research will go is the thing I predict least well. [laugh]
Good. So I think that’s a good stopping point for today.
This is David Zierler, oral historian for the American Institute of Physics. It is July 8th, 2020. I am so happy to be back with Professor Paul Steinhardt for round four of our epic discussion. [laugh]
Paul, thank you so much for joining me again.
Oh, thanks for having me back. You're infinitely patient! [laugh]
[laugh] Let’s pick up on the story in the interlude, 1997 to 1998, when you are invited to Princeton to give a talk. Let’s set the stage there. First of all, what were you invited to speak about, and did you have any inkling that this was sort of the beginning of your eventual move over to Princeton?
I was invited to give a colloquium, a physics colloquium, the weekly colloquium, to talk about the work I had been doing with Jerry Ostriker on the idea that there could be a substantial amount of dark energy in the universe that accounted for 70% of the energy of the universe. It wasn’t dark matter, it wasn’t ordinary matter, but that would have to be there to account for the observations that we had in hand at the time.
Is this before or after Mike Turner sort of coined the phrase “dark energy”?
That’s a good question. I don’t exactly know when he coined that term.
I believe it was 1998, but there’s always—
That’s what I think.
The phrase is out there, but it’s sort of credited as being sort of coined in an article that might have come after the actual use of that phrase.
I know Mike did it, but I just don’t remember which he had in mind.
But obviously these are ideas that are sort of bubbling around in your circle at this point.
A little bit. There were a few of us. So there were two related efforts --most people were talking about cosmological constant, a specific form of dark energy. That was a possibility. One was the paper that Jerry and I wrote, and another was a paper that Mike Turner and Larry Krauss had written. Both papers had something in common, and something importantly different. What both papers had in common, was that they both pointed out there wasn’t enough matter in the universe when you added up dark matter and ordinary matter. There wasn’t enough to account for the total energy density you would need to add up to the critical density.
And so there were two logical possibilities at that point. One, is that there is no more energy; the rest of it is accounted for by the curvature of the universe. That we live in an open universe, pretty open, 70% empty space, curved space, and 30% matter and ordinary matter. And the other logical possibility, was that there was another energy component, dark energy.
But the two papers at that point diverge, because in the Krauss and Turner paper—they wrote, “We're going to assume that the universe is flat. That means we're going to assume there is a critical density, and therefore there has to be a dark energy.” Based on that assumption, not data. Jerry and I didn't want to assume; we wanted to ask if the observations forced us to that. So our paper showed that there were additional observations that Krauss and Turner didn't consider, namely the microwave background and what we knew about the evolution of structure at that time, that, we showed, already forced us to the possibility that it couldn't be the open option; it had to be the dark energy option. Based on observations. Not an assumption.
So we were more definite, and we weren’t relying on a theory. They were assuming, “Oh, inflation must be correct. And if inflation is correct, it must be total energy density is equal to the critical density. And we're going to go with that.” We said, “No, we want to ask observationally, empirically, what do we know to be true about the universe?”
And specifically what observations are you relying on, up to this point? What are the missions? What are the telescopes? What’s out there that you are relying on empirically to make these calls?
So for the matter side of things, there’s lots of different pieces of evidence. There’s what you know about the expansion rate of the universe, the Hubble parameter. There’s what you know about the emission of X-rays in clusters of galaxies. There’s what we know about the amount of baryonic matter from nucleosynthesis. There’s studies of large-scale structure, clustering of large-scale structure, that the number of clusters of galaxies that we observe in the universe. All of which constrains the amount of matter we have in the universe, usually in combination with some other degree of freedom, some other unknown. Like maybe we don’t know the Hubble constant exactly, and we don’t know the matter density, but they constrain different combinations of those.
So by putting the different data together, there emerges what we called the concordance picture—you know, bringing the data into concordance -- you could have imagined that they produced conflicting results, but they actually lay on top of one another and all agreed that the matter density added up to no more than 30, 35% of the critical density.
And how do you calculate a number like that? How do you arrive at 30, 35%? What does that even mean?
Critical density is related to the Hubble expansion rate. So according to Einstein’s equations, if you're at the critical density, then the expansion is driven entirely by whatever the totally density is. And that’s called the critical density. If, on the other hand, the universe is curved, or the universe is anisotropic—is expanding in different directions, in different ways—those also affect the expansion rate. And if they make a significant contribution, then that means the matter density is different than the critical density. It could be greater or less, depending upon signs.
So the first question you're asking is, “Are there any contributions to the expansion other than whatever the total matter energy density is?” And so you can assess that part by figuring out individually what the different contributions are to the total density, and see if they all add up to the critical. So the first part that we had done -- and Krauss and Turner had done a sort of weaker version of that -- was to show that it didn't add up to the critical density. If you put all the constraints in that were known at the time from different types of astrophysical observations, they were all pointing forcefully to significantly less matter than the critical density. Not just less than half, but less than probably a third of the critical density. Which means something else was missing. There had to be something else in the universe. Maybe it was curvature. Maybe it was anisotropy. Maybe it was some other form of energy. So then you need an additional set of observations.
And this is what Jerry and I did that was different. I think it was an important addition to the argument. Because it didn't rely on theoretical prejudice; let’s put it that way. It just relied on observation. We showed that if you take what were then the observations of the microwave background fluctuations—so this is 1995; we're past COBE. COBE has made some initial observations. So we know about that. Other experiments had been putting constraints on what the fluctuations could be on different angular scales. Not yet the wonderful plots that we have today, but the first crude measurements. But those were good enough for our purposes.
We also knew that if you introduce curvature versus introduce some form of energy, it affects the fluctuations in the microwave background on different scales differently. We could compare that to the observations and show that the open possibility, the idea that there could be curvature—there’s nothing other than matter—didn't work. I think it was something like five sigma, five standards of deviation away from fitting the data at that time. Even at that time. Nowadays, it would be many, many more sigma.
And so that left us with only the possibility that it could be some form of cosmological constant or dark energy, some energy component. So when we wrote the paper, we were trying to make two points. Number one, there’s enough data now—no single piece of data will tell you, but there’s a way of putting them all together that it can tell you this story. That was our first message. And the second point was that there had to be 70% of new stuff, and it had to be something like a cosmological constant. And I guess astronomers would normally assume, because somehow that’s how they've been trained, that “Oh, that it must be a cosmological constant.” Even today, many people assume that the dark energy is a cosmological constant. But there are various reasons theoretically why that’s not a great idea, or at least not a required idea.
So almost immediately, I began working on the idea that there may be some kind of time-varying component. A cosmological constant is a form of energy that, as the name implies, is constant. It was there since the beginning of time. It hasn’t changed. It has no dynamics. Its only effect is when finally the matter and radiation density are spread out enough through expansion. Only when you finally reach a stage where its constant energy density becomes significant does it have any physical effect. And the physical effect is to speed up the expansion of the universe.
But it doesn't have to be that way. The data was equally good, equally acceptable, if you had an energy density which was varying with time. So by 1997, in fact in July of 1997, my postdoc Rob Caldwell and student Rahul Dave and I actually wrote a paper, which we submitted, saying, “There’s a possibility we should be thinking of, which is not only is there this other form of energy, but it could be time-varying.” And we called this new form of energy quintessence. Fifth essence. Fifth form of energy in the universe. We know there’s ordinary matter. We know there’s dark matter. We know there’s neutrinos. We know there’s radiation. This would be the fifth essence, if you like, a quintessence. And that’s what we proposed. So that was one important development going into 1998. The paper hadn’t yet appeared -- it had appeared on the arXiv, but hadn’t yet been published.
The second development, which is an entirely different subject, was in the area of quasicrystals. And I want to mention that too, because you'll see how that plays into what happened in 1998, 1999. With my student Hyeong-Chai Jeong, we had shown something surprising about quasicrystals that we hadn’t expected. Up to that point, the view that we, and everyone else, had about quasicrystals is that they're analogous to Penrose tilings, which is a tiling composed of two different size tiles that can be forced to form a quasicrystal or quasiperiodic structure. And the idea was that if you wanted to make something periodic, we know we can do that with just a single repeating unit like a square tile. But if you wanted to make something quasiperiodic, then, based on the experience with Penrose tiles, it looked like you needed at least two, because you want to have two competing length scales, or two competing frequencies in order to make something quasiperiodic. It turns out that’s not true, and that’s what we showed.
A very clever mathematician named Petra Gummelt had suggested you could do it with just a single repeating unit. Not a tile exactly, but what she called a covering. That is to say a unit which would repeat, but in such a way that you're allowed to cover part of one unit with the another. They’d overlap. So it’s not the kind of thing you would want to build for your bathroom tiling [laugh] because you don’t want your tiles to overlap. Not to be recommended. But what it suggested to us was another concept -- which is that you could have repeating units, which have the property that they share atoms. And so you could rethink the structure of a quasicrystal --- not trying to figure out separately which atoms correspond to one tile, which atoms correspond to another tile, but it would be more like for the case for a crystal. You just have a single unit. You have to decipher how the atoms are arranged in just that one unit, and once you figured that out, you know the rest of the structure. Following the overlap rule, everywhere, would define the rest of the structure -- much in the same way that for a crystal, once you decide what are the atoms that correspond to the square or the unit cell, you've figured out the entire structure, because you know how the squares fit together.
So it suddenly made the story of figuring out where the atoms sit in a quasicrystal much simpler, much closer to what you had for a crystal. Except more constrained, because you're not allowed to put the atoms any which way in the unit cell. You have to put them in such a way that neighboring unit cells nicely overlap, that the atoms can be shared in a nice way. That the arrangement of atoms in one unit match nicely with the ones in the overlapping unit. So it actually makes determining the atomic structure even more constrained, which makes the problem solving easier. And then we had gone on to actually try this. We worked with a group in Japan that had done atomic imaging of quasicrystals. And we had shown that this approach does a beautiful job, at least for one of the best samples that has been measured, did a beautiful job of explaining where all the atoms were in the sample. So that was very exciting and meant that somehow quasicrystals were now simpler in some sense, conceptually. It also made it simpler to understand why they form. Quasicrystals are not so different from a crystal as you might have thought.
OK. So those are two separate threads which are going into 1998. So a sequence of events occurred—I'm going to describe it chronologically for this period, because it’s going to sound crazy. But those events started different threads of research, each of which continue to this day.
Paul, so I understand correctly, did both of these threads compel you to see Princeton as really the place to be? Or was it really more on the cosmology side, and then these other aspects—
It was definitely more on the cosmology side, at the time. It turned out to be really important on the other side, too.
But it was cosmology as the sort of motivating force behind the move, as far as you were concerned?
Yeah. Because what I was doing on the dark energy side, that was really exciting. [laugh] Because that’s something that could be tested with the cosmic microwave background and other observations. And Jerry was at Princeton, and the microwave background group was at Princeton. All the resources on the theoretical and observational side were there to explore what I thought was going to be a really important and influential idea going forward. So January 1998, I get the call from Princeton. They say, “Oh, would I be interested in coming to Princeton?”
And it’s like an anonymous call, or it’s a name that’s worth putting on record, in terms of who’s making this offer?
It’s from the chair, Stew Smith, a wonderful person, a wonderful experimental physicist, really wise person. He called me. I didn't know him at the time, maybe just to say hello. But I hadn’t been thinking about Princeton. This was like just out of the blue. So that immediately grabbed my attention. And as we discussed last time, it didn't take me that long to decide that this would be a good thing to do. The timing was right. I thought I had put a lot of work into Penn, into building a group there in astrophysics. I thought it was a very good time for them to sort of take off on their own, anyway. I had been thinking about how to handle that. This was also very good for me intellectually, scientifically. So it seemed like a good transition. So that was event number one.
January 1998 was also the month in which two different supernova groups announced their results, that they had observed that the expansion of the universe is accelerating. Which is exactly what you'd expect, if you had some form of dark energy in the universe. So suddenly the idea that we had been working on – beginning with the work with Jerry Ostriker and onto the work with Caldwell and others on time-varying dark energy -- which wasn’t being strongly noticed, because there was a strong prejudice against the idea of dark energy, and frankly which has been mostly forgotten by many people in the field since – I mean the fact that we had all that work done in advance -- rather than as a response to the supernovae groups —was nevertheless verified.
And not only did the supernova groups say the universe was accelerating, but it could be explained by a cosmological constant, which corresponded to roughly 70% of the energy density of the universe, leaving roughly 30% in ordinary matter and dark matter, right in line with what Jerry and I had concluded on the basis of completely different lines of evidence. So that was exciting. That suddenly meant this was a real subject, not just completely far out.
And also by that time, within a few weeks, our paper on time-varying, the quintessence idea, appeared in print, which turned out to be very influential even to the present day. It’s a really important idea that’s being explored, driving a lot of experiments and also being suggested by recent developments in string theory. It continues to be an essential part of what I work on nowadays, as part of even more ambitious ideas about the evolution of the universe.
So that was, I guess, January. And then by September of that year, I had moved to Princeton. During that year, it was kind of a funny—I was asked to give a colloquium again, this time as a new faculty person -- a little bit like what happened at Penn when I first got there. I decided I would not give one on cosmology. I decided to give one on these interesting results we had in quasicrystals. The results we just talked about.
So I gave this talk, and at the end of the talk, a fellow came up to me, whom I didn't recognize, and introduced himself. His name was Ken Deffeyes. He was on the faculty in the geology department, and he wanted to know if anyone had ever discovered a natural quasicrystal, one made in nature -- going back to the idea I originally had in 1984, when I had started looking in museums for possible quasicrystals that had not yet been identified. Ken was asking, “Has anyone found a natural mineral quasicrystal?”
I told him “No, but I have a good idea of how to look for one.” Because this idea that began in 1984 kept rattling in my mind. And a few years earlier, I had discovered that there’s a catalog, an international catalog of what are called powder diffraction patterns, including every mineral and synthetic material whose diffraction pattern has been measured. The diffraction data is sent to this international center and they put it in a big database. Materials scientists—for the most part, materials scientists-- use this database.
Because if you make something in a laboratory, you want to know if it’s something new or something familiar. So you measure its diffraction pattern and compare it to the catalog, and if it matches, then you know, “Oh, I didn't discover something new.” If it doesn't match, well, there’s a good chance you have discovered something new. So it’s a standard tool of the field.
I had tried to use the catalog to look for quasicrystals – to find candidates whose diffraction pattern would look like a quasicrystal. But the way it’s set up with their software, it’s a very clumsy tool to use, because you have to use their front end. They hide the data in the back, to keep that private, because this is how they make their money, I guess. So you could only look at one sample at a time. I even had an undergraduate once try checking one at a time, but it went so slowly as not to be practical.
But this was now several years later, and I thought, “Well, we probably can break into that database, one way or the other. And if we can, then we can search literally 10,000 or 15,000 patterns all at once, and find those candidate quasicrystal minerals.” Because the catalog included 8,000 mineral diffraction patterns that might include promising quasicrystal candidates. “Then, we can go out and try to find the actual mineral, and when we study at a piece of it to see if it really is a quasicrystal. That was the crude concept I had.
And Ken got pretty excited about that. He said, “This would be a great project for a senior thesis project at Princeton. And I know just the person who would be interested in doing this. There’s a physics undergraduate here named Peter Lu, who also happens, since he was in high school, to have been an expert in minerology, and who has done a lot of projects in minerology. He has worked with me. He knows how to take diffraction patterns and he’d be a good person to work with.”
And so the next day, he introduced me to Peter. He introduced me also to Nan Yao, who is the head of our Imaging and Analysis Center at Princeton, which could be used to study diffraction data. And I explained to them the idea that we had. Peter was excited, and Nan was willing to give his time in the laboratory to help us explore any samples we should come up with. And that began a project to look for natural quasicrystals, and that’s a project which continues to this day. So that’s going to be another thread that we'll be talking about. So I think I'll put the threads down, and then we can decide which order you want to do things.
The next summer, summer of 1999, I had made an arrangement to co-chair a workshop in Cambridge University at the Newton Institute with Neil Turok, who was then a professor there, to bring together string theorists and cosmologists, to see if this was a moment in which string theory might have something interesting to say about cosmology or vice versa. There was, in the back of my mind, and apparently it was shared by Neil, the idea that there had been interesting developments in string theory during the last few years, which might make contact with cosmology. It was actually early days to look for such connections. Within a year or two, this became a very popular topic, but at the time, it was a little bit edgy to do something like that.
And so in August of 1999, we brought together a combination of astrophysicists, cosmologists, and string theorists to give talks about what’s going on in their respective fields. And there were two talks that were particularly influential in terms of determining my future research directions. One was a talk by Joe Silk. His talk was about was how the then-conventional view of dark matter consisting of weakly interactive interacting massive particles, so-called WIMPs, was running into trouble with observations. The WIMP idea works fine if you only consider observations of the universe on a large scales, on the scale of galaxies and larger, but when you consider recent observations and look on smaller scales, it runs into trouble, he argued. For example, he said that whereas simulations, computer simulations, of WIMP dark matter suggested that the density of dark matter becomes more and more concentrated as you go to the center, producing a kind of cusp of density in the center, there is significant data that suggest the opposite, that there are no such cusps . That instead, galaxies are observed to have what we call a core, in which the density rises to a certain level as you measure closer to the galactic center and then the density kind of flattens out as you measure even closer to the center. The conflict between the WIMP prediction and observations is what’s called a cusp-core problem.
And then there’s another problem, which is in the WIMP dark matter picture -- the structure of the universe is self-similar. And what I mean by that, is whatever structure you see on a given scale, you should see a similar structure if you look on yet a larger scale. So you have dwarf galaxies, which have smaller bits of stuff in orbit around them. You have ordinary galaxies like ours, which have dwarf galaxies in orbit around them. You have clusters of galaxies, which are themselves clusters of galaxies which have clusters of dwarf galaxies around them, clusters of clusters. Superclusters. And up to a certain scale, you have this kind of self-similar structure.
Now, we know that when we observe superclusters, they have a substructure containing hundreds or thousands of clusters. So therefore if you look at a galaxy, you should have dwarf galaxies that number in the hundreds or thousands. But when astronomers actually looked for these dwarf galaxies, they only found a dozen, roughly speaking. So where were the missing dwarf galaxies? Something’s funny that they don’t seem to have formed. That’s called the satellite problem. Where are the satellites in orbit around our Milky Way? We know some, but we don’t have very many, not as many as you'd expect, based on the simulations. Simulations said there should be hundreds and thousands, and we're seeing only a dozen. Nowadays, we might say 30 or 40. And that’s called the satellite problem.
And there were other things Silk mentioned. His talk triggered a discussion between David Spergel and me. David Spergel had come to the meeting and given some talks. After considering all the problems that Silk mentioned, we suddenly thought, “Oh, there’s a possible dramatic solution to this.” Which is that we give up on WIMP dark matter. That’s the wrong idea. If you want to address these problems, you could address them if the dark matter is what we call strongly self-interacting. Particles that scatter off of one another very strongly, almost like billiard balls. This is the opposite of weakly interacting particles that pass near one another without any effects. If the dark matter were strongly interacting, then for example, instead of clumping together to form a cusp, they would tend to bump off one another and scatter outwards, spreading out to form a core with a nearly uniform density of dark matter.
Another consequence would be that, if you had a dwarf galaxy, a satellite galaxy, orbiting a much larger galaxy, like our Milky Way, something interesting would happen if the dark matter is strong self-interaction. The dark matter orbiting our own galaxy is trapped gravitationally by its large mass, which keeps it in orbit even though the dark matter is moving rather quickly. The dark matter in this satellite galaxy is being trapped by the rather weak gravitational force with this small satellite galaxy, so dark matter is only trapped if it is moving comparatively slowly. Now if the satellite galaxy moves through the dark matter of a more massive galaxy, the "hot" or fast moving dark matter of the massive galaxy can collide with the "cold" or slow moving dark matter of the satellite galaxy. We described as similar to putting a snowball in an oven. The colder dark matter is going to "melt," or more precisely, be scattered away from the satellite. The satellite will lose a lot of its mass and will then not have enough gravitational force to hold itself together. It will disappear. That would explain another of Silk's issues regarding WIMPs --“Why do we observe many fewer satellite galaxies around our Milky Way than computer simulations based on WIMPS tell us should be there?” So we hatched the idea that instead of WIMP dark matter, if you imagine strongly self-interacting dark matter, you could solve these and perhaps other problems. And that was a new research direction in cosmology that got started at that point. And that’s an idea that has developed and continues to be quite lively today.
And then the bigger thing that happened in that meeting was a talk that was given by Burt Ovrut, who had been my colleague at Penn. I was, by now, at Princeton. And what he talked about, is the recent idea that had been introduced of what we call M-theory in string theory, and the idea of branes -- a sort of structure to spacetime that was being suggested at the time by string theory.
And the idea was that, as is always true in string theory, you have to have extra space dimensions. String theory relies on the idea that there are more dimensions than the usual three space dimensions and one time dimension. In particular, in M-theory, you can think of the universe as being composed of two `membranes.’ So we shorten that, and we call them branes, being short for membranes, two parallel membranes that extend in three space dimensions separated by a finite distance of empty space along an extra space dimension; empty except that gravitational fields can traverse the space between the branes.
And what Burt was explaining was that if you have a spacetime, which has this structure in string theory, you can explain a lot of the properties of elementary particles that we observe to be true in the laboratory. So we drew a picture with these two static parallel planes, which are supposed to represent these branes.) And then there’s this one extra dimension between them. And so he explained how this was leading to a new way of explaining all the gauge symmetries and particle properties we observe—a very, very promising idea.
Now, at the time, in that audience, I remember that Neil Turok and I were sitting on opposite sides of the audience, but at the end of that talk, we both converged on Burt from different directions, and we both had the same question, which is, “You've drawn those branes as if they are static. Is it possible they can move? Is it even possible they can collide? And could that, for example, be what we think of as the big bang?” Burt thought for a moment and he said, “Oh, that sounds possible. It sounds like it’s possible.”
We got very excited, but it was time for the next talk. We didn't have a chance to discuss it. But that evening, we were all supposed to travel to Cambridge -- from Cambridge to London -- to see a play, Copenhagen, that was playing in London. And we decided to set a time when we’d all get on the train at the same time, and we'd flesh out this vague idea, this vague thought and idea. So we began to brainstorm on that hour-long train ride.
And the brainstorming went something like this: It seems imaginable that we can first of all replace the big bang, which we normally think of as a beginning of time, with a collision. So it’s not true the bang would be the beginning of space and time. It would be an event that happened in time. It would be one in which space would collapse along one direction, momentarily, and then it would hopefully rebound or reopen. We're brainstorming. We're making up ideas. No calculation. We're on a train. We're just saying, “What if? Is that possible? Could that be?”
Paul, if that’s where this is headed, does that render the big bang as not the best metaphor for what’s happening now?
We're going to end up there, yeah. Not with this particular idea, but this is going to inspire what I think are eventually better ideas, yeah. But back to the brainstorming. Almost stream of consciousness, but out loud, and going from one to the other of us: Of course for the brane to collide and rebound, there would have to be something that would draw these branes together. “Could there possibly be a force between these branes that draw them together and cause this collision? A springlike force?”
“Sure, there are different ideas that could happen in string theory that might cause such a springlike force. So that idea isn’t completely crazy. Could we explain why the universe is smooth and flat?” Because you have to reproduce all the successes of big bang inflation. We had an idea there, which I don’t hold to today, but which is, “Oh, maybe just the branes naturally start off far away, and they're flat to begin with. Flat and parallel would look like, from a three-plus-one-dimensional observers’ point of view, as if you lived in a universe that was smooth and flat. So maybe it just happened to be there for reasons of symmetry to begin with. Is that possible?” Burt thought, “Yeah, that’s possible. That’s plausible.”
And then we thought, “OK, but now we have to explain how we get the deviations from smoothness. How are we going to get these deviations from smoothness?” And I guess from my work in condensed matter physics and my colleagues, especially at Penn, had been thinking about membranes of biology -- you know, formed by lipids, in lipid bilayers. And I suggested, “Well, these membranes we're talking about are a little bit like these soft lipid membranes that soft condensed matter physicists make and study in the laboratory. They wiggle and squiggle all the time, due to thermal fluctuations. So maybe as they're approaching, the membranes we're talking about wiggle a little bit due to quantum effects, and then they wouldn't collide exactly at the same time, and they wouldn't bounce exactly at the same time, either. That would leave an imprint that may become the fluctuations we need to explain what we see in COBE and in the cosmic microwave background.”
So by the time we finished the trip, we had sort of put together vague concepts, little stories. That’s the way theories often begin—little stories that you could put together in a model like this. And that’s as far as we got at that meeting. [laugh] But I said I would go back—and of course with Burt who was going to be at Penn; I would go back and try to see if we could develop some of those ideas, make them more concrete, and see if we could make something interesting.
And I have to say that an important decision I proposed from the start, was that we should not try to reproduce big bang inflationary cosmology with branes, which is what people spent a lot of time doing in the years since. That was boring. If you introduce something like extra dimensions and membranes, you should be able to do something else entirely different. So we should try to do everything different, to see if we can make a theory which is, in as many ways as possible, different from inflation.
Is this based on the confidence that other people are working on this, or you didn't care about that?
No, I didn't care about that. I just thought that it often happens in science when some new element gets introduced, people just try to paste it into the current idea. Like dark energy is an example of that. What have most people done with the story of dark energy? They said, “Oh, we didn't know about dark energy before. We'll just paste it into the standard model as an added form of energy and that’s that.” The cosmological constant, or dark energy, as an addition to the ingredients that were there. It doesn't change our story about the past that much. And it doesn't have much effect. Whereas my reaction would be -- you just discovered something really profound that you didn't know to be true. Surely it’s going to have a more important or profound effect than just that.
So I thought this new idea -- that time didn't have to have a beginning, and that you were replacing it with a collision, that there could be a “before and and after” instead of just a beginning— there’s a chance you could find other ways of explaining the observed properties of the universe, other than when we assumed there were only three spatial dimensions, when we assumed there was a big bang and we thought we had no choice other than to have inflation to smooth and flatten the universe. So the principle was, since we're making a dramatic change, it opens the possibility that there’s another way of solving the fundamental problems of cosmology. And that would make it much more interesting. Otherwise, you're just making another version of inflation. There’s already a thousand versions of inflation, so now you've made a one thousand and first version of inflation. So that’s not interesting. It doesn't produce anything fundamentally new.
So that put a pressure on us to stay novel—and I always tried to keep that pressure on us. Because it’s always easy to say, “Oh, we have these problems. Let’s introduce some inflation.” My response would be: No, let’s not introduce some inflation. Let’s force ourselves to see if we can solve this by some other means. And that kind of exchange happened many times over the next few years.
Neil wasn’t that much involved during most of this first period. I picked up a student at Princeton, named Justin Khoury, and he and I would meet frequently to try to develop this idea. Burt would meet with us, usually once a week. He’d come to my house, and we’d work together with Justin on this idea. And what we wanted to show is how this attractive force that would bring the membranes together could arise naturally from the structure of string theory. Not just something put in ad hoc.
When we describe this theory as having an extra dimension, I should say that you should really view the spacetime from two points of view. One is you see all the dimensions. You're a microscopic being, able to see the extra dimension, even though the extra dimension itself is extremely tiny, much smaller than an atom, much smaller than a nucleus. You can imagine that picture. But you should also be able to pan back. If you were to pan back, you wouldn't notice the extra dimension. In some sense, you'd integrate out the extra dimension. You'd think of yourself as a usual being in three space dimensions and one time.
So you have to view the universe up close, microscopically, the string picture, where it looks like it has an extra dimension. But you also also have to be able to view it from what we call a four-dimensional effective theory, a theory in which you would—as a macroscopic being -- interpret what’s going on. So you have these two different points of view, and you have to explain how what you see in one picture corresponds to the other. After all, real observers don’t know about the extra dimension. They're too big. We do measurements on macroscopic scales. So we need to be able to relate the microscopic picture to observations on macroscopic scales. So you need a translation that explains “How do you go from the microscopic picture to the macroscopic picture?” So we had to work that out. To understand the relationship between the full microscopic picture to observations.
At some point, I called back Neil. He helped us work out some of the other details in the story. And we ended up writing a first paper on this idea of this colliding brane picture of cosmology. Although this is not a picture that I particularly pursue today, it’s what got me and my colleagues on the road to the ideas that I do think about today, which I think are much, much better. It opened my eyes up to the idea that there didn't have to be a beginning, a big bang. I think that was the key conceptual thing. Because the more I thought about it then, and the more I've thought about it in years since, the big bang is actually what causes all the problems that we have in cosmology.
What is? Just the idea that the big bang connotes a beginning?
Well, number one, it’s a very strange thing, [laugh] right? I think the first time you come across the big bang, any of us hears about it, we already feel it’s a strange thing. We've heard it enough, and enough scientists speak about it with such confidence, that you might think it’s a really well defined thing.
But actually it has never [laugh] been a well-defined thing. It’s a hypothetical thing, a hypothetical notion, that somehow you can begin from nothing—including no space, no time—and grow into something, a universe filled with space and decided by time. It’s already a strange idea, because we know of no other thing like that in physics. Everything else in physics repeats. This would be a unique phenomenon where you go from nothingness to somethingness -- that’s a one-time only, that somehow is crucial to the universe? That’s already a strange idea.
But Paul, isn’t it possible that there’s just a singularity in physics and that’s it? Why is that unsatisfying? Why does the big bang have to be like the rest of physics that comes after it? Why can’t it sort of invent the rules and be somehow separate from those rules? Why is that not satisfying?
I'm not going to give you a proof, because I'm not going to say you can prove it’s impossible. But there are reasons why you should be very disturbed by it. First of all, you properly called it what it really is—a singularity. It’s a breakdown in your equations. The proper way to interpret that, is to say that the equations you used to extrapolate from the present to the past and give the bang -- they're not valid. They're mathematically inconsistent. That’s what a singularity means. And you should be curing that. You should be replacing it with some idea.
Now, many people would say, “But when you go back far enough in time, you don’t really hit a singularity first; you first get to a regime where quantum gravity physics takes over.” There are different euphemisms that people use, metaphors that people use. Like they said, “Oh, there might have been a quantum foam stage, where the universe is defined entirely by quantum physics, which somehow settled into a universe that’s classical, described by equations of Einstein’s theory of general relativity. That’s a logical possibility.”
There are people that talk about emergence of spacetime. That you might go from a stringy quantum universe, to a universe that’s classical. By classical, I mean described by classical deterministic equations of motion. Like Einstein’s theory. His theory, a theory without quantum mechanics, it does a really good job of explaining the universe after a certain point. So you also have to have this quantum-to-classical transition. Somehow, if you're going to follow this line of reasoning, you’d have to say, “There would have to be a phase one, which could only be described with quantum physics. And somehow change to a phase two described by classical physics.”
People also talk about the beginning being described by a wave function of the universe. There are all kinds of metaphors they use. And then somehow, it would have to change from that to classical. And although there are all these metaphors, they are actually no calculations there. We actually don’t have a mechanism that takes us from totally quantum to classical. It has to be hypothesized that there must be one, if you're going to have a bang.
So to summarize, you have a second problem. You have to explain this quantum-to-classical transition. Which we don’t know an example of. We’re used to systems in the laboratory, where, on the scales we observe as observers, we can treat the universe classically to a very good approximation, and we can study quantum phenomena within our laboratory. But imagine everything, including your laboratory, is quantum. Now there’s no classical framework in which to project out which are the classical degrees of freedom. So that’s an unsettled question in the big bang picture.
A big bang is also fundamentally non-unitary. That is to say, it violates the laws that probabilities are conserved, since you go from nothingness to somethingness. And so somehow, there would have to be this one-time, non-unitary phenomenon, which takes us from quantum to classical. But not just any classical. It had better be a universe that looks like it’s going to match up with the universe we observe. So it has to have very special properties. In fact, you’d have to produce a universe which explains why the universe is smooth and flat, which is a very special condition. And why should that come out of some violent big bang quantum uncertain random probabilistic thing, out of all the things that could happen? There’s nothing in the quantum physics that says any particular thing should happen more than something else. Why should it come out that it was smooth and flat?
Nevertheless, all this does not stop people from thinking about this big bang idea [laugh]. It has still been a dominant thought in cosmology. People assume that’s the only logical possibility. But then, it runs you into yet more troubles. One can’t, from this big bang mechanism, naturally explain why the universe is smooth and flat. Anything could have occurred. It’s not impossible, but there’s an infinite number of other things that could have happened. So why this one? Smooth and flat is a rather special condition. “Why not something that indicates this wild quantum origin? Why don’t we see that instead?”
So that’s what triggered the introduction of inflation back in the 1980’s. The big bang alone is just going to produce something, anything. Well, we want to be able to turn anything into smooth and flat. That’s what inflation was supposed to do. But by this point, we also know that’s trouble, because inflation itself requires special conditions to start. So you just pushed the problem that you had with the big bang to another place. Coming out of the big bang, there was no reason why smooth and flat had to come out. Now you're saying, “I'm going to introduce inflation to make it smooth and flat, but I’d better have special conditions coming out of the big bang that would give me inflation.” And it turns out those conditions are exponentially unlikely. So you haven't really explained something by introducing inflation. All it has done is produced another puzzle, which is, “How did you go from big bang to classical, and not just classical, but the very special conditions you need to begin inflation?” And then even if you get those special conditions, inflation itself has a fundamental quantum instability that once inflation starts running, it doesn't really just simply smooth the universe out. That’s what it would do if you ignored quantum physics. But when you include quantum effects, it produces quantum fluctuations—rare ones, but some of which drive the universe into continuing inflation long after you might have guessed. And then further, such fluctuations keep it running yet longer and longer and longer. So instead of inflation being an epoch which comes to an end, it’s an eternal process. Inflation never ends. It’s eternal.
These were all things we had learned in 1983, when the discovery of eternal inflation and the multiverse were coming out. Inflation leads to a multiverse of possibilities, because although most of the universe is inflating, there are occasional patches that stop inflating. But these properties depend sensitively on the history of quantum fluctuations that created them. And since quantum physics explores all possibilities, and you've given it an eternal amount of time to do this explore all possibilities over time, it will produce an infinite number of every conceivable cosmological possibility. So instead of producing a universe that’s smooth, it’s patchy.
And not only is spacetime patchy, but the patches are different from one another. Yes, there are some that are smooth and flat, but there’s an infinite number that aren’t smooth, and an infinite number of every possible kind of non-smoothness. There’s an infinite number that aren’t flat, and every infinite possibility of things that are not flat. So there’s no particular reason to expect the universe should be smooth and flat, any more than it should have been smooth and flat was coming out of the big bang.. So inflation, by producing a multiverse, does not really accomplish this goal of explaining why the universe is smoother and flat. Because it could have been smooth and flat; it’s just that there were an infinite number of other possibilities.
So, to avoid the pitfalls of the big bang with or without inflation, we had to replace the singularity with something else. I would love to say that this was clearly in my mind when I began working on the colliding brane idea, but it wasn't. The issue came into focus much later when I began to work on a much simpler idea that did not require branes or extra dimensions.
As the idea got simpler, I realized there really is an alternative possibility. And the reason why it’s important to have competing ideas, is because you learn from each. Each one helps you understand the flaws of the other and then decide which direction to go.
Even though I had been thinking about alternatives to inflation for some time, most of them died. They just didn't work for one reason or another, and so I had to abandon them. This one was different. It kept going and going and getting simpler and simpler. And while my original goal was to find an alternative that would be as good as inflation, I came to realize it had more and more significant advantages relative to inflation. That is, the alternative made clearer what the problems inflation has, and provided an example of how they could be overcome by avoiding inflation. I never anticipated this. I should have been smarter, but I wasn’t. I learned so many things about cosmology generally from this, over the next decade or so. Things that people commonly assumed, but just weren't true. It was, and continues to be, a deeply rewarding experience.
Paul, I want to ask about this idea of different ideas. Were you following the work of James Hartle at all? Did you collaborate with him on any of these ideas as you were developing them?
No. Because that's an example of `wave function of the universe’ thinking, how you go from quantum to classical. I had trouble with what I call step one of that [laugh] analysis, which is they assumed there exists a wave function of the universe. That's a strong assumption. And they assumed that it evolves according to a Schrödinger-like equation, which, instead of having time in it, like the Schrödinger equation does, it has the Friedmann-Robertson-Walker scale factor. Now, why is that worrisome? Well the Friedmann-Robertson-Walker metric is a metric in general relativity which describes a smooth universe. And so essentially, built into their formulation was an assumption that you could treat the universe as smooth. So instead of showing why it had to be smooth, instead they were beginning with a formulation which only made sense if it were in some sense smooth to begin with.
And I just didn't see that as being a successful way of explaining what needed to be explained. And then the more it developed, I thought there was a lot of arbitrariness to the rest of the construction. This is called quantum cosmology. I never bought into this approach.
But there is a basic shared sense that the concept of a definite beginning to the universe is problematic.
Yes. But then they assume a particular form for it, which is smooth—closing off the universe with a sphere. A sphere is a particular smooth object. And that’s what we're trying to explain, is why it became smooth. So that seemed like a very strong assumption. We had at the beginning of our brane idea a similarly strong assumption. We assumed that the branes began far away, flat, and parallel. That’s the same, assuming the smoothness and flatness to begin with. And I didn't hold to that idea, either [laugh] because it’s not explaining. You're putting smoothness in as input, instead of obtaining it as output.
It's perhaps the most important feature you need to explain in any new theory of the universe, because we observe the smoothness and flatness to be real features, and we also know that past attempts to explain it have failed. For example, the big bang theory alone. or inflation with its multiverse, imply that a smooth and flat universe is very unlikely. Until we find a theory that explains why it is likely, we are missing something important about the history of the universe. Now most cosmologists today are focused on “How did the tiny deviations from perfect smoothness come to be?” That's an important question, too. But their ideas about that presume that something made the universe flat and smooth in the first place. They often link the deviations to quantum fluctuations during inflation, assuming that inflation makes the universe smooth and flat. But we know that this is an unlikely outcome in inflation, so that's not a justifiable assumption. On the other hand, if we knew a true smoothing mechanism, we might also learn the true means by the deviations from smoothness were generated.
So one question is, if you were thinking or being influenced by Hartle. I'm also curious, as your views on inflation are changing, are you in contact with Guth, and what is his reaction to where you are on this topic?
I have not discussed it with Guth. Alan is wrapped up in inflationary theory, as is Linde. But as our ideas developed over the next few years, one thing that I did wonder about, was the story about the multiverse. Because Alan himself had written about the multiverse and explained how it’s a problem since it produces an infinite amount of every outcome. He asked, “Why is it that we're smooth and flat? Is there some way of weighing different patches of the universe, what we call a measure, that would explain why what we observe is more likely than the alternatives?”
And actually, that measure approach of trying to explain one’s way out of the multiverse problem already began in 1983, after I, and then also Alex Vilenkin and later Andrei Linde, had shown that inflation in general has this eternal inflation and multiverse issue. I hadn’t been following subsequent developments. I knew that at various times, various people—and Vilenkin in particular—would claim, “I now think I have a plausible argument why we would be more likely in the universe like ours than anything else.” And then, you know, maybe a year or so later, I’d read a paper—“Oh, there’s something wrong with that argument. It actually doesn't work.” But I wasn’t following closely. I was really concentrating on the microwave background and predictions that would come from that during those the years. And, of course, other research I was doing.
But I realized that one thing that happens during a contracting universe - which you would have before a bounce -- is that you can’t produce a multiverse. And the reason is, you're not ever inflating. The reason why you get a multiverse, is because you have rare quantum fluctuations which keep inflation going, which means gravity stretches them by a huge volume, so that they soon occupy most of the volume of the universe. And then quantum fluctuations on top of fluctuations keep repeating that process.
In a contracting universe, you can have rare fluctuations that keep you contracting, but you're contracting -- so those regions aren’t going to ever become important relative to regions that bounce and start expanding. So you immediately solve the multiverse problem. And when I realized this simple solution, I thought, “Well, hold it. By now, surely people have solved this multiverse problem in inflation, but I can’t find it in the literature.”
So I started asking around. I remember calling Michael Turner. That call was really influential to me. Mike had been a key collaborator and mentor to me during the early years of inflation, introducing me to a lot of standard cosmology and astrophysics that I had not been introduced to. So I was counting on him to assuage my worries. I said, “Mike, I know you're still a big aficionado of inflation.” “Yes.” I knew he didn't like thinking about alternatives like bouncing models and ideas like that. I don’t even know if he thinks about them today. But I said, “One thing that bothers me is this multiverse problem. What do you say about that?” And he said, “Oh, the multiverse is a real big problem.” I said, “It’s a real big problem, but isn’t it like a really big problem? Doesn't it mean that the theory doesn't really work? It doesn't really explain why the universe is the way it is. It says it could be any which way. Isn’t that a big, big, fundamental problem?” He said, “Yeah, but I just figure someday the theorists will figure out how to solve that problem.”
I thought that was striking.” It’s not that people hadn’t been working on it. People had been working on it since 1983. I was talking to Mike probably in 2001, so this was 17 years later. They had been trying lots of ideas, and they had been failing. What they were doing, is they were making different assumptions about how to weigh different patches in the multiverse, and seeing if you could find out that a patch like ours is more likely than anything else. And what they were finding in the end, when you really worked it out, is we didn’t end up being more likely, quite the opposite, even given their generous assumptions about how to weigh patches.
This failure proved two things. Number one, they could get different answers, depending upon what measure they would use. That’s really bad news. That means the only predictions you’re getting are based on your assumption about measure -- but for your measure, you're using the information that you want a universe that is smooth and flat. So there’s nothing fundamental about your assumption about measure. You're just saying, “I'm going to add another assumption to my theory to make sure it comes out right.” And even when you do it, not only do you not get the right answer, but you get different wrong answers, depending upon which weighing rule you choose. That’s really sick. That means inflation has really done nothing. You began with the idea of the big bang producing any possibility -- and you just replaced it with the big bang followed by inflation, and the result is that you produce any possibility. That’s not an improvement. That’s not even a cure to the cure.
So that surprised me, that that was Mike’s point of view. And then I started asking other people. Another person whom I have respect for, is Slava Mukhanov at Munich, who was one of the first people to work on quantum fluctuations and inflation. I've known him for many years. And he’s a very rigorous-type person. In other words, I didn't expect he’d try to snow me on this one.
What he said is, “I think it’s metaphysics. Maybe there’s something funny about quantum mechanics in cosmology on large scales.” I thought to myself, “Wow. Slava would consider modifying quantum physics to solve this problem?” That’s big. Because people are relying on quantum physics all the time. We know of no other reason to modify it. And in fact, we're using quantum physics to predict the fluctuations. And now you're going to tell me somehow in the early universe that quantum physics is different, yet not so different in such a way as to change the fluctuation predictions based on conventional quantum mechanics? I have enormous respect for Slava as a deeply thoughtful physicist, so I do not believe he meant for me to take this suggestion seriously. But the fact that he gave this response made it clear that even he didn't really have a solution to the multiverse problem and that it must be even more serious than I had been imagining. And I thought, “Wow. Inflation is in serious trouble.”
So the more people I asked, I realized there actually was no good answer to this question. I should have been thinking this all along, but those conversations really brought it home to me, that this was a much more serious issue, and that we really must find a way to defeat this multiverse problem. And that meant doing something other than inflation to set the properties of the universe – those conversations forced the issue. In my mind, that was the end for inflation. It has only gotten worse over time. It never recovered from that moment for me.
Paul, another issue that I’d like to hear about, whether it has gotten better or worse over time, particularly in the mid to late 1990s, which was at the tail end of the height of this sustained criticism on string theory—you know, string theory, particularly after John Schwarz’s and Mike Green’s breakthrough in 1984, and the sort of counterreaction to that, led by people like Shelly Glashow and people of that ilk -- where are you in these intramural debates about questions of testability, relevance to larger questions? Where are you in terms of the validity and value of string theory at that time, and in the years since?
I would say, certainly at that time, I had a much more generous [laugh] attitude than people like Shelly and others.
Because you were more hopeful that it would prove to be useful? Is that basically what it was?
Yeah. I liked some of the ideas in it. I liked the idea of strings and extra dimensions. That was always an idea I was interested in. I hadn’t worked on it at the time, but I liked the elements. I liked the promise. It seemed to have certain aspects which were attractive regarding making quantum gravity finite, which is one of the fundamental problems in quantizing gravity.
I never had the optimism, I never fell for the [laugh] story that was going around in the early 1980’s, that it would be solving everything in ten years, that it would be a theory of everything. Because I just don’t think that’s the way human development of science takes place. That’s just way over-the-top ambitious. So it didn't bother me that it didn't yet connect to observations. It had some suggestions about observations. It suggested we should see supersymmetric particles. It suggested that dark matter might be WIMPs. Up to that point, up to let’s say 1998, and you'll see why in a second—I would say I was hopeful about that. And that was part of why I was pleased to try to utilize ideas from string theory to create a new kind of cosmology.
Because if string theory were right, and there were these extra dimensions and all these dramatic properties that are different than we had been thinking of up to this point, surely it’s going to have some sort of profound cosmological effect. So I would say up until, yeah, including the early developments of the colliding brane theory, I was, I’d say, being lenient [laugh] on the theory.
[laugh] Paul, what about the response that there were a few people working on this in 1970, 1972, a few dozen in the eighties, and now there’s thousands of people all over the world working on string theory? Is that compelling to you, in terms of the validity of it and thinking longer-term than simply being—I don’t know what the right word is—impatient?—that some of the ideas—
My thoughts today are different than back then, because of events that occurred in the next few years. So let’s just continue along that line a bit.
So the discovery of dark energy was a serious problem for string theory, because dark energy, if it were cosmological constant, is something that, at least in 1998, was thought to be impossible to incorporate in string theory. String theorists were really happy with the idea there would not be a cosmological constant, because supersymmetry makes it very difficult, along with the other constraints of string theory, to find a self-consistent theory which has a positive vacuum density. It’s very easy to make a negative vacuum density, but very hard to make a positive vacuum density in string theory.
In fact, I remember that in 1998 I would go to talks—let’s say, for example, at the Institute for Advanced Study—in which people would be presenting the evidence that there is accelerated expansion, and that there is this dark energy. Now, because I had been working with Jerry and been thinking about that idea for some time, my view was that the supernova data was not the first discovery of dark energy; it was the last brick to fall into place. I had studied the data very closely. I tend to do that anyway. So to me, this was “Yeah, of course. This confirms what we already have strong evidence for.”
But there would be the string theorists in the audience, and they’d show up, and they were not happy. They were very skeptical that the data from supernovae might have been misinterpreted. As I said, people didn't tend to follow the stuff that had already been done by Krauss and Turner or by Jerry and me. They were now focusing only on the supernova. And they weren’t very happy. In fact, for the next few years, they weren’t very happy.
But then in 2003, a group at Stanford showed, or claimed to have shown, I should say, that you could actually have energy states, vacuum states, with positive vacuum energy in string theory. It was a collaboration that is called by their initials KKLT—Kachru, Kallosh, Linde, and Trivedi. What they claimed to have shown, is that if you had string theory with extra dimensions, you can take those extra dimensions and introduce all kinds of complications, so-called flux lines, and anti D-branes and construct them in particular ways, a kind of plumbing-like solution, so that what would have been a vacuum state with negative energy, which is really easy to achieve in string theory, could be lifted up to state of positive vacuum energy, which is what you needed to explain cosmic acceleration. A form of dark energy that produces cosmic acceleration has to have a positive potential energy.
Now, this construction, though, was very complicated. It had many moving parts. So there wasn’t just one solution; you could find many, many solutions. Each one of them would lift negative energy vacuum states up by different amounts. So you didn't have just one vacuum with one dark energy density that you could compare to observations. No. The idea was, you had an exponentially large number of vacuum states. At first, they said ten to the 500, sometimes now people say ten to the 5000. Some say it’s even much bigger. Within the full collection of vacuum states, you could find every possible vacuum energy that you could imagine. And one of them would be ours. That was their claim.
And they called this the string landscape, referring to an energy landscape. So the energy landscape would have many valleys, each corresponding to a different possible "vacuum state" with different types of particles and forces, compared to what we observe. The vacuum state determines the physical properties. Our universe would correspond to a particular vacuum state. But there would be a huge, exponentially large number of different vacuum states, according to the string landscape picture. They would span a huge range of different physical properties and have different cosmological constants. The cosmological constants would correspond to how high the vacuum states were above zero energy. Our particular vacuum would have a height, or energy, above zero that would have to account for the dark energy density we observe. It would be purely an accident of our universe corresponding to this vacuum state rather than another. And this is what was called the string landscape picture.
This is a really bad idea, conceptually. It’s just like the multiverse problem. Because it doesn't explain why the universe has the particular vacuum density it does. It doesn't even explain why it has any physical properties that it has, because each one of these vacua would have different physics, different masses of particles, different kinds of particles, different forms of forces in them, and things like that.
So this is a testability nightmare.
In the same sense as the multiverse. It has an additional problem to it, which is you have to explain, “How did any of these states, vacua, come to be occupied? Why isn’t just one of them occupied?” Since there would be nothing special about ours, it would just be one of these many, many vacuum states, you have to explain, “How did that vacuum state come to be occupied?”
And they only have one answer, which is what they stick to, to this day—it’s the multiverse. It’s inflation. They took the very thing that was a problem for inflation, the multiverse, and they said, “Oh, that’s a good thing for us. The multiverse produces an infinite amount of every possible outcome. It’s going to eventually populate every one of these vacua, including the one we live in.” So they took a defect of string theory—I would call it a defect of string theory, which is the landscape idea, which was needed to explain dark energy—and they married it to a [laugh] defect of inflation, which is it produces a multiverse.
And they said, “Guess what? We all have to change our views about science. We shouldn't expect a falsifiable theory. We shouldn't expect we'll be able to understand everything. We should expect that we live within this multiverse landscape picture, in which a lot of the properties that we observe in the universe are just a happenstance of our particular environment, the fact that we live in this valley, rather than in that valley. The fact that we live in this part of the multiverse, rather than that part of the multiverse.” Et cetera, et cetera.
So if you really follow this to the extreme, it would take all the explanatory power out of string theory and inflation. Except they would kind of cherry-pick. They’d say, “Oh, we know we live in a flat universe. Well, inflation gives us a flat universe.” They forget to tell you it also gives you curved universes. But they say, “Oh, we declare that to be a victory. A proof” “Oh, string theory explains something about gauge symmetry, so we'll claim that as a victory for string theory.” But of course, other vacua would have given us something different. So there was this kind of game that began to be played, that required you to rethink what you can get out of science. This is the best you can do, is this kind of environmental science. And that kind of idea was a—how shall I put it?—it was a dominant idea for a considerable period.
Dominant among who?
String theorists supporting the landscape idea and cosmologists. So inflationary physicists, cosmologists, would argue that string theory proves inflation, because string theory needs inflation to make sense of the landscape. And the string theorists supporting the landscape idea would say that inflation proves string theory to make sense of the multiverse. So there became this marriage of two, in my view, sick ideas. But, things don’t always go the way you would expect them to go!
Something interesting has occurred in the decades since, and I'm involved in that as well, which is going back to this complicated plumbing-like proof that you could get all these landscape vacua. If you look more closely at the original papers, you might notice that they don’t actually complete the proof that they exist. That’s OK. People argued at the time that the part that’s unproven—that can be done. That’s not a big deal.
So you might ask, “OK, it’s 2020. You told me there’s ten to the 500, ten to the 5000, ten to the whatever number of these vacua. At least in 2020, how many can you show me today definitely exist?” That is using the rules of string theory, you do a calculation, and conclude, “Yes, there’s definitely a vacuum state with positive vacuum density in your energy landscape.” And the answer today is—zero. Not one is proven to exist. And this has led, within the string theory community, to a kind of rebellion, where there’s a fraction of the community that says, “There’s probably a reason why we're not finding them—because they might not exist. String theory might not allow them. They may be inconsistent with quantum gravity.” This is called a swampland idea - that the vacua they were hypothesizing might exist actually in the swamp that’s forbidden by string theory. You can’t have such a situation in string theory.
Now, although I had always liked this idea of extra dimensions, my student, Daniel Wesley and I, in 2007, 2008, we showed that, in fact, if you have a theory with extra dimensions -- which is described by Einstein gravity and which is supposed to compactify to a theory that looks like our universe and which is also described by Einstein gravity -- you can’t do that and accelerate, not under a broad range of conditions. You can do it if the universe is decelerating—is slowly expanding. But if you're trying to introduce any kind of element that causes the spacetime to accelerate in its expansion, it also causes a back reaction on the extra dimensions, causing them to either collapse or expand. That would change the physics of your effective 4D theory, so it would no longer look like a universe with accelerating expansion. In other words, these theories were incompatible with a sustained period of accelerated expansion, whether it be due to inflation or it be due to dark energy.
Meanwhile, the string theory group that’s developing the swampland ideas over the years, especially in recent years, has come to the same conclusion, but using a different line of argument. In some ways, it’s more restrictive than ours, and in some ways, more expansive than ours, but it reaches the same conclusion. “You can’t have a cosmological constant,” they would say, “or a vacuum density which has a positive energy density, in string theory. It would be inconsistent with certain principles,” they argue. They conjecture.
So now where has the debate gone? The landscapers would say, “Yes, we haven't proven that they exist, but surely they do. Surely there’s enough freedom left in the parts we haven't been able to compute that it will help us to get the energy conditions we need.” And the other group that says, “Prove it! Just prove one—show me one darn example, please! Until you do, as far as we know, and we're looking quite extensively, we're not finding that to be the case, and our arguments that it won’t be the case, can’t be the case, are getting stronger and stronger by the day.” So this debate has been brewing in the last few years. This is a growing development within the string theory community.
So to complete the loop to my own thinking, I think the dark energy problem has been—I already felt it back when I did the work with Wesley—an existential threat to string theory and the idea of extra dimensions. Maybe there’s something else that none of us yet know about, that will save the day. But at the moment, I think the challenge for string theory should be to focus on the dark energy problem, and determine whether string theory is compatible with it or not, because that is a key litmus test.
Right now, accommodating dark energy in string theory is hard enough. Inflation is much harder. Both involve cosmic acceleration. But the acceleration due to dark energy has only begun recently and has only lasted for a short period. The universe has only stretched by a factor of two or so since the acceleration began. Whereas inflation has to be for a sustained for a long time, enough for the universe to expand by ten to the power thirty -- an incredible amount more accelerated expansion. That turns out to makes it much harder to accommodate inflation than it is dark energy, and dark energy is not yet accommodated.
So you're not yet at the point to say that string theory has become so divorced from observable reality that it is essentially operating as a set of zombie ideas. You're not quite there yet.
Yeah. But I think the onus is on string theorists to address this problem. And so my disturbance with string theory at the moment, is that instead of declaring this to be an existential problem, and all hands on board—thousands of people that are working on it, this is what everyone should be working on—you'll find almost nobody is working on this. They're working on one abstract problem or another that’s inspired by string theory, rather than working on what I would call the existential problem. That bothers me.
And you think that working on the existential problem is doable. I mean, the presumption is that people should be working on this, because it can be worked on.
Yes. The fact that only a few of the best people are working on it [laugh] and the majority of the community ignores the issue is not a good sign. It’s probably not true that they haven't thought about it. It’s probably true that they haven't found a good idea to address it. But it would be nice if they said that out loud.
I think that it’s important to do so. The string theorists, I feel, is an example of a community that when they get into trouble, or they don’t like something, they don’t like to talk about it. Which I think is completely the wrong attitude. When you're a young person in the field, it helps to know what the key problems are in the field. And then if you solve those problems, you'll know that you’ve really done something. You've accomplished something. By not talking about this, and not declaring it as urgent, “OK, everyone drop everything, this is what you should all be brainstorming on,” I think that obscures the problems with the theory. It delays progress. And it’s not as if it is a minor issue; it is, potentially, an existential threat to string theory.
What I would hope is that in an effort to try to cure the problem, if you ever do find a cure, it’s going to be really important, not just to solve the dark energy problem. It will also tightly constrain string theory. So instead of getting anything like a landscape of possibilities, it may give a unique possibility. That would be great. But you'll never discover it, if you never go after the dark energy problem. So that’s my concern – that most of the community is not paying sufficient attention to what is a serious existential threat. I shouldn't say everyone. There is a swampland community, and that includes some outstanding theorists like Cumrun Vafa at Harvard, Hiroshi Oguri at Caltech, and others. There is a group that works on it.
But it’s this business that—you know, one segment of the community is saying, “There’s a problem. There’s a problem. There’s a problem.” Other segment of the community—quiet. “We're not going to talk about that. It’s just not discussed.” It feels like it’s socially unacceptable to have that discussion. Instead, you're going to hear from that segment something about anti-de Sitter space, and wormholes, and things that are far from observation.
This is the first time that there’s a clear observation that is difficult, if not impossible to be accommodated by string theory. You see, they originally provided a lot of motivation for supersymmetry. They pushed hard for the LHC, to look for the supersymmetric particles. And then we haven't seen those supersymmetric particles. So you might say, “Doesn't that mean string theory is in trouble?” No, because the string theorists immediately turned around and say, “Well, maybe the supersymmetry breaking scale is higher than we imagine and that is inaccessible to the LHC.”
Right. So Paul, what would you say to the idea that maybe we'll find supersymmetry in an ILC, if that ever happens?
Might happen. I'm open-minded about that. But that’s hypothetical, whereas the dark energy issue is right in front of your face right now.
They’re not even questioning the data that the universe is accelerating, since we now have multiple ways of getting the same conclusion. We definitely are living in a phase of dark energy domination. We don’t have to talk about hypothetical inflation, because maybe that, you can replace. But dark energy is definitely there and must somehow be accounted for within string theory.
So you're saying there’s more fundamental work that should and can be done now, that’s just not being done.
Yes. Not being done by the community at large, only the subset which is recognizing the problem, and which is not accepting the landscape picture. The answer I often get about the landscape is, “Oh, yes. In addition to all the other forms of energies we can calculate that would lift these vacua from states of negative energy density to states of positive energy density, there are so-called non-perturbative corrections, which could also help lift it. We can’t calculate those. Those are too hard to calculate. Those would take us away from what we call perturbative string theory, and we don’t have mechanisms for doing that.”
I say, “Fine, but you're going to tell me it’s going to happen ten to the 500 times, and you can’t produce yet one example? And furthermore, all your arguments for string theory are based on perturbative string theory, and now you're going to tell me to explain the vacua of our universe, somehow non-perturbative corrections are going to be important, and yet they're not going to affect any of the things that you already held dear about string theory based on perturbative string theory, that you thought were successes? Does that make sense?”
So going back to the dark energy issue and string theory, I think it’s a very, very serious problem, and it’s very concrete. And so I'm disappointed that there isn’t more of a clear focus on it. So for example, if you go to the Strings meeting from this year, you can ask how many people discussed this existential problem; well, I challenge you to find one. Even though I would say it’s what every talk should be about! [laugh] Or at least most of them should be about. It’s not what people are focusing on. So the idea of extra dimensions I think is now problematic, in my mind, because of the dark energy. And similarly, string theory, which may or may not require it, is usually phrased in terms of extra dimensions, but maybe it doesn't have to be—is also problematic in my mind.
Paul, given that we're at sort of a crossroads in this area, what are the technologies either available or imagined in the future that might help us move past where we are?
Do you mean experimental? Is that what you're referring to?
Yeah. To keep things observable. To keep things testable. To keep things focused on the fundamental questions.
What am I keeping my eyes on?
So I think first of all, one of the most important ones, is looking for so-called B-modes, a polarization signal in the cosmic microwave background, which would be a signature if the smoothing process in the early universe created gravitational waves or shears in spacetime, through quantum effects, much like it produces fluctuations in density. Because that’s a key test for distinguishing what I would call today’s bouncing cosmology, from big bang inflationary cosmology. Should I say some words about that?
If you were to go the big bang way, then everything we observe in the universe, including all its large-scale properties, have to be produced after the bang. In fact, shortly after the bang, you already need a universe which is smooth and flat, so it has to be some process that smooths and flattens when the temperature and density of the universe is still quite high.
Now, the laws of physics don’t let you make something perfectly smooth. Classically, they do; you can make something as smooth as you like. Quantum mechanically, you can’t. So there will inevitably be quantum fluctuations that take you away from the smoothness, occurring at energy densities—like in this first instance—when the energy density is quite large. The fluctuations will include fluctuations of the metric, the spacetime metric. And those metric fluctuations can come in various forms. If they're small fluctuations, we can nicely divide them into what we call scalar fluctuations, or. equivalently, what we call curvature fluctuations, fluctuations of the local curvature. Versus shear, or tensor fluctuations. So tensor-like fluctuations, shears of spacetime, which we often refer to as gravitational waves, because they propagate as gravitational waves at some point after you produce them. If they're on small enough wavelengths, they begin to oscillate and propagate as gravitational waves. So you should produce, at high energies, a combination of those two—curvature and gravitational wave. Or scalar and tensor. And whatever your smoothing process is, they should leave a signature, among other things, in the microwave background, but different signatures so you can distinguish them.
The curvature ones produce fluctuations in density. If you change the curvature, you're changing the local energy density, so it’s synonymous to saying, “I've changed the local density or the local temperature.” Well, we do observe temperature fluctuations in the microwave background. So that’s consistent with the idea so far. But attempts to measure the tensor fluctuations have failed. We have not observed these B-modes so far. Down to a level which is well below the level of the curvature fluctuations. And that’s not good news, because—how should I say it? Quantum physics doesn't know a scalar from a tensor; it makes everything fluctuate. So if quantum fluctuations were responsible for this, and there’s no extra tuning you’re introducing, you’d expect them to be at comparable levels, where already our constraints are well below those comparable levels. But we have not observed any sign of the tensors. They would leave a distinctive polarization signature in the microwave background that we call B-mode.
Now, that doesn't stop theorists from doing what theorists do—introducing extra parameters, introducing extra fields, so that the calculated tensor contribution would fall below the level we can experimentally detect. And of course that makes the experimenters go and make better experiments to try and reach those lower levels. And so, there’s a cat-and-mouse game that’s occurring right now on the theory side.
But stepping back, you should realize there’s a big problem here, because you're already past the point where you would naturally have expected to observe them if you did not introduce special tuning, where even textbooks said you would have expected the tensor fluctuations or B-modes to be detected by now. And that’s why the game is one of tuning, and parameter-fitting, and remodeling, and things like that. So, what does it mean that we're not seeing these B-modes? How could it be that we have quantum fluctuations in one degree of freedom, and not the other degree of freedom? How could that happen? Especially at these high energies, because there’s enough energy to produce fluctuations in both of them.
Well, it suggests that maybe this process of smoothing didn't occur at high energies. Maybe it occurred at very low energies. At low energies, gravitational waves are so weak, what you’d produce would be so weak that you wouldn't detect them. That’s what happens in a contracting universe. In a contracting universe, the energy density begins very low, like at today’s energy density. And it’s during that period that you'd have to produce quantum fluctuations. The quantum fluctuations may produce gravitational waves during this smoothing process, but their amplitude would be very weak, because the energy density is so small, that they would be way below the detection limit that you would expect to see.
So to me, the absence of B-modes has a strong implication. As long as we don’t detect these modes -- the most sensible explanation is that our concept that there was a big bang, and we produced them after the bang, doesn't work. The natural explanation that doesn't require any work at all, is that you smoothed the universe before a bounce, where the energy densities are so low that, yes, you produce these gravitational waves, but they’d be at a much smaller—you know, 50 orders [laugh] of magnitude smaller amplitude. Not a little bit smaller; hugely smaller.
So I think that’s an important development to watch. There are experiments today being constructed, most famously the Simons Observatory in the Atacama Desert in Chile, which is supposed to push the limit on B-modes, bring the sensitivity down by several orders of magnitude. Suppose you were to detect them. That would be inconsistent with the idea of slow contraction. And I understand that many theorists would say, “Oh, that’s proof of inflation.” But it’s not proof of inflation. It’s actually just as much a problem for inflation, as it is for slow contraction. Because inflation would have naturally expected them to be at a much larger amplitude which we should have already detected. In fact, that’s the reason why BICEP-2 had such an impact back in 2014, when they claimed to have detected the B-mode signal you expect from inflation. Why did everyone bring out the champagne glasses, and why was it international news? Because it was at the level that everyone had anticipated, that the textbooks said that it should be at. It was viewed as the proof of inflation.
Somehow, it didn't bother people when it turned out to be a dust effect, rather than due to B-modes. If before you thought you proved inflation, doesn't the revised analysis mean you basically disproved it, or at least the theory is now in trouble? You won’t hear that very much, though. But yes, that’s actually what it means. It means now that the inflationary theory is in serious trouble. So if you were to now detect B-modes at this very low level, I wouldn't say it’s proof of inflation; I’d say you've disproved the slow contraction idea and the bouncing idea, and there’s some other source of gravitational waves, some other idea that’s needed to naturally explain why they would appear at a level which is not what you'd expect at the high-energy densities associated with inflationary smoothing, nor at the low energy densities you'd expect with slow contraction. It’s going to need another idea, to really explain it. So the Simons Observatory is important either way. Either it detects B-modes at a low level that you would not expect, given any of our current theories, in which case we have to rethink. Or it detects no signal, which is exactly what one of our current ideas -- bouncing cosmology with slow contraction -- tells us to expect.
And it does not naturally fit the other idea – a big bang followed by inflation. To explain no signal with inflation, we would have to crank, crank, crank, crank, – fix parameters and fields ‘just so’ to evade the test -- pushing models into a corner where we didn't expect to have to go before the experiment. And that’s usually the way science often proceeds. You don’t rule out an idea altogether. But you move towards the theory that naturally explains the experimental result, and away from the theories where you have to crank, and crank, and crank to make it fit.
Paul, shall we pick up some of the other threads at this point?
OK. Let me continue with the bouncing model a bit, because that has changed quite a bit. So for the first few years, a group of us—including Neil Turok and myself—worked a lot on this brane idea. Somewhere around the mid-2000’s, we began to realize that actually, we didn't need those branes, or the extra dimensions, or that stuff. They were inspirational, and I'm not saying they're impossible, but they weren’t needed. You could get by with just the usual three spatial dimensions and time. And everything the branes were doing for us were essentially being done by quantum fields.
Just like inflation, where we have a scalar field called the inflaton, which is supposed to drive inflation, we could do the same with a scalar field rolling down a potential. We originally just assumed the branes began flat and parallel. But by this time, my students Daniel Wesley and Joel Erickson and I suggested a whole different mechanism, a very natural mechanism, for explaining how you can make something flat and smooth, although it is very counterintuitive at first, and that's by having not a period of accelerated expansion after a bang, but by having a period of slow contraction prior to a bounce. So, you can flatten and smooth the universe effectively, either of those two ways. In a series of detailed analyses using the tools of numerical relativity, it has recently been shown that this slow contraction not only works, but it turns out that slow contraction is more effective than inflation in smoothing and flattening beginning from wildly unsmooth and curvy initial conditions. In fact, the paper we've written showing that if you really want to smooth and flatten the universe, there’s four different properties it must have. Inflation has one of them, but not the other three. Slow contraction has all four. So I would say in 2020, my statement would be: Now I think that the only mechanism we have that actually works to smooth and flatten the universe, that satisfies all the criteria you need, would be slow contraction. Maybe there are other ideas to be invented, but I'm talking about ideas that we know now, what we have in hand.
So that’s a powerful reason to think more and more about this slow contraction idea. Slow contraction can be achieved just by a field rolling down a potential. Whereas in inflation, the potential is largely positive. In this case, the potential begins very small—like I said, low energy—and goes negative. It’s this negative value of the potential energy density that changes you from expansion to contraction. And if it’s steep enough, the steeper the potential is, the slower the contraction is, the more powerfully and rapidly it smooths the universe. And it smooths the universe in such a way that you don’t have quantum runaway effects, you don’t have multiverse, you don’t have the tensor modes that you didn't want. You don’t want to have the B-modes. So it’s extremely powerful—it’s the only mechanism we know which would truly smooth the universe in an absolute way, and brings you to a bounce under an ideal condition.
Now, what happens next? Now, somehow you have to go from this contraction to expansion. And for a long time up to this point, driven by this idea of colliding branes, perhaps, or just my own theoretical prejudice about the way it had to go, I was convinced you had to go through some kind of quantum phase—you know, the universe would contract to become infinitesimally small, smaller than the Planck length, and then have to somehow bounce.
But in 2012, I encountered a young woman, Anna Ijjas, who was visiting Harvard. I was on leave at Harvard, and I heard her give a talk about inflation. I gave her a really hard time in that talk. She was introduced as Dr. Ijjas, so I had assumed that this was like an advanced postdoc or maybe young faculty. And I had also assumed, when I went to the talk, that she was going to talk about all the good things about inflation. And I thought, “Well, I'll push a little bit. I'll point out the various problems that I now think inflation has.” So I probably gave her a really hard time. But in fact, her talk was really about all the problems with inflation. She didn't buy inflation at all. I was kind of surprised. And she actually gave very intelligent answers to all the questions that I asked. So I was pretty impressed. She was probably pretty upset with me. In fact, I know she was pretty upset with me because I had been so tough.
But afterwards, I asked Avi Loeb, who had invited her to this talk, “Who is this person?” And it turns out, although she is a Dr. Ijjas, she was a doctor of philosophy at the time. She had one doctorate. And she was now preparing a second doctorate in physics, in cosmology. She was actually a first-year physics graduate student. It was really remarkable, the depth of her knowledge. So we began this collaboration, which continues to this day.
Anna’s view from the very beginning was, number one, she never believed inflation. She had learned inflation as a student of Slava Mukhanov, whom I think I mentioned earlier, who was a strong inflation fan. But the moment he mentioned the multiverse, she immediately became skeptical of the idea. She was convinced that idea was wrong. And then we began to talk about bounces and things like that. She was convinced that you did not need, and you did not want to have, a singular bounce. You didn't want to have such a "big crunch" as it is often called. She was convinced that you could have a bounce which was classical. That is, the bounce occurs before the universe gets very small, so small that quantum gravity effects become important. I was really skeptical. I told her about all the past attempts along these lines that had failed.
Fortunately, she didn't listen closely to me. [laugh] She pressed on. And she did some reading. She said, “Well, there are these ideas that gravity could be modified at high enough energies, and maybe some of these modifications would allow us to bounce before we get to that point.” This sounded like an awfully long-shot idea. But to make a long story short, over the course of a few years, she actually showed that this idea works. To finish off the proof, there are still things to be done, but I would say all the roadblocks that I thought were in the way have been superseded.
You want to complete the idea. And to complete the idea, you have to essentially do a numerical calculation that we're in the process of developing now. But I would say it’s a very high probability that this idea works. I would bet strongly that it works.
Now, that’s a game-changer. Because suddenly in which both because of the bang, and then again during inflation, the universe must go through a phase where quantum physics dominates over classical. Now, you can go to a theory where quantum physics never dominates over classical. The entire evolution of the universe never contracts to a volume small enough that quantum gravity effects dominate or encounters a situation like quantum runaway, in which quantum physics dominates over classical. Which makes this theory entirely deterministic and predictive —where here, I am referring to the average, or coarse-grain properties of the universe.
So it’s not that we've turned off quantum physics. Quantum physics plays a role. It sets some details. Like, “Is there a galaxy sitting here, or a galaxy sitting there?” But the coarse-grained properties—the smoothness, the flatness, the isotropy—can all be explained in a classical deterministic way, which never has quantum runaway, never has a multiverse, never has any phase in which you have quantum effects become so large, like you might have had at a singular bounce. In this non-singular bounce, you don’t have any of those effects that would mess up anything or leave uncertainty about the coarse-grained properties. It’s a conventional, predictive theory in the sense that we're used to in science. Which means it’s do or die, also. It makes definite predictions.
So it’s not that if tomorrow they discover gravitational waves or B-modes in the microwave background, we could say, “Oh, I can adjust this parameter and do that.” I'm sure you can do something, but it would so ugly it would not be worth doing. So you're forced. Which is good. This is what I think one wants in a scientifically meaningful theory. It’s also—and that’s what we've really shown in the last few months—it’s the only mechanism we know of that truly smooths and flattens the universe. That is to say, it’s not enough to say that if I begin smooth, I stay smooth. That's not even true for inflation if you include the quantum runaway effects that lead to a multiverse. It must also be, if you begin smooth and you include quantum physics, it stays smooth. That’s not true for inflation. It ends up in a multiverse. But it is true for slow contraction. The smoothing mechanism should also be robust in the sense that if the universe begins with some very wild initial conditions, the mechanism should be able to force the universe to become smooth. You should be able to give virtually any conditions you like, and if slow contraction begins. Boom, it smooths it out.
That’s what we've shown using numerical relativity techniques. But that is not all. You want the smoothing to happen fast, fast enough that you don’t just smooth the universe, but you smooth it long enough before the bounce to produce the little fluctuations you want to see in the microwave background. And this is the only smoothing mechanism we know that has all four of those properties. That’s what we've shown. And since we observe the universe as smooth and flat, I’d say now it becomes a challenge to come up with any competitor idea that satisfies all four. Inflation definitely doesn't.
That now becomes a much more powerful reason to think that we must have gone through a phase of slow contraction. But if you were to buy that argument, you'd say, “Well, then there must be something connecting it to expansion. Oh, that must be a bounce. Therefore, there can’t be a bang followed by expansion. There can’t be the cosmic singularity.” So now that is inconsistent, if you like, with the smoothness and flatness we observe.
If I want to say it in the strongest way possible, it looks like the big bang is inconsistent with resulting in a smooth and flat universe —and I’m saying that in a much stronger sense than I would have said in the past. Because there’s no way to go from there, without ending up through quantum uncertainties, with something that could equally well be otherwise. So I think it’s a very important recent development.
And then it led to a surprise, which is, “OK, I want to have a period of slow contraction, and then a bounce before we collapse to zero size.” Suppose we say, “Well, if the bounce happens once, couldn't it happen more than once? Why can’t the evolution be cyclic? How about that idea?” People have had the idea of a cyclic universe before. Back in the 1920’s, people thought about that idea. They knew it had problems. They knew it would lead to crunches, in which matter would crunch together into a dense mass. And how do you get out of that? They knew it had a problem with entropy. They knew it had a problem with what we call chaotic mixmaster behavior.
But there’s a problem with what they were thinking about, a basic conceptual flaw, which we bumped into. We didn't think about it in advance. It’s something we bumped into. Which is that they assumed their picture of this cyclic universe is a universe which is vaguely analogous to a balloon which expands and contracts, and expands and contracts, and expands and contracts. In that kind of cyclic universe, the universe contracts to a point at each bounce, which makes things crunch. Also, every time it contract, it triggers chaotic mixmaster behavior, which messes up smoothness. Neither can occur in the new kind of cyclic model we are considering.
And Paul, this is an ongoing process of expansion and contraction, or this happens at a particular moment in time?
This would happen throughout cosmic history. That's the idea that people had when they talked about a cyclic universe. So they would imagine that we're right now living in an expansion phase, and then at some point, the universe would begin to turn around and contract, and do this repeatedly. That was back in the 1920’s, people already had this idea. But they also had the crunch. They showed that as you begin to collapse, you'll tend to have this so-called chaotic mixmaster behavior, which completely unsmooths the universe, which is bad news. They had a problem with the Second Law of Thermodynamics with this picture. And nowadays, you’d say the problem of, “Hold it. You have this accelerated expansion. How do you manage to turn that around to contraction?” In the picture I described today, all those problems are defeated at once, in a surprising way.
In particular, what happens in this picture is that, after a bounce, when the universe is filled with matter and radiation, it expands at the usual rate we predict by the big bang model. Between then and today, that is a lot of expansion, an increase in the radius of the observable universe by something like 60 orders of magnitude over a nearly 14 billion year period. That takes us up to a period like the present. But imagine that the vacuum we live in is not stable. The dark energy density decreases, eventually so much that the universe switches from expansion to contraction.
But the contraction is very slow. To fully smooth and flatten the universe and to get to the bounce, you actually need very little contraction. So the black holes, galaxies and other cosmic structures we see would hardly have moved together at all by the time the bounce is reached.
But if we were around at the bounce, we would have lost sight of what happened to all that stuff we can see today, because the part we can see and keep track of, what is called our Hubble radius, shrinks to a very tiny microscopic size as the bounce approaches. All the black holes, galaxies and structure would still be out there, but whatever light or gravitational waves they were emitting at the time would not have a chance to reach us before the bounce.
But the universe that forms next is going to be born from the volume within this tiny little Hubble radius. So space overall has hardly contracted at all, but the part we can observe and keep track of has contracted by a huge amount. In other words, we don’t actually see the black holes, galaxies, etc. move together; we just lose sight of their movements as we approach the bounce. We can only observe a tiny volume of space. And then, after the universe bounces, that tiny volume will expand and evolve over the next 14 billion years into an observable universe similar to what we observe today. The black holes, the galaxies, and entropy that was observable a cycle earlier has, due to the same expansion, moved far beyond where we can observe. We never get to see them again. Effectively a new universe is created from the energy that drove the contraction, that decays after the bounce into hot matter and radiation that creates new stars and galaxies, for the next cycle, and then it all begins again.
So what really happens in this picture is that the universe grows a lot during expansion, shrinks a tiny bit, grows a lot more, shrinks a tiny bit, grows a lot more, shrinks a tiny bit. There’s no crunch-like behavior. There’s no place where space collapses to a tiny region. What’s cycling is the temperature and density and how much of space you can observe and keep track of.
An observer today sees the same sorts of things with the same temperature and densities as an observer would have seen a cycle ago. So in that sense, the universe is cyclic. But if you're asking about the geometry of space, that's not cyclic; space is going through this process of – lots of expansion, then a little contraction, then lots more expansion, going on forever. You might call it a cyclic universe, or maybe better a self-similar universe, that solves all the problems that people had with cyclic universes in the past.
The fact that we did not have this idea of coming up with a new kind of cyclic model, or of resolving all the problems with cyclic models in mind in the first place – that we were led to it, just by putting together the two ingredients -- slow contraction and a smooth bounce – that were introduced only to explain smoothness and flatness —is kind of mind-blowing. It’s also mind-blowing to realize that this cyclic model has other novel features that could not occur in earlier types of cyclic models.
Because, for example, just to give you an idea, because space does not really contract to a point—in fact, it hardly contracts at all—there’s nothing to say you can’t send signals across from one bounce to the other. Because, you know, there’s space and time there. There’s nothing to say that something can’t pass through from one side to the other. Black holes that existed before, would pass through, from one side to the other. Gravitational waves, they would pass through. Maybe other things. So then maybe, when we finally understand this better, we can also look for signals or remnants that have passed through the bounce in future observations. That’s one of the ideas we'll be going after. So that tells you the arc of the story on the bouncing cosmology side.
And I should emphasize that, when I say we, Anna Ijjas continues to be the leading force when it comes to conceptual developments but most especially when it comes to all the advanced mathematical and numerical relativity developments which are key to pursuing this new direction in cosmology. I feel fortunate to be a collaborator and co-author. As the senior scientist, I am often given more credit than I deserve. But there is no way where I could have done it without her.
Which takes us up to the present day.
Yes. Takes us up to the minute.
We're funded these days by a generous grant from the Simons Foundation. We just presented to Jim Simons on Monday, these latest developments, and I think he was very excited. He likes the cyclic universe very much. And that’s part of why he has invested in the Simons Observatory, to see if he can test these ideas.
Paul, let’s pick up on condensed matter. I think that’s the next stop. And here, would we go back to your joining Princeton? Would that be the right place to pick up?
Yeah, let’s go back to the colloquium and Ken Deffeyes, and him introducing me to Peter Lu and Nan Yao.
So the first thing we did with Peter Lu, was we went to this computer catalog of diffraction patterns. We went to the company that sells the software for it. We explained to them what we wanted to do, that we couldn't work with their front end, because it required going by hand, file by file, and taking data, and it was just too slow. We wanted to be able to do a computer search, a matching search against an algorithm for looking for quasicrystal candidates, given the data. And we asked them if they’d agree to let us get direct access to their database, which they kindly did, and so then we could apply this idea. And we soon found we could identify something like 50 or 100 minerals which would be, say, possible quasicrystal candidates. That is to say, they gave diffraction patterns which were not exactly like a quasicrystal, but close enough to be potentially interesting. And everything else gave something very unlike a quasicrystal. So it left us with a finite number of potential minerals to go after.
And the next part of the project was to actually try to find the minerals, beginning with the most likely candidate, next most likely candidate, et cetera. And to make a long, long story short—there were wonderful adventures in trying to find those samples, and trying to test them, but they all failed. This was 1999—2001. At that point, Peter had left Princeton and gone to Harvard for graduate school, so we wrote a paper in which we explained that we had this idea of searching the existing database for quasicrystals. We had only been able to check out a few of our best candidates. So far, we had failed, but we knew how to search. And we invited anyone that wanted to help join the search to contact us, and we would be happy to share more of our candidates with them, and work together on it.
But no one answered the call, until six years later. By this time, Peter is at Harvard for a number of years, and he’s sort of disconnected from the project, working on other things for his PhD. We get an email from somebody I had never heard of, a fellow by the name of Luca Bindi, who was a mineralogist at the University of Florence—curator of their mineral collection at the time. I never heard of him before, but he volunteered that he would be willing to look for samples in his museum’s collection to see if any of the ones on our list were in it, and to test them out. So we tried that.
Now, I should say, testing a sample takes a lot of time. You have to find it in your collection. You then have to take a really small piece of it. You have to prepare it in a very special way. You have to get time on your electron microscope. You have to then study it. Because you know, a typical rock or mineral is going to have a collection of minerals in it. You have to search quite a bit. So it takes on the order of two to three months, just to do just one study. After the course of a year, we came up empty. And we thought about writing a paper saying, “We've tried a bunch more, and we're still failing so far.”
But when Luca answered the call and chose to join us, I did not know it at the time, but in retrospect, I call it one of the most luckiest events one could possibly imagine happening. Because not only did it turn out that there was something he had in his collection which was not anticipated, but Luca himself became an immediate fanatic on this issue. Total outright dedication. As nutty as I was, I would say, if not nuttier. And it started a series of Skype conversations between us that would happen on a regular basis, that became more and more frequent, and shortly after that, began almost a daily communication, including to the present. So that was fortunate. And it also turned out that Luca has incredible skills in the laboratory that led to one discovery after another for us, often saving us from what seemed to be a dead end. I came to call him the Miracle Man, L’Uomo dei Miracoli. So much of the success of the years following traces to him.
But at first, it didn't look so good, because after a year it looked like we had failed once again. But then he said, “You know, I have some things in the collection which aren’t in this international catalog, some minerals whose diffraction pattern never made their way there.” And there was one particular sample he thought we should look at, because it had in it metallic aluminum. It was a mixture of metallic aluminum and copper, was what they claimed was the main mineral in there. It was supposed to be a crystal mineral, but he knew that some quasicrystals, some of the synthetic ones that had been studied in the 1980’s, had metallic aluminum and copper in them. And so he thought that would be a good thing to try. So sure enough, he sliced and diced the sample so he could do the studies of different regions of the sample. And sure enough, it did have this aluminum-copper mineral in it that’s called khatyrkite, which is a crystal, as the box claimed it contained. And although it may seem obvious that if a museum has a box that says it has “X” in it, it should have “X” in it, you'll see in a moment that’s not so obvious, actually. That was luck, that it actually had this mineral in it.
But he also found some other minerals that didn't classify. And he tested at one of those minerals, one of the little grains in this rock, and he said, “Well, this looks vaguely like the properties you might expect for a quasicrystal.” At that point I said, “Well, you've got to send it to us.” Because we have the right instrumentation at Princeton to do high precision work. And so he did that. And so by the time I got to see the sample—it began as a few millimeters size—by the time I see the sample, there were a few tiny powdery grains of the stuff on the edge of a glass needle, barely visible to the naked eye. So you couldn't tell much from that. We tried to see what we could do without removing it from the needle; couldn't do much that way.
I was now working again with Nan Yao, whom I had worked with earlier, when I was studying diffraction patterns with Peter. But we had a problem, which is people could sign up for the electron microscope. Although Nan was the director of it, he had to let students and others use the electron microscope. And he told me we had a problem, which was that it was all booked up for several months. But this was around winter break. So I asked him, “Hmm, is it possible we can do it over winter break?” And he said, “Well, the only date available is January 2nd, and only very early in the morning.” “How early?” “Oh, five or six in the morning,” he told me. I said, “Are you willing to come?” He said he was willing to come. So that’s when we set up to do it.
The first challenge was getting those little powdery grains off the needle. We almost lost the sample there. We managed to get them off the needle. We popped it in the electron microscope, and within a matter of moments, Nan found a grain in which appeared a fantastic, amazing diffraction pattern, as perfect as anything I had ever seen of a quasicrystal. Just the signature pattern. Snowflake pattern, rings of spots with tenfold symmetry, in perfect alignment. Actually much more perfect than the synthetic sample that Shechtman had originally produced back in the early 1980’s that had helped start the subject off.
So at that moment, I was sure that I had observed the first natural quasicrystal to be discovered. Really exciting time. So although it was now early in the morning and freezing cold, I had a wonderful ride back home thinking that we had actually found a natural quasicrystal. I wrote this to Luca, and he was very excited. And the story could well have ended that we published the results, everyone accepted the results, and victory! We had found what we had been looking for. But that’s not what happened. A much stranger story emerged.
There was no question that what we had was a quasicrystal. When we began to do more measurements of the sample and rotated it different angles, we found that it had an icosahedral symmetry, just like some of the early synthetic quasicrystals did. And then, when we measured its chemical composition, we discovered it had the chemical composition which we recognized immediately -- it was exactly the same chemical composition that had been observed by the Japanese group that discovered what I would call the first bonified quasicrystal in 1987, that is, the first highly perfect synthetic quasicrystal.
But when they had made their sample back in 1987, they had done it under highly controlled conditions. Purified the elements, brought them together with just the right composition, cooled the liquid slowly under controlled conditions. This sample we found was in a rock, which had all kinds of other minerals in it. And they were mishmashed together like meatballs or something. A really complicated mess. And somehow, nature had managed to make something that appeared as perfect as something that had been produced under highly controlled conditions. “How is that possible? How did nature manage to do that?” That was the puzzle I could not get out of my mind.
What did that tell us about quasicrystals? Maybe they're more robust than we thought. They're easier to make, and nature has found a way of making them that we haven't thought of. Or, maybe it’s telling us something about geology. After all, this would be the first example in the history of geology of something which is non-crystalline and not glassy. Something which is quasicrystal.
So I wrote to Ken Deffeyes, who had started us off in this direction, after my colloquium. He was retired now. He was in San Diego. And this was a little bit beyond what he could help us with, but he pointed me to a well-known petrologist, a geologist whose expertise is in deciphering how a rock formed, based on what you observe in it. His name is Lincoln Hollister. He was, at the time a professor at Princeton, and is now emeritus. Lincoln was one of the first people to study the lunar samples coming from the Apollo missions. So someone with a prestigious international reputation, and quite expert.
And so I called Lincoln up and asked him if he’d be willing to meet with me to talk about this idea. He said yes. Of course, I was a theoretical physicist coming to talk to a geologist about this crazy idea. I went to his office. He’s tall, and looks just like I would picture a geologist. Just like your classic picture of a geologist who does field work. I didn't know at the time how legendary he was. Both in terms of funny stories as well as scientific stories. Like how he was famous for firing a rifle in Harvard Yard when he was a student.
Going after squirrels. He comes from a legendary family, the legendary Hollister family from California that at one time owned most of California. But anyway, he’s a geologist.
I got to his office, and I told him the whole story of what we had done, and I asked him what he thought. And he said—he gave me a strange look, and he said, “Well, I'm sorry to tell you that what you have there is impossible.” And I interrupted and I said, “No, it’s not impossible. We know quasicrystals exist.” He said he was totally unfamiliar with the idea of quasicrystals, but again -- what we had there was clearly impossible. And then I said, “No, no, it’s not impossible. We know quasicrystals exist. In fact, a metallurgist in 1987 made the same alloy in the laboratory in Japan, we know this particular one is possible.”
And he interrupted me and said, “No, no, no. That may be true. There may be nothing wrong with the idea of quasicrystals. I can’t help you with that,” he said. “But what you told me is that you have a sample, a mineral sample, which contains a mixture of metallic aluminum and metallic copper.” He said, “You know, there’s a lot of aluminum on the earth, but there’s no natural metallic aluminum. All aluminum on the Earth is an oxide. We spend a lot of energy in aluminum foundries to separate aluminum from oxygen. There’s a whole history about the history of aluminum, how we learned to do that. First it was very expensive. Eventually, it became very inexpensive. But no one has ever credibly observed anything with metallic aluminum in it in nature before. And surely what you have there is some kind of slag, some kind of man-made substance that came out of a laboratory -- it came out of a foundry, a by-product of a laboratory, or something like that.” He said this with such definiteness and such seriousness that I almost thought he was prepared to kick me out of his office.
[laugh] At that point. I certainly thought he wasn’t going to say anything.
Paul, had he ever dealt with the kinds of ideas that you were bringing to him? Is this his first entrée?
First entrée. Never heard of quasicrystals before. He could just tell me about the geological interpretation. And also—and I wouldn't say I'm an impertinent person, but I have learned over the years that whenever someone tells me something is impossible, I don’t take it for granted.
In fact, that’s exactly what I said. I asked him the question I often ask when someone tells me, that something is impossible. I have been told “A bounce is impossible.” “Slow contraction is impossible.” Et cetera. I've often been told an idea I am pursuing is impossible. I respond, “When you say it’s impossible, do you mean like it violates fundamental principles of science that we know cannot be violated? Or, do you mean it’s the second kind of impossible, something which, based on experience, we haven’t seen before, and we think is unlikely, but we can’t really rigorously argue is impossible?”
And at that point, I really thought Lincoln might throw me out of his office. [laugh] But fortunately, he didn't. He thought. And then he said, “Well, OK. If you force me. If I were forced to come up with an explanation for this, I could imagine there could be conditions deep under the surface of the Earth where the pressure is high enough that you could separate aluminum from oxygen. It would have to be quite low, near the core-mantle boundary, so thousands of miles below the Earth’s surface. Then you could imagine making the mineral you claim. Of course, you'd have to figure out a way to get it to the surface. Because you found it in a museum. It obviously got to the surface somehow. So, how could that happen?”
“Well,” he continued, “one of my colleagues here, Jason Morgan, who has since retired, is one of the founders of the plate tectonics theory. And one of the ideas he had was at one time, in the Earth there were what you call superplumes, plumes that would have gone deep under the Earth and brought material up to the surface of the Earth. Now, we know some plumes exist that formed Hawaii, the Hawaiian Islands, but they're shallow.” He was talking about ones that went all the way down to the core-mantle boundary. And if that were the case, and you managed to form the plume extended all the way down to the Earth's core, it could have caused material, including a quasicrystal, to shoot up to the Earth's surface.
I thought to myself, “Ah. It’s not the first kind of impossible.” It’s not like one plus one equals three. It’s the second kind of impossible—highly unlikely but potentially really interesting. So at that point, I had another idea in my head, which I had been flirting with. And I asked him, “Well, how about meteorites? There is no oxygen in space. Is it possible that a collision of meteorites could have caused this thing?” Now fortunately for me, Lincoln didn't know much about meteorites, because if he did, he would have said, “You're an idiot. There’s plenty of oxygen in space. Meteorites are full of oxygen.” [laugh] I didn't know that. I was just thinking of iron meteorites.
Fortunately, he didn’t know it either, so he didn't call me an idiot. He said, “Actually, I don’t know much about meteorites, but I know someone who does. A former Princeton graduate student who is now head of the meteorite section of the Smithsonian Museum in Washington.” And so a week later, we took a train ride to visit Glenn MacPherson at the Natural History Museum in Washington. And I had not known it at the time, but before we had gotten there, Lincoln had talked to him and given him some preview of what we were going to talk about. So when we got there, waiting at the door on Constitution Avenue, was Glenn --not even waiting for us to enter the museum, ready to tell me, right off the bat, “Before you go any further, I just want to tell you one thing. What you've got there is impossible. Can’t exist. Doesn't exist in any meteorites.”
And for the next few hours, the story went on and on like this. “I have seen every possible meteorite that exists. We have them here in our collection. I study meteorites from different ages, especially ones from the early solar system. We've never seen metallic aluminum in any of them. Furthermore, your sample has some other peculiar properties.” And we spent the afternoon going through all the peculiar properties that he said were simply inconsistent with any meteorite sample that has ever been seen. Or any natural mineral sample that had ever been seen. So by the time Glenn was through, it was like taking the few sentences from Lincoln that was saying it was impossible, and extending it over hours and giving me many reasons, and Lincoln many reasons, why it was impossible. Glenn’s conclusion, like Lincoln’s original reaction, was that the sample had to be a piece of slag.
And by the time I left, I'm pretty sure Lincoln thought he’d never hear from Luca and me again, and certainly Glenn thought he would never [laugh] hear from us again. And as we took the train ride back, and probably Lincoln and Glenn both thought that was the end of the story. But I write to Luca; we have a series of Skypes. First of all, he’s not convinced by these arguments. And secondly, my thought is, even if they're right, even if some person by accident made it, they still managed to make the quasicrystal highly perfect. So it’s kind of a win-win situation. Even if we figure out it’s some kind of slag, some kind of industrial by-product, we discover a new way of making quasicrystals. And also, although Glenn gave us a bunch of arguments, they amounted to a bunch of stories. They were like second kind of impossible stories, based on previous experiences, why it hadn’t been seen. So, you know, maybe it’s the second kind of impossible, not the first kind. Maybe it’s the kind you can overcome.
So that left the challenge for me and Luca to essentially prove the case. And the way I thought about it, conceptually, and convinced Luca to think about it, is that we should think of the four of us as now forming a red team and a blue team. We were the blue team, Luca and I. We're going to try to push this idea that it’s natural, as far as possible. Lincoln and Glenn are going to be our red team, even if they don’t know it. We're going to present data to them, and they're going to keep shooting down our ideas. And either we convince them, or they convince us. You have to worry as a theorist that you have a theoretical bias, and the only way to correct that theoretical bias that I know of, is to make sure you have people who are critical of you, that you can go to for honest disagreement.
Glenn and Lincoln were both esteemed scientists in their different fields—in their knowledge of meteorites and geology generally. If we couldn't convince them, we're dead. If we can convince them, we should win. And that’s just how it went – the next year was an intense back and forth between the red and blue teams. Fortunately, Lincoln and Glenn were willing take part. As a result, the plan worked beautifully.
So that essentially began a process of Luca and me trying to figure out what was going on. And the process we decided on divided into two strands. One strand would be to take those few little grains we had left, from the tip of that needle Luca had sent me, and examine each one of them in fine detail to see if we could find evidence in the laboratory that it was slag. Because slag should have certain properties. We learned a lot about slag during this period, what to look for. See if we could find any evidence of that, or to the contrary.
And the second strand we followed, was to go back and ask, “Well, where did this sample come from – the sample that landed in the museum?” We could turn this into a detective story and trace where that came back from.
Now, it turned out both those stories took about a year and a half to develop. The detective story is like an international story of intrigue. I'll try to give you a brief impression of it. And the laboratory story is continuing in parallel. You have to imagine every day, there was news on one front or the other —that’s why we were Skyping every day. Sometimes good news, sometimes disastrous news, going backwards and forwards. But just the detective story is kind of the wildest part of it. So, what did we do? We went back to the museum records to determine, “Where did this sample come from?” Well, it turned out it was sold to the museum in 1990 by a collector who lived in Amsterdam, along with several thousand other what they call microsamples, small samples of minerals. OK, so, “ Let’s go find the collector.” So we looked for the collector. By looking for the collector, I mean, it’s the day of the internet, so you can go via internet and visit people in Amsterdam without physically going there. You can even speak Dutch if they don’t speak English, because you can use Google Translate, and try to search for this collector. We didn't find him.
The other thing we could do, is we could send an all-points bulletin out to museums and collectors around the world, and ask, “Do you have any of this sample?” Because there was no particular reason to believe this sample was rare. It was just a sample in a museum. There’s nothing special about the Florence museum. Maybe other museums have it, and we can test those samples. And, in fact, we found three or four that were in Europe or the U.S. that claimed to have samples, along with a museum in Russia, that also claimed to have a sample. The ones that were outside Russia were willing to send us their samples to test. We tested them. Each of them was labeled as having this khatyrkite, this mixture of aluminum and copper in it. When we tested them, actually none of them had it, any of it. They were all fakes.
When I mentioned earlier that we were lucky that our sample that claimed to have khatyrkite in it really had it, this is what I meant. It turns out there’s a lot of fakery in the mineralogical game. It’s much cheaper to buy a mineral than it is to test it. It’s not like art. The art is very expensive; it doesn't cost so much to test, comparatively. Of course you test it. Here, if a mineral collector sees someone has a peculiar mineral, they don’t have an electron microscope handy, usually!
So they're going to buy it. It’s not so expensive. They're going to take it. They're going to put it in their collection. That collection may be sold to a museum, like in Florence. They're not going to spend the time or money to test it. So over many years, you can have more and more fakes end up in museums. And some of these sources were museums, and some were private collectors.
And Paul, you're getting a crash course in the underworld of mineral collecting in real time now. [laugh]
Yes, that’s right. In fact today, I'll warn you, since we've had this discussion, that you can go to mineral shows, and you will find this same mineral for sale. Whenever we've tested those minerals, we find they're fakes. So because it has now become a `thing’, this mineral, the faking continues to be done. But the mineral in Russia we knew had to be real, because that was the original mineral from which this khatyrkite was first discovered.
What I mean by that is the following. We had found our sample in the Florence museum. It had a name associated with it, a mineral name, khatykite. You can look that up in the International Mineralogical Association. It is described as being a crystal of aluminum and copper. The quasicrystal we had was not aluminum-copper; it was aluminum-copper-iron. That was the natural quasicrystal. But the main component was supposed to be was this crystal mineral khatyrkite that we knew that existed. Now, someone had first reported the discovery of that mineral in 1985. When you find a new mineral, if you want to have it accepted, you have to do a couple of things. You have to write a report describing your new mineral, describing all its properties. You have to send it to the International Mineralogical Association. A panel of 30 geologists from around the world have to approve your report. They then allow you to name it. They work with you on the name, but they have to allow it to be named. They report it. But you also have to put a sample of it in some museum someplace. And it’s called the holotype sample.
The material in Russia was the holotype sample for this aluminum-copper khatyrkite crystal mineral. So we knew that it had to be real. But it was also true that the director of that museum would not permit it to be studied. Partly because it was holotype, and I think partially because he was just a stubborn person and wouldn't allow it to be studied.
So what could we do next? Well, by now Glenn and Lincoln are just getting more and more skeptical, so we're kind of stuck, and this trail has ended. We haven't found anything in our investigation of the sample in the laboratory back in Princeton that is convincing yet. But just by chance, one of those miracles happened that happen many times in this story. Luca was having dinner with his sister one evening, who brought a friend over, and telling him the story of how we had gotten to this point and where we were stuck. And at some point the friend asked, “What’s the name of this collector in Amsterdam?” He said, “Because I live in Amsterdam.” That’s where he had come from. Luca gave him the name of the collector. He said, “Oh, that’s too bad. That’s a very common last name. It’s like Smith. So there’s going to be lots of people with that last name. There is an old woman who lives down the street—I help her get groceries. She has that last name. When I get home, I'll ask her if she happens to know anything about this collector.”
Twenty-four hours later, we get an email from the friend, or Luca gets an email from the friend, saying, “Guess what? She’s the widow of the collector.” So suddenly, we are on the trail of the collector again. Again, I'm just trying to give you highlights. There’s so many threads; this is like a detective story. The dead ends are as interesting as the live ends, but I'm just giving you a sense of the live ends.
So Luca goes to Amsterdam and asks her, “Does she know anything about her late husband’s collection, how he got his samples?” No, she knows nothing at all. Her husband used to collect it. She knows nothing at all about—her husband gave the collection, or sold the collection to Florence. That’s the last she heard of it. She knows nothing, nothing at all. In fact, she won’t even let Luca stay in the room. She only will talk to the friend. She asks Luca to leave. She’s very wary and suspicious of what he’s doing there. Scared of having this stranger there.
But finally the friend persists, and finally she says, “Look, I really don’t know anything about what my husband collected. But he used to keep a diary. And while the collection went to Florence, I have the diary. I'll let you look through the diary.” The friend looks through the diary, and sure enough, this sample appears in there. And it describes in there how her husband went to Romania, met someone there—only described as Tim. Tim the Romanian—
—and he made a deal with Tim the Romanian, which got him the samples. Now, it’s described in somewhat obscure words, because selling minerals at those times -- the 1980’s, in Soviet Russia -- was strictly illegal, and would get you sent to Siberia or something like that. So it’s written in some sort of coded language, but it’s clear that’s what happened. When I got this news back, I thought, “Great. Nothing should be easier than to find Tim the Romanian who’s a smuggler.”
So we tried to track down Tim the Romanian. We didn't find him. After six weeks, we didn't find him. As a last desperate act, Luca went back to Amsterdam. Maybe using the word “Tim” would excite something in his widow’s mind. No. She knew nothing about Tim the Romanian, knew nothing about her husband’s trips, knew nothing, nothing, nothing. But finally, she pointed out that her husband used to keep a secret, secret diary, as well. And now we know it’s probably because of transactions that were less legal, he kept a second set of books to describe those.
This time, she did allow Luca to look at it—and it was all described. How Tim the Romanian was getting his samples. He was getting his samples from the same guy who had published the original khatyrkite sample, and who had put the sample in that museum in Russia. Now, we had tried to contact this guy before, this scientist. He had emigrated to Israel. We had a terrible time with him. He wasn’t willing to help unless I was willing to pay him a significant reward. And by this time, we had heard a lot of scurrilous things about him, so I wasn’t sure we could trust him. So we had given up on this guy. Now, we suddenly understand our sample is genetically related to the sample that’s in the Russian museum, and to this guy. They came from the same place.
And where did they come from? Well, according to the paper they published, they came someplace in Far Eastern Russia, north of the Kamchatka Peninsula, about as far east and north as you can get in Russia, in the Okrug, or region, which is called Chukotka. Very desolate region. Less populated than the Western Sahara. And hard to get to. And we didn't really believe that this guy, who among other things had high political and KGB connections, would have ever landed himself somewhere as remote as this. We were convinced that somebody else must have actually done the work and brought the sample to him.
And so we began to investigate and ask all kinds of people, “Who would that likely be?” And in the original paper, in addition to the authors, there was a name mentioned in the first paragraph of some obscure person, Valery Kryachko, who had been doing some digging and found something. But we had been told by Russians that this would be a fake name, a fake person. The fellow we knew – the scientist who had emigrated to Israel -- had been the head of the Soviet Union’s Institute of Platinum in Moscow. His job was to look for platinum, something very valuable. He would not want to give away the location where he was searching in a little article about some obscure mineral. So he would make up some story with some imaginary people. This would be an imaginary person. Others told us, “No, I think I remember a guy like that, and I think he passed away.” So he was either imaginary or dead, one of those two.
And then, by accident, several months later, we found an article about someone involved in mineral explorations in Chukotka who had the same name. So suddenly Kryacho went from imaginary to someone real. It didn't give us enough information how to find him, but there were other authors to the paper, so we tracked down those authors. All of this is all by internet, and using Google Translate. All of this was done remotely, and over a period of months.
And one of the people that we contacted, Vadim Distler, told us that, in fact, he had been the PhD thesis advisor of Valery Kryachko. That, in fact, he had heard that from Valery about being sent to this Far Eastern Russian place by the fellow in Israel.
And then came a crucial moment when—because I thought, you know, it’s now many years later. It was 1979 when Kryachko was sent there, and we're talking in 2010. So I finally asked, “Well, is Valery still alive?” After a moment that seemed like an eternity, Vadim said, “Oh, yes. He’s still alive. In fact, he’s coming to visit me next week. Do you want to talk to him?” And suddenly, we went from this imaginary, possibly dead person, to someone very alive. And although he doesn't speak English, we were able to communicate again by Google Translate, and Valery gave me the whole story, the whole detailed story on how this fellow, who’s now in Israel—his name was Leonid Razin, who was the head of the Institute of Platinum, had sent him and another fellow to this remote region of Far Eastern Russia, in the middle of nowhere, in the Koryak Mountains, to a stream where gold had been found. And where you found gold, you often find platinum. Their job was to look for platinum.
Valery believed Razin was very scary that he was working for. He had KGB connections and he was believed to send people he didn't like, arrange for them to be sent to places you don’t want to send people, Siberia or some equivalent. So he’s afraid of him, and he hadn’t found platinum in his weeks there. He had dug and dug and dug,and sifted and sifted and sifted. But all he had found were some shiny rocks which he knew weren’t platinum. And to show that Razin had at least done something, to show him something tangible, he brought them back and gave them to Razin, and that’s the last Valery had heard of them.
He didn't know the guy had taken them back to Moscow and then to Saint Petersburg, had them tested, found new minerals in them, apparently put some of those samples in a museum, apparently helped smuggle some of them—or someone helped smuggle some of them--- out, and that they ended up in Amsterdam, and then in Florence. He didn't know anything about that.
But, by now, Valery had heard about us, because our first article claiming to find a natural quasicrystal had now appeared in Science. It was described as having a connection to Russia. And now he realized he was personally connected to the story. So that got him very excited. He offered, if we ever wanted to, to take us back to the spot and show us where he had found them. Although it was obviously this [laugh] incredibly remote spot in the middle of nowhere.
And then I explained this to Glenn and Lincoln—and the great thing about the site was, this was really the middle of nowhere. There’s no aluminum foundry—there’s nothing there [laugh], OK, that could have faked this. So that was great. And that really began, I think, to turn Lincoln’s mind, as to take more seriously that this might be something real. I'm not sure we convinced Glenn so much, but we certainly convinced Lincoln. He had been a great foil all along, making all sorts of important criticisms and suggestions. And now it just got better. In the meantime, in the laboratory, Luca had discovered something surprising. He discovered a little tiny submicron grain, which had a quasicrystal in the middle embedded, and growing around it, a piece of what’s called stishovite. Now, stishovite is silicon dioxide, the same molecule that makes up sand and glass. The same thing chemically. But stishovite doesn't have the same structural form, the same crystal form, as sand or glass, because stishovite is a form of silicon dioxide that forms under very high pressures that might occur in a meteorite impact or that might occur in an explosion or something like that.
And because the quasicrystal was entirely embedded in this piece of stishovite, it meant that somehow there had been some enormous pressure, a hundred thousand times or more atmospheric pressure, that had been needed to form the stishovite, and the quasicrystal had to have already been there in the first place because it was embedded inside the stishovite. So it’s not something that could have been manufactured in a laboratory someplace, because you don’t reach anywhere near those pressures. It couldn't have been formed accidentally in a foundry or slag. It had to be something formed where you'd get those extraordinary pressures.
And by this time, I and Luca and the team had invented maybe a dozen or more different possible theories for how the quasicrystal may have formed, but there were only two theories that were possible that would produce those high pressures. One, deep under the earth, and the other, in space. And so that led to the next test. “Is there some way to tell which it is?” You can. You can tell which it is by measuring the oxygen isotope ratios in the material, in the oxygenated minerals.
And there are only a few places in the world you can do that test. One of them is at Caltech. I was a graduate of Caltech. I made connections there and arranged for us to work with John Eiler and Yunbin Guan, who had the right kind of instrument, an ion microprobe, that does just this kind of analysis. It’s how you differentiate Mars rocks from asteroidal rocks, from other kinds of minerals, terrestrial minerals. And we prepared to do this now expensive test, if you like, to test which our quasicrystal was.
And when the results came out—it took a long time to just get the instrument tuned up enough to do the job—when they finally came out, it came out that our sample was unquestionably meteoritic. And not just meteoritic, but a special subclass of meteorites, which are called CV3 carbonaceous chondrites. Those are famous meteorites, because those are the earliest meteorites to have formed in the solar system. Those are the most interesting meteorites that people who are interested in the history of the solar system wanted to study. The most studied.
The world’s expert, if you're going to name the single world’s expert on CV3 carbonaceous chondrites, was Glenn MacPherson, the fellow at the Smithsonian Institute, the very person that had been skeptical up to this point. When he saw the data from the microprobe, he responded, “Wow. This is obviously meteoritic and natural. And furthermore, it’s bizarre, because we've never seen this kind of mineral in a meteor before. I now have a bunch of other things I'm going to be able to measure about these samples. This investigation is mine now. This is my territory!” And I said, “Hold it, Glenn. You understand that to get to this point, we used every little grain of material [laugh] we had left?” I said, “Furthermore, we're not about to drop [laugh] out of this project now!” So it was a funny exchange, after all the serious exchanges we had had over the preceding two years.
But the point was, this was overwhelmingly convincing. The red team had officially conceded. I knew almost immediately that meant one thing. We had to go back to Far Eastern Russia and see if we could find more samples. That was the only way we were going to be able to do it. And I had already been thinking about that idea. We were obviously going to need people who were willing to go on this obscure mission, and we were going to need funds.
I don’t know how much of that story you want to get into, but I first went to Princeton to see if I could get them to provide some funding for us. They were in the middle of a capital campaign. They told us, “No, we can’t really help you with this.” I asked them, “What if I find somebody, a private donor, who’s willing to give money?” They said, “No, no, you can’t do that. Because that same private donor could give money to Princeton.” I kind of knew that’s the way administrations worked, so I was already ready to ask the next question, which was, “Suppose I find a private donor who would in no way give money to Princeton, except for this.” They said, “Sure. Go ahead and try.” [laugh]
But I already had an idea of how to do it, and I'm not going to reveal my secret. Two days later, I called them back and said, “Guess what? I have such a donor. He prefers to remain anonymous. But I have such a donor.” They said, “Well, we have to know the name. We have to check it out. So I got permission from the donor that for this one purpose, I could give his name. A few weeks later, they called back, almost quizzically, and said, “You know what? You're right. He’s not going to contribute to Princeton [laugh] in any way other than for this! OK, you can go ahead and do this.” So that’s how we got the funding for it.
How did they confirm that independently?
Oh, they had their ways.
They know the family trees of every person who is connected to the university. And I knew this in advance. I had considered that the criterion when choosing this person. So when I asked around, I had to find someone with no Princeton connections, and who had no interest in contributing to Princeton. That was my criteria. And I won’t go about the secret for how you do this, but there is a way you can do this. So then we had the cash. Then the next thing was to pull together a team. Valery was more than willing to help us. He put me in contact with his advisor, Vadim Distler, and his advisor’s director, Marina Yudovskaya, and they were willing to help us. So we had the money, we had the Russian contacts. They were going to get us all the permissions we needed. Just like a stack of permissions a foot high.
And then we just had to find people who would be willing to give up their next summer and go on this wild goose chase. Many I spoke to said, “Look, just because someone found a little grain this size in 1979, you can go back there, and the most likely thing is you're going to find nothing.” But, you know, if we didn't go, and if we didn't go then, who knows if Valery would be able to go. He was now in his sixties. And if we didn't ever go, we’d never know for sure what we could find.
So I pulled together a team. Again, to make a long story short, we come in our story to July 20th, 2011. We're sitting in Chukotka, ready to board trucks to cross the tundra, to the Koryak Mountains to see if we can find something.
My original plan, by the way, I should say, was not to go myself. I had a brilliant plan where I would send others to go. I thought that was a great plan. I would get them a helicopter and arrange to get them to the site. Unfortunately, I couldn't get a helicopter. Couldn't arrange it on that end for various reasons. And by the time we got far enough along, Valery convinced me that the only way you could go there was by, well, what he called trucks. They were really more like tanks with tops that looked like vans. Really funny-looking vehicles. And he said, “I'm going to get two of them, and you have to go.” And Lincoln Hollister, whom Luca and I both looked up to, whether it came to science or planning advice, said, “Yeah, Paul, you have go to.” [laugh]
I said, “But I'm not an outdoor person! [laugh] I don’t go camping. I don’t do any of those things.” “Doesn't make a difference. You want this team to go? You better go with them.” Lincoln insisted. And that was that. So I did end up having to go with them. Lincoln was not healthy enough to go, but he sent a undergraduate Mike Eddy to come in his place. But Glenn came with us, a sign of his conversion from the red to the blue team. And Luca, of course. He was key. I got to also bring along a wonderful geologist, Chris Andronicos, whom Lincoln recommended and who was an expert on structural geology, so he had studied the geology of the area. And he had also worked in regions with grizzly bears, and that was important, because in the area we were headed, there’s Kamchatka brown bears, which can be very, very nasty bears. And so he was going to be our bear expert as well as our structural geologist. I also got to bring along my son Will, who was, in fact, at the time at Caltech studying geology.
After graduating and going to Harvard.
Was this totally unconnected, his interest in what you were doing?
Totally unconnected. In fact, it was important that he went, because whereas I had zero camping experience—
—he, by this point, had significant camping experience. So this was a hilarious occasion for him, I think, because I was now the child compared to him, when it came to the outdoors. And he wouldn't let me forget that. And we got to camp together. That was a really wonderful, wonderful, wonderful aspect of the experience.
All you're doing when you go there is you're digging, digging, digging. You can’t really measure things when you're there. Again, I'm compressing a long story, because I know we've gone quite a long time. But you're digging and digging, and you're panning and panning and panning. Because you can’t bring back the raw material; you have to pan the materials. Just like you pan for gold, you're panning for quasicrystals. But gold, you can recognize. In fact, we found some golden nuggets there. But you can’t recognize a quasicrystal by eye.
You collect all the panned materials, you bring them back, you manage to get them out of Russia back to laboratories in the U.S. and Italy. And then Luca basically has to go through literally millions of grains, one by one, and looking to see if any samples of meteorite are to be found. Six weeks later—again, I'm making a long story short—he reports, sure enough, he has found a sample which has quasicrystal in it, and has the other minerals we had seen.
And where and how was he able to determine this?
Again with electron microscopy. Through by X-ray diffraction, and by an electron microprobe measuring the chemical composition.
So obviously this is not being determined in the field. This is being brought back to the lab.
Can’t determine it in the field. We did bring along a crude optical microscope, and we used that to help guide us. We looked for shiny bits of mineral or oddities, and that helped a little bit. In fact, this particular first sample Luca found was one of the first we had found—actually, Luca picked the sample—we know exactly when and where this sample was found, because he found it on day one in the field, and he immediately suspected it was a quasicrystal. The other geologists on the team were very skeptical. But six weeks after we got back, in fact, he turned out to be right, as Luca often was in this story.
And eventually he found nine different samples, and each one of them had a little story associated with it. But finding the first was the most exciting. Because I just told you a completely nutty story about how we tracked down this sample. And if that’s as far as the story got -- you, like we, would have been skeptical that we had reconstructed the story correctly. Because I’d also have to tell you about all the other dead ends that we followed as well. You'd say, “Well, I'm willing to bet 10% [laugh] that the story is right and the sample in the Florence museum containing quasicrystal comes from Chukotka like you say it does.” But now, we personally went there under controlled conditions, picked something out of the ground, and found quasicrystals. Suddenly, there’s no question that we got the story right.
Furthermore we found that first sample in layers of clay that hadn’t been exposed for over 10,000 years. So it couldn't be something that was put there recently. We found lots of valuable information from this one sample. And we're still reconstructing the story based on studying the complete set of samples today. The latest we're doing is now, we're looking for trace elements, in the metals, materials that—a few atoms of material that will distinguish if—first of all show that it wasn’t made in a laboratory, but it will also help us reconstruct something about the history of how this meteorite formed.
And what we think, is that there were collisions occurring in space in the early solar system as meteorites aggregate together to form planetesimals. Or perhaps a planetesimal was broken into pieces by a collision with another one, and that was under the very high pressure conditions that the quasicrystal very rapidly formed —even though it was in a mishmash of other materials.
At Caltech, there is another group, who work with Paul Asimow, who does a sort of ‘cannon experiment’ where you literally shoot a metal projectile into a stack of minerals, and try to reproduce those high pressure conditions. And sure enough, we have been able to produce quasicrystals that just look very similar to what we see in our samples. In fact, that turns out to be an interesting way of making quasicrystals, because we've also made novel quasicrystals that were never known before. That is, we discovered, along the way, a new way of making quasicrystals. So that’s where that story is at present. Lincoln and Glenn continue to be important contributors to the science that Luca and I lead. And several other talented scientists have joined as we have gone along, depending on the measurements involved. We're just in the process of publishing a paper which will discuss these trace elements results, along with that we think is a more and more plausible story of how the meteor might have formed in the early solar system. It’s still a subject of study, so we'll see where it takes us. Nature really did find a way of making quasicrystals that we hadn’t thought of before, so that was cool.
This is an Indiana Jones story in some ways.
Definitely an Indiana Jones story. [laugh] And I haven't told you—there are many wild parts to it. We really did encounter Kamchatka brown bears. Someone on the team really did get a mild case of hypothermia. We really did almost have a serious fire and get caught in the middle of nowhere, in one of our trucks. So it’s a nice story when you're done. [laugh] But, when you're in the middle of it, it’s a bit crazy.
The fact that I was there turned out to be important. Because I guess I was responsible for the money and pulling the team together, somehow the team was looking to me to make various decisions. And there were some important decisions that had to be made in the field. Things didn't start off just as we expected them to do. And that turned out to be important for making the success. So it was actually a good idea in the end.
And now that I survived [laugh], I have no complaints. But at the time—I think I was probably worried and tense throughout the entire expedition. My main concern was safety. You know, I'm looking for natural quasicrystals. That’s a cool idea. But I kept thinking, “What if someone gets injured as a result of this crazy experience? Or worse, you know? Maybe it’s even my son.”
You're not even an experimentalist. You're a theorist. You're not even used to working with your hands.
That’s right. I was very much participating in a lot of the laboratory work at Princeton. So I liked being able to do that. I wasn’t turning the knobs, per se, but I was there and definitely directing many times what we should be doing, as we were doing it. Similarly, in the field. Directing at times. And in the end, it was a wonderful, wonderful experience. But I personally only felt relieved when I saw that we had just gotten back to Anadyr, the capital of Chukotka, where we had started from, and I knew that I was no longer responsible for the well-being [laugh] of everyone on the trucks. That’s the only time I really felt relaxed, after all that.
But nevertheless, it was a great experience. And it did introduce me to being outdoors, which I hadn’t had that experience before. And ever since then, I do a lot of hiking and things like that. Nothing as daring [laugh] as this trip, but just enjoying the outdoors, which I didn't do before. So it left me with that gift as well. That’s where we are at the present on that leg of the story.
There’s one other thread. Maybe I should just mention it briefly. So in the mid 2000’s—this gets us back to quasicrystals again—I got together with an experimentalist at Princeton by the name of Paul Chaikin, whom I had known, because he had once been at Penn with me. He had moved to Princeton. Now I had moved to Princeton. We were back together again. We had worked back at Penn a little bit on some issues with quasicrystals, and we had a discussion in which we asked whether or not quasicrystals might be an interesting design for photonic solids. Photonic solids are like semiconductors for light. They play the same role, if you want to make a light-driven circuit, a photonic circuit, as what a semiconductor does for electrons. Namely, it has a photonic band gap, which blocks light waves within a certain band of frequencies just like a semiconductor blocks electrons within a certain band of energies.
There’s a whole field of photonics, and what we call photonic crystals, which are crystals which people design to act like these semiconductors for light. But a problem with photonic crystals is the fact that because they're crystalline, they're highly asymmetric. That is to say, there are some directions which light flows differently than in other directions. And the differences are quite large. And so we had the idea, “What about a photonic quasicrystal?” Quasicrystals can be more spherically symmetric. Not exactly so, but much more nearly—an icosahedron almost looks like a round ball. A soccer ball, if you like, is an example of an icosahedral shape. It’s almost round. So maybe it would also have a band gap. Maybe it would also be spherically symmetric. And Paul had a bright student, Weining Man, a wonderful, dedicated, hardworking woman, who decided that yeah, she’d work on this project. In fact, she’d make one of these photonic crystals using what was at that time the best-you-could-have 3D printer. So not like 3D printers of today; this would have been an easy project today. This is a 3D printer which you had to baby for several days. Basically, she had to stay up 72 hours to make the first examples of this photonic quasicrystals. They were about this size, the size of a pair of open hands put together. And they were designed to act as photonic solids for microwaves.
Why microwaves? Well, number one, it was easy to print something that could block light waves of that wavelength. If you wanted to print something for visible light, it would have to be done with a very expensive lithographic machine, which doesn't even exist at the present time. But this you could do for microwaves, and you could test the sample by shining microwaves. Where are you going to get the microwaves? Well, again, this is one of those peculiar things. I live next to a group that studies the cosmic microwave background. They have a laboratory which generates microwaves and has detectors to look at the transmission of light, to absorb, to produce, and then detect microwaves.
So we actually used the cosmological laboratory to test whether microwaves would pass through our manufactured photonic quasicrystal in the way we hoped they would produce a band gap. And the result of that was yes, it did, even though our material was a very crude example. But it was enough to convince us, yes, this really worked. And that started me on a whole other thread of interest in what we call photonics.
A year or so later, when we were developing this idea, I met someone from our chemistry department by the name of Sal Torquato, another Princeton professor, and he was very interested in optimization questions. And I wanted to work with him on designing materials with the largest possible photonic band gaps.
And that led to the question, “Well, do we need a crystal or a quasicrystal to have a band gap? Is it possible to have something disordered but still have a band gap?” If you studied the literature, the answer was ambiguous. It wasn’t clear. But Sal had been working on the idea of what he called hyperuniform disordered solids, a material which, on the one hand, if you look at it locally, on a microscopic scale, it looks like it’s disordered, but there’s funny correlations in the distribution of material or atoms or molecules, as you average over larger and larger scales, that are like that of a crystal. So it’s kind of a mix. It’s neither crystal nor glass. It’s kind of a funny hybrid.
And after a while, working with a postdoc, Marian Florescu, we designed the first example of this type of hyperuniform disordered photonic solid and showed that it could have a large photonic band gap. But not a gap that was nearly spherically symmetric. Rather, a gap that was exactly spherically symmetric. And since they are disordered to begin with, you don’t have to align the parts of the design as perfectly as a precisely ordered photonic crystal or a photonic quasicrystal. And this experience started us on a whole line of research that we still work on, of designing new kinds of photonic solids. I guess by now, we have like over ten patents in this area and we spawned a startup called Etaphase with the support of some dedicated investors. We're still trying to develop this as a practical application. Photonics is a slowly developing field, but this is growing interest in replacing electronics with photonics, because you can pack more information with light and have less dissipation. But it hasn’t yet developed to be used extensively.
And so that’s another thread, if you like, which will ultimately connect back to help me understand the physical properties of quasicrystals as well as these other kinds of novel materials. So now we keep working on what I would call more and more novel kinds of materials, novel arrangements of matter, novel arrangements of material that weren’t known before, that have secret kinds of order that were not known previously.
I think it’s a very interesting period now for materials science. I'm very excited about it, in the following sense. When I was first working on quasicrystals, I was mentioning it to you, back in the 1980’s with Dov Levine, we had this idea, but people kept telling us, “Unless you can find some way that you can make that material, it’s just an hypothetical idea. It’s not a scientifically important development.” And we were lucky, because nature did make—I mean, in the laboratory, people did manage to make some of these materials. But you had to wait. But this is a new age for materials science. This is an age where you can 3D print a form for matter. And we're getting to the stage where we can manipulate matter on atomic scale.
So it’s no longer a matter of having to wait for nature to accidentally make that material. If you can imagine it, you can figure that it can be made somehow. And if you can make it, and it has interesting new physical properties—well, then you've discovered a new useful kind of matter, a new useful kind of material. So it’s now more about what you imagine. It now relies on what is in your head, what you can imagine, --- how imaginative you can be.
So far, most of us have been limited by what materials we observe in nature or can make in the laboratory. But now, if we can imagine them mathematically, we can make them through new technologies, and make them real. And I find that a very exciting direction. I'm having a lot of fun with it. So that’s another thread. So, I think I've covered a lot of threads.
You get a sense of—life has been busy.
Seriously. Well, Paul, in the last portion of our talk, I want to ask a few broadly retrospective questions about your career, to sort of help tie it all together—
Good luck! [laugh]
—since we've been on this epic journey together. So the first one, sticking with quasicrystals, do you see quasicrystals as sort of the connective tissue intellectually between your wide-ranging interests in Earthly physics and cosmological physics? Is that sort of one of the things that ties it all together for you?
You mean in cosmology? Is that what you said?
No, no. I would say it’s the fact that it’s so different is what’s exciting to me. What I like to work on is different things. I don’t look for a fusion. Occasionally, there are these funny fusions that occur, where working in one area inspires something in another. But it’s not what I'm looking for. I'm looking for a good puzzle. So the quasicrystals emerged from a puzzle of what were the limits on making something icosahedral over a longer range? Was there a fundamental limit, or could you make it infinitely icosahedral, and something infinitely large, with infinitely many elements, arranged everywhere with icosahedral symmetry, in contradiction to what had been the long-standing crystal lore.
So that was the hook in that idea. Could we violate what had been the 200-year-old theorems of crystallography? And each one of the problems I work in, I’d say there’s a hook in it. There’s something that, “Gee, if we can do this, we're going to be showing —we're going to be surprising—we're going to be overturning something that people have believed for some time.”
I'm just always looking for good puzzles. I’ll always try to ask myself the question—I try to tell students the same thing—you should ask yourself the question, “Imagine you can actually do what you're imagining. How will you feel? Will you be really excited about it, or will it just be ho-hum?”
Because very often, people work on what I would call ho-hum questions. They'll say, “I'm going to solve this equation under these conditions, and I'm going to see the following outcome.” I'll ask, “Really? That’s what you're going to spend your time doing? Why, exactly? What excites you about that?” And often, they can’t answer that question, and I send them back—“Try to find an answer to that question, or try to find a different question.” Because you can only work on a certain number of questions in your lifetime, and you should be working on the ones that you can imagine, when you start, that there’s at least a small chance that it will succeed, and if you succeed, you'll be really excited by it.
Now the hard part about that, or the mysterious part about that, I think, is having the intuition that you can possibly solve that problem. Because you can think of lots of questions which you can’t answer [laugh], but you also have to have the intuition there’s a chance that you will find an answer to that question. And that is kind of a sixth sense. I don’t know how to describe it. It’s a very weird feeling. I've had it more than once. But I start thinking about an issue in an almost subconscious way, and I can’t even articulate the thinking. In fact, I don’t tell people what I'm thinking. [laugh] Because if I tried to articulate it, I just feel like it would sound like, you know, garbage. Wouldn't be sensible. But nevertheless, I have a really strong feeling that it’s important to pursue this direction. I should drop everything for a while, and give it a good go. And the hit rate on that is surprisingly high. It’s not random. [laugh] Far from random. So there’s something. I don’t know how to describe it. Something going on in one’s head, where somehow I was thinking ahead somehow, into believing something is possible.
Like when I was talking to Lincoln and talking about, “Well, are you sure it’s impossible? You think it can’t be something like this?” And got him thinking as well. Or again in this story with Luca. One of the strangest experiences I've had is pretty early on, when Lincoln and Glenn were telling us that they didn't believe this could possibly be a quasicrystal, I had read the paper by Razin in Russia saying that they had found the rock with similar composition in Far Eastern Russia. We didn't know it was connected to ours yet. But they had found it in Far Eastern Russia.
And I remember I wrote to Luca one morning, and I said, “I had a really strange dream last night.” I don’t usually remember my dreams; I hardly ever remember my dreams. But in this strange dream, I saw us in front of a hill, and we were there cheering each other. And it was clear this hill was in front of a stream, like the stream that was in that story in the paper. Now, I had no idea that we were connected to that stream, or that I’d be there two years later. I mean, it was just a very strange thing going on. I don’t know how to describe that. That’s probably the strangest.
Usually it’s more like a less definite feeling, like when I went to IBM in the middle of working on inflationary cosmology, because I just had this feeling that Dov and I had reached a point that it was important to drop everything and give this completely different topic some attention. Don’t ask me to articulate it. I tried to do my best when we were discussing it, but I can’t really articulate it. It’s a very strange pull, or—you know. Once you have enough positive experience, you just say, “OK, I don’t get it. I just go with it.”
In fact, that’s very much the story with Luca and me. There were many times terrible things that happened, that you and I didn't discuss, where it looked like everything was going to collapse on us. And our goal—our thought process at one point was, “We're just going to go all in. We're just not going to stop. Something strange about this story says just go all in. Whatever test you can do, whatever experiment you can do, wherever you can go, wherever you have to travel, just do it, and ask yourself later why you did it.” [laugh] So it’s that kind of feeling. And so that’s more how it works with almost everything I do.
Paul, obviously a major theme of our talk has been this intellectual style of yours to sort of follow your nose and see what is intellectually important and curious to you. And I wonder, particularly because it’s a unique style particularly among physicists today—I mean, most people do not have the kind of research agenda that you have. And so I wonder if you ascribe to an intellectual tradition, maybe if you have an old soul, in the way that physicists used to work, that were not so self-limiting and concerned about hyper-specialization, and whatever benefits that that confers. So beyond obviously you just following your instincts, I wonder if there’s a tradition that you feel a part of, and that you feel is important to maintain in the modern era.
Hmm. [pause] Well, I do feel that there are too many physicists who narrow themselves as you described, decide at some point they're driven by particular questions, and they essentially burrow and go straight ahead working on those particular questions. I think there’s various forces that stop them from doing things the way I've learned, or taught myself to do research. One of them is insecurity. If you're going to try to enter another area—I mean, I knew nothing about minerals when I started this search for natural quasicrystals. I learned a lot. Lincoln and Glenn and Luca and Chris taught me so much. That was part of the fun. But I was completely a stupid idiot, as a student. I knew nothing. Less than an undergraduate major in the subject. So I had a lot to learn. You have to be willing to start from scratch – to embarrass yourself asking a lot of dumb questions.
So one of the things is insecurity. I think people don’t like—as they age somehow, many scientists feel it’s inappropriate for them to be asking those kinds of questions. Maybe it intimidates them.
Then there’s the social thing. You have to leave your scientific social network. There’s the fact that the social network you're moving to is not particularly welcoming. Each social network likes to protect its own, in some way. Their first response isn’t going to be a friendly response, in most cases. I mean, individuals will be friendly, but on the whole, the community will be very suspicious and skeptical. Every one of these directions I take, I get huge pushback from the community. Takes a long time to get them to really listen to what you have to say.
There’s also funding. We do have the funding issue. Fortunately, as a theorist, almost everything I do is cheap. And as I mentioned, I've been fortunate with especially the Department of Energy in the early stages, that they were willing to overlook the fact that I was going far afield in many of these directions from what you'd call the typical high-energy physics funding areas. And more recently, the Simons Foundation has been remarkably generous in helping on this bouncing cosmology idea, which is really taking off. I can’t say it can’t fail, but it just has so much going for it. The way it’s building up right now, and so quickly, it just—if you talk about a strong feeling, I have a very, very strong positive feeling about this. I don’t mind that people aren’t [laugh] jumping in, but if I were a young person, I’d be jumping into this, because this has so much impact in so many different areas of fundamental physics, and new ideas associated with it.
But I don’t know, I think it scares people to work this way. I think people think it’s harder and scarier than it really is. And there aren’t many models for it. I can’t be prescriptive. Some people say—sometimes ask me, “Do you think I should be looking at something at the interface between”—I don’t know—“condensed matter physics and string theory?” I say, “No, you should be looking for a good question.” If that happens to take you there, fine. But find a good question. Find something that you care about. That you're willing to stay up all night, if you have to, for many, many nights in a row, if you have to. Do whatever you have to do to get to an answer. Willing to go through a wall in order to get the answer to that question. Whatever it takes. That’s the question you should work on. Then, it will involve some areas of physics, some of which you may know, some of which you don’t know.
But you'll find that if you have a wedge question, a question that people haven't asked before—could there be a meteorite that makes a quasicrystal, and people haven't asked that before—or could there be a bounce – questions people haven't really asked that before—you'll find it doesn't take you that long to get to the frontier of that subject. Because you don’t have to know the entire subject. You have to know enough at the beginning to start to ask your question. That’s relatively little, especially since it’s not yet an explored question. So it’s relatively little you have to know.
And then, if it turns out it looks like it’s making some headway, you'll get the feeling, “It’s time to broaden my knowledge. I have to know more.” And you learn more and more as need be. You learn it on the fly. You don’t have to be an expert who could give a course in geology. I couldn't give a course in geology. Yet I know a lot about geology that few geologists know, about my corner of it, what was relevant to me, and what I needed to explore in my problem. And so I think that’s another reason why most don’t take this approach — people think that they have to be an expert to start in the subject. You don’t have to be an expert. You really can just jump in the middle of the pool and learn to swim.
It’s self-evident in listening to you describe the benefits of this approach, that condensed matter helps you understand cosmological issues and vice versa, right?
So that part is clear. Has it ever presented challenges in taking this approach? Just from a resource perspective. There’s only so much time in the day. There’s only so many graduate students you can work with. There’s only so much funding out there. Have there ever been times when you felt like you've bitten off more than you can chew?
I wouldn't say that. Ideally, you like to time these problems so that one problem is in cruise mode, while the other one really needs your attention for invention mode, or getting over a barrier mode. And what’s beautiful is if you can time these things so that everything is in cruise mode except the most important thing for which there is a roadblock you have to surmount. But that doesn't always happen. Sometimes problems collide. And there are moments when things have collided, and, OK, you get less sleep [laugh] for a period of time. But they haven't—they don’t maintain synchrony for long periods of—I haven't had a long period where that has occurred. There have certainly been moments. Especially when you have collaborators both in Italy and Japan, [laugh] that you're communicating with on different problems. So there’s always someone up at every hour of the day.
Those times have been quite intense, something like that going on. But I've managed to—it hasn’t been bad. It’s a good problem to have. Let’s put it that way. That’s a good problem to have, because it means there’s exciting things happening on both fronts. You do have to be able to pick up something, get yourself immediately focused on it, and then when you're ready to switch, drop it and get immediately focused on the next topic. And that’s not something I knew as a student, or a graduate student, or as a postdoc.
I would leisurely—and I think that’s another aspect—you can get to be leisurely about research. You grab your cup of coffee. You relax a little bit. You draw some pictures. You read the paper. You know, you do some things, and then you start to work, and that kind of thing. But if you have several projects going at the same time, it’s more like, “Bam! I'm switching to this project right now! I'm immediately giving it 100% focus.” You wouldn't know that I have the other projects going. And then, if you look at me later in the day, “Bam!” I’ve switched to something else. Giving it equal focus.
So in some ways, I feel like I sometimes fool some of my collaborators and they think I'm focusing 100% on my project with them, [laugh] when I'm doing a lot more of this switching. And sometimes it runs into a little bit of trouble, but it has been manageable. I'll just say it has been manageable.
Paul, I want to take one comment that you said in an earlier discussion and use it as a starting-off point for a much broader question. I'm thinking back to your criticism of—the issues related to multiverses and saying that, to a certain degree, when it’s so untestable, we're outside of the realm of science. It’s not science, right?
So a philosopher of science, or a historian of science would say, “Well, what about the naysayers to Einstein in 1904, who said, ‘This isn’t science yet’?” What mechanisms are you using to be certain, or as certain as you can be, that things that are untestable now are not science, versus it’s not science yet. Right? Without having that crystal ball in the future where obviously there are going to be advances, there are going to be game-changing technological discoveries, theoretical advances, that are going to make the impossible possible. So when you say something specifically about with multiverses, it’s not science, how and where do you draw the distinction between it’s not science, versus it’s not science yet?
I think there’s a clean distinction. I'm not concerned if you can’t test it today. If you can’t test it yet. I'm concerned if you tell me the logical structure of your idea is such that no matter what observation I find, it can never—no matter what I find, whatever I measure ever -- it can never disprove your idea.
The issue with the multiverse is, it predicts literally that there are patches of space which manifest every possible conceivable outcome that the laws of physics allow. Now, if you make an observation, it obviously has to obey the laws of physics. That means anything you observe would be consistent with such an idea. So, for example, the goal of inflation was to explain, among other things, why the universe is spatially flat. But in the multiverse, there’s an infinite number of regions which are open and closed. And in fact, I shouldn't say it that way—I would say which have different degrees of openness, and different degrees of closedness, and each one of them has an infinite number of possibilities. Now, I go out—
—make a measurement, and I discover, oh, my measurement says the universe is flat. Or, I made a different measurement, and I discover it’s open by 30%, or 90%, or closed. Which one of those measurements, in principle, would disprove your idea? The answer is none of them, because they're all possible. And some of the proponents of the multiverse actually boast about that idea. They say, “You can’t disprove our idea, because it allows all possibilities.” I say, “Yeah, that’s exactly what’s wrong with your idea. That’s the problem with it.”
So if an idea is constructed like that, so that it is -- some philosophers would describe it as insulated against any kind of empirical observation -- then that lies outside the boundaries of normal science. Then you're doing some other activity. You're allowed that other activity, but you're not doing normal science.
So it’s immune from history, essentially.
Immune from the future, from any kind of observation. So a usual path in science is you have a theory, you go out and do an empirical test. It agrees; thumbs up. That increases your confidence in that theory. Or two, it fails the test. If it fails the test, you often don’t give up the theory. We know, in the real history of science, that’s not what happens. What happens is theorists come in, and they amend the theory. They immunize it from that particular observation. But they leave other predictions you could test. Then you do another test. If it fails again, OK, again, you can immunize it again, and you can immunize it again. But what happens as you're immunizing it, it’s losing its power. And at some point, if you decide it’s not a very powerful idea, you decide you ought to consider another idea. Or maybe another idea comes up, which doesn't require immunization.
So if inflation were normal science, didn't have the multiverse in it, you might have said, “Inflation predicts that the gravitational waves should be of a certain amplitude.” We discover it’s not, OK? We discover instead this other idea that would explain why you shouldn't have seen them. You have the option of immunizing inflation, tuning it, or going to the other theory. And at some point, you'll decide when you're going to go from one to the other. That’s the way normal science proceeds.
But with a multiverse, you're beginning with an idea that, as a matter of principle, makes no prediction. So you could simply say, “OK! BICEP-2, it found the gravitational waves. Great, I'll celebrate.” And then later, “Oh, it didn't find the gravitational waves after all? Great, I'll celebrate.” Because either of them could happen in a multiverse. Even without tuning extra parameters.
So the problem with that is just what I said—as a matter of principle, there’s no way you can falsify this idea. We don’t prove ideas in science, but we do falsify them, and we force them to be immunized or dropped. And this theory, if you like, is infinitely immunized to begin with, which means it is completely powerless to explain anything. What does it explain? Simons Observatory is about to make a measurement. Do we have a firm answer from inflation as to what they're going to find? No! It could be anything!
You can contrast that with the bouncing pictures. Do they give a firm answer? Yes. Zero B-modes detected! They better not find anything if the bouncing pictures are to survive. That’s the difference between a non-testable theory and a testable theory. And that’s the problem with the multiverse.
So it’s way beyond the question of whether you're technologically capable today of testing the experiment. If Einstein had a theory—and he wouldn't do this, but if he had a theory which in principle, there could not exist an experiment that could test it, then he would also be doing something outside the boundaries of normal science. But that’s not what he did. [laugh]
General relativity was difficult to test. We're still in the early stages of testing it. There’s nothing wrong with general relativity as definite science, even though it has taken us a long time to—
Early stages of testing it is not to say that it’s not testable.
That’s right. But you should in principle be able to perform tests where you should be able to say, “Oh, it’s right”—or that you have to change it or drop it.
All right, Paul. Last question. And I'm a little sad, because it means that all this time we've spent together is coming to an end. But it’s going to have to happen. You've already made clear your current research agenda, and obviously this is going to take you into the future.
My last question is sort of future-oriented. And that is, in all of these threads that you've drawn during our time together, do you see them converging in a way in the future within your career or even beyond your career, that might lead to—you know, these big questions about unifying physics? That everything in physics is working towards unifying all of these disparate theories. Now, in the way that you've discussed it, these are separate threads because they're separate disciplines. And yet physics is working towards its own singularity. And so I wonder if you see either because of your work, or contributing to it, that these threads ultimately at some point in the future are going to merge, or that they should merge?
I'm trying to think of how to interpret your question—that question could be many things. I think there’s various aspects to it. To what degree can everything in nature be reduced to scientific ideas? I don’t know the answer to that. There may be things which are not reducible. They're not subject to science. So I should say, my view is that science is something invented by humans. Before humans invented science, they had various ways of figuring things out. But when the scientific method came along, it proved to be a remarkably powerful way of learning things you didn't know before. That was the importance of science.
People had competing ideas for explaining all kinds of phenomena. There were very intelligent people, just as intelligent as we have today, but they didn't have a good way of sorting out which idea was better. There was mathematics. There was philosophy. But that wasn’t strong enough. So humans invented the scientific method. And that has been a very successful way of learning up to this point. But it’s still a human invention. And it may be limited by our humanity. After all, it’s limited by our senses.
We have to be able to sense something, in order to test it experimentally. Or maybe not. Maybe as computation grows, there will be some new ways of learning things—the power of science is how rapidly we can learn new things. And since it was invented, of course, we've learned science just keeps accelerating the rate at which we learn new things. But I wouldn't promise that that is the ultimate fastest one can do, and that there aren’t ways of enhancing it or doing better than that, that would be more effective.
I'm sort of stepping around your question a bit. I think [pause] the idea that science can unify is another human ambition. But again, there’s nothing to say that it has to go that way. It may be that physicists are only drawn to certain kinds of questions that fit our notion of what makes for interesting physics. That is, we're screening out many phenomena that aren’t easily reduced to the way physicists like to think. If you ask how a car works, or some device works that you're looking at, at a distance, which is more of an engineering question, we're not so good at those kinds of questions, because they're not general universal questions.
There are certain kinds of questions which physics-type thinking is very amenable to. We're looking for genericity. And we don’t know that everything of interest fits within that genericity. So I guess I'm saying—I'm not even sure the notion of unification is a key idea. I think we have a lot more to learn about nature. I always think it’s interesting how some of my colleagues have sometimes claim we're really close to understanding the theory of everything, or some phrase like that. And I always think to myself, we've only been doing this for a few hundred years.
Really? Really we're going to understand everything? Really, is the universe that boring? [laugh] You know? It has no more secrets? Really? It’s the end of science? I mean, sometimes people talk about the end of science. I see no evidence of that. Every time I answer a question, it generates ten other questions. So I just don’t believe in that. So I tend to be, if you like, in this sense, more modest, in terms of how far I think humans have gotten and how far they can get. I do think science is a human enterprise, and it’s something we as humans enjoy doing, and we learn a tremendous amount from doing science. But we're also sort of limited by our humanity as to what models we have, internal ideas we consider to be reasonable. We're come up against that all the time.
You mentioned using condensed matter physics all the time. What does condensed matter physics provide? It provides phenomena that we don’t encounter in our everyday lives, but that are found in the laboratory so we know they exist. Like superconductivity; it exists. We don’t encounter that in our everyday lives. Once you know it exists, you can say, “Oh, maybe there’s something like superconductivity happening in some other phenomena.” It gives us a model, something physical that we can say beyond what our everyday experience has been, that allows us to extend the possibilities of what we might imagine.
So I very much think of science as a human process. And I don’t know what its limits are. But I suspect it is limited. And it may take enhancements beyond the current scientific method to go beyond those limits. There may be things we're missing, because of the current scientific method. We need something stronger, more powerful than simply the scientific method. I wouldn't give up the scientific method [laugh] but I would look for enhancements.
Paul, it’s another way of saying, of course, that there’s a lot to be excited about in the future, and that there’s a lot more fundamental research to be done.
Yes. I think, as I said, every time I think a question is answered,—especially if it’s a good question, it should seed new questions. And that’s kind of my measure of how good the question is. I always had that problem with people, writers who talk about the end of science. I always feel like they don’t get it. Good science doesn't end, because it just seeds new questions, and better and better questions. It’s like a chain reaction. It’s a runaway chain reaction. It’s an uncontrolled chain reaction. So I don’t see it coming to an end in the foreseeable future.
Well, on that note, maybe we'll have to check in, in ten or 15 years, and see where everything is then.
Very good! Hopefully I'll have made some progress.
I hope so.
Thanks very much, David. It has been a real pleasure to talk to you.
And thanks for your patience.