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Interview of Robert M. Wald by David Zierler on October 7, 2020,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Interview with Robert M. Wald, Charles H. Swift Distinguished Service Professor of Physics at the University of Chicago, where he also has appointments with the Kadanoff Center and the Kavli Institute for Cosmological Physics. Wald recounts his childhood in New York, he describes the tragedy of losing his parents in an airplane crash when he very young, and he explains the ongoing legacy of his father Abraham Wald who was a prominent professor of statistics at Columbia. He describes his high school education at Stuyvesant and his decision to pursue a physics degree at Columbia, where he became close with Alan Sachs, who supervised him at Nevis Laboratory. Wald explains his decision to focus on general relativity for graduate school and his interest in working with John Wheeler at Princeton. He describes the excitement surrounding recent advances in approaching astrophysics through relativity, the significance of the discovery of pulsars and the field of black hole uniqueness, and he discusses his postdoctoral research with Charles Misner at the University of Maryland. Wald describes the impact of Saul Teukolsky’s discovery of a variable Weyl tensor component that satisfied a decoupled equation, and he explains the circumstances leading to his faculty position at Chicago, where he was motivated to work with Bob Geroch. He reflects on the experience writing Space, Time, and Gravity, the advances in black hole collapse research, and he explains why he felt the field needed another textbook which motivated him to write General Relativity. Wald discusses his work on the Hawking Effect and his long-term interest in quantum field theory, and he explains the influence of Chandrasekhar on his research. He describes his contributions to the LIGO collaboration, and he explains what is significant about the Event Horizon Telescope’s ability to capture an image of a black hole. Wald explains the state of gravitational radiation research and the accelerating universe, he prognosticates on what advances might allow for a unification of gravity and the Standard Model, and he explains why dark energy is apparently a cosmological constant. At the end of the interview, Wald discusses his recent work on the gravitational memory effect and, looking to the future, he explains his interest to continue working to understand the S-matrix in quantum electrodynamics.
Okay. This is David Zierler, Oral Historian for the American Institute of Physics. It is October 7, 2020. I am so happy to be here with Professor Robert M. Wald. Bob, thank you so much for joining me today.
I’m happy to be here.
Okay. So to start, would you tell me, please, your title and institutional affiliation?
Well, I’m a professor. The official title is Charles H. Swift Distinguished Service Professor of Physics at the University of Chicago. I have affiliations with other institutes at Chicago, but I think that is a mouthful already.
[laugh] Now what is the connection to Charles Swift and your chair?
This one happened to be available, I suppose. Charles Swift was a donor, a major donor 100 years ago or so to the University and endowed this chair. It was held by Enrico Fermi and other distinguished people, so it has a distinguished line to it. But I’m not sure there was any special reason that this was, you know, why I was designated with this chair when I was given a chair 20 years ago.
Now administratively and also physically, how does the appointment with the Enrico Fermi Institute work? Do you spend time there? Is it like a 50-50 kind of thing? How does that all work?
Well, okay. So, I’m a member of the Enrico Fermi Institute. I’m also a member of the Kadanoff Center and of the Kavli Institute for Cosmological Physics. The University of Chicago has a very unusual setup that is hard to explain—especially when people start mixing up the Fermi Institute with Fermilab, which is a different entity.
Right, of course. Totally different.
But at least in physics, everyone is a member of, of course, the Physics Department, but they’re also a member of an institute. Basically, the people in particle physics, astrophysics, general relativity who are in the Physics Department are, by and large, members of the Enrico Fermi Institute. People in condensed matter physics and related fields are members of the James Franck Institute.
In principle, the institutes are responsible for lab space, or office space in my case, and things related administratively to research, whereas the departments are the only entities that are concerned with teaching-type issues. Now, in practice, of course both the Department and the Institute are interested in getting the best faculty. They have to cooperate on this, of course, because they have to act jointly in making new appointments. So, the whole lines of authority and who takes the lead on this is not really very clearly spelled out, and it tends to oscillate with time.
But there are separate faculty meetings of the Physics Department and of the Fermi Institute, and we, in principle, independently decide on appointments, although we have to coordinate so that the person we are hiring is going to be both in the Fermi Institute and the Physics Department. So it’s confusing to explain. If one were setting it up from scratch, I don't think one would do it this way, but it does work overall, and having two bodies involved has—well, it has some redundancies, but it also has some usefulness to it. I can't see that changing particularly anytime in the foreseeable future.
And nowadays with the pandemic, it’s good to be a theorist where presumably you can carry on with all of your work and institutional responsibilities remotely. There are no labs for you to be worried about to be present at.
I think my experimental colleagues were really-- I mean, they were shut down literally from mid-March until, I think it was about the end of June or early July. I mean, no one could go into their lab, so they just couldn't work. While life was unpleasant for me, I could still function fully. I could meet with my students over Zoom. I could do my own work. I got probably a lot more work done than I normally would have because otherwise I would have been traveling and distracted and--
[laugh] You're not the first theorist to say this that I’ve heard, of course. This is actually probably a very productive time for many theorists.
[laugh] Well, Bob, let’s go all the way back to the beginning. I know that it’s a tragic story and it’s a very painful story, of course, but it’s important for the historical record. I’d like you to talk about your parents. Tell me a little bit about them and where they were from.
Well, my father, Abraham Wald, as I was saying in the chat before you started recording, seems to be becoming more and more famous and well-known as time goes on. When my parents tragically died in a plane crash in 1950 while they were visiting India and I was three and a half years old at the time, he was a professor at Columbia of statistics. So, I have very few memories of my parents.
My mother was born in the United States. My grandfather on my mother’s side had died a few years before I was born. My grandmother came from Latvia and immigrated to the United States around the turn of the 20th century. She was born in 1884. My grandmother did a lot of childcare for me and my sister, who is four years older than me, while my parents were alive. She was taking care of us during the whole month-long trip that my parents took in late 1950. My parents went to Europe where there were some conferences, and then my father had been invited by the new—it was only a few years old—government of India to spend several weeks in India touring the country there. It was at the very end of the trip there, after they had been gone over a month, that their plane crashed in a fog in southern India. Since I was only three and a half years old, I have very few memories of my parents, and by now the ones I have are probably more reconstructed than direct memories.
So, your mother was American-born, but your father was born in Hungary.
Yes, my father was born in 1902 in what’s now Cluj, Romania. It was part of Austria-Hungary when he was born, and it would alternatively go by the Hungarian name of Kolozsvár or the German name of Klausenburg. My father’s family was ethnically Hungarian. The area that he came from was a Hungarian area, and Hungarian was his native language.
Did he grow up in a secular household, or were they a religious family?
The family was very religious. Well, my father’s mother, if I have this straight, was the daughter of Rabbi M.S. Glasner, a prominent—actually Zionist—leader in Europe and chief rabbi of Kolozsvár. And my father’s grandfather on his father’s side was also a prominent rabbi of Kolozsvár. The family observed the Orthodox Jewish traditions.
But not Chadishe [Chasidic; “ultra-Orthodox”]?
No, I don't think so. David Glasner would probably know this much better than me. I mean, again, what I know is really just what I’ve read because I didn't have my parents to tell me this. Well, the other part of the full tragedy is that essentially my father’s entire family—except for my father and except for one brother who survived a concentration camp—were killed by the Nazis in World War II.
So, your father survived during the war in Europe. He did not come to America before the war.
He came to America after Anschluss but before the war. My father’s brother did survive the war. The Hungarian Jews were not rounded up to concentration camps until about six months before the end of the war, and he managed-- I mean, there are stories there, too, but he managed to survive Auschwitz for the six months. But my father had left—I’ll call it Kolozsvár—to go to Vienna in about, I’m not sure of the exact date, but roughly 1930 or so to pursue a PhD under Karl Menger in mathematics.
So, his mathematical abilities were well-developed growing up in Europe. This was not something that he began to pursue in the United States.
Yes. Well, the fact that he went to Vienna for his PhD is already--
That isn't something one would normally do if one wasn’t exceptionally talented. Well, he was part of and even ran the Menger colloquium in mathematics, which is quite well-known. It had some connections with the Vienna Circle that was going on at the time, and there were a number of major developments at that colloquium. In fact, Karl Sigmund put out a volume recently of the papers from that colloquium. Again, I know this from biographical things that I’ve read as opposed to things that only I would know.
Bob, is your sense that your father maintained his Jewish observance as an adult or not?
Oh, no. No, not at all.
Was he a bit of a black sheep in his family?
Was he a black sheep in his family in that regard, having these mathematical abilities and not keeping up with his Yiddishkeit [Jewish observance]?
Well, I don't know how observant he was or wasn’t in Vienna. I have no idea, but my own family when I was growing up was not at all observant. Of course, I was brought up by my grandmother, and my grandmother had been originally brought up in the Jewish tradition, but they became quite lax. Anyway, my grandmother was completely nonobservant. My mother and her sister were completely nonobservant, and we—“we” being my sister and I—as brought up by my grandmother, were completely nonobservant.
In fact, the neighborhood I grew up in in northern tip of Manhattan, the Inwood neighborhood, was mostly Jewish at the time. It was actually Jewish and Catholic, but the Catholics mostly went to a parochial school, so the public school was about 98% Jewish, I would say, at the time that I went to public school. I believe I was the only one of my friends who never went to Hebrew school. All my friends after school would go to Hebrew school, so that illustrates how nonobservant we were. And I’m sure this would have come from my parents. If my mother and my father had been at all observant, I’m sure my grandmother would have carried that on.
Now when did your father arrive in America? Was it right after the war?
It was right before the war, and well, of course, being in Austria-- Before the war, it was already very nontrivial for a Jewish person to get a job, but he did things like tutoring a businessman and was okay in that regard until Anschluss. At Anschluss it was clear that Jews had better get out of there if they could, and he was lucky enough very early on to get a fellowship to come to the United States. The Cowles Commission is the name of the organization that offered this fellowship. He was supposed to go to Colorado Springs, I think, but I don't know really even whether he went there at all. But he quickly ended up at Columbia and that’s where he stayed. So, he arrived in the United States in 1938, I guess—I mean, not very long after Anschluss. Of course, he never went back, and he was quite fortunate in being able to escape.
Where did your parents meet?
Well, in New York City, but I don't actually know any details of how. My mother was a high school math teacher. She actually had a master’s in mathematics. In fact, going through old things some 40 or 50 years ago, I came across her master’s thesis. That may have provided some sort of connection, but how they actually met I have no knowledge at all.
What language would they have communicated in initially? Would it have been Yiddish? Did your father have any English coming to America?
Well again, I can't really say how well he spoke English—I mean, he spoke English and wrote in English and taught classes in English. My mother was American. I don't think she would have spoken any other language but English, so there’s no question they would have communicated in English.
You said that you have only vague memories of your parents, and even those might be reconstructions. What do you remember when you try to think of your parents in your memory? What images come to mind?
Okay. There’s one story that is definitely a memory, although the specific way I think of it now could easily be somewhat reconstructed, but this definitely happened, and this is, I think, quite amusing. My father, when he was deep in thought—which he was quite a bit of the time—used to pace back and forth quite a bit. I have been told that I would very frequently ask him for a piggyback ride when he paced, and so he’d put me up on his shoulders while he would be pacing back and forth. On this one occasion that I remember, I was done with the piggyback ride and I wanted to get down but he was so deep in thought that I couldn't get his attention to put me down. [laugh] I believe I started screaming, and I do have a memory of my mother coming into the room and picking me off his shoulders to get me down.
Bob, of course there’s no way of proving this for sure, but you didn't grow up with the benefit, obviously, of learning about them. But to the extent that mathematical ability has a genetic component, do you feel like your talents in physics and theory sort of come from what your parents were able to accomplish?
Well, I mean I have no way of knowing that any more than anyone on the outside would have a way of knowing it. Obviously I wasn’t tutored by my father, so it’s not like I got a big head start on account of that. On the other hand, one probably should also take into account that my father was obviously revered in the family, I mean the extended family. So, the idea that I might want to do something like study physics rather than become a doctor or an engineer or open up a business or something—I think there are a lot of families where they think their kid is crazy if they want to study physics or study mathematics rather than make some money as a businessman. But in my case, I would only have positive reinforcement to the extent I was interested in pursuing an intellectual career. But yeah. I would think that my case might be a good argument for genetic transfer of, say, mathematical ability or something because it is clearly a case where it isn't from my being tutored, but on the other hand, there is a counterargument that I did get a lot of reinforcement to develop my intellectual interests in physics and mathematics.
Bob, would you say that your childhood was happy despite this tragedy? Growing up in your grandparents’ home, did they do the best they could to stand in for the parent figures that you lost?
Well, yeah, although it’s kind of hard for me to know what things would have been like had my parents lived. Now “grandparents” is my grandmother because my grandfather had already died before I was born, so it was just my grandmother, although her other daughter, my mother’s sister-- Well, within the year after my parents died—I don't know the exact date or amount of time—we moved in for a brief amount of time with my aunt and uncle (her husband) and their two children who were about the same age as me and my sister. We all lived together in this small apartment for a brief period of time, and then we got an apartment—that is, my grandmother, my sister, and I got another apartment in the same apartment building. So when I grew up, there was an extended family around of my aunt and uncle and my two cousins, as well as my sister and my grandmother and me. But yeah, it was mostly just my grandmother taking care of my sister and me. I mean, she was a really wonderful person. She was very caring, kind, sweet, very permissive, too.
Did you have any father figures in your life?
I didn't have the feeling as I was growing up that I was greatly deprived. I didn't have the feeling of “Why am I in this situation and all my friends are happy?” I felt basically normal and as though I was in a normal family. In a sense, of course, I was, but it’s really hard to say how different I would have felt if my parents were alive.
Did your uncle or anyone else serve as a father figure in your life?
No, unfortunately not. My aunt was also very warm and caring, but my uncle was sort of much more distant and not-- He had a sense of humor that would go over very well with adults, but not very well with kids, I mean sarcasm and so on. He was not very kid-friendly to me or my sister, I think particularly my sister, really. So yeah, I really did have the absence of a father figure, I would definitely have to say.
Bob, at what point did you start to get interested in science? Was it even before your formal exposure in middle school and high school to science?
I can't point to a time when I wasn’t interested in science, although I don't really remember what I was or wasn’t that interested in in kindergarten or first grade. I was always good in math in elementary school. I didn't have much trouble with arithmetic and algebra and so on as that went on. I recall that I was in a special science sixth grade class, so I had demonstrated in some way that I was interested and able in science by sixth grade to be in that class, but I’m sure I was interested in science before then. I’m sure I wouldn't have been able to say physics, math, chemistry, or whatever, or even biology possibly (although I don't think I was ever that interested in biology), but yeah. By high school, I was definitely interested in—well, I think by then it was probably physics, I would say. When I went to college, I don't think there was ever any issue in my mind when I entered or any time I was there of being a physics major.
Where did you go to high school?
I went to Stuyvesant High School.
Was that the obvious choice and not Bronx School of Science?
No. It’s a funny thing. A person who was my best friend at the time decided to go to Stuyvesant and maybe one or two other of my friends, and that was how I made the decision. I was living closer to Bronx Science, although you couldn't get there as easily by mass transit, so it was a kind of comparable commute. A few other friends of mine at the time went to Bronx Science. I don't recall giving it any real thought beyond what some of my friends were doing and what I heard other people had done.
Was there an entrance exam?
There was an entrance exam, but that was for all three. There were three high schools that required an entrance exam—Bronx Science, Stuyvesant, and Brooklyn Tech. It was the same entrance exam, but I think maybe when you took it, you designated which school you wanted to go to or something like that. I don't really even remember how it worked. I undoubtedly could have gone to Bronx Science if I had chosen that, although I’m not—I mean, my memory of all this is incredibly hazy, so I could easily have some facts mixed up. I don't think I lost anything by going to Stuyvesant. I think I got a good education there. There were some crazy teachers there, but there were undoubtedly some crazy teachers at Bronx Science too.
[laugh] Did you have a good physics teacher at Stuyvesant?
No. I’m trying to remember. I had a few physics teachers in different courses. There was an advanced placement course I took that had a quite a bad teacher. Yeah, I think I had a couple of really quite bad teachers, but again, I haven't thought about these things for many decades. However, there was a summer course I took at Manhattan College—I think it must have been the summer after my junior year. The National Science Foundation was sponsoring summer courses for high school students given at colleges. It was a six-week intensive course. I think the mornings were calculus and the afternoons were introductory physics. It was like at least a one-semester course, maybe a bit beyond that in both of those subjects. So that’s where I really learned calculus and introductory physics. That’s what really gave me a good head start toward college, not the courses I had in high school.
Now when you were applying for colleges, did you know at that point that you wanted to pursue physics? Were you set on physics even before you got to school?
Yes. I don't remember when I made the decision. It certainly wasn’t like one night I was thinking about this or that and said, “Well, let’s try physics.” There was never kind of any doubt about what I wanted to do. Of course, it’s possible I could have gotten to Columbia and not liked the physics classes and really liked the math classes and switched to a math major or something, but I definitely came in as a physics major. In any case, I really loved the first-year honors physics class I had and never thought of switching.
Bob, did you specifically want to stay close to home? Did you apply to schools outside of New York?
It’s hard to believe what the admissions process was like then, with the current way it is now. Nowadays it seems if students don't apply to ten colleges or something…
Right. I mean you can't go wrong by Columbia if you want to study physics, but I wonder if you also applied to places like Princeton and Harvard or even beyond.
Well, we were not allowed to apply to more than three schools. Stuyvesant wouldn't send the transcript to more than three places. It was largely unheard of to apply to schools well outside the New York area. I mean, Harvard or Princeton or schools within a 400-mile radius, fine, or maybe even Michigan, but I don't know of anyone who applied to Stanford or Caltech or even University of Chicago, for that matter.
One of my applications was to City College, and there you would automatically be admitted with a B average or better, so that was my safety school. Then I applied to Columbia, and the third school I chose was Harvard, but I didn't get admitted to Harvard. At Columbia, because my father had died while a faculty member, they made the decision to consider me to be the son of a faculty member and waived the tuition.
Oh, that’s great!
And at Columbia I could and did live at home, too. Plus, I got a Regents Scholarship, which normally is reduced to the amount of tuition or something, but if you have a tuition scholarship (which mine was considered to be), you got the full amount. So, I’m the only one of the people I knew who ended up making money going to college without working. [laugh]
Bob, even from the beginning, did you know that you wanted to pursue theory? Did you try your hand in the world of experimentation and do lab work and things like that as an undergraduate?
[Pause] What I’m trying to think of is what I was thinking in terms of experiment or theory. I think when I came in, I may not have had a clear idea, but of course, I also didn't have a clear idea of what experimentalists really do, and for that matter, what theorists really do. I spent the summer following my freshman year at Nevis Labs. I was helping out in an experiment, but I spent much of my time reading things, and the biggest contribution I made is I came up with a suggestion of how to wire something series versus parallel to get the same magnetic field in case you would accidently put on a couple of extra turns of the wire.
I remember the faculty advisor being extremely pleased with my pointing that out, that if you connected them in parallel rather than series, then the errors would largely compensate out, as I figured out. So even there I was more doing a theory contribution. Anyway, by the time I went to graduate school, there was no question that I wanted to do theory. In fact, there was little question that I wanted to do general relativity theory, even though I only had the vaguest idea of what general relativity was from reading popular books.
What professors as an undergraduate did you become close with?
As an undergraduate, I had an advisor who I liked a lot and who I felt was very helpful. His name was Alan Sachs. I think he may have been supervising me at Nevis. There were a bunch of post-doc type people I worked with at Nevis, and actually one of them was John Peoples, who became director of Fermilab. On the theoretical side, I didn't do any research projects or thesis-type thing or anything like that at Columbia, so I just took courses. There were professors whose courses I liked a lot and who certainly had important influences on me, but I wouldn't say that I got close with them.
Did you ever interact with I. I. Rabi?
No. He taught some science in society course that I took, so I heard his lectures, but that was a large class and I never had anything close, at that time, to personal interaction with him. I did meet him many years later when I came back to Columbia for a visit. He was emeritus but still coming in for talks and so on, and I did meet him then, once, but I didn't interact with him other than shaking hands or whatever.
And you said that when it was time to think about graduate school, you were specifically thinking about general relativity.
This would have been in 1968, right? Where was general relativity at that stage? I know that the subfield had gone through ebbs and flows throughout the decades. Where was general relativity in terms of how interesting it was to professors at the time?
In fact, general relativity was starting to undergo a really major revolution that just completely changed the subject, but I had no idea of that at the time.
Nor would any of the professors that I was interacting with have known about the revolution taking place then. General relativity had been a real backwater-ish subject before then. The Nobel Prize announcement yesterday, in fact, is a very good indication that Roger Penrose’s 1965 paper was a true landmark in the field that really initiated developments that went on over the next decade that totally transformed the field, but I had absolutely no idea of that. So really, John Wheeler at Princeton was, at that time, the only high-profile figure in the United States that was actively involved in general relativity and had a large group.
Which is amazing to think about, that it’s really only Wheeler in the whole country.
Well, that’s not really true. There was Peter Bergmann at Syracuse and Ted Newman at Pittsburgh. Chandrasekhar at Chicago had started working in general relativity around 1960 or so, and he had published a number of papers at that time. And then there were people seeded by Wheeler: Charles Misner, Kip Thorne in particular were forming their groups at Maryland and at Caltech. And, of course, there was a lot of activity in England, Cambridge particularly. Well, Penrose, who was really at a college in London at the time, I suppose. He later moved to Oxford. Dennis Sciama’s group in Cambridge included Hawking and Ellis and Carter. I’m sure I could add quite a number of others. Well, and Bondi a bit earlier than that and Pirani and others. So it’s not like there was nobody doing relativity, but in terms of people with a high profile—
—who if you went to advisors at Columbia or any other school, you know, “What’s a good place to go to for relativity?” I think the answer you’d get would be, at least in the United States, “Oh, Princeton, John Wheeler.”
Was that the advice you got? Did your mentor say specifically, “You should go study with Wheeler”?
I don't really remember, but I certainly knew of Wheeler. I certainly knew that Princeton was a place where relativity was being done, and that put Princeton certainly at the top of my list of where I wanted to go for graduate school. I’m not sure I was dead-set that I wanted to do general relativity, but I think I was pretty well set that I wanted to have the option to do general relativity.
Bob, on the social side of things, you had left Columbia right as things were starting to get very intense with the anti-war movement, the civil rights movement.
I mean, I was there when things got-- I mean, the spring of ‘68 is when the riots and all the disruption took place, so I was there—well, I would say in the middle of that, but because I was living at home, I was not. I mean, I was certainly not on campus at three in the morning when the police cracked down on demonstrators and so on. For at least a week or two after that, I literally could not get on to campus. They were not letting students into the campus who were not living on campus. But of course, I had lots of friends who were. Well, a number of friends who were involved in the building takeovers and other friends who were there when the tactical patrol force attacked the students who were gathered on the south lawn at two in the morning or whenever it was.
Was the draft something that you had to contend with?
Yes. I mean, the Vietnam War was at its height then, and the student deferment for college was in effect and remained in effect, but there had been, until maybe the year before I graduated, a student deferment for graduate school. That was eliminated. Plus they were, at that time, drafting by the oldest eligible people, which means the people who got the college deferments were the most vulnerable. You know, they’d be first on the list for the draft because they would go before people who were just turning 18 years old. What happened is that I was able to put things off after I graduated from Columbia. I won't get into the delaying tactics, but I was able to delay things for about a year and a half until the lottery system went into effect. Given that I can still remember what my lottery number was, that is an indication of how traumatic the whole situation was. My lottery number was 353 out of 365.
Oh, wow. That’s cutting it close.
So I was safe.
Yeah. When you got to Princeton, did you develop a relationship with Wheeler right away, or that sort of developed over time?
No, it developed over time. This story has a couple of cute elements with it. Princeton at the time, maybe even now, had offered general relativity as a course every year, but in alternate years, it would be a one-semester course versus a two-semester course. The year that I arrived it was a one-semester course, so I decided why don't I put off taking general relativity till the two-semester course? There was all this other stuff—solid state physics, all this other stuff I really need to learn. I was kind of looking at it as you spend your first two years sort of preparing for the general exam, which is true. That’s how people did things then, and then you really only start your research after that. The attitude now is you start your research as a sophomore in college, and you can't even get into graduate school if you don't have some research accomplishment by the beginning of your senior year when you're applying. Then when you get to graduate school, you kind of try to join a group the first week.
But anyway, that wasn’t my attitude, and it wasn’t anywhere near as prevalent as an attitude or practice for anyone at that time. So, I put off taking general relativity until the second year and I was really looking forward then at the beginning of the second year to taking it from Wheeler. Then I learned that Wheeler was not teaching at least the autumn semester! Some guy from University of Maryland who was visiting who I’d never heard of was going to be teaching the class, and I mean I was just outraged. Well, that guy was Charles Misner.
[Laughs] That’s a pretty good substitute!
Well, he taught a great course.
I mean, I learned an enormous amount of general relativity that autumn semester, autumn of ‘69. Princeton had Saturday classes then. They had Monday/Wednesday/Friday classes and Tuesday/Thursday/Saturday classes, and I think the earliest one was at 8:00. It’s possible it was 8:20 or 8:30, but anyway, I had relativity from Misner three of those days at 8:00 or something, and cosmology from Jim Peebles the other three days at the same early hour.
[laugh] That’s pretty good!
Yeah. That was a great course, too. But the relativity course—that really jumpstarted me into understanding general relativity. Then Misner was only there for the autumn semester; Wheeler then taught the spring semester, and I found that a total letdown. I was really disappointed—
—at how imprecise and heuristic Wheeler was being in presenting the stuff.
In what way? How was he heuristic?
Yes, he was heuristic. I mean, Wheeler’s real strength was his physical insight. He kind of had some intuition about what would happen with a black hole or what the theory should be saying about this or that. In fact, at the time I really didn't like that style very much. As the years went by—I’m talking more about the 10, 20 years after I left Princeton—I began to appreciate more and more the strength of Wheeler’s way of doing things and how valuable it is to always be asking physical questions—I mean, what happens if you lower this box near a black hole?—as opposed to just try to prove some mathematical result about black holes. Even though I wasn’t that enamored of his overall style at the time, it really did pervade my thinking and really helped me a lot in my approach to research by always thinking about the physics side of what does this observer then see or feel, always asking that kind of question rather than just how do you solve this equation or whatever.
Bob, did you spend much time at the Institute? Was that a place that there would be seminars and things like that that would be interesting to you?
No. I mean, I very occasionally went there for a seminar, but that was pretty rare. There wasn’t, at that time, any general relativity being done at the Institute itself. It was all in Wheeler’s group in the physics department. Well, Peebles, Dicke, and so on were doing things related to relativity, but--
How did you develop your dissertation topic? How closely did you work with Wheeler in settling on the area for you to work on?
Really very, very little. In fact, someone told me that Wheeler’s letter of recommendation for me for my postdoc applications said, “A self-starter if there ever was one.” [laugh] There was just an enormous amount of intellectual activity and ideas about black holes that were being promoted by Wheeler. I mean, the whole black hole uniqueness ideas which caught my attention were something that Wheeler was very strongly promoting.
What were those ideas? What was going on with black hole uniqueness at that point?
Well, Israel had already proven that the Schwarzschild black hole, which is uniquely characterized by its mass, was the only kind of static black hole you could have. Well, Israel actually had thought that probably indicated that you wouldn't have black holes if you didn't have spherically symmetric objects or something, but again, I don't know whose idea came in where. But Wheeler took this idea that he interpreted correctly as showing that a collapsing star would lose its information about its multipole moments when it formed a black hole. He took that as an indication that it would also lose its memory of everything else—baryon number, lepton number—and you wouldn't have these conservation laws and so on.
One of my main interests at the time was to prove that the Kerr black hole was unique. That was later proven by Carter and Robinson, but before Carter’s proof, I obtained a perturbative proof about Schwarzschild of the uniqueness. That was probably the main thing that went into my thesis. I don't really remember exactly where the idea for that approach came from. But the whole idea of “a black hole has no hair”—the way Wheeler would phrase it—was strongly promoted by Wheeler. Wheeler was emanating, radiating those sort of ideas, and putting a lot of enthusiasm into how important it is to do these things.
One thing that Wheeler was absolutely wonderful about is the way he treated graduate students. He treated me (but I think everyone else would say this) as though he were honored to be able to hear my opinion of something. I mean, he was extremely supportive in that regard. If I was telling him something, he would sometimes take notes, and it’s not just me. It would be so easy for someone in his position to do exactly the opposite—I mean, kind of treat students as his minions and tell them to do things and be annoyed with them if they didn't succeed or whatever. He was totally the opposite, and I think the feeling that my efforts would be appreciated was-- I’m not sure that was something I would have consciously noticed at the time, but I think that was very important. That also was important, I’m sure, for all his students and is undoubtedly a big factor in why he was so successful in producing so many students who were extremely successful.
Bob, of course this is a time of amazing advances in physics generally, and I wonder if you could talk about, perhaps peripherally, how some of those advances in perhaps particle physics, in astrophysics, cosmology, observational astronomy—what was going on more generally in the world of physics that may have been relevant as you were developing your dissertation?
Well, actually there was a real lull in particle physics. I mean, papers had been written on electroweak unification and so on, but that-- The Standard Model was really more--
A few years away.
Well, it was verified by the late ‘70s and early ‘80s, but it was not in place when I was a graduate student. And the breakthrough on QCD, I mean asymptotic freedom, was also, I think, around 1973. The period I was in Princeton was ‘68 to ‘72, so particle physics was really in a lull. In fact, I can vaguely remember some kind of townhall meeting between faculty and students at Princeton where some of the particle theory faculty were decrying the fact that there were more students going into relativity at that time than particle physics.
This was a big time in astrophysics, especially astrophysics related through relativity. Pulsars had just been discovered. That was a huge thing when I arrived at Princeton. The discovery of pulsars was ‘67, I believe, so that discovery was about a year old when I arrived at Princeton. And then I think it was probably ‘70 or so that the first x-ray satellite went up, the Uhuru satellite. I don't remember exactly, but by 1971 it had discovered x-ray binaries that likely contained a black hole. So that was a really big thing at the time.
In cosmology, the microwave background had been discovered in ‘64 or ‘65; I can't remember the exact year. So that was a big thing. The big splash it had made had been kind of absorbed by the time I arrived in ‘68, but there were then measurements to try to see whether it was thermal and so on that were going on while I was at Princeton. But microwave background things really became a dominating topic in cosmology only after the inhomogeneities could be measured beginning with the COBE satellite.
How mathematical was your dissertation looking back?
There wasn’t a lot of abstract mathematics in there. I mean, it had this perturbative argument of Kerr uniqueness, and it had a similar thing with electromagnetism, and it had electromagnetic perturbations of Kerr, and it had things about radiation from a charged particle falling into a black hole and so on. The perturbative uniqueness argument was a proof, and I was careful as I could have been at the time to dot i’s, but it wasn’t a theorem that was using some sophisticated geometric methods or whatever. Those were the kinds of things that were indeed being developed exactly at that time—you know, Penrose, Hawking, Geroch—but I hadn’t mastered those methods at the time. The results in my thesis were all mathematical-type results. Well, there wasn’t particularly any data to tie into, at least not the kind of thing where one might say, “This feature shows that this object must be a black hole.” Not that kind of thing at all.
Besides Wheeler, who else was on your committee?
Well, on my committee—I mean, the committee didn't do much other than administer the oral exam, which was fairly, as it turned out, perfunctory. They did not give me a hard time. So, I remember Jim Peebles. I’m picturing the room. I remember Jim Peebles there, and I think Karel Kuchar, but I’m not actually sure who else was there. But if the question is who else was involved with my research, the people I interacted with were mainly the students.
Yeah. In Wheeler’s group, you mean.
Wheeler’s group, and there was an amazing array of students at that time. In fact, the two years that I was doing research, Wheeler was actually on leave my third year while he was writing Misner, Thorne, and Wheeler with Misner and Thorne. Then my fourth year he was back, but he was traveling so much that he was actually, I thought, around less than he had been the year that he was on leave. So, I would really only see him maybe once a month on average for a meeting where I would try my best to bring him up to date on what I was doing, and he would of course offer some comments. Again, he was marvelously supportive and so on.
We would sometimes have these group meetings where everybody in the group would be there, and everyone would give a five-minute report on what they were up to. And of course, if I wrote something up, Wheeler would read the paper and offer comments and so on, but I didn’t get a great deal of direction. I mean, it was partly my choice because I had chosen my own problems to work on, although they were all very compatible with things that Wheeler was interested in. But I was not getting a lot of research direction from Wheeler, which is not a criticism of Wheeler. That’s just the way things operated, and I think by contrast, he was involved in a very significant way in suggesting to Jacob Bekenstein to look at black hole area and its possible relation to second law of thermodynamics.
But the people I interacted with—I mean, Jacob Bekenstein I talked to nearly every day, and we would tell each other about what we were working on. I had fairly limited interaction with Bill Unruh. He was a year or maybe two years ahead of me. I’ll briefly run through a list of others. These were all people that I had some interactions with, but when you sum them all together, it really adds up to a lot. Claudio Teitelboim—he now goes by Claudio Bunster. Bei-Lok Hu. Steve Fulling, who was a student of Wightman’s. I had a lot of interactions with him. A fellow by the name of Bahram Mashhoon I interacted with a lot. He became a professor at University of Missouri. I didn't interact that much with Demetrios Christodoulou, but I overlapped with him a year or two. Others at Princeton with whom I had some interactions and who went on to successful careers were Marc Davis, Niall O’Muchadha, and Stu Shapiro.
Did you cross paths with Bill Press at all during those years?
No. Bill Press was a student at Caltech at this time. He came to Princeton as a faculty member several years after I had left. In the year or two after I graduated, when I was a post-doc, Bill Press, Saul Teukolsky at Caltech were people that I interacted with a great deal, but mainly by seeing them at conferences.
Bob, as a graduate student, you know, you're so focused on your own project, but to the extent that you thought about sort of the major questions in gravitation, general relativity, black holes, how did you see your dissertation sort of being responsive to those broader questions in the field at the time?
Oh, the black hole uniqueness was one of the really major issues at that time. That got largely settled by Carter in 1971, although Carter only considered the axisymmetric case. But anyway, my work certainly fit into what was considered one of the major problems in general relativity. But I was just amazed with what particularly Hawking, Penrose, and Bob Geroch were putting out at a rapid pace in the late ‘60s and early ‘70s and fantastically interested in that, although global methods was not something I was fully up to speed on and ready to do my own work on. But that was something I was strongly following and strongly interested in.
Now your post-doc at Maryland—was Misner specifically your motivation for going to College Park?
Yeah. Well, I think I applied for six postdoc positions. Six is kind of the number I remember of applications I sent out. There weren't that many places, and I got an offer from Maryland. I don’t think I got an offer from any of the other places I applied to. I recall that Jacob Bekenstein got the position at the University of Texas, Vishveshwara got the position at Boston University, and Doug Eardley got the position at Caltech—so it was a pretty competitive job market! I was not the least bit disappointed to be going to Maryland—I mean I wouldn't have been disappointed with the other places, but Maryland looked like it would be (and was) a great place to go.
What were you working on during your Maryland years?
In other words, were you expanding on your dissertation, or this was an opportunity to take on new projects?
I’m a little torn as to how to answer that because in some sense my dissertation was already two or three different projects that I put together. You know, they were related enough that I put it together, and while I was at Princeton there was another project that I worked on on the motion of spinning bodies that I didn't put in my dissertation, but that was a paper I completed while at Princeton. So when I went to Maryland, I continued in the same style and I’ve continued in that style, you know, for the roughly 50 years since then. […]
When I went to Maryland, Saul Teukolsky had just made a really major breakthrough of finding a variable, a particular Weyl tensor component that satisfied a decoupled equation, and the question arose of could you reconstruct-- You know, did that uniquely determine the whole perturbation, because that’s just one component of one object. I realized that that was related to some work on exact solutions that had previously been done, and I was able to adopt that work to show that that component does essentially uniquely determine the whole perturbation. So that was probably one of the major things I did at Maryland. It’s disjointed from my thesis in that there’s no direct intersection, but it’s a very similar kind of question. Obviously knowing a lot about the Kerr metric and so on, which I had to know for my thesis, was helpful for this.
There was another paper involving what the electromagnetic field would look like if you had a Kerr black hole in a magnetic field, but it really was just a little side project. I had realized a kind of trick that would enable one to get some solutions and realized that this solution would be one of the ones you could get from this trick. That paper now has 500 or so citations because the result led to a number of other important ideas.
Now when you moved to Chicago, that was initially a post-doc, but did you accept it on the basis that hopefully it would turn into a faculty position?
Yeah, there was a possibility expressed of a faculty position. But I would have accepted it anyway. I really wanted to work with Bob Geroch, who I just thought was an ideal person to interact with. I mean, he just knew so much, understood so much, could explain everything so well.
Did you know Geroch before you got to Chicago, or you just knew him by reputation?
He gave a colloquium at Princeton maybe when I was a third-year graduate student, and I got to talk to him for at least an hour or so, maybe as part of a larger group, but anyway, I got to interact with him a fair amount there. That led to some questions which we corresponded about—you know, letter writing—over the next year or two, and I think I was able to invite him to come to Maryland to give a talk. He also invited me to Chicago for two visits of about two weeks each. So, we really had interacted a lot before I came to Chicago. He was interested in getting me to Chicago and indicated he would be trying to get me a faculty position. Obviously he couldn't promise that, but I was correspondingly extremely interested in coming to Chicago.
I did not like the idea of being in Chicago or in Hyde Park. It had a largely deservedly bad reputation at the time. As it turned out, it really has improved a lot. It’s a very nice place to live. I’m very happy to have now lived in Hyde Park for over 45 years and have no thought of moving. I like Chicago as a city, but at the time it was at the bottom of my places of where I would want to live, but it was way at the top for where I would want to go.
In fact, I had applied and was shortlisted for a faculty position at Stanford, one that went to Cliff Will, but I remember I was thinking if I were offered this position, I could hardly think of turning it down. But I really wanted to go to Chicago, so I remember thinking that I would ask if I could delay coming for a year so that I could go to Chicago for at least a year or something. I mean, that never came to pass; I didn't get the offer, but that shows how much I really did want to come to Chicago.
Yeah. [laugh] Bob, did you conceive of Space, Time, and Gravity from the beginning as a book that would be oriented toward a more general audience?
That book came about because the Fermi Institute started a new lecture series, the Compton Lectures, to be given by post-docs for the public. Bruce Winstein gave the very first one in the winter quarter of 1976, I guess it would have been, and I was invited to give the spring quarter one. I went to one of Bruce’s talks to just see what they were like, and I noticed he was recording it. I asked him, “Are they recording the lectures?” and he said no, he was just recording it himself because he was thinking he might write this up as a book. My reaction was, “Oh, that’s an interesting idea!” So, when I gave the lectures a month or so later, I very much had in mind writing them up. I may have mentioned it to the director of the Fermi Institute, and they made some contact with the University of Chicago Press. I don't remember exactly how this all came about, but then when I gave the lectures, the arrangements were in place. Then I just wrote it up that summer.
What were some of the most important ideas about Einstein that you wanted to communicate to a broader audience?
The subtitle of the book is “the theory of the Big Bang and black holes.” It was the Big Bang and black holes that were the things I was interested in. Einstein’s name probably barely appears directly in the book because it’s not about what he was thinking or what he thought. There is a chapter on special relativity and a chapter on general relativity in general, but the rest of it is what general relativity says about cosmology, what a black hole is, what its properties are, and what the general relativity predictions about cosmology and black holes are. Then the last chapter is on the Hawking effect, I mean the particle creation by black holes and the fantastic implications that that has. That was what I was intensively working on beginning when I arrived in Chicago. So that was a real change because I had never done anything research-wise in quantum theory or quantum field theory before.
What were some of the developments in gravitational collapse at this point? What were some of the big questions that were being raised?
Well, do you always get a black hole rather than a naked singularity was probably the biggest question in that. That’s another thing I did at Maryland, was look at Gedanken experiments to destroy a black hole. But anyway, I think that would probably by that point have been the major question because the singularity theorems were largely established and there was no question you got singularities. But would they always be hidden in a black hole? I mean, what the nature of singularities are was, and still is, a major question, although not something that I worked on especially.
I think after Hawking’s work in ‘74 on particle creation by black holes, for me that and its implications really became the major question. From the mid-70s on, there was very little work in mathematical classical general relativity, at least compared with what happened from the mid-60s to the mid-70s. There were some major exceptions: proof of the positive mass theorem and so on. Nowadays, I mean the last decade or so, there are a lot of mathematicians that are really starting to prove global existence theorems and things like that that are, in some sense, carrying on the program of determining general properties of solutions to Einstein’s equation.
The work that was done mid-60s to mid-70s was only using Einstein’s equation to get inequalities on the Ricci tensor. The developments of the last few decades are really looking at Einstein’s equation as a system of partial differential equations and using techniques of partial differential equations to say things about the solutions. They can tell you that you won't develop a singularity in certain circumstances, and if you do, more about what the nature of the singularity would have to be. There has been major progress in this direction in recent years and there probably will be a lot of major progress in the not-too-distant future.
Bob, when you joined the faculty, did you start taking on graduate students right away?
Well, I was open to taking on graduate students right away. I joined the faculty in ‘76. There was a large group of students already working with Bob Geroch. Gary Horowitz, whose name you might have heard--
--entered at the time that I started my faculty appointment and I worked closely with him. We wrote several papers together. His official advisor, though, remained Bob Geroch. So, I think my first official student was a little bit after—probably around 1980 or so. I can't remember when he would have started working with me, but it wasn’t until the early 1980s that I started to get a steady flow of my own graduate students.
In terms of teaching undergraduates, what were some of your favorite classes to teach during the early part of your faculty career?
I rarely taught undergraduate classes. Well, in the first 20 years or so of teaching, I was pressed into teaching freshman electromagnetism once, which I did, but I didn't find that a lot of fun. I don't imagine that the students found it a lot of fun. It was a very standard course. I also taught a physics for poets type class but I don't think it was terribly successful. I probably shouldn't divert too far in this interview, but the trouble with those classes is there are-- Well, it was a large class—I mean, 130, 140 people—and there would be 10 or 15 students who were very interested and very talented, another 20 students who were interested and probably talented but kind of afraid of math if you wrote down an equation. Then at the other extreme, there were about 40 students who were only interested in copying the homework and turning it in to get credit. Then there were students in between—you know, not total laggards. They were going to try to do their work, but not very interested and probably not very talented at it. I could not figure out who to teach to.
[Laughs] I guess it worked out well if you didn't have to teach so often.
Yeah. I don't think there is a solution to that problem. I mean, if you're going to try to really teach a physics class to non-science majors, you can teach a kind of history anecdote class and then everybody kind of likes that, although the top group of students will feel cheated. Anyway, I haven't taught that class again. I’ve taught undergraduate general relativity. That class only came into existence about 20 years ago, and now I’ve taught that probably four or five times. That’s been a very good experience, but aside from that, I’m not sure that I’ve taught any undergraduate classes. I mostly teach graduate courses.
What were your motivations in the textbook General Relativity? What was missing in the curriculum that you felt this textbook needed to be introduced?
This is going back far enough in time that I have to try to distinguish between what I was thinking before I wrote the book, what I was thinking during the time I was writing it, and what I’ve thought in the 35 years since--
I mean, was there a standard textbook that needed updating, or was there really nothing of its kind?
Well, okay. Until Misner, Thorne, and Wheeler, there were no modern books, I would say, that incorporated the recent developments—the 1965-onward type developments of general relativity. Well, Weinberg’s 1971 book certainly incorporated developments in cosmology and a few other things, but I certainly wouldn't call that a kind of modern book in relativity. So Misner, Thorne, and Wheeler was the standard text in relativity, and I had no thought or idea of trying to compete with that.
But I found that book kind of hard to read. It digressed so much, and the kind of-- I mean, the book is of course very good. With those three authors—or even with one of those three authors participating—you wouldn't have a book that’s bad or that has incorrect statements all over the place or whatever. But the mathematical layout ideas were really, to me, fairly confusing.
But I wasn’t feeling like, “I think the field needs another book.” That wasn’t at all my thought. I was definitely writing it mostly for me to get my own thoughts all clear because I kind of knew all of the stuff, or much of the stuff that went into the book, but things like the global methods that we’ve already alluded to with Roger Penrose’s work and Hawking and Geroch—I mean, I kind of knew almost all the arguments, but I wasn’t sure. I was vague about how they fit together.
So for the early parts of the book, I thought I could just do a much clearer job of kind of saying exactly what’s true and how this works and so on, but for part two of the book, which is probably two-thirds of the book on advanced topics, I really wanted to kind of, for myself, write everything down and go through all of the arguments. It was a tremendously good experience in that regard. I mean, I really did get to see very clearly what really was shown and known and how the arguments fit together and that sort of thing.
Purely for myself I could have read more and so on; I didn't have to take the effort to write a book. I pictured the role of the book as being very helpful for students who wanted to go into general relativity. I didn’t think that it would be used as a course text. But they could use it as a kind of secondary reference to get some of the advanced topics that aren’t covered very well in Misner, Thorne, and Wheeler, and get a kind of much clearer, to-the-point discussion of some of the more, you know, a more mathematically straightforward discussion of the topics that are discussed in Misner, Thorne, and Wheeler.
I just never had any idea that it would become a standard text in courses, and what I really, really never had any idea of is illustrated by when I went to Brazil a year ago and gave a talk, I had 12 people coming up to me after my talk—I think 12 is probably literally about right—asking me to sign their copy of my book. [laugh] I mean I never expected this would be used internationally. That never crossed my mind.
Bob, given the amount of literature for you to review in preparing the textbook, I wonder if you came across any debates within the field intramurally and how you might have covered them in the textbook.
I wouldn't say that. I wasn’t putting any speculation into the book. The book is 35 years old, and a lot has happened in the last 35 years, but there’s actually very little in the book that I would need to revise. I mean, of course there are more recent developments in some areas that would be nice to have included, and the cosmology section where I talk about current observations is definitely out of date. I do have a section on quantum gravity, but there I’m really just mentioning a few ideas.
I’m not coming down on whether string theory is right or wrong or whatever. String theory was extremely new as a theory of gravity at the time I wrote the book, and it’s mentioned in there. But I wouldn't want to do more than just mention it. So, I only was talking about solidly established results, and none of them have been overthrown or significantly modified. The whole book is written with “This is what general relativity is,” first of all, in the first part, and “This is what general relativity implies about this or that” in the second part. It isn't about “This is what’s really true in nature,” you know.
Bob, the book comes out just on the cusp of the second string revolution, so to speak, so I’m curious how closely you were following developments in string theory and how compelling you found string theory as an explanation for quantum gravity.
I was aware of the developments, and I was certainly following the headlines then, and again, now I am certainly at least trying to follow the headlines. Even following the headlines is difficult enough with literally many dozens of papers on the archive every day.
Did you have colleagues at Chicago who were involved in string theory at the time?
Yeah. Well, Friedan and Shenker were there at the time who were not necessarily so much involved directly with string theory at the time, but with the developments that very much played a big role in the string theory developments. They left not long thereafter, but then Emil Martinec—and not long after that, Jeff Harvey—came to Chicago. In fact, Martinec may have come before Friedan and Shenker left. So there always have been string theorists, and of course, Martinec, Harvey, Sav Sethi, David Kutasov are all at Chicago now, so there is a good representation of string theorists.
What were you taking on in the mid-1980s? What new projects were interesting to you?
Well, probably the most significant were tied in with the Hawking effect, but also Bekenstein’s ideas about black hole entropy and this whole Wheeler idea of what happens when you throw something into a black hole? Can you violate this second law, even taking into account the increase in area? That’s Bekenstein’s work. But Wheeler’s idea was it could violate the second law and how would one get out of that? You could just violate the second law by throwing entropy in.
So the idea is if you just throw a box of matter with entropy into a black hole—you know, do a quick back-of-the-envelope calculation—it will increase the area of the black hole by a lot more than the entropy lost and the generalized second law that Bekenstein had proposed would be valid. But if you carefully lower the box to very near the horizon, then it would seem that you can make the area increase of the black hole as small as you like, and then you could violate the generalized second law when you drop the box in. Bekenstein tried to evade this by proposing that the matter in the box would have to satisfy a bound on its entropy relative to the size of the box—well, and its energy.
We don't need to get too much into the details, but that bothered me a lot, and in the early ‘80s I was thinking about that and came up with an idea that although the Hawking radiation might be small, the fact that this box near the horizon that you're lowering is accelerating would cause it to feel an effective radiation as in the Unruh effect. I realized that that effect would rescue the generalized second law, without the need for Bekenstein’s bound.
So, I was incredibly pleased with this result, and just by chance I was scheduled to visit Vancouver where Bill Unruh is a few days later (within the same week as I had discovered this). So, I was really excited to tell him about this. I was actually going to stay with him and he picked me up at the airport, but I didn't want to barrage him with this on the car ride to the office. So, we talked about various things in the car ride like housing prices in Vancouver and that sort of thing, and continued that discussion in the tea room. Then finally we went into Bill’s office and I said, “Well, I’ve just done some work that I’m really excited to tell you about.” Bill said, “Yeah, and there’s some work I want to tell you about.” I said, “Mine has to do with black holes,” and he said, “So does mine.” I said, “Mine has to do with the Bekenstein bound,” and Bill said, “Yeah! You don't need it!” [laugh]
When he said that, I remember I made eye contact with him, and I think for a microsecond or so, millisecond maybe, I had a real flash of anger of “How did you find out about this?” or something. Then for another millisecond or maybe a few milliseconds I had a flash of panic because I thought he would think that I stole his ideas, and my notes were back in Chicago and all that. And then I realized that neither of those could possibly be true. Then we talked about the idea, and it turned out there was an issue related to it—which came up as we were just chatting about it—that was an incredible puzzle. It made no sense. How would an inertial observer interpret what’s going on when you lower the box? We spent two or three days, the whole time I was in Vancouver, just intensively talking about that night and day, and finally figured it out just as I was leaving.
So we wrote this up together, of course, and that led to a collaboration that went on through the ‘80s. There were related issues. When an accelerating observer who Unruh had previously shown feels he’s in a thermal bath, absorbs a particle, how does an inertial observer interpret that? So that was another very nice paper that came out of that. I can think of some other things I was working on in the mid-’80s, but the collaboration with Unruh was probably the most major.
When does quantum field theory become really a major part of your research agenda?
Well, exactly when I arrived at Chicago in 1974. Hawking’s result had just come out—I think the preprint probably had come out six months earlier or so. I was still at Maryland then. That just seemed like such an amazing result. I decided that that’s what I was going to work on when I got to Chicago, and that’s what I did. So I quickly--
Yeah, and sort of broadly, you’ve remained with quantum field theory ever since. How has the field changed over the past 20 or so years?
Well, in the past 20 or so years some new mathematical techniques, specifically microlocal analysis, have entered the field, which has changed things in terms of enabling one to formulate and analyze how you would do renormalization in curved spacetime in ways that couldn't have been done with the kinds of techniques that people use in flat spacetime. So that’s been definitely a major advance. That’s a thing I was working on intensively with my post-doc at the time, Stefan Hollands, when he arrived. I wouldn't have been able to do this by myself at all, but he knew these techniques and knew an awful lot about quantum field theory and curved—knew a lot about everything! But I was able to direct his energies on this problem and collaborate with him on it. The series of papers we wrote over a four-year period then I think is certainly my most significant work in the quantum fields in curved spacetime domain.
Bob, I wonder if you could talk about your relationship with Chandrasekhar, in what ways he might have served as a mentor to you or what you learned from him or how you may have collaborated with him over your career. Did you know him before you got to Chicago at all?
Well, yeah. I was in Maryland for two years, but each of those two years Bob Geroch invited me to visit Chicago for two weeks, I think both times in early December. So I had spent, well, a week or two; I can't remember now. But I spent several weeks in Chicago while I was a post-doc in Maryland, and of course I met Chandra and talked with him then. Before then, there was some point when I was surprised to hear that he was alive—either when I was a graduate student or when I was just starting as a post-doc, I don't remember. Probably when I was a graduate student, you know, because he’s somebody you read about his work in 1931 and you were surprised he was still alive in 1970 or whatever.
Was he active? Was he still active on the faculty?
Yeah, extremely so. Well, he never stopped working. He did become emeritus sometime in the mid-80s, and I would say that he slowed down maybe the last five or ten years of his life, but slowing down for Chandra would be still working much harder than the average faculty member in their most active period. I mean, he wrote a book on Newton’s Principia. That was just finished before he died. But he was still putting out papers in general relativity even in that period.
What was he like as a person?
Yeah. That’s a very good question to which I do have, I think, a lot of insight because I really did get to know him extremely well. When I first arrived in Chicago, Chandra being there was certainly a plus, but I didn't see him as somebody I was likely to interact much with. I was coming to Chicago because I was enthusiastic about being in Chicago, because I really was interested in interacting with Bob Geroch, who I really did learn a tremendous amount from, particularly the first couple of years I was in Chicago. You know, Chandra I sort of viewed as a kind of very formal, distant person who was very-- When I interacted with him, he was very nice and all that. I never had an unpleasant interaction with him, but you would see him at seminars where he asked rather sharp questions. Anyway, what became very clear within a year or two of my being in Chicago is that, first of all, he’s about as anti-establishment as anyone I’ve ever met.
Which means what? What’s the establishment that he would be anti- of?
Well, okay. What I would say is what he really has a strong allergic reaction to is a kind of groupthink, and if somebody is working on a problem because other people think it’s an important problem, you’ll get some question from Chandra that will probe why you think it’s an important question. You shouldn't be working on something because somebody else thinks it’s important. You should be working on something because you think it’s important, and you should be taking responsibility for whether or not it is important and whether you're working on the right question. There is no one I know who has that strong a view on this issue. Now that isn't so much what I had in mind, but it’s closely related to when I said anti-establishment. Everybody should be an individual on their own, not kind of a group. You shouldn't be taking any orders, I mean marching orders type orders, from higher-ups about what you should be doing or what you should be thinking. You should be your own person.
Although in Chandra’s case, who is the higher-up, though? He is the higher-up.
Well, that’s why it came as such a surprise that he is so against the higher-ups having any control over the situation. I’m not expressing this terribly well, I’m afraid, but it is this kind of level of personal responsibility that wouldn't be inconsistent necessarily with his external appearance or whatever. But it certainly wouldn't be clear until you know him reasonably well that that is such a driving force in his attitude toward science, and just the whole way he lived his life.
So, Bob, what were those most compelling issues to Chandra at the end of his life? What was he working on before he died?
Well, I think the last ten years of his life, his main effort was to understanding Newton’s proofs in the Principia and how they would compare with modern proofs. In general relativity, he was interested in properties of plane wave solutions and solutions related to these by mathematical transformations. In the last ten years his main collaborator was Valeria Ferrari from Rome, who visited here many times during the collaboration. I can't remember exactly what issues were the primary things driving what he was working on in the last decade of his life besides the Newton Principia work, which really was the main thing. But he was continuing to write papers, relativity papers. He never stopped, even though he claimed, I think, many times that he was stopping or was going to stop.
What was your inspiration for the symposium honoring his life in 1996?
Well, I’m not sure how to answer that question. He was somebody who if he passes, you're not going to say, “Okay, too bad. Now time to get back to work.” I think I certainly felt the need and many others felt the need to recognize his existence and his passing and to memorialize that in some way. Then we had another symposium in 2010 to commemorate the hundredth anniversary of his birth, and again, the same—we haven't forgotten him, and we shouldn't forget him. I think it was appropriate to do that. The symposium shortly after his death—I mean, he had requested that there be no memorial function, so that really was strictly a scientific symposium. There were no talks about Chandra himself. It was all talks about scientific work of interest to him—I mean, talks in general relativity that one might have thought would have been of interest to him. We bent that a little bit by 2010. I think his prohibition of no memorial service, I think, after 15 years, we could bend. It was appropriate to bend a bit on that and include some historical talks and talks that made direct reference to him personally.
And in 1996, given that you were able to convene people like Stephen Hawking and Penrose and Martin Rees, really it’s a state of the art opportunity to talk about the cutting edge of the field at this point.
So, I guess on that point--
We had, I believe, zero declinations of the invitations. Yeah, and if you look at the list of speakers, it’s--
Yeah. I wonder—So, Bob, what came out of that symposium just as a historical marker in terms of where the field was at that point?
Well, I’m not sure that the symposium has some historical significance in the way that Solvay conferences would where some new development that nobody had known about before came up and was discussed. I don't think there were any startlingly new ideas that were presented at the symposium. There were a series of really very good talks, up to date, state of the art by the leading people for sure, but—I was extremely pleased with that as a way to memorialize Chandra without having a memorial function.
But it’s not like there was some new-- It wasn’t the kind of working conference where some new ideas would get developed. It was talks by leading people to an interested audience, but not a kind of working conference the way Solvay meetings of the early 20th century were.
Bob, was there any point in your career when cosmology was sort of front and center in your research agenda?
Well, it’s been sort of front and center on a few occasions for lines of research. I did some work with Bill Unruh after we had started the collaboration that I described, and with Gene Mazenko who is at Chicago—this was also in the mid-80s—on conditions for inflation and arguing that if you had inhomogeneities, you wouldn't have the appropriate conditions for inflation to occur.
About ten years ago, I had a student, Stephen Green. In collaboration we looked at the issue of whether large density inhomogeneities as observed in the universe could affect the expansion of the universe. We argued that it couldn't, but other people had been arguing that it could. So that line of work with Stephen Green—we wrote I think three fairly lengthy papers—was the main thing I’ve done in cosmology recently. That certainly is cosmology—maybe not cosmology closely tied in with observations or galaxy formation or things like that. This was more of a general relativistic theory application to cosmology, but that’s again another situation where I would say that for a three- or four-year period I was working mainly on that cosmological project.
When did you become involved in the LIGO collaboration?
Oh, I joined the collaboration about three years ago. I’ve been a member, and if people get this transcript, I can probably say I’ve been definitely a member in good standing and I pulled my weight appropriately, my weight being I’m at the 10% level, which is the lowest level allowed. 10% is supposed to be that 10% of my research time is devoted to LIGO-related things. That may be a stretch, but not too much of one.
But the reason that I joined is-- Again, I think I probably won't get kicked out for saying this. My former student, Daniel Holz, who is now a faculty member at Chicago, is a prominent member of the LIGO collaboration. The first year or so after the discovery, it was a very awkward situation because I’d want to talk to him and he’d want to talk to me about some of the things that were going on, but he’s not allowed to talk to somebody outside the collaboration about any of the new observations. If there was some new puzzling event that they saw, he would have loved to bounce off, you know, “Do you think this could be this or that?” I’d love to hear these questions. Okay, but he can't do that. He’s not allowed to tell me. He can come in and hint at, “What if hypothetically one were to find this or that,” you know, or “Hypothetically, do you think it’s possible for…” And then I can't go to his group meetings because they’re going to discuss LIGO stuff, and I have the same problem talking with his students. So, it just solved all the problems to have me be a member of the collaboration.
Was the detection of gravitational waves in the course of your career—was this the most satisfying experimental demonstration of a theoretical prediction in your career?
Well, I don't know. I think the binary pulsar had, certainly to my satisfaction, demonstrated the existence of gravitational waves. I mean now--
Mm-hmm. That begs the question, then, what’s the big deal with LIGO, of course.
The big deal with LIGO is astronomy and astrophysics and cosmology. I mean, this is a new tool for observational astronomy and astrophysics. I don't want to say that we didn't need to see gravitational waves. I mean, it’s fantastic that LIGO saw gravitational waves. It’s amazing and it’s technologically truly, truly amazing, too. It’s a wonderful achievement. A Nobel Prize is the least one could do for the kind of thing that’s been achieved, so it’s not-- I don't want to sound like I’m poopooing it, but what’s interesting is that we’ve learned that there are black hole binaries and lots of them of 20, 30, 40 solar masses. We may learn from that how they’re formed, formation mechanisms. We can use the gravitational wave observations for many other things. Particularly for neutron stars, if there is an optical counterpart, and even if not, we should be able to use it to measure the Hubble constant. It certainly might be at least competitive with other methods for measuring the Hubble constant. I mean, this is a new window of astronomy, and that’s what’s exciting to me.
Bob, earlier this year when a black hole was finally observed, what was your reaction to that as somebody who has been working with black holes for so many decades? Did it change anything for you, that there was now something that was not purely theoretical?
Well, okay. So when you say black hole was observed, are you talking about Event Horizon Telescope, you know, the image of a black hole that was obtained a year and a half ago? Well, the Nobel Prize was just awarded yesterday--
--to Penrose and to observers who over the course of the last two decades, observed stellar orbits around the center of our galaxy and thereby established that there is some 4-million, I think it is, solar mass object there that’s within 1,000 Schwarzschild radii. So, what could that be other than a black hole? Well, they’re receiving the Nobel Prize for showing that there’s a black hole at the center of our galaxy. It was already known for M87, the one that the Event Horizon Telescope took the image of, that there was a billion or so solar mass—extra amount of mass in the center there, and it’s an active galactic nucleus and there isn't-- There’s no plausible explanation of that other than it being a black hole.
So what I’m saying—I’m not poo-pooing the Event Horizon Telescope. That’s incredibly exciting, and I’m incredibly excited about it. LIGO is incredibly exciting and I’m incredibly excited about it, but LIGO is incredibly exciting from my point of view, as I’ve just said, not because it directly detected gravitational waves, though that is really nice, but because you can do astrophysics with it.
And the Event Horizon Telescope, as far as I’m concerned, is not incredibly exciting just because it found a dark spot at the center that corresponds to what we would expect with a black hole there and thereby gives further confirmation to the presence of a black hole, although that is really nice. I mean, that’s absolutely great. But from my point of view, what’s really exciting about it is now we can study the astrophysics of the matter that’s around the black hole. So that bright area, that’s the interesting thing, and that can test our theories of black hole accretion and formation of jets and so on. That can teach us a lot about astrophysics.
I have to say the view that you're expressing—you're not really expressing a view, but kind of where the question was coming from—seems to be how nearly everyone else in the physics is reacting. I mean, wow, there’s the black hole! Now we know there’s a black hole. Well, as far as I’m concerned, we already knew there was a black hole there, and if you're going to go out on a limb to say that the previous evidence didn’t show that there was a black hole there, I don't know why you should believe it now just because there’s a picture with a dark spot in the middle. I mean, you’d have to be saying general relativity is wrong; all this other stuff is wrong.
But Bob, it’s sort of like saying, you know; “We always knew the Higgs was going to be there, so what’s the big deal of finding it when we do?” Is that a fair comparison?
It’s not really because we believed that the Higgs was there, but we didn't know its mass and didn't know for sure what its properties are. There are lots of different Higgs models, and of course, maybe the whole idea is wrong.
So, you're saying that the observation of a black hole doesn't necessarily teach us more about black holes?
Okay. So, this is a good question. And what’s the difference between observing the Higgs and observing black holes? The main difference is here in the black hole case, we have a quite well-established theory. General relativity, now, of course it’s not established in all circumstances. Certainly we don't know what happens near singularities, but that shouldn't be relevant if we have black holes. It’s not proven that the singularities always have to be contained in a black hole, but there’s lots of theoretical evidence for that and lots of reasons to believe that. So if you believe in general relativity, then you should expect a black hole to be there, and there’s plenty of the circumstantial evidence that it’s there—I mean, much more circumstantial evidence than there was for the Higgs particle or something, to push that analogy.
So why is the image of a black hole—I’m asking a partly rhetorical question—why is that stronger evidence than the evidence that Ghez and Genzel got the Nobel Prize for studying the stellar orbits near the undoubtedly black hole at the center of our galaxy? I think there are a lot of issues one could raise about the image reconstruction by Event Horizon Telescope if you really wanted to doubt that there was a black hole there. You could probably point to more things with the Event Horizon Telescope image of what they could have gotten wrong than what you could point to with Ghez and Genzel, where there’s nothing major you could point to that they plausibly could have gotten wrong. You have to come up with how could there not be a black hole when you have all this mass within 1,000 Schwarzschild radii?
But if you had a theory where you have four million solar masses or whatever it is in 1,000 Schwarzschild radii without there being any bright emission or anything like that from this object, if you have a theory of that, I would think you can make up a theory as to why Event Horizon Telescope would end up with a dark spot in their image. Again, I think the Event Horizon Telescope is incredibly exciting and I am really excited about it, but it’s not like I doubted that there was a black hole before, and this proved to me that there was.
I think their-- I think essentially no one seriously doubted that there was a black hole there, and it is really nice, then, to have the image be in complete agreement with what you would have expected. But if somebody didn't believe the black hole was there, I’m not sure why they should after the Event Horizon Telescope…
If they’re worming out of it in all these ways from the other evidence, I can't imagine they wouldn't be able to worm out of the Event Horizon Telescope evidence, either. But I think the Event Horizon Telescope really is exciting because now we can actually start to see details of the accreting matter.
Maybe we’re able to see details of jet formation—that’s not well understood at all—and really learn a lot about astrophysics. You know, the Event Horizon Telescope people will tell you, “Now we can test general relativity,” but I think that’s, at this point, nonsensical. We ought to assume general relativity and test astrophysics, and if the astrophysics doesn't make sense, then maybe we go back and see whether we need to consider the possibility that maybe general relativity is wrong. But we understand general relativity; we don't understand the astrophysics.
I gave a talk a year ago to the Event Horizon Telescope people at the Black Hole Initiative place and had this sort of discussion. I wanted to really emphasize this point. I had some more technical results to be talking about as well, but I had a half-hour to an hour discussion with Event Horizon Telescope people just saying, “What is really exciting is not the black hole but testing the models for accretion.”
Well, I’m really glad I asked the question because clearly this is something you’ve been thinking a lot about. Slightly different area, Bob. What’s the state of your research on gravitational radiation?
Well, I haven't done terribly much on gravitational radiation. What I have done a lot of work on what you might call radiation reaction effects. In general relativity, a really small, very low mass body will move on a geodesic of the background metric. That was actually a hypothesis originally that Einstein made, which now you can really prove within the theory. You don't need to assume it as an extra assumption as he originally did back in 1915 or so. But to the extent that the body’s mass is not zero, that won't be true. There will be deviations from geodesic motion, which you can think of as due to forces that the body exerts on itself, which you can also think of as being associated with radiation that the body is emitting. So, I’ve done a lot of work on that—some work with my student Ted Quinn a little over 20 years ago, and then a lot with my student Sam Gralla a little over ten years ago. I have not done anything significant on this since Gralla left.
Bob, in what ways has your research been important to work on the accelerating universe?
Well, at least if you believe the conclusions that Stephen Green and I drew, which you should because they’re correct, there has to be a cosmological constant, or maybe it’s some other dark energy that’s really a form of matter or something that isn't quite a cosmological constant, but there has to be something like that. It can't be caused by the density inhomogeneities that we observe in the universe. We were countering the proposals that had been made that these large density inhomogeneities would change the large-scale behavior, the expansion of the universe on large scales. I don't think much of the cosmological community had believed those arguments, but I was very pleased with our work because we came up with a nice perturbative scheme to treat these high density inhomogeneities that could be useful for other purposes.
Well, we actually adopted an idea that a former student of Bob Geroch’s, Greg Burnett, had originally introduced 30 years ago, but anyway, that could be useful for other applications as well. But I don't think this had much impact on the cosmological community because I don't think they believed the people in the first place who were claiming that the large density inhomogeneities would produce an effect. But I think it’s nice to have looked at that and I think shown quite convincingly that density inhomogeneities cannot be responsible for the observed acceleration.
Bob, this is necessarily a forward-looking question because, of course, there’s much work that needs to be done here. What, in your view, is necessary to get to a more fully quantum theory of gravity? What work remains to be done in that field to get there?
Yeah. Well, it’s possible that the approaches that are being taken—I mean string theory most prominently or loop quantum gravity also quite prominently, you know, that those have or are taking us there, but I’m not at all sure. There has definitely been important and interesting mathematical work done in pursuing these approaches. There has been an enormous amount of work that’s been done in the last 20 years that’s relating conformal field theory to anti-de Sitter spacetime and so on. There’s been an enormous amount of interesting ideas, but I’m not sure where this has taken us. You know, there are basic questions in quantum gravity of are there local observables? If so what are they, and if they’re not local observables, then what is the theory even about, because you can talk about S-matrices and so on, but that’s really some idealized observation of some idealized observers. I mean what I’d like to know is what I see. What predictions does the theory make for what I observe, I personally observe the universe to be? That is what I’d like the quantum theory of gravity to tell me.
Now maybe the quantum effects aren’t important now, but if I really imagine myself still alive but near the Big Bang, what would I see? But to within my ability to understand present theories, there isn't any presently available theory that’s even capable of posing the question of what a local observer sees. You’ll find people making statements like that, but they’re kind of inferring that from some S-matrix-ish thing or some other more abstract thing, and it’s not clear that the inference is justified. Quantum field theory in curved spacetime has a well-defined set of local observables and is exactly of the nature of quantum theory as one would understand it in other contexts and so on, but it treats gravity classically.
I’d like to see quantum gravity be able to address these questions, and I do mean address as opposed to answer. I mean, I’d like to see an answer, too, but I would be very happy with just addressing questions relating to what a local observer will see, which I would think would mean defining local observables of the theory. But there are severe problems with doing that arising from the fact that the metric itself is the dynamical variable. Those problems were there when I first heard of quantum gravity as a graduate student, and those problems are there right now as far as I can tell.
Bob, an even broader question than the last one. Is that to suggest that these fundamental questions surrounding gravity—do those need to be understood as a precondition to figuring out how to unify gravity with the Standard Model? In other words, is that grand unified theory not even plausible before working out these ongoing questions within gravity itself?
Yeah. I mean I would think so. Who knows? Of course--
Or the other way of looking at is could you--
I wouldn't stop people from trying to get the grand unified theory first and then trying to answer the questions that I just talked about second. Things can work differently than one would imagine. Eventually, to say you have a quantum theory of gravity, you have to be able to say what a local observer would see, or at least for me to recognize it as a quantum theory of gravity, I think you have to do that. But it doesn't mean that you have to answer that question fully first in a pure gravity context and then move on to grand unified theories. Maybe you do the grand unified theory without having an answer to that question, and then you kind of get the insight you need for the other questions. The way that all works and fits together gives you some clue as to how to answer these other questions.
And similarly, do you think further advances in understanding what either dark energy or dark matter are more likely to shed further light on gravity, or do you think it would more likely work the other way around?
Well, I think dark matter seems to be ordinary matter—I mean, not ordinary matter that we know about, but some matter obviously not interacting with electromagnetism and not interacting much, if at all, with itself. But it’s probably some new type of particle, and if we can find out what it is, that will be great for particle physics. That will be a major breakthrough in particle physics, but it may not tell us anything we don't already know about gravity. I’d be very surprised if it tells us anything about gravity. I don't think it’s a modification of general—you know, that there’s no dark matter, really, but general relativity is wrong. I mean, there are some MOND—if you’ve heard of that—proposals modifying gravity, but I don't think those work. The overwhelming prevailing view is that those don't work. So I think there’s overwhelming evidence for dark matter and it will be a breakthrough in particle physics when it’s discovered.
Dark energy seems to be a cosmological constant, and if that’s the case, then of course that raises the question why does it have this bizarre value—you know, this bizarre, tiny, but nonzero value? I don't know that we’re going to be able to answer that without some other breakthroughs in physics. If it’s not a cosmological constant, it’s certainly very much like a cosmological constant, so that, again… Again, I don't think there’s any chance that this is a modification of general relativity, but some other form of matter, a scalar field with some very tiny self-interaction potential is an awful lot weirder to me than a cosmological constant, even though the cosmological constant certainly seems to have a very weird value.
But anyway, if one could distinguish between the two and find that it’s really a scalar field, that would be another breakthrough in particle physics. Again, I’m not sure it’s going to tell us anything about gravity and I’m not sure that there’s anything more to be learned about gravity until we get to the quantum regime, which as far as the present expansion of the universe is concerned or the structure of galaxies is concerned, I don't think we’re anywhere near a quantum regime. But the major questions in cosmology are the ones you mentioned. What is dark matter, and is dark energy a cosmological constant or something else, I think are the questions most people-- They would be at most people’s top of the list, including mine, of what things would you like to have answered.
Bob, throughout the discussion, you’ve mentioned sort of in the narrative some of the graduate students that you’ve collaborated with. Who are some other graduate students that you’ve had that have been very successful in their career, in their work?
Yeah. Well, I mentioned Gary Horowitz, who is technically or officially not really my graduate student, but we collaborated a lot. David Garfinkle is a faculty member at Oakland University in Michigan. Curt Cutler was another student in the 1980s who is a JPL scientist and continuing to work in gravity, particularly gravitational wave physics. Steve Anco was a student of mine around 1990 or so and is on the faculty of Brock College in mathematics. Michael Seifert is a professor at Connecticut College. Daniel Holz, has certainly been extremely successful and is a fellow professor at Chicago now. Sam Gralla, who as I mentioned, I collaborated with on self-force, is on the faculty of the University of Arizona now.
I’ve had several recent students who are post-docs now, Stephen Green and Kartik Prabhu. They were excellent students and should have careers in physics if there’s any justice. [laugh] I’ve also had many excellent students who decided not to continue in the field. Vivek Iyer and Ted Quinn decided, largely for personal reasons, not to go into the field. They each could have at least gotten post-docs. Vivek collaborated with me on black hole entropy work, probably my highest-cited work. And Ted Quinn worked with me on self-force back in the late 1990s. Again, I had many other excellent students who just did not go on in the field at all.
Bob, just to bring the narrative up to the present, what have you been working on in recent years? What are the things that are most interesting to you currently?
Well, I’ve worked a lot in the last five years on the gravitational memory effect. I’ll just say what it is and then say what I think is particularly interesting and what I’m working on now with one of my current students. When a gravitational wave goes by, if you have a pair of test particles, they will kind of oscillate relative to each other. The ones here will oscillate out of phase with these in the polarization I’m drawing. If you have a faraway detector (to leading order in 1/d from the source), after the gravitational wave has passed, these test particles will go back to being at rest with respect to each other, but they won't go back to their original configuration. They’ll be sort of sheared relative to their original configuration like you might see in a snapshot of them while they’re oscillating, but they’re done oscillating.
Well, it turns out that when you do a quantum analysis of the gravitational radiation, when you think of this in terms of a graviton state, the memory effect will occur if and only if in the quantum theory there is an infrared divergence in gravitons. In other words, this effect of the permanent displacement is expressed in the quantum theory by there being an infinite number of very low energy gravitons emitted. So it’s a kind of strange description, and this, though, gives rise to the question of how you deal with this in a scattering description.
This issue has come up in quantum electrodynamics. My interest in this came from the gravity side, but there’s an analog of this that’s been known since the early days of quantum electrodynamics. People have found various ad hoc ways of dealing with that—well, even some non-ad hoc ways of dealing with the infrared divergences in quantum electrodynamics. I think my student and I are coming to the conclusion that the one nice way of dealing with that in quantum electrodynamics looks like does not work in gravity, and it seems like there may not be any way to make it or anything else work, either, which to me would suggest one shouldn't think about the S-matrix as fundamentally describing the theory.
There’s no problem making the predictions all in terms of local observables. This ties back to what I was saying earlier. So you can describe what’s happening at late times seen by distant observers all perfectly well in terms of what all the local observables are, but giving a description in terms of free gravitons may not be possible or sensible. Anyway, I’m not yet claiming that’s the case; that’s what we’re looking at and that’s what we believe at the moment.
Well, Bob, for the last part of our talk, I’d like to ask sort of a broadly retrospective question and then one that sort of looks to the future. So in your field, the many fields that you’ve worked in, right, mystery is sort of front and center, you know, the great unknowns about how the universe works. So I wonder if you can reflect over the course of your career—you know, obviously not going back to Einstein, but in your career—what are the things that you’ve worked on where, from your time as a graduate student, really were not understood well at all, and over the course of both advances in theory and in observation are really well understood now? And then on the flip side of that, what are the things that—and we’ve touched on this a little already—that remain sort of as mysterious or poorly understood as when you first came up against these concepts in the late ‘60s and early ‘70s?
Well, again, almost everything I’ve done is in general relativity, and that has the anomalous property of the theory is completely well-defined. We are unable to mathematically work out all the predictions of the theory and even its general properties. As I mentioned much earlier, a lot of mathematicians are now looking at Einstein’s equation as a system of partial differential equations and trying to get a lot of general properties. But we have the theory and are just trying to work out its consequences. So that’s unusual in physics.
Of course, particle physics has had the Standard Model for quite some time, and that kind of works too well in some sense because you kind of understand everything that you are able to observe in experiments using the Standard Model. But the Standard Model, one knows for sure, is not going to keep working at higher and higher energies. Now maybe you have to get up to Planck scale or grand unification energies to see it break down; maybe it will break down earlier. Prior to the Standard Model, there were all sorts of questions like why do we have this kind of particle? It seems to fit in this pattern, but how does this all really work? Before QCD, what’s the basic mechanism of the strong interaction? There were just a lot of total unknowns that now I think one could say one understands all the outlines of and could probably calculate almost anything with a big enough computer or whatever.
But general relativity has in some sense always been in that situation since the time I was a graduate student, so the bigger questions really just have to do with do you always get a black hole when you have gravitational collapse? The singularity theorems tell you that you always have a singularity, but must it be in a black hole? Well, I mean that might get answered eventually with the partial differential equation techniques, but there are little things you could do to test that and probe that.
So, let’s see. I’m not giving an especially coherent answer to your question, but I guess more to the point of your question, there aren’t that many mysteries about general relativity. There are mysteries about cosmology and there are certainly mysteries about particle physics and there are definitely mysteries about quantum gravity. But most of those are too ill-defined to really work on directly. Like you could ask what happened before the Big Bang, or was there even a before? Well, that’s a good question, but how are you going to answer that? What is quantum gravity? Do you have local observables? That’s what we were talking about before. Well okay, but I don't know how to attack that.
I mean, cosmology, we’ve just learned so much more about the details of the universe and have constructed a simple model, the standard model of cosmology, that does an incredibly good job of fitting all the data with only a few parameters. But you can start asking did inflation really occur or was it something else? Again, you might stumble on the answers to those questions by some weird detail in the cosmic microwave background being discovered that can't be explained nicely with inflation, but could be explained with some other theory that somebody else comes up with. Who knows how this will work?
But those kinds of things are usually—I mean, those big questions are not things that are usually terribly fruitful to try to work on directly. Definitely in my own experience, what’s really fruitful is you have this little question that has some twist to it that doesn't seem to make sense: how do you explain that or how do you even go about calculating this or how does this much smaller idea work? That’s what often leads to the bigger ideas. Very often some kind of side question in looking at a more mundane, smaller idea spins off into something that really gets very interesting and leads to some new idea. But that’s hard to predict, so…
Well, I’m definitely not trying to give advice to others or anything, but looking back, that-- Well, the judgment call of what to work on is by far the hardest thing to do. Usually what is most fruitful is finding some sort of smaller question that has some mysterious aspect of “I don't really understand how this could work,” or a situation where one argument would tell you, “You should get this result,” but this other argument would tell you, “You should get that result.” Which is right? Finding a good question like that is what, in my experience, leads to the most fruitful outcome and often some new unexpected idea.
Bob, on that note, looking ahead either in general relativity or in the way that improving our understanding of general relativity will be useful to physics more generally, for you personally, what are the outstanding questions as you look to the remainder of your career that are most compelling, that you want to spend your time on, not just because they’re most interesting, but because there is plausible chance of really continuing to make fundamental discovery in the field? What are those topics that are most compelling to you as you look to the future?
Well, okay. So, I think what I’ve just been saying is that I’ve kind of never approached the research that I’m doing in terms of what is the most likely thing to lead to some fundamental advance in the field. It’s always been, “Gee, this is a little odd. What really does happen under this or that circumstance?”
But there are still choices you have to make. You still have to choose what to work on.
Right. Well, for example, as I just described, I’m right now looking at the ideas that have been used to make sense of an S-matrix in quantum electrodynamics, and as I say, the belief is that that won't work in gravity. What are the implications, then? If you don't have an S-matrix, what would be an efficient way of describing scattering and what states should be allowed and things like that. That to me is a very important question. Now, that’s not going to tell you what happened before the Big Bang or how to quantize gravity or what’s dark energy or whatever. But should we be giving up on S-matrices except as some side comment in the theory for special cases where it might be useful to introduce an S-matrix? That isn't the prevailing view in physics. That could lead to some major shifts in viewpoints that could lead to other things.
Anyway, it definitely is of interest to me. So I think that is a very good example of the kind of thing that… Well, it is an example of what I actually am working on now, but a good example of the kind of thing that I like to work on. It’s a finite-sized question that should be possible to answer, and the answer might very well have some broad implications. That is certainly the way I would approach things. Now if you ask me to make a list of questions I’d like answered, probably not plausibly in my lifetime, then I’d go back to my earlier list of what happened before the Big Bang, etc. But those are not things that I’m going to work on because I don't have any ideas that are likely going to lead to an answer to that.
Well, we’ll all have to stay tuned for all of that. [laugh] Bob, it’s been such a pleasure speaking with you today. I’m so glad that we connected. Your insights over so many areas are so vital for the historical record, and I just really want to thank you for spending this time with me today.
Yeah! Okay. Well, it’s been interesting for me too because there have been at least a dozen thoughts that have come up in this discussion that haven't entered my mind for decades, so it’s nice to think about some of this stuff.
Well, in that regard, mission accomplished. That’s great.