Warner Miller

Miller:

Well, I first met John Wheeler, actually he wants me to call him Johnny now; he says he's reached that age and has that stature that I should call him Johnny or else I pay him a nickel every time I forget and call him Professor Wheeler. I first met Johnny in the fall of 1981. He came to the University of New Mexico in Albuquerque and gave a seminar on the foundations of quantum mechanics and the gates of time and very deep issues in physics.

I had just finished undergraduate school at the University of Maryland and was an active-duty Air Force officer at Kirtland Air Force Base, also a full-time graduate student at the University of New Mexico. I was a little anxiety-stricken knowing that there was more in physics for me than was there at the university and in the Air Force, and it was sort of a serendipitous state of affairs that someone,that Johnny, came and gave a superb lecture. That didn't settle me at all. In fact, it made my anxiety level go up another few notches, and set me off on developing what was to be sort of my introductory pitch to John Wheeler to become a student (it was an ultracold neutron delayed choice experiment). And that experiment was the longest lived, largest great smoky dragon, as Wheeler puts it, in quantum theory, that was available at the time.

It was practically doable at the time. That was just the beginning. I then went to a conference in San Antonio sponsored by Prigogine's group. I went as a student of Marlan Scully (he was at the University of New Mexico). I went down there with Marlan Scully and shared a room with Professor Manfred Fink, which was at the hotel. Manfred Fink was a professor at The University of Texas.

Well, John then did a number on me. I guess my anxiety level went up another few notches being with him. I knew in my heart that Texas with John Wheeler was the place that I really wanted to be and where I could really grow. He has this magic about him. As a student, you hear this so many times, that as a student, when you come into John Wheeler's presence, he makes you feel like you're a valued colleague, a lifelong valued colleague.

Well those aren't just words, that is an honest-to-God truth, and I'm a witness to that. Being with him at San Antonio really set me off onto the course of moving to Texas. Fortunately, the Air Force cooperated and sent me to Texas; unfortunately, with Manfred Fink. I worked in his laboratory, as I was an experimentalist, but in the back of my mind I knew that John Wheeler was the person I needed to see, and eventually got in to meet with John Wheeler (got my courage up and presented my idea of an ultracold neutron delayed choice experiment).

Well, John Wheeler was already in his seventies. It was in the early spring of 1982. I told John that I was interested in sharing an idea I had with him, and sat down with him and began to go through this experimental procedure. I worked at Argonne National Lab, I knew the ins and outs of the accelerator, how to produce the neutrons. I knew the ins and outs of the delayed choice experiment because after interacting with John Wheeler at the conference I gave a talk back at Kirtland Air Force Base on delayed choice experiments and the Einstein-Podolsky-Rosen experiment.

There was energy seeping in to me from that early time, and I gave him this very elaborate experiment. All the details were there, and I mentioned the word moderator at one point, because you needed to send these neutrons through a moderator to get the lower energy neutrons that I needed. There John very quietly mentioned that he introduced that word moderator into the physics language. Then I went on and talked about the neutron interferometer and delayed choice experiment.

The delayed choice part of it was an idea, a concept, that John Wheeler captured to really bring the mysteries of quantum mechanics out in the open, illuminate those. I put all these pieces together and said, "Well, I would like to become your student," and John said, "Well, this is very interesting. I want to see you pursue this research, but I'm getting a little older and I'm reluctant to take on any new students." Then I mentioned a little bit about the situation I was in where I had an opportunity to work on experimental high-energy physics and measure the mass of the neutrino,(I was actually involved with Tom Dombeck in the neutrino experiment at Los Alamos, the predecessor of the one that actually measured the neutrino oscillations recently. And I mentioned my interest in his probing of the foundations of quantum mechanics in the theoretical physics area that I had never really been exposed to.

He basically told me, "Well, you'll have to make decisions in your career and plan them out, and those are very important." That sent me out of his office energized with the delayed choice experiment and thinking about making decisions in my life and knowing that he just was really not in a position to take on a new student. I went off and thought and came back to him, scheduled another appointment to see him.

I was crafty enough to say that I wanted to talk to him once again on this idea, give him some feedback. I came back into his office and basically told him I made my decision. "You told me to go off and think about what would be the best decision for me," I told Johnny. "The best decision I can make would be to work with you."

[Addressing JAW now as the reader of this transcript] I didn't expect your response, but you sent me out to Zelda Davis, the secretary, and you put me on the payroll. That was the best decision I ever made in my life, and brought me in with fellow student Arkady Kheyfets and with Ignazio Ciufolini and Roberto Bruno. The environment that you, Johnny, created at The University of Texas I haven't experienced anywhere else in academia or in the national laboratories, and I am continually searching for that environment. People say that you can't teach anyone anything, but you can provide the environment in which they can learn. I guess that's one of the things, John, that I think you create, an environment where people feel very much like pioneers in science, and explore the strange nature of the world around us. As a student(let me go on a little bit) as a new student of yours, let me just highlight three important interactions we had. As a new student, you took me for a walk across the campus of The University of Texas to the LBJ Library Museum and you pulled out a videotape from the Sesquicentennial celebration, and you emphasized the "can-do" attitude that you felt at The University of Texas. But more importantly, you made it absolutely clear to me that the students . . . That was the beginning of our scientific relationship. I never forgot that, and I'm hopefully going to build that type of environment at a university myself and mold it after your good example. I'll find a way to bring a student for a hike, a new student, and instill that into that student also.

Second, I remember that you would sit down with me (I don't remember exactly where it was, it was at a fountain somewhere on campus) and you told me, "Warner, in physics you can go down well established avenues and work on problems that are of interest today, but what you really want to do, and what we really ought to do, is take an odd-angle cut across physics. Bits and pieces of information from very diverse areas you wouldn't expect to filter into your problem are what sometimes provide the major breakthroughs." So I've never forgotten that second feature, of taking an odd-angle cut across nature. It doesn't help so many times with careers, with my own career, but it's the way I do physics and it's very personally rewarding. I wouldn't do it any other way. So I have to thank you for that.

The third thing I learned from you early on as a student is that "a picture is not a picture without a frame on it." One part of this is that you have to push the envelope, schedule yourself for talks, give yourself deadlines, deadlines with publishers. I remember that picture you had showing a scene from revolutionary times. I don't know the exact date of the picture or what it's all about, but it's in colonial [times] and shows a firing squad with a poor guy being shot. You said, "If I don't meet the deadlines of my publisher, this is what's going to happen to me, Warner." So that's very important, and it all ties in. A picture is not a picture without a frame on it. Along those lines, you always instilled in me the importance of language. When you start a research topic the language is an integral part of that research, and you have to give it a title. And I can ask you, Johnny: What's the title of the book you're writing with Ken Ford? But you have to have a title for the research that you're working on. You sort of paint in your mind's eye. First you put up the banner, the title, on this lot, and then, in your mind's eye, you construct the different buildings and what you are going to do with the land, the raw land that you are dealing with. The construction tools are not the tractors and the bulldozers and the masonry, but the English language, and the use of the words in new ways. I have learned a lot from you. I have my black notebooks around, which you gave me to start me off as a new student. I put all my thoughts and daily interactions into them. I also keep the thesaurus and dictionary right next to me when I'm writing papers, and I thank you for that.

Those are the three important things that you taught me. Now I'll now shift gears. My research, my interaction with you at Texas: Johnny: You decided to cultivate my research. It ended up not being foundations of quantum mechanics, it ended up being theoretical work in general relativity. We forged our topic at High Island. I remember the title you first gave it, "Harbingers of Einsteinacy." I guess that was your way of showing me how important a thesaurus was, but at the same time Janette vetoed that topic, and thank God we settled down on 4-geodesy, or spacetime geodesy, which later on became null-strut calculus. You decided that it would be good for me, and I thank you for this. It really helped me, my communication skills.

You decided that we would do our research in this four-dimensional spacetime triangulation, this 4-geodesy, entirely in the car, without me being able to pick up a piece of chalk and go to a blackboard and draw pictures for a while. So you would have this daily schedule with me, where you would call me up in the morning. (I'm going to let you in on something that I've never let you in on!) You would call me up in the morning at 7:00 or 8:00. Kathy tells me it was 8 o'clock, but it was early for me. (I'm telling you this very reluctantly) 8 o'clock in the morning and the phone would ring. I would be in bed asleep, and I would clear my throat the best I could to sound bright, because if I didn't sound bright I knew you would feel guilty and wouldn't come by and pick me up because you'd think I needed the sleep or something. You would say, "Is this a good time, Warner?" Every morning the same line, "Is this a good time, Warner?" and I would say absolutely, "Yes, Johnny, I've got a lot of things to say to you." At that time it was "Professor Wheeler," but, "Johnny, I have a lot of things to say. Come on down, I'm ready." I would jump into the shower, take a 10-second shower, and rush down to the sidewalk, because I knew you were only a few minutes away. And I would have to completely get ready for the next question, the same old question every day, day in and day out, "Warner, what's new?" That takes a clear mind.

If you just woke up a few minutes earlier, that's a tough thing to learn, but I thank you for that. That really teaches you to be on the ball. I thought I was in the military before I came to Texas, but you, I guess, really taught me what military life was about. So we would get in the car, and we would discuss what was new, and the next question is, "What do we do next?" We discussed what I would work on during the day, and we developed quite a language. Many facets of our research together taught me that the language we use is an integral part of science. And I don't think people appreciate that as much as they should. And that's one of the biggest contributions I would think that you've given to physics, through coining the phrases black hole to moderator, and I just can't begin(we could build a dictionary on the terms you've introduced into science).

In so many ways they form a paradigm for all the other scientists, for how they view nature. This is your insight and your intuition that has been on the mark for so many years that you come up with the correct words that enable us to make advances, and with those, forge the right paradigms in which we work and think. Well anyway, we would go to school and Johnny, I would sometimes just have to catch the bus and go home to sleep because I was up 'til 2:00 in the morning working on the question of "what's new?" for you. It really helped, and that's a little bit of our interaction. Also I should mention to you that you've instilled in me the history of the United States and the importance of trains and railroads, because every time we'd pass under the railroad tracks on the way to school when a train would pass by you would just light up, and the energy would jump a few notches; that would be always an exciting time.

On our trips to Aspen, Colorado together you would always seek out the nearest railroad and the history of the railroad in the town, because that was your way of mapping in your mind's eye the development of the growth of the state and the towns and cities we were in. That's just a side bar. Johnny, among the things that come to mind here is your involvement in explosives, involvement with explosives on the 9th floor of a 17-story building. One morning Roberto Bruno was working on the relationship between topology and Mach's Principle in general relativity, and you were so excited about some connection that you two made in a discussion, that you came out in the hallway with excitement in your eyes and said, "Warner, here's five dollars," as you took it out of your wallet, "Go get me some firecrackers, because there's a breakthrough here." I ran out and there were no firecrackers to be found in Austin. But I had some fireworks at home.

Any good student of yours would have fireworks at home stored in a box somewhere. They weren't actually firecrackers; they were these big Texas bottle rockets. So I brought in the Texas bottle rockets, and was a little bit disappointed that they weren't firecrackers, but you didn't care. You ran out into the hallway(we couldn't believe it). In fact, I would be interested to learn from you, you could send me a postcard, whether you had any fire marshals call you up the next day. So you went out in the hallway, told the secretaries to stay in their office, and sent the graduate students, I was one of them, down the hallway to make sure there were no other students or faculty members that were going to pass through the hallway, and you let that bottle rocket off in the 9th floor of the physics building, and it shot down the hallway from north to south and stuck in the bottom of a door on the opposite side of the hall.

Well, we learned a little bit about the excitement of a breakthrough in physics, and hopefully I can get away with that maybe some 20, 30, 40 years in the future. I'll never forget that. There were other stories that we heard, secondhand in my case, of you setting off fireworks in classes that you taught at The University of Texas, Roman candles with the sparks flying on the floor and students up on top of their desks avoiding the sparks. Anyway, that was exciting. And when you invited me as a new student to Maine, I don't know if this was a way for you to test me [laughs], but you gave me matches and a firecracker. It was just after Janette went to take her nap, and you sent me to the hallway and you said, "Why don't you go in that hallway there and light off this firecracker?" Oh yeah, Johnny, I would do anything you asked me to do. So I guess that was your test.

I don't know, I may have failed it. So I went, and as I was going to break the match off, I looked over my shoulder and you were running out the back door. I was abandoned. But I lit the firecracker and ran out I wasn't going to stick around. Thank God it was a dud. I guess maybe you knew it was a dud. You'd just see how far I would go. I'll never forget that; it was exciting. As an afterthought: We started my dissertation research on null-strut calculus there at High Island. I mentioned that earlier.

Let me shift gears a little bit here and talk about the research group. I mentioned earlier the research environment you forged at Texas. That was the best environment that I've ever had, and my colleagues that I keep up with, the ones to whom you introduced me, also say that. Arkady Kheyfets, now a professor at North Carolina State University with tenure, was in the group. He was an odd fellow. He ends up now being my best friend, and we write papers together all the time. You forged the beginnings of that friendship.

It's sort of ironic that an Air Force officer during the Cold War would become best friends and colleagues with a Russian immigrant. We had a unique perspective on the world and peace, and I can tell you we predicted the end of the Cold War much sooner. I got to respect the Russian people more than I think any of my fellow Air Force officer colleagues had a chance to do. Arkady was very much a mathematical physicist, and that was some of the vitamin C content that you always talked about(a good group always has to have good vitamin C content.) What you meant by that is diversity.

Arkady was a very mathematical physicist, mathematically oriented, but with keen physical insight. I guess he's the Roger Penrose our generation, and you saw that in him. I don't know how, but you saw that in him. There was myself, with a background of high-energy experimental physics, I suppose with a lot of energy and eager to learn and not afraid to ask people questions. Then there was Roberto Bruno; I mentioned the work earlier that he was involved in. I don't know where he is now. I haven't kept track of Roberto, and I don't know whether he actually received his Ph.D. from you. He may be down in the Panama area now.

Then there was Wolfgang Schleich, who was a postdoc you brought in. He was a former student of Marlan Scully. He added a totally different perspective to our group in the Center for Theoretical Physics there at Texas. He was a hard worker, German through and through, showed great respect for us students. I was surprised. I guess that rubbed off a little bit on you. He would talk to us and interact with us, and he took some of your comments(you were working on squeezed states with him, quantum states which were squeezed in momentum space, stretched out in configuration space). Wolfgang would sit down, listen to your intuition, and I never saw so many pages of detailed calculations that ended up in an actual result, confirming your intuition and your simple "poor man's" way of looking at it. I learned a lot from Wolfgang. I learned to sit down and do lengthy calculations.

Continuing with the group: There was Philip Candelas. We students never really interacted too much with him at The University of Texas. The fields were a little bit different, our directions were a little bit different. Then there was Benjamin Schumacher, Ben Schumacher, who is now at Kenyon College in Ohio. He was the one of us in the group that sort of carried on the torch that you started with Bill Wootters on information foundations of quantum mechanics; how much information you can push down a quantum channel, distinguishability arguments in quantum mechanics. The diversity in your group was tremendous. Another person that I interact with on a weekly basis still, or monthly basis, is Ignazio Ciufolini. Ignazio came from Italy, worked previously with Ruffini, I believe, and was very much interested in measuring the gravitational field(very much in my heart, with my experimental background).

He came up with the idea of the Lageos 3 satellite experiment to measure the frame-dragging effect, or the gravitomagnetic effect. That still hasn't been measured, but that idea that came from Ignazio's mind while he was working in the group there at the Center for Theoretical Physics has involved many years of my life since then. In fact, I'm still pushing for a launch vehicle with Ignazio. We're writing a joint proposal this month to push that experiment further. Just the interactions and the circuitry of interactions that you established during those few years in Texas were amazing.

There are others I'm leaving out. Bill Wootters would come to visit. In fact, you would always have an influx of visitors, with again a diversity that you established there in that research group. Bill Wootters would come in and charge us up and get Ben Schumacher going. Bill Wootters and Ben Schumacher are very close colleagues right now, friends, to this day. I believe Bill Wootters is at Williams College. Then perhaps the biggest impact you had on my life was inviting Professor James York from the University of North Carolina out to The University of Texas, because he taught me what you taught me: that if you want to start on the subject, such as general relativity, you don't start on Page 1 of the bible of general relativity(the Misner, Thorne and Wheeler book(you just jump in with two feet right in the middle of things). And where you jump in is geometrodynamics.

Johnny, I think that geometrodynamics is your school of general relativity. Only a couple of schools exist, and I'm proud to be a member of that one. So I learned from Jim York, who solved the initial value problem under your direction, under your guidance at Princeton. He taught me what I know about general relativity. I didn't have much time to learn it. I started studying general relativity in the late fall of '82 and had to give my qualifier on null-strut Regge Calculus in March of '83. So I had to pick up the subject of general relativity in just a few months.

But your geometric approach, your multifaceted way of looking at general relativity, your little tidbits emphasizing the work of Gauss, that you didn't have to think of spacetime as embedded in some higher dimensional object. Those gems of thought that reach back into the history of science are so important, they lay the foundations, the strong foundations, for studying a subject such as general relativity. The way you taught me general relativity seems sometimes so simple, so much easier than the astrophysics that I'm involved in with Stirling Colgate. That's because you made it clear; you unraveled the subject.

I think, in all honesty John, you brought relativity into the census; in other words, from some esoteric theory into a practical tool. Let me use your own words. I asked you in a recent Marcel Grossman meeting, "What's the future of general relativity in your opinion?" You mentioned that it may be an engineering science, that we may use it in gravity wave astronomy to probe nature, more of an engineering science. That would not have happened if it wasn't for your geometrization of that subject and your multifaceted way of looking at things, looking at things from many different angles, and only then understanding the true beauty and the depth of the subject.

Ford:

Let me interrupt with a question regarding the research group. To what extent did Wheeler interact significantly with other faculty members as opposed to his own group of students and postdocs? Steven Weinberg, for instance was there. Did they have much to do with one another?

Miller:

There were vehicles for interaction at The University of Texas. One was the lunches at the Center for Theoretical Physics. John would have us all come in, the students and some professors. Richard Matzner would show up; other members of the Center for Relativity would show up on occasion. Those lunches were amazing. We would come up and no one would know what the subject of the day was; it would just evolve. And be spontaneous.

The students would be put on the spot. I had to derive the ground state of the electromagnetic field one day on the blackboard. I don't know how you got me to do that, Johnny, but it was a learning experience. That was one mode of interaction. Another mode of interaction was through the astrophysics lunches that we had at The University of Texas at the Faculty Club, and I thank you for bringing me to a few of those.

I remember at the astrophysics lunches you would have discussions with Steven Weinberg. He would go to the lunches. Also Richard Matzner, Prigogine on occasion would be at these lunches, and of course Craig Wheeler and the astrophysics group at The University of Texas. As far as other interactions with a professor, you had professors in your office, they would come to you, and I noticed that. It was my perspective, I was a student, but I would notice that the professors would come to you and interact in that mode also.

John, as far as I recollect the research that was alive and kicking and evolving at The University of Texas when I was there, my work was primarily centered on null-strut calculus. That was to take Regge calculus, which you worked on with Tullio Regge in the late '60s, early '70s at Princeton, take that and build a tool, a computational tool, that would solve Einstein's equations in astrophysically or cosmologically relevant situations. The whole goal of this research was to really build a tool that we could solve problems with.

Once again this view of engineering, relativity as an engineering science. However, along the way interactions with other colleagues led to much deeper insights for me in relativity. In fact, I have a very unique perspective on studying relativity through that research. So that was one area, null-strut calculus. The second was the work of Arkady Kheyfets with you. The theme of that research was austerity and the laws of physics. In particular, you were quite animated at the bottom, at the foundation. There was nothing, a tautology, a trivial identity, zero equals zero, some topological identity. The closest thing you came to that that I'm aware of is this boundary of a boundary principle; that is, literally, zero is equal to zero, the topological identity. That occurs, as you mentioned, twice over in each theory, each field theory we know(once in its 1,2,3-dimensional form and then again in its 2,3,4-dimensional form.

Arkady worked on this issue of austerity in the laws of physics, and in many ways with you nailed that problem and unified electrodynamics with general relativity. On the surface, they look very different(in MTW [Misner, Thorne, and Wheeler] for example, the book on gravitation(but it was Arkady and you who really unified that, and took a reinterpretation of the Maxwell tensor as a scalar value 2-form, transforming that in a 2-form value scalar, using very deeply Cartan's geometry, the geometric picture of space and time. Ignazio Ciufolini came up with what became the top ranked experiment in the space test program within the Department of Defense, and a very active satellite experiment, still a proposed experiment, is his Lageos experiment to measure the frame-dragging effect around the earth.

The idea behind that is that just as a current in a wire produces a magnetic field, a dipole magnetic field, so too Einstein says that a current of matter spinning(the earth, for example, produces a dipole gravitational field or gravitomagnetic effect. That causes a precession in the orbital plane of satellites, over and above the procession due to the oblateness of the earth. In the case of Lageos it's 1 part in 107. This dipole gravitational field, 1 part in 107, is a very difficult effect to measure, but Ignazio came up with an idea of canceling the classical perturbations, launching two satellites, a tandem pair of Lageos satellites. One was launched in 1976, the other one, Lageos 3, would be hopefully launched by the turn of the century. So the effect has never been measured and is astrophysically quite relevant to the Bardeen-Peterson effect. Accretion disk alignment mechanism around black holes, for example. Wolfgang Schleich worked with you on quantum optics, on understanding squeezed states in quantum mechanics. A beautiful way of looking at it.

Once again you've done the job, and given a poor man's way of looking at it in terms of phase space in Bohr-type diagrams and intersections, and Wolfgang's augmentation of that with quite detailed calculations that predicted some new effects which they measured later on. They're still having meetings at the University of Maryland on this subject to this day, and you were right at the beginning of it. That tied in quite a bit with Kimble's work at The University of Texas at that time. He was doing some squeezed state measurements of light down in the basement of the RLN physics building. I'm leaving people out here. It's difficult, there's so much diversity in the group at Texas it's hard to keep track of what everyone did.

Roberto Bruno, as I mentioned, was working on the deep relationship between topology and Mach's Principle: Was there some way of having, yes, topologies and no, topologies in quantum gravity or in general relativity by using Mach's Principle as a sieve to rule out some and not rule out others? I didn't follow that research. Harry King came in. I can remember only a little bit what Harry King was doing, as he came in almost at the end of my tenure there. He was not in this photograph that I showed Ken Ford. But Harry King came in, a former engineering student who left his career in engineering to start physics, just like Jim York in a way, who left his career in engineering and came to you as a postdoc at Princeton. Quite impressive.

Harry King worked on taking Jim York's initial value equation, his steering equation, the constraint equation, for the conformal scale factor in general relativity, and, term by term, understanding geometrically what that was all about(a "poor man's" way of really getting a handle on that equation and understanding that equation. Jim York is still animated by that research topic that you set out for Harry King. A very deep subject. Ben Schumacher worked on how much information one can pack down a quantum channel. Very close to your own heart in looking at the information-theoretic foundations and underpinnings of quantum mechanics in your attempt to get a deeper understanding of Bohr's view of the world and his understanding of quantum mechanics. Maybe a view deep enough, built on the concepts of distinguishability and bits of information, yes's and no's, that one could marry those deeper concepts with the deep concepts of general relativity. Maybe that's what is where our understanding of space and time from a quantum point of view will be born. I agree with that, and I think that it's going to take many, many years for people to appreciate. I'm tainted(?), Johnny. I have to agree with you on that one. I may be crazy, just as crazy. I think that gives pretty much an overview of the types of research that were conducted at the Center for Theoretical Physics.

Ford:

Warner, have you any knowledge or understanding of John Wheeler's change of perspective on the black hole from the time when he thought a true singularity could probably not exist to the time when he became a believer.

Miller:

John, I was not around at that time, when you were discussing these issues, but I can tell you my perspective, for whatever it's worth. If it's helpful then good; if not, then you can ignore this. You follow Bohr's style of research so many times, and you capitalize on paradoxes. I can't think of a more severe paradox in physics than a singularity in the fabric of space and time. But you also have this tendency to push a theory to its extremes.

You do this in quantum theory, you do this general relativity, you do it in everything you've touched. And so it was sort of obvious to push general relativity to its logical conclusion, to these singularities. And black holes you call them, or the gates of time, where the fabric of space and time then lose their meaning, break down. Again, I don't know your thoughts on this, but I very well suppose that you embraced that prediction of general relativity when you realized that nothing could stop the gravitational collapse classically. Quantum mechanically the jury is probably still out. I haven't studied this well enough, but I could if you wanted me to look into it.

The fact that time and space lose their meaning means there must be something deeper, more fundamental, something more fundamental that transcends time and space. When I came to work with you, I guess that's the mode you were thinking in, that's the paradigm you presented us students with(something deeper that transcended the concepts of space and time. I remember you introducing me to the book Critique of Pure Reason by Kant in this connection. In fact, among books you introduced me to, here is another one I have sitting on my desk in front of Ken Ford and myself. I guess you thought I was lacking a little bit of skills in diplomacy and so you had me pick up and read the Autobiography of Benjamin Franklin. That's a good guide for an autobiography, because it really helped me out. I hope your book helps other people out in the future.

Ford:

Can you give me a kind of a layman's general explanation of the phrase that Wheeler has used, "the boundary of a boundary is zero."

Miller:

Let me describe the boundary of a boundary in terms of Einstein's theory of general relativity. I'll start off with the earth. Say you're an equatorial man, and you have a spear, and you decide one day that it's just too hot down on the equator and you want to head north. So you take this spear and you head north, always carrying the spear in front of you, never moving it to the left or to the right. I'm speaking of a gyroscope, but I won't mention that word. You carry it up to the north. Following the longitudinal line, you get up to the North Pole, and you decide then it's too cold, so you take a right hand turn, and you know that you didn't have any scary moments, events that happened on your journeys to the north, nothing dangerous, so instead of taking the effort to tilt that spear around, you keep it where it's pointing and just turn right yourself, you make a right hand turn, and you head down to the equator again, always carrying the spear at your side, with the pole pointing to your left. You carry it in two hands.

Again, you never rotate that spear. So you walk down to the equator, you get down there and you decide, "Yes, this is where I want to spend the rest of my days." But you're homesick. You want to go back to your village, and you're now a quarter of the way around the equator because you took a right hand turn. So you go back along the equatorial line and now you know you don't carry the spear in front of you along the equator, but you'd better carry it pointing behind you, because people are jumping you from behind. So you take a right hand turn once again, and luckily for you, you don't have to turn the spear. It's pointing behind you now, because you took a right hand turn. You walk back to your village, and it's fortunately uneventful.

You greet your friend there, and he says, "You've turned your spear. It was pointing up north when you left. You turned it 90 degrees. It's now pointing along the equator, toward the east." And you say, "No, I can assure you that I didn't turn this spear once in my journeys around the earth." Well, it turned 90 degrees, /2, and you circumnavigated an area (/2)r2 of the earth, where r is the radius of the earth. So the angle that that spear turned, or that vector turned, divided by the area circumnavigated is 1/r2, which is the curvature of the earth. So curvature makes these vectors or spears turn. And that's the measure of curvature. Well, relativity is about curvature of space and time. Let's look at this room we're in. It has walls and corners and faces. So take a vector(and let's not deal with these spears, let's take a gyroscope for this vector(and we parallel transport it. In order words, just like we're walking up on the earth, and bring it around the ceiling of the room and bring it back to the corner. Ordinarily there's curvature. Just like on the earth, it's going to be rotated by an amount.

You take that same vector and you bring it around the other five faces of this room, with due regard to the orientation, and you bring it back to that same point, is there going to be a net rotation? No. There is going to be no rotation. It's going to be zero. That's because you went down an edge of the room an equal number of times as you went up the edge of the room. Zero net rotation. That is, the one-dimensional boundary, the edges of the room, of the two-dimensional faces, the walls and ceilings of the room, of the three-dimensional cube, the room we're in, is zero. The boundary of a boundary is zero. There are no unexposed edges. You go up an edge and down an edge an equal number of times. That, in formal language, if you wrote out all of the equations with the curvature tensors, gives you the contracted Bianchi identity in general relativity. It sounds high-falutin', but it's nothing more than an identity, that the boundary of a boundary is zero.

If you try to build Einstein's tensor, it was Elie Cartan, and Wheeler taught this. This is not taught in graduate school, Johnny. This should be taught in courses in general relativity. You want to build Einstein's tensor for this room. Well then you taught me that you pick not the rotation, this bi-vector, this rotation vector you get from the ceiling of the room and how you build the Einstein tensor, but it's a moment of rotation, built up (?) as a torque. The sum of torques for the room. So pick a point in this room, say Ken Ford's nose, as a fulcrum, and take a vector from the tip of his nose to the center of the ceiling, and take a vector and rotate it around the ceiling of the room. You get a bi-vector, and then you have this other vector from the fulcrum, from his nose to the ceiling, and that forms a parallel pipette.

If you sum all those moment of rotations or torques up for all the six faces of the room and take its dual, that's equal to the amount of energy momentum or density of books, us, or my computer, or my desk, the telescope, the pictures, my black notebook(that's equal to the amount of density of mass energy in this room. The Einstein tensor has two indices. One index is this dual of moment of rotations, the other index is the orientation of this room. In this case it's a timelike oriented volume. And the moment of rotation, we can ask for the timelike component of that, and we'll get this g00 tensor, which is 8 x r, the density of mass energy in this room. I mentioned that earlier. That's the way to see Einstein's tensor with this rotation. And you can go on and talk about conservation of energy and momentum by employing a 2,3,4-dimensional form of this boundary of a boundary principle. But I'll forego that now on this tape. It's just too involved.

Ford:

Okay.

Miller:

Johnny, I guess I dictated this piece for you, and it was very personal. I used your name throughout the entire session. I suppose one thing I would like to have you recall is your Daniel Boone pioneer type of outlook in physics; you're very much in many ways a pioneer in physics, forging a new school in general relativity and the way of looking at things which led to numerous breakthroughs.

Your emphasis on introducing the correct language and terms and phrases into physics. And I guess most importantly, your insights recently since I've known you in Texas on "it from bit" and getting underneath quantum mechanics and the deeper issues, trying to build everything we know, everything in existence, from yes's and no's.

I don't know whether you remember this, but when you came to my house when I was a new student of yours and you sort of put these ideas on the board before you had your meaning circuit developed fully, and you were trying to draw analogies between the work of Benjamin Franklin, you would phrase it in terms of the shades of Franklin, and this new way of dealing with physics, this "it from bit" approach to physics, building everything from yes's and no's, distinguishability being the key point there, and probabilities for yes's and no's being the key points in that.

I think that that is going to be appreciated years and years from now, and that's one of the major advances. I see you doing to quantum mechanics and to the foundations of physics what you did to general relativity in so many ways. There are a lot of parallels. You're pushing the theory to its extreme, getting down to the basics with the paradoxes that it presents us with. And as you said so many times to me, there is no progress in physics without real paradoxes around. I guess that's, through you, my experience of Niels Bohr in my life. Anyway, thank you, Johnny