No Boundaries to Hartle

0:00 In this talk, I want to tell you a bit about working with Jim Hartle and what we managed to do together. I found Jim to be the ideal collaborator. He saw what the fundamental questions were, and he knew about quantum field theory, of which I was completely ignorant, having entered research from classical general relativity. Although we only wrote four papers together, two of them brought about major changes in the field. I will tell you about them along with a few anecdotes about Jim and the times we went through together I have known Jim since almost before the flood and certainly before the great flood of papers on general relativity and black holes We first met at one of the few Texas conferences that actually took place in Texas. Nowadays, Texas has extended its borders to include Chicago and Paris, but this conference was in Austin in 1970. There were various new observational results at the meeting, but they were just refinements of previous discoveries, and I can't remember what they were. On the other hand, there was great excitement on the theoretical side. We were in the middle of one of those changes of emphasis that had been fundamental to the development of 20th century physics. Up to then, attention had been concentrated on what happened to the star in a gravitational collapse. The object that was left after the collapse was referred to as a frozen star and was considered dead. However, it was discovered that one

2:30 could extract energy from these objects, but that the amount one could extract was limited by the area increase of the horizon. This made them interesting dynamical objects in their own right, independently of how they were formed. This was recognized by the adoption of the term, Black Pole, instead of the dreadful name, Frozen Star. Immediately after the Austin, Texas, conference, Jim came to Cambridge on a Sloan Fellowship at the Institute of Theoretical Astronomy, of which I was a member. He and I had a lot of discussions on classical black hole theory, which was unrapidly developing. During this period, we wrote the first of our joint papers. It was quite a tour de force, though I say it myself. In modern language, which hadn't been invented then, it was about multi-centered DPS solutions of Einstein-Maxwell theory. The simplest case was the multi-particle solution, discovered by Papadou and Magyantra. Gemini showed that they represented charged black holes that could remain at constant distance from each other because their gravitational attraction was exactly balanced by electric or magnetic repulsion. The irony of this was that to the end of this life the Papadu didn't believe in blackpoles.

5:00 In our paper, Jim and I also considered a generalization of the Papadu-Megnanda solutions obtained by Israel and Wilson. In these, the harmonic function, V, was allowed to be complex, and there was a one form, omega, defined by V, up to a constant of integration. These solutions were later to play an important role in Euclidean quantum gravity, but at the time, they didn't seem of much interest, because they had not charred and closed time-like curves. Nevertheless, we found the coordinate transformations needed to remove the apparent singularities. This meant that when U2 in quantum gravity came along a few years later, we could just look up our paper and analytically continue the results. Jim spent six months at the Institute of Theoretical Astronomy, and then took me to Heathrow and his E.W. Beetle. As you know, beetles don't have a proper boot or trunk, so the wheelchair had to be beside me in the back. It was quite a squash. We were going to, I think it was GRV-5, in Copenhagen. This was a memorable conference in many ways. The previous GRV conference happened in Soviet Georgia in 1968, shortly after the Soviet invasion of Czechoslovakia. I had been intending to go, but canceled because of the invasion. I now think this was a mistake on my part. My protest didn't hurt the Soviet Union, but it deprived Soviet scientists of some of their badly needed contacts with the West.

7:30 Other people canceled because Israeli scientists had not been given visas. There was an unholy argument about this at Copenhagen, with demands to reform and democratize the International Committee, which often then had organized PR conferences. I was more interested in science than scientific politics and didn't believe in democracy for organizing scientific conferences, but Jim went to the meeting and saw Soviets walk out of the conference. Jim and my second joint paper was also based on discussions we had while he was at the Institute for Theoretical Astronomy. It is probably the least significant of our foreign light paper, but it was based on a neat idea. We showed the horizon could be treated as if it were a soap film of a viscous liquid. A planet or moon orbiting the black pole would raise tides on the horizon. If the black pole was rotating, these types would move relative to the generators, causing the shape of the small pencil of race in the horizon to change with time. This in turn would cause the horizon to expand at a rate that could be calculated from the Newman-Penrose equations. One could interpret this as the dissipation of the rotational energy of the black hole, the two irreducible mass, as represented by the area of the horizon. After Jim's stay at the Institute of Theoretical Astronomy in 1971, we didn't meet again until I accepted Pipthorn's invitation to spend the year 74-75 at Caltech.

10:00 The Sherman Fairchild Foundation provided us with a large American station wagon. Into it we loaded my first electric wheelchair, two children and a tame graduate student, and headed up the 101 to Santa Barbara. we stayed at the faculty club and fell in love with Santa Barbara though I remember sitting freezing on the beach trying to have a picnic in a gale at that time or maybe a few years later Jim and his first wife, Judy lived in a converted barn in Montecito south of Santa Barbara Judy was an artist, and I think the burn was her idea. It was quite impressive, but I think it can have been very comfortable. Later, it spontaneously collapsed, though not when anyone was in it. To get back to physics. Earlier that year, I had discovered to my surprise that even non-rotating black holes would radiate with a thermal spectrum. Nowadays, something like that would have triggered an avalanche of other papers within a few weeks. but those were quieter times before HEPTH and about a year passed before there was much response this was partly because particle physicists were working on gauge theories and didn't take seriously anything that couldn't be described by Feynman diagrams But it was such a break with existing ideas that many people didn't believe it.

12:30 How could anything get out of a black hole? By definition, a black hole is a region of space-time from which nothing can escape. So they were sure something must be wrong with my calculations. In my original paper, I obtained the radiation by considering zero-point fluctuations in the initial vacuum state that were amplified by the collapse that formed the black hole. However, the fluctuations also receive a very light redshift by hovering just outside the horizon. And when I say large redshift, I mean really large. A redshift of V to the 10th of the 40, for a black hole that will evaporate in the age of the universe. This meant the radiation from the black hole seemed to come from the amplification of modes that of the Planck frequency. Surely, people said, the theory would break down at such high frequencies, and one could not believe any conclusion based on them. If one took my original calculations literally, one might think that the amplified vacuum fluctuations formed a sheet of very high energy density just outside where one would have expected the horizon to be. Anyone who tried to fall into the black hole would have to cross the sheet, and it might seem that they should interact with it strongly. Although a few people still believe that objects falling into a black hole will be hit by a sheet of radiation as they try to cross the horizon, this has never been my picture of

15:00 what is happening. Instead, I believe that black hole radiation is a continuous process that takes place at rather than something that was produced in the gravitational collapse just before the horizon and gradually leaked out. How would the local physics know where the event horizon was going to be? The event horizon is a global structure that is determined by the future history of the space-time. It can be way outside the apparent horizon, which is all that can be determined locally. My picture was that vacuum fluctuations in the region outside the black hole gave rise to pairs of virtual particles that appeared and disappeared together. One member of the A pair would have positive energy, but the other would have negative energy. This meant that it could not remain in existence in normal spacetime, but it had to seek out its positive energy partner and annihilate with it. However, a black hole contains negative energy states Thus if the negative energy member of a virtual pair fell in a black hole it could continue in existence without having to annihilate with its partner The positive energy member of the pair could then escape to infinity, where it would appear to be radiation given up by the black hole. One can think of a negative energy particle falling into the black hole

17:30 as a positive energy particle coming out of the black hole but traveling backwards in time. When it gets to where the virtual pair first appeared, it would be scattered into traveling forward in time. Thus the positive and negative energy members of the virtual pair are really the same particle, which can be thought of propagating out from the singularity through the horizon. I wanted a mathematical treatment of black hole radiation, as low-energy particles leaking out of the horizon at late times, rather than as a high-energy process during the collapse. I therefore wanted to use path integrals to calculate the amplitude for a particle to propagate from the future singularity of the black hole to an observer at infinity. All I knew about path integrals was a book by Feynman and Hibbs, which dealt only with the non-relativistic case, and only in flat space. But Jim showed me how one could use path integrals to calculate the propagation of scalar particles in curved spacetime. Together, we puzzled how to apply them to particles in a black hole metric. In order to make the path integral converge, it seemed necessary to complexify the space-time, and this had the advantage of connecting the past and future singularities of the black hole through complex values of the coordinates it enabled us to relate the probability that a particle escaped from the black hole to the probability that one fell in

20:00 The emission and absorption probabilities for a particle of energy omega were related by the Boltzmann factor e to the minus omega over t. This was precisely the relation needed for the blacked hole to be in equilibrium with thermal radiation at temperature T. Thus we had shown that blacked holes give off thermal radiation without the questionable use of frequencies above the Planck value. We also confirmed that the radiation corresponded to energy leaking out of the horizon at late times, rather than something that happened during the collapse. Even more important than these results, this paper was the first to use Euclidean methods. We showed that the Schwarzschild solution could be analytically continued to a section on which it was Euclidean, that is to say, on which it was a positive definite metric. The natural choice of propagator was in the unique green function on this Euclidean section. When one analytically continued this propagator back to the Lorentzian Schwarzschild solution, it had poles periodically in the imaginary time coordinate. This puzzled us, but Gary Gibbons and Malcolm Perry recognized them as a characteristic signature of thermal green functions.

22:30 This meant one could extend the proof of thermal emission to interacting field theories as well. Any field theory on a black hole background will behave as if it was at a black hole temperature. It would not have been possible to show this with my original method of calculation. Our path integral paper inspired an Euclidean approach to quantum gravity. For years, this was regarded by the outside world as a Cambridge eccentricity, but the methods and ideas are now generally accepted, and applied to M-theory, which is a politically correct name for 11-dimensional supergravity. gravity. Much of the early work on Euclidean quantum gravity was carried out in Cambridge with people like Gary Gibbons, Chris Pope, and Don Page. But Jim and I are responsible for extending it to cosmology, with our no-boundary proposal, which was the subject of our fourth, and most cited, paper. Jim had moved from Santa Barbara to Chicago in 1981. He said it was to be part of a bigger science community than the then rather small and isolated physics department in Santa Barbara. But I suspect it was also an account of Judy's desire to be part of a larger artistic community. The teaching load at Chicago was less than that at Santa Barbara.

25:00 This meant he had time to make regular visits to Cambridge in this period, which was a time of great excitement in cosmology with the development of the inflationary model. I have got in trouble before now with the signing credit for so-called new inflation, which seems rather old-head now, so I won't repeat that mistake. but I managed to get nearly all the principal players in the field to come to an affield workshop on the very early universe in Cambridge in June 1982 that was a very timely conference when a generally accepted picture of inflation emerged The main observational prediction was that there should be small fluctuations in the microwave background produced by quantum processes in the early universe. Ten years later, this prediction was confirmed by the Cosmic Background Explorer satellite, COPE, and the measurements of the fluctuations were further refined by later experiments. The so-called new inflation scenario was that the universe started out very hot at a singularity. Had it expanded, it would have cooled. By some means that was never properly established. This was supposed to have left the universe with a scalar field that was constant in space, and was sitting at a local maximum of the potential. The energy-momentum tensor of this scalar field would then have acted like a cosmological constant and caused the universe to expand in an exponential manner.

27:30 As the universe expanded, the scalar field would roll down the potential, but the rapid expansion would slow the roll down and delay it long enough for the universe to inflate The new inflationary scenario was rather implausible. In a hot chaotic universe that was cooling, one would not have expected the scalar field to be spatially homogeneous, when sitting at the maximum of the potential. but it was unsatisfactory at a deeper level than this because it began with a singularity at which all the equations broke down it is sometimes said that it doesn't matter how the universe began because once inflation takes over, it erases all traces of the initial conditions. However, this can't be true, as can be seen from the following thought experiment. Pick any state for the universe at the present time and run the evolution equations backwards. By the singularity theorems, there will be an initial singularity. Thus there will be singular initial data for any state now, no matter how inisotropic, or unlike the universe we live in. One cannot argue that inflation will cause most initial data to evolve to an isotropic state now because one does not have a measure on singular initial data sets.

30:00 thus inflation is not a substitute for a theory of initial conditions which is required if cosmology is to make predictions Jim was at the Nuffield workshop, and he and I discussed this problem of the universe, using the Euclidean methods that had been developed for black holes. Our starting point was the ground state of the harmonic oscillator. One can express the ground state wave function at a point x by a path integral over all paths in Euclidean 1 plus 1 space from the point x that approach the minimum of the potential in the infinite future. This suggested we define the wave function for the universe at some free geometry, HIJ, by a path integral. The path integral would be over a family of Euclidean four geometries that had the three-geometry, H.I.J., as their boundary. The choice of the family of Euclidean geometries specified the quantum state of the universe. So what family should we choose? There were two natural choices. The geometries could be asymptotic to flat Euclidean space, or they could be closed without any boundary other than the free geometry, H.I.J.

32:30 The first choice is appropriate for scattering, where one sends particles in from infinity and measures what one gets back out at infinity. But the universe is not asymptotically flat, and we are not making measurements at infinity, but in a finite region in the interior. So for cosmology, the appropriate family is closed, compact geometries, whose only boundary is the three-geometry, H.I.J. This choice of family of Euclidean four geometries is called the No Boundary Proposal. It can be paraphrased as, the boundary condition of the universe is that it has no boundary. After the Nuffield workshop, I went to Santa Barbara for five weeks with the whole family and another graduate student. By then, we had our third child, Tim, then aged three. I remember him gazing at the mountains and saying, It's a big country. Jim was still on the faculty at Santa Barbara, having kept a foothold by going to Chicago on leave of absence. This turned out to be a wise move. The attraction of Chicago decreased as his marriage to Judy broke down. Meanwhile, the attraction of Santa Barbara increased, with the founding of the Institute of Theoretical Physics, in which Jim played an important role, and was later director for a time.

35:00 Jim and I discussed the wave function of the universe in Santa Barbara that summer. We found it much less obvious than it now appears with hindsight, and did not finish the paper until Jim visited Cambridge the following spring. The paper created quite a sensation, and started a wave of interest in quantum cosmology, that is still with us. There have been alternative proposals for the initial conditions of the universe, such as the tunneling hypothesis, or the pre-Big Bang scenario. But neither of these kids are complete prescription for calculating quantum fluctuations about a homogeneous isotropic background. So neither can be regarded as serious rivals, because they don't make observationally testable predictions. When Gemini first formulated the no-boundary proposal, we naively thought the universe was four-dimensional. But one can equally well formulate a no-boundary proposal for M-theory or large extra dimensions. It is by such a marriage of ideas that I expect further progress in quantum cosmology. Since our 1983 paper on the wave function of the universe, Jim has shown he has no boundaries in other directions. With no man, he has studied decoherence, and the transition from quantum to classical. The universe may have had a quantum origin, but it is pretty classical now. How did this change come about?

37:30 And Jim again showed he had no boundaries in another sense when he took on the post of director of the ITP at Santa Barbara. He took the opportunity of instigating several programs on gravity, but took my advice, and got out while he was still scientifically alive. So let me salute my friend, Jim Hurdle, a man without boundaries. Thank you.