Quantum Man: Richard Feynman's Life in Science Page 21
Physics is, after all, a human social activity, and at any time there is often consensus about what the “hot” problems are, and which directions are most likely to lead to new insights. Some view this faddishness as a problem, as for instance, the fascination of much of the community over the past twenty-five years with string theory, a mathematically fascinating set of ideas whose lack of direct contact with the empirical world has been outweighed only by the increasing confusion about what it might predict about nature. (Nevertheless, in spite of this, the mathematics of string theory has led to a number of interesting insights about how to perform calculations and interpret the results of more conventional physics.)
It is inevitable that groups of people with similar interests will get excited about similar things. And ultimately, fads in science don’t matter, because first, all of the activity inevitably reveals the warts as well as the beauty marks quicker than would otherwise have been the case, and second, as soon as nature points out the right direction, scientists will jump off a sinking ship faster than rats in a storm.
In order for science to be healthy, it is important that not all scientists jump on the same bandwagon, and this was the point that Feynman focused on, almost to obsession. He was so talented and so versatile that he was able, if necessary, to reinvent almost any wheel and usually improve it in the process. But by the same token, reinventing the wheel takes time and is rarely worth the trouble.
It wasn’t just that he could take this road; it was that he often felt he had to. This was both a strength and a weakness. He really didn’t trust any idea unless he had worked it out from first principles using his own methods. This meant that he understood a plethora of concepts more deeply and thoroughly than most others, and that he had a remarkable bag of tricks from which he could pull magic solutions to a host of varied problems. However, it also meant that he was not aware of brilliant developments by others that could have illuminated his own work in new ways, leading him further than he could have gotten on his own.
As Sidney Coleman, a brilliant and remarkably well-respected Harvard physicist who had been a student of Gell-Mann’s at Caltech in the 1950s and who had interacted with Feynman throughout his career, put it, “I’m sure Dick thought of that as a virtue, as noble. I don’t think it’s so. I think it’s kidding yourself. Those other guys are not all a collection of yo-yos. . . . I know people who are in fact very original and not cranky but have not done as good physics as they could have done because they were more concerned at a certain juncture with being original than with being right. Dick could get away with a lot because he was so goddamn smart.”
Feynman did get away with a lot. But could he have done much more if he had agreed every now and then to build on well-trodden paths rather than seek out new ones? We will never know. However, an honest assessment of his contributions to science from 1960 or so onward demonstrates several trends that continued to repeat themselves. He would explore a new area, developing a set of remarkably original mathematical techniques and physical insights. These would ultimately contribute to central developments by others, which would lead to a host of major discoveries and essentially drive almost every area of modern theoretical and experimental physics. This ranged from his work in condensed matter physics to our understanding of the weak and strong interactions, to the basis of current work in quantum gravity and quantum computing. But he himself did not make the discoveries or win prizes. In this sense, he continued to push physics forward as few modern scientists have, opening up new areas of study, producing key insights, and creating interest where there had been none before, but he tended to lead from the rear or, at best, from a side flank.
Whether or not this would have disturbed him is unclear. In spite of his natural tendency to showboat, as I have described, he was ultimately more interested in being right than being original, and if his work led others to uncover new truths, he might remain skeptical of their results for a long time, but eventually the satisfaction of having provided illumination in the darkness gave him deep pleasure. And by concentrating on difficult problems the mainstream would not approach, he increased his chances of providing such illumination.
FEYNMAN’S FIRST FORAY well off the beaten path involved his desire, beginning around 1960, to understand how one might formulate a quantum theory of gravity. There were good reasons for his interest. First, while developing such a theory had thus far eluded all who had thought about it, he had already been successful in developing a consistent quantum theory of electromagnetism when others had been stymied, and he thought his experience with QED might lead somewhere useful. Second, Einstein’s general relativity had long been considered the greatest scientific development since Newton. It was, after all, a new theory of gravity. But when one considered its behavior on small scales, it appeared to be flawed. The first person who could set this theory straight would surely be viewed as the rightful heir to Einstein. But perhaps the biggest attraction for Feynman was that no one else, at least no one who really mattered, was thinking about the problem. As he put it, in a letter to his wife from a conference on gravity that he attended, in Warsaw in 1962, “This field (because there are no experiments) is not an active one, so few of the best men are doing work in it.”
That was probably somewhat of an overstatement, but in truth the study of general relativity had become a field unto itself since Einstein’s great discovery of his classical field equations in 1915. Because general relativity implies that matter and energy affect the very nature of space itself, allowing it to curve, expand, and contract, and that this configuration of space then affects the subsequent evolution of matter and energy, which then continues to impact on space, and so on, the theory is both mathematically and physically far more complicated than Newton’s theory of gravity had been.
A great deal of work was done to find mathematical solutions to these equations in order to explain phenomena ranging from the dynamics of the universe to the behavior of the last moments of stars as they burn out their nuclear fuel. The equations were complicated enough, and their physical interpretation confusing enough, that tremendous ingenuity and mathematical prowess were required, and a small industry of experts had developed to investigate new techniques to deal with these issues.
To get a sense of how complicated the situation actually was, it took a full twenty years and lots of detours down blind alleys and errors, including some famous ones by Einstein himself, before scientists realized that general relativity was incompatible with a static and eternal universe, which was the preferred scientific picture of the cosmos at the time. In order to allow for such a universe in which our galaxy was surrounded by static empty space, Einstein added his famous cosmological constant (which he later called his biggest blunder).
The Russian physicist Alexander Friedmann first wrote down the equations for an expanding universe in 1924, but for some reason the physics community largely overlooked them. The Belgian priest and physicist Georges Lemaître independently rediscovered the equations and published them in an obscure journal in 1927. While Lemaître’s work did not receive general notice, Einstein certainly was aware of it, and wrote to Lemaître: “Your calculations are correct, but your physics is abominable.”
It was not until the 1930s, after Edwin Hubble’s observation of the expanding universe through the motion of distant galaxies, that Lemaître’s work was translated to English and began to receive general acceptance, including by Einstein. In 1931 Lemaître published his famous article in Nature outlining his “primeval atom” model, which eventually became known as the big bang. Finally, in 1935, Howard Robertson and Arthur Walker rigorously proved that the only uniform and isotropic space (by then it had become recognized that our galaxy was not alone in the universe, and that space was largely uniform in all directions with galaxies everywhere—an estimated 400 billion in our observable universe) was the expanding big bang described by Friedmann and Lemaître. After that, the
big bang became the preferred theoretical cosmological model, although it actually took another thirty years—after Feynman began his work—before the actual physical signatures resulting from a Big Bang were seriously explored, and the discovery of the cosmic microwave background radiation put it on an unequivocal empirical footing.
While it took two decades to sort out the cosmological implications of general relativity, the most familiar of all situations associated with gravity, the gravitational collapse of a spherical shell of matter, remained confused for far longer, and is still not fully understood.
Within a few months of Einstein’s development of general relativity, the German physicist Karl Schwarzschild wrote down the exact and correct solution describing the nature of space and the resulting gravitational field outside of a spherical mass distribution. However, the equations produced infinite results at a finite radius from the center of the distribution. This radius is now called the Schwarzschild radius. At the time, it was not understood what this infinity meant, whether it was simply a mathematical artifact or reflected some new physical phenomena taking place at this scale.
The famous (and eventually Nobel Prize–winning) Indian scientist Subrahmanyan Chandrasekhar considered the collapse of real objects like stars and argued that for stars larger than about 1.44 times the mass of our sun, no known force could stop their collapse down to this radius or smaller. The famous astrophysicist Arthur Eddington, however, whose own observations of a total eclipse in 1919 had provided the first experimental validation of general relativity (and catapulted Einstein to world fame), violently disagreed with this result and ridiculed it.
Ultimately Robert Oppenheimer demonstrated that Chandrasekhar’s result was correct after a slight refinement (about 3 solar masses or greater). But the question still remained, What happened when stars collapsed down to the Schwarzschild radius? One of the strangest apparent implications of the theory was that from the point of view of an outside observer, as massive objects collapsed, time would appear to slow down as the Schwarzschild radius was approached, so that the objects would seem to “freeze” at this point before they could collapse further, leading to the name frozen stars for such objects.
For these reasons and others, most physicists believed that collapse inside the Schwarzschild radius was physically impossible, that somehow the laws of physics would naturally stop the collapse before the Schwarzschild radius was reached. However, by 1958 scientists understood that the apparent infinities associated with the Schwarzschild radius were mathematical artifacts of the coordinate system used to describe this solution, and that nothing unphysical would happen as objects traversed this radius, now called the event horizon because once inside, objects could no longer communicate to the outside world.
While nothing untoward might happen at the event horizon, in 1963 Roger Penrose demonstrated that anything that falls through the event horizon would be doomed to collapse to an infinitely dense “singularity” at the center of the system. Once again, dreaded infinities were cropping up, this time not just in calculations of the interactions of particles, but in the nature of space itself. It was speculated, though it has not been proved, and indeed several tentative numerical counterexamples have been suggested recently, that all such singularities are shielded from outside observers by an event horizon and therefore cannot be seen directly. If true, this would have the effect of sweeping under the rug the problem of what actually happens inside such an object, but it would clearly not resolve the key physical question of whether such singularities exist.
In 1967 John Wheeler, Feynman’s former supervisor, who had earlier argued most strongly that collapse inside the Schwarzschild radius would be impossible in a sensible universe, gave in to the possibility and forever enshrined such collapsed objects with the enticing name black holes. Whether it is their name that has provoked such interest, black holes remain at the center of all modern controversies concerning our understanding of gravity at small scales and strong fields.
These issues surrounding the interpretation of classical solutions of Einstein’s equations and the nature of gravitational collapse were the focus of activity in the community of theorists studying gravity when Feynman began to turn his attention to this field. What was most striking, perhaps, was how the study of gravity had evolved to become almost a separate and isolated field of physics. After all, Einstein had seemingly demonstrated that gravity was completely different from all of the other forces of nature. It resulted from the curvature of space itself, whereas the other forces seemed to operate quite differently—based on the exchange of elementary particles moving through space, for example. Even textbooks tended to treat general relativity as an entirely self-contained field that could be understood apart from almost all of the rest of physics.
Feynman, however, rightly believed that such a separation was artificial. At small scales, quantum mechanics reigned, and ultimately if one was going to attempt to understand gravity at small scales, one would need to use the tools that Feynman and others had developed to understand how classical theories like electromagnetism—which on the surface seems similar, being a long-range force that falls off with the square of distance out to infinity—could be made consistent with the principles of quantum mechanics. Perhaps by approaching gravity, then, as he and others had approached QED, they might be able to gain valuable new insights.
Feynman began thinking about these issues seriously in the mid-1950s, shortly after he had finished his own work on QED, and had discussed them with Gell-Mann during Christmas of 1954, by which time he had already made great progress. However, it was not until 1962–63 that he completed and formalized his thoughts, during a year-long graduate course he taught at Caltech. His lectures on the subject were turned into a book much later, released for popular consumption in 1995 and not surprisingly titled The Feynman Lectures on Gravitation. This title was especially fitting because he taught this graduate course at the same time that he was developing and teaching the second year of his famous introductory course on which the more well-known Feynman Lectures was based. It is no wonder that he was exhausted at the end of this period.
He explained the motivation for his approach in a 1963 scientific paper that summarized his results, and apologized for considering the quantum aspects of gravity, which were then, as they are now, far removed from any possible experimental verification: “My interest in it [the quantum theory of gravitation] is primarily in the relation of one part of nature to another. . . . I am limiting myself to not discussing the questions of quantum geometry. . . . I am not trying to discuss any problems which we don’t already have in present quantum field theory of other fields.”
It is difficult, in the current climate, where such great interest has developed in unifying the different forces of nature, to realize how revolutionary Feynman’s approach was. The idea that gravity might not be so special or self-contained, was almost heretical, especially to the closed community of scientists who treated it as a special jewel, to be worked with special tools not available to ordinary physicists. As might be expected, Feynman had little patience for such an effete viewpoint; it flew in the face of all of his beliefs about science. While at the second conference on gravity that he attended, in Warsaw (the first, in Chapel Hill in 1957, was presumably more enjoyable), he wrote to Gweneth:
I am not getting anything out of this meeting . . . there are hosts (126) of dopes here—and it is not good for my blood pressure—such inane things are said and seriously discussed—and I get into arguments outside of the formal sessions . . . whenever anyone asks me a question or starts to tell me about his “work.” It is always either—(1) completely un-understandable, or (2) vague and indefinite, or (3) something correct that is obvious and self-evident worked out by a long and difficult analysis and presented as an important discovery, or (4) a claim, based on the stupidity of the author that some obvious and correct thing accepted and checked for years is, in
fact, false (these are the worst—no argument will convince the idiot), (5) an attempt to do something probably impossible, but certainly of no utility, which, it is finally revealed, at the end, fails, or (6) just plain wrong. There is a great deal of “activity in the field” these days—but this “activity” is mainly in showing that the previous“activity” of somebody else resulted in an error or in nothing useful or in something promising. . . . Remind me not to come to any more gravity conferences.
Feynman began by arguing that gravity was even weaker than electromagnetism, and therefore—just as one could try to understand the quantum theory of the latter by considering first the classical theory, and then adding small quantum corrections order by order—the same procedure should work for gravity. Hence, it was worth investigating whether the infinities that resulted when one went beyond the lowest-order approximation in electromagnetism also appeared in gravity, and whether one might remove them in the same way as one had done in QED, or whether new complications might result that could give insight into the nature of gravity itself.
In electromagnetism, forces result from the interaction of charged particles and electromagnetic fields, the quanta of which are called photons. Remarkably, as far as I can determine, Feynman was the first to suggest that one might treat quantum gravity just like any other quantum theory, and in particular like the quantum theory of electromagnetism, which on the surface has a great deal of similarity to gravity. To do this he explored a remarkable idea: Let’s say Einstein had not come up with general relativity. Could someone have instead derived Einstein’s equations just by thinking about the classical limit of quantum particles interacting with quantum fields? While Feynman was not the first to explore such a possibility or to draw a positive conclusion in this regard—in fact, Steven Weinberg performed the most general and powerful exploration of this question in 1964, and elaborated in his beautiful text on gravity and cosmology in 1972, and again in a later paper in 1979—Feynman’s original analysis created the modern mindset for the more recent reappraisals of the theory.