Quantum Man: Richard Feynman's Life in Science (21 page)

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.

The claim is remarkable: Forget all about geometry and the fascinating notions about space and time that seem to be at the basis of general relativity. If one considers the exchange of a massless particle (just as a photon is a massless particle that conveys the electromagnetic force), then if the massless particle in question has quantized spin 2 instead of spin 1 as a photon does, the only self-consistent theory that results will, in the classical limit, essentially be Einstein’s general relativity.

This is a truly amazing claim because it suggests that general relativity is not that different from the theories describing the other forces in nature. It can be described by the exchange of fundamental particles just like the rest. All the geometric baggage comes out after the fact, for free. In fact, there are subtleties in the actual true statement of the claim, coming from what is meant by “self-consistent,” but these are really just subtleties. And Weinberg, as I have indicated, was able to prove a more general version of this claim, relying simply on the properties of the interactions of a massless spin 2 particle and the symmetries of space that arise in special relativity.

But these subtleties aside, this new picture of gravity and general relativity created a completely novel bridge between general relativity and the rest of physics that was not there before. It suggested, just as Feynman had hoped it would, that one might use the tools of quantum field theory not only to understand general relativity but also to unify it with the other forces in nature.

First, what are these massless spin 2 particles and what do they correspond to in nature? Well, recall that photons, the quanta of the electromagnetic field, are just quantized versions of classical electromagnetic waves, the waves of electric and magnetic fields that James Clerk Maxwell first showed result from jiggling an electric charge, which is the source of the electromagnetic field. These fields we experience with our eyes as light, our skin as heat from the sun, as radio waves with our radios, or microwaves with our cell phones.

Einstein had shown, shortly after he developed general relativity, that mass, which is the source of gravity, could produce a similar effect. If a mass is moved in just the right way, a new type of wave will be emitted—a gravitational wave, which is literally a wave in which space compresses and expands along the wave, and will travel out at the speed of light, just as photons do. In 1957, when Feynman first discussed his ideas at a physics meeting, many in the audience were dubious that gravitational waves even existed. (In fact, Einstein himself was earlier deterred by H. P. Robertson from publishing a paper denying their existence.) However, in 1993 Joseph Taylor and his former student Russell Hulse received the Nobel Prize for convincingly demonstrating that a pair of orbiting neutron stars was losing energy at the exact rate predicted by general relativity for the emission of gravitational waves from this system. While scientists have yet to directly detect gravitational waves, because gravity is so weak, large terrestrial experiments have been designed to do so, and plans are underway to build a very sensitive detector in space.

Gravitational waves are emitted only from objects in which the distribution of mass is changing in a nonspherically symmetric way. Physicists call the kind of radiation emitted by such a distribution
quadrupole
radiation. If one wanted to encode this kind of directional anisotropy by associating particles with the emitted waves, these primary “quanta” would have to have a spin 2, which is precisely why Feynman first explored this option. The quantum of gravitational waves is called a
graviton
, in analogy to a photon.

Having demonstrated that gravity can result simply from the exchange of gravitons between masses, just as electric and magnetic forces result from the exchange of photons between charges, Feynman then proceeded to use precisely the kind of analysis that had stood him in such good stead with QED to calculate quantum corrections to gravitational processes. The effort was not so simple however. General relativity is a far more complex theory than QED because while photons interact with charges in QED, they do not interact directly with each other. However, because gravitons interact with
any
distribution of mass or energy, and since gravitons carry energy, gravitons interact with other gravitons as well. This additional complexity changes almost everything, or at least makes almost everything harder to calculate.

Needless to say, Feynman did not find that a consistent quantum theory of gravity interacting with matter, without any nasty infinities, could be derived by simply treating general relativity as he had electrodynamics. There still is not such a definitive theory, though candidates have been proposed, including string theory. Nevertheless, every major development that has taken place in the fifty-odd years since Feynman began his work in this area, involving a line of scientists from Feynman to Weinberg to Stephen Hawking and beyond, has built on his approach and on the specific tools he developed along the way.

Here are a few examples:

(1)
Black Holes and Hawking Radiation
: Black holes have remained perhaps the biggest theoretical challenge to physicists trying to understand the nature of gravity, and they have produced the biggest surprises. While suggestive observational evidence has accumulated in the past forty years of the existence of massive black hole–like objects in the cosmos, from the engines of energetic quasars to million and billion solar mass objects at the centers of galaxies, including our own, the detailed nature of quantum processes that operate in the final stages of black hole collapse has produced surprises and controversy. The biggest surprise came in 1972, when Stephen Hawking explored the detailed quantum mechanical processes that might occur near the event horizon of a black hole, and discovered that these would cause black holes to radiate energy in the form of all types of elementary particles, including gravitons, as if the black hole were hot, at a temperature inversely proportional to its mass. The form of this thermal radiation would be essentially independent of the identity of whatever collapsed to form the black hole, and would cause the black hole to lose mass and perhaps eventually evaporate completely. This result, which is based on the type of approximation Feynman first used to explore the quantum mechanics of gravity—namely, approximating the background space as fixed and approximately flat, and considering quantum fields, including gravitons, propagating in this space—not only flew in the face of commonsense classical thinking but also presented major challenges to our understanding of quantum mechanics in the presence of gravity. What is the source of this finite temperature? What happens to the information that falls down the black hole if the black hole eventually radiates away? What about the singularity at the center of the black hole, where conventional quantum field theory breaks down? These major conceptual and mathematical problems have driven the work of the greatest theoretical minds in physics over the past forty years.