ATTEMPTS TO QUANTIZE GRAVITY?


“I am not getting anything out of the meeting. I am learning nothing. Because there are no experiments, this field is not an active one, so few of the best men are doing work in it. The result is that there are hosts of dopes here, and it is not good for my blood pressure. Remind me not to come to any more gravity conferences!” [Richard Feynman in a letter to his wife, written while attending the 1962 Warsaw Conference on “The Theory of Gravitation.”]  Feynman's big contribution to the field was a convincing argument that gravitational radiation was observable and that efforts should be made to construct practical detectors of it.



By the late 1950s, there were two prominent attitudes toward quantum gravity. One was that a quantum theory of gravity would never be needed, since quantum gravitational effects could never be observed. Another was that there were obstacles to a quantum theory of gravity that could never be overcome. The gravitational field was not a gauge vector field (its bosons would have spin 2) and its coupling constant G had a dimension, which caused “an infinite number of infinities” at every order of perturbation theory. Furthermore there seemed to be an inherent incompatibility between gravity and quantum physics... in quantum physics, time is just a parameter, whereas in Einstein's Theory of Gravity, the geometry of space-time itself is the result of an elaborate calculation. So would quantum physics itself have to be redone from scratch? Beyond that, in relativistic quantum field theory, the fields occupy a passive space-time, whereas a quantum field theory of gravity would somehow also have to reformulate quantum field theory from the ground up, somehow placing fields within fields.


Two pioneering figures in quantum gravity have strong University of Texas roots... John Archibald Wheeler (left, 1911 - 2008) and Bryce DeWitt (right, 1923 - 2004). Despite their pioneering efforts, there has really been little or no significant progress in quantizing gravity since their early and seminal work. Of course the inability to do experiments or make astrophysical observations relevant to quantum gravity is the major stumbling block, and there is some reason to hope this situation may change. However, the current state of quantum gravity research is accurately described as dismal. Here is a quick summary of the situation. And here is a broader survey of current work. But the problems are of such a fundamental nature that it's hard to imagine much progress in the foreseeable future. Here is an interesting set of recent proposals.


Black holes are a famous consequence of Einstein's classical field theory of gravity. Now consider an interaction between a black hole and a quantum system. In quantum physics, time evolution of the state is generated by a unitary operator, which also has an inverse. In other words |ψ(t)⟩ = U(t,t0)|ψ(t0)⟩, and we can freely go backward or forward in time.  The basic principle of quantum physics is that the state vector contains all the information that exists about the state being described.  Now suppose the system described by that state falls into a black hole.  Where is the information that the state carried?  We can no longer reverse time and back the state out of the black hole, and the whole concept of a classical black hole centers on the idea that it has nothing inside except a singularity. This puzzle is the black hole information paradox, previously mentioned.  You will notice it is actually a problem involving both time reversibility and information! [And it's further complicated by black hole evaporation!] Since it was originally posed in the mid-1970s, it has generated an avalanche of suggestions and hypotheses, but there is very general agreement that the original question remains untouched. The inability to find an answer that the majority of researchers in the field can agree upon is a very clear symptom of a field in crisis. Feynman would not be surprised. After more than 40 years, it is impractical even to itemize the huge number of “solutions” to the puzzle which have been proposed, much less describe each of them in a sentence. It's hard to think of experiments that might help. Here is someone's attempt at a quick discussion. Here are two obvious comments from me: (1) it is in no way surprising that a classical field theory is an uneasy fit to quantum theory! They should NOT be consistent. (2) The unitary operator U(t,t0) has a generator, and that generator is the system Hamiltonian H. There is no way to put a black hole into the Hamiltonian, since it has no quantum representation. It seems clear to me that the whole "paradox" is of no real interest, except in emphasizing that a classical field theory of gravity will always be inconsistent with quantum physics!

Tremendous theoretical effort has been devoted in the past 50 years to trying to find promising approaches that lead toward a quantum theory of gravity, that is hopefully testable, and reduces to Einstein's theory in the classical limit.  There is general agreement that no real, definite progress has been made.



SOME MILESTONES IN QUANTUM GRAVITY:

SUPERGRAVITY (1976)--- interest in such approaches has waxed and waned over the years, with most theoretical attention going to more general string theories.

LOOP QUANTUM GRAVITY (beginning 1986)--- The major current contender to provide an alternative to string-theory-based approaches to quantum gravity. It is basically a “brute-force” direct quantization of space-time itself. There is no boson for gravity in LQG. Where the quantization of space-time leaves the rest of quantum field theory is an unsettled issue. Some versions of LQG incorporate supersymmetry.

TENTATIVE IDEAS--- After so many years, dozens of different ways to approach quantum gravity have been suggested, without much of interest resulting.

Here is a summary of current research at one of the major centers for QG studies.  A main problem is of course that Einstein's Theory of Gravity works so well... there are no failures pointing out any way to go beyond it.  Similarly, the Standard Model works incredibly well everywhere it is tested, and again there is nothing pointing out any way to go beyond it.