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 spacetime 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
spacetime, 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,t_{0})ψ(t_{0})⟩, 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 mid1970s, 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,t_{0})
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 stringtheorybased
approaches to quantum gravity. It is basically a “bruteforce”
direct quantization of spacetime itself. There is no boson for
gravity in LQG. Where the quantization of spacetime 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.