Classical Theory by S. W. Hawking
Classical Theory by S. W. Hawking
In these lectures Roger Penrose and I will put forward our related but rather different
viewpoints on the nature of space and time. We shall speak alternately and shall give three
lectures each, followed by a discussion on our different approaches. I should emphasize that
these will be technical lectures. We shall assume a basic knowledge of general relativity
and quantum theory.
There is a short article by Richard Feynman describing his experiences at a conference
on general relativity. I think it was the Warsaw conference in 1962. It commented very
unfavorably on the general competence of the people there and the relevance of what
they were doing. That general relativity soon acquired a much better reputation, and
more interest, is in a considerable measure because of Roger’s work. Up to then, general
relativity had been formulated as a messy set of partial differential equations in a single
coordinate system. People were so pleased when they found a solution that they didn’t
care that it probably had no physical significance. However, Roger brought in modern
concepts like spinors and global methods. He was the first to show that one could discover
general properties without solving the equations exactly. It was his first singularity theorem that introduced me to the study of causal structure and inspired my classical work on
singularities and black holes.
I think Roger and I pretty much agree on the classical work. However, we differ in
our approach to quantum gravity and indeed to quantum theory itself. Although I’m
regarded as a dangerous radical by particle physicists for proposing that there may be loss
hep-th/9409195 30 Sep 94
of quantum coherence I’m definitely a conservative compared to Roger. I take the positivist
viewpoint that a physical theory is just a mathematical model and that it is meaningless
to ask whether it corresponds to reality. All that one can ask is that its predictions should be in agreement with observation. I think Roger is a Platonist at heart but he must answer
for himself.
Although there have been suggestions that spacetime may have a discrete structure
I see no reason to abandon the continuum theories that have been so successful. General
relativity is a beautiful theory that agrees with every observation that has been made. It
may require modifications on the Planck scale but I don’t think that will affect many of
the predictions that can be obtained from it. It may be only a low energy approximation
to some more fundemental theory, like string theory, but I think string theory has been
over sold. First of all, it is not clear that general relativity, when combined with various
other fields in a supergravity theory, can not give a sensible quantum theory. Reports of
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the death of supergravity are exaggerations. One year everyone believed that supergravity was finite. The next year the fashion changed and everyone said that supergravity was
bound to have divergences even though none had actually been found. My second reason
for not discussing string theory is that it has not made any testable predictions. By
contrast, the straight forward application of quantum theory to general relativity, which I
will be talking about, has already made two testable predictions. One of these predictions,
the development of small perturbations during inflation, seems to be confirmed by recent
observations of fluctuations in the microwave background. The other prediction, that
black holes should radiate thermally, is testable in principle. All we have to do is find a
primordial black hole. Unfortunately, there don’t seem many around in this neck of the
woods. If there had been we would know how to quantize gravity.
Neither of these predictions will be changed even if string theory is the ultimate
theory of nature. But string theory, at least at its current state of development, is quite
incapable of making these predictions except by appealing to general relativity as the low
energy effective theory. I suspect this may always be the case and that there may not be
any observable predictions of string theory that can not also be predicted from general
relativity or supergravity. If this is true it raises the question of whether string theory is a genuine scientific theory. Is mathematical beauty and completeness enough in the absence