Three Roads To Quantum Gravity

WHAT CHOOSES THE LAWS OF NATURE?
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Planck dimensions, then we would expect the elementary
particles to have similar dimensions. The fact that protons
and neutrons are nearly 20 orders of magnitude lighter than
the Planck mass seems very hard to understand. But since the
theory would be unique it would have to get this right.
String theory was invented with the hope that it would be
this ®nal theory. It was its potential uniqueness that made it
worth studying, even as it became clear that it was not soon
going to lead to predictions about the masses of particles or
anything else that could be tested experimentally. After all, if
there is one unique theory it does not need experiments to
verify it ± all that is needed is to show that it is mathematically
consistent. A unique theory must automatically be
proved right by experiments, so it does not matter if a test of
the theory is several centuries away. If we accept the
assumption that there is one unique theory, then it will pay
to concentrate on the problem of testing that theory for
mathematical consistency rather than on developing experimental
tests for it.
The problem is that string theory did not turn out to be
unique. It was instead found to come in a very large number of
versions, each equally consistent. From our present-day
perspective, taking into account only the results on the table,
it seems that the hope for a unique theory is a false hope. In
the current language of string theory, there is no way to
distinguish between any of a very large number of theories:
they are all equally consistent. Moreover, many of them have
adjustable parameters, which could be changed to obtain
agreement with experiment.
Looking back, it is clear that the assumption that a uni®ed
theory would be unique was no more than that ± an
assumption. There is no mathematical or philosophical
principle which guarantees there to be only one mathematically
consistent theory of nature. In fact, we now know that
there can be no such theory. For example, suppose that the
world had one or two spatial dimensions, rather than three.
For these cases we have constructed lots of consistent
quantum theories, including some which have gravity.
These were done as warm-up exercises for various research