Three Roads To Quantum Gravity

192 THREE ROADS TO QUANTUM GRAVITY
can be applied very widely, and give a general and completely
detailed description of what a horizon would look like were it
to be probed on the Planck scale.
While this work applies to a much larger class of black holes
than can be addressed by string theory, it does have one
shortcoming compared with string theory: there is one
constant that has to be adjusted to make the entropy and
temperature come out right. This constant determines the
value of Newton's gravitational constant, as measured on large
scales. It turns out that there is a small change in the value of
the constant when one compares its value measured on the
Planck scale with the value measured at large distances. This
is not surprising. Shifts like this occur commonly in solid state
physics, when one takes into account the effect of the atomic
structure of matter. This shift is ®nite, and has to be made just
once, for the whole theory. (It is actually equal to the H3/log
2.) Once done it brings the results for all different kinds of
black holes in exact agreement with the predictions by
Bekenstein and Hawking that we discussed in Chapters 6 to 8.
Thus, string theory and loop quantum gravity have each
added something essential to our understanding of black holes.
One may ask whether there is a con¯ict between the two results.
So far none is known, but this is largely because, at the moment,
the two methods apply to different kinds of black hole. To be
sure, we need to ®nd a way of extending one of the methods so
that it covers the cases covered by the other method. When we
can do this we will be able to make a clean test of whether the
pictures of black holes given by loop quantum gravity and
string theory are consistent with each other.
This is more or less what we have been able to understand
so far about black holes from the microscopic point of view. A
great deal has been understood, although it must also be said
that some very important questions remain unanswered. The
most important of these have to do with the interiors of black
holes. Quantum gravity should have something to say about
the singular region in the interior of a black hole, in which the
density of matter and the strength of the gravitational ®eld
become in®nite. There are speculations that quantum effects
will remove the singularity, and that one consequence of this