Three Roads To Quantum Gravity

BLACK HOLES AND HIDDEN REGIONS
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lengthened as the frequency is decreased. This is because the
wavelength of light is always inversely proportional to its
frequency. As a result, if the frequency is diminished, the
wavelength must be increased by the same factor.
But this means that the black hole is acting as a kind of
microscope. It is not an ordinary microscope, as it does not act
by enlarging images of objects. Rather, it acts by stretching
wavelengths of light. But nevertheless, this is very useful to
us. For suppose that at very short distances space has a
different nature than the space we see looking around at
ordinary scales. Space would then look very different from
the simple three-dimensional Euclidean geometry that seems
to suf®ce to describe the immediately perceptible world.
There are various possibilities, and we shall be discussing
these in later chapters. Space may be discrete, which means
that geometry comes in bits of a certain absolute size. Or there
may be quantum uncertainty in the very geometry of space.
Just as electrons cannot be localized at precise points in the
atom, but are forever dancing around the nucleus, the
geometry of space may itself be dancing and ¯uctuating.
Ordinarily we cannot see what is happening on very small
length scales. The reason is that we cannot use light to look at
something which is smaller than the wavelength of that light.
If we use ordinary light, even the best microscope will not
resolve any object smaller than a few thousand times the
diameter of an atom, which is the wavelength of the visible
part of the spectrum of light. To see smaller objects we can use
ultraviolet light, but no microscope in existence, not even one
that uses electrons or protons in place of light, can come
anywhere near the resolution required to see the quantum
structure of space.
But black holes offer us a way around this problem.
Whatever is happening on very small scales near the horizon
of the black hole will be enlarged by the effect whereby the
wavelengths of light are stretched as the light climbs up to us.
This means that if we can observe light coming from very
close to the horizon of a black hole, we may be able to see the
quantum structure of space itself.
Unfortunately, it has so far proved impractical to make a