Three Roads To Quantum Gravity

CHAPTER 9
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HOW TO COUNT SPACE
The ®rst approach to quantum gravity that yielded a detailed
description of the atomic structure of space and spacetime
was loop quantum gravity. The theory offers more than a
picture: it makes precise predictions about what would be
observed were it possible to probe the geometry of space at
distances as short as the Planck scale.
According to loop quantum gravity, space is made of discrete
atoms each of which carries a very tiny unit of volume. In
contrast to ordinary geometry, a given region cannot have a
volume which is arbitrarily big or small ± instead, the volume
must be one of a ®nite set of numbers. This is just what quantum
theory does with other quantities: it restricts a quantity that is
continuous according to Newtonian physics to a ®nite set of
values. This is what happens to the energy of an electron in an
atom, and to the value of the electric charge. As a result, we say
that the volume of space is predicted to be quantized.
One consequence of this is that there is a smallest possible
volume. This minimum volume is minuscule ± about 10 99 of
them would ®t into a thimble. If you tried to halve a region of
this volume, the result would not be two regions each with half
that volume. Instead, the process would create two new regions
which together would have more volume than you started with.
We describe this by saying that the attempt to measure a unit of
volume smaller than the minimal size alters the geometry of the
space in a way that allows more volume to be created
Volume is not the only quantity which is quantized in loop