Three Roads To Quantum Gravity

CHAPTER 8
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AREA AND INFORMATION
At the beginning of the twentieth century, few physicists
believed in atoms. Now there are few educated people who do
not believe in them. But what about space? If we take a bit of
space, say a cube 1 centimetre on each side, we can divide
each side in two to give eight smaller pieces of space. We can
divide each of these again, and so on. With matter there is a
limit to how small we can divide something, for at some point
we are left with individual atoms. Is the same true of space? If
we continue dividing, do we eventually come to a smallest
unit of space, some smallest possible volume? Or can we go
on for ever, dividing space into smaller and smaller bits,
without ever having to stop? All three of the roads I described
in the Prologue favour the same answer to this question: that
there is indeed a smallest unit of space. It is much smaller
than an atom of matter, but nevertheless, as I shall describe in
this chapter and the next three, there are good reasons to
believe that the continuous appearance of space is as much an
illusion as the smooth appearance of matter. When we look on
a small enough scale, we see that space is made of things that
we can count.
Perhaps it is hard to visualize space as something discrete.
After all, why can something not be made to ®t into half the
volume of the smallest unit of space? The answer is that this is
the wrong way to think, for to pose this question is to presume
that space has some absolute existence into which things can
®t. To understand what we mean when we say that space is