Page 88 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 11
(though this is not yet known for certain). String theories, however, have a bigger problem: they seem to be
consistent only if space-time has either ten or twenty-six dimensions, instead of the usual four! Of course, extra
space-time dimensions are a commonplace of science fiction indeed, they provide an ideal way of overcoming
the normal restriction of general relativity that one cannot travel faster than light or back in time (see Chapter
10). The idea is to take a shortcut through the extra dimensions. One can picture this in the following way.
Imagine that the space we live in has only two dimensions and is curved like the surface of an anchor ring or
torus Figure 11:7.

Figure 11:7

If you were on one side of the inside edge of the ring and you wanted to get to a point on the other side, you
would have to go round the inner edge of the ring. However, if you were able to travel in the third dimension,
you could cut straight across.

Why don’t we notice all these extra dimensions, if they are really there? Why do we see only three space
dimensions and one time dimension? The suggestion is that the other dimensions are curved up into a space of
very small size, something like a million million million million millionth of an inch. This is so small that we just
don’t notice it: we see only one time dimension and three space dimensions, in which space-time is fairly flat. It
is like the surface of a straw. If you look at it closely, you see it is two-dimensional (the position of a point on the
straw is described by two numbers, the length along the straw and the distance round the circular direction).
But if you look at it from a distance, you don’t see the thickness of the straw and it looks one-dimensional (the
position of a point is specified only by the length along the straw). So it is with space-time: on a very small scale
it is ten-dimensional and highly curved, but on bigger scales you don’t see the curvature or the extra
dimensions. If this picture is correct, it spells bad news for would-be space travelers: the extra dimensions
would be far too small to allow a spaceship through. However, it raises another major problem. Why should
some, but not all, of the dimensions be curled up into a small ball? Presumably, in the very early universe all
the dimensions would have been very curved. Why did one time dimension and three space dimensions flatten

file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (7 of 11) [2/20/2001 3:15:56 AM]