Page 88 - A Brief History of Time - Stephen Hawking
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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




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