Three Roads To Quantum Gravity

THE SOUND OF SPACE IS A STRING
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information about these relationships can be used to learn
something about the structure M theory must have, if it exists.
For example, it gives us some information about the symmetries
that M theory will have. These are symmetries that
extend the idea of duality in a major way, which could not
be done within any single string theory.
Another very important question is whether M theory
describes a universe in which space and time are continuous
or discrete. At ®rst it seems that string theory points to a
continuous world, because it is based on a picture of strings
moving continuously through space and time. But this turns
out to be misleading, for when looked at closely string theory
seems to be describing a world in which space has a discrete
structure.
One way to see the discreteness is to study strings on a
space that has been wrapped up, so that one dimension forms
a circle (Figure 37). The circle which has been wrapped up
has radius R. You might think that the theory would get into
trouble if we allowed R to get smaller and smaller. But string
theory turns out to have the amazing property that what
Hidden dimensions
Ordinary dimensions
An ordinary string
A string wrapped on the
circle which is in the direction
of a hidden dimension
FIGURE 37
A cylinder is a two-dimensional space in which one direction is a circle. We
see a string wrapped on the circle. This is typical of ideas of how the extra
dimensions are hidden; the horizontal direction is typical of the three
ordinary directions, while the vertical direction stands for one of the hidden
dimensions. Time is not indicated here.