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If the strings have Grassmann dimensions as well as their ordinary number
dimensions, the ripples will correspond to bosons and fermions. In this case,
the positive and negative ground state energies will cancel so exactly that
there will be no infinities even of the smaller sort. Superstrings, it was
claimed, were the TOE, the Theory of Everything.
Historians of science in the future will find it interesting to chart the
changing tide of opinion among theoretical physicists. For a few years, strings
reigned supreme and supergravity was dismissed as just an approximate theory,
valid at low energy. The qualification "low energy" was considered
particularly damning, even though in this context low energies meant particles
with energies of less than a billion billion times those of particles in a TNT
explosion. If supergravity was only a low energy approximation, it could not
claim to be the fundamental theory of the universe. Instead, the underlying
theory was supposed to be one of five possible superstring theories. But which
of the five string theories described our universe? And how could string theory
be formulated, beyond the approximation in which strings were pictured as
surfaces with one space dimension and one time dimension moving through a flat
background spacetime? Wouldn't the strings curve the background spacetime?
In the years after 1985, it gradually became apparent that string theory
wasn't the complete picture. To start with, it was realized that strings are
just one member of a wide class of objects that can be extended in more than one
dimension. Paul Townsend, who, like me, is a member of the Department of Applied
Mathematics and Theoretical Physics at Cambridge, and who did much of the
fundamental work on these objects, gave them the name "p-branes." A p-brane
has length in p directions. Thus a p=1 brane is a string, a p=2 brane is a
surface or membrane, and so on.There seems no reason to favor the p=1 string
case over other possible values of p. Instead, we should adopt the principle of
p-brane democracy: all p-branes are created equal.
All the p-branes could be found as solutions of the equations of supergravity
theories in 10 or 11 dimensions. While 10 or 11 dimensions doesn't sound much
like the spacetime we experience, the idea was that the other 6 or 7 dimensions
are curled up so small that we don't notice them; we are only aware of the
remaining 4 large and nearly flat dimensions.
I must say that personally, I have been reluctant to believe in extra
dimensions. But as I am a positivist, the question "Do extra dimensions really
exist?" has no meaning. All one can ask is whether mathematical models with
extra dimensions provide a good description of the universe. We do not yet have
any observations that require extra dimensions for their explanation. However,
there is a possibility we may observe them in the Large Hadron Collider in
Geneva. But what has convinced many people, including myself, that one should
take models with extra dimensions seriously is that there is a web of unexpected
relationships, called dualities, between the models. These dualities show that
the models are all essentially equivalent; that is, they are just different
aspects of the same underlying theory, which has been given the name M-theory.
Not to take this web of dualities as a sign we are on the right track would be a
bit like believing that God put fossils into the rocks in order to mislead
Darwin about the evolution of life.
These dualities show that the five superstring theories all describe the same
physics and that they are also physically equivalent to supergravity. One cannot
say that superstrings are more fundamental than supergravity, or vice versa.
Rather, they are different expressions of the same underlying theory, each
useful for calculations in different kinds of situations. Because string
theories don't have any infinities, they are good for calculating what happens
when a few high energy particles collide and scatter off each other. However,
they are not of much use for describing how the energy of a very large number of
particles curves the universe or forms a bound state, like a black hole. For
these situations, one needs supergravity, which is basically Einstein's theory
of curved spacetime with some extra kinds of matter. It is this picture that I
shall mainly use in what follows.
Excerpted from The Universe in a Nutshell by Stephen Hawking Copyright 2001 by Stephen Hawking. Excerpted by permission of Bantam, a division of Random House, Inc. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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