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Because energy density is, like matter, a source of gravity, this infinite
energy density ought to mean there is enough gravitational attraction in the
universe to curl spacetime into a single point, which obviously hasn't
happened.
One might hope to solve the problem of this seeming contradiction between
observation and theory by saying that the ground state fluctuations have no
gravitational effect, but this would not work. One can detect the energy of
ground state fluctuations by the Casimir effect. If you place a pair of metal
plates parallel to each other and close together, the effect of the plates is to
reduce slightly the number of wavelengths that fit between the plates relative
to the number outside. This means that the energy density of ground state
fluctuations between the plates, although still infinite, is less than the
energy density outside by a finite amount. This difference in energy density
gives rise to a force pulling the plates together, and this force has been
observed experimentally.
Forces are a source of gravity in general relativity, just as matter is, so it
would not be consistent to ignore the gravitational effect of this energy
difference.
Another possible solution to the problem might be to suppose there was a
cosmological constant such as Einstein introduced in an attempt to have a static
model of the universe. If this constant had an infinite negative value, it could
exactly cancel the infinite positive value of the ground state energies in free
space, but this cosmological constant seems very ad hoc, and it would have to be
tuned to extraordinary accuracy.
Fortunately, a totally new kind of symmetry was discovered in the 1970s that
provides a natural physical mechanism to cancel the infinities arising from
ground state fluctuations.
Supersymmetry is a feature of our modern mathematical models that can be
described in various ways. One way is to say that spacetime has extra dimensions
besides the dimensions we experience. These are called Grassmann dimensions,
because they are measured in numbers known as Grassmann variables rather than in
ordinary real numbers. Ordinary numbers commute; that is, it does not matter in
which order you multiply them: 6 times 4 is the same as 4 times 6. But Grassmann
variables anticommute: x times y is the same as –y times x.
Supersymmetry was first considered for removing infinities in matter fields and
Yang-Mills fields in a spacetime where both the ordinary number dimensions and
the Grassmann dimensions were flat, not curved. But it was natural to extend it
to ordinary numbers and Grassmann dimensions that were curved. This led to a
number of theories called supergravity, with different amounts of supersymmetry.
One consequence of supersymmetry is that every field or particle should have a "superpartner" with a spin that is either 1/2 greater than its own or 1/2
less.
The ground state energies of bosons, fields whose spin is a whole number (0, 1,
2 , etc.), are positive. On the other hand, the ground state energies of
fermions, fields whose spin is a half number (1/2, 3/2 , etc.), are negative.
Because there are equal numbers of bosons and fermions, the biggest infinities
cancel in supergravity theories.
There remained the possibility that there might be smaller but still infinite
quantities left over. No one had the patience needed to calculate whether these
theories were actually completely finite. It was reckoned it would take a good
student two hundred years, and how would you know he hadn't made a mistake on
the second page? Still, up to 1985, most people believed that most
supersymmetric supergravity theories would be free of infinities.
Then suddenly the fashion changed. People declared there was no reason not to
expect infinities in supergravity theories, and this was taken to mean they were
fatally flawed as theories. Instead, it was claimed that a theory named
supersymmetric string theory was the only way to combine gravity with quantum
theory. Strings, like their namesakes in everyday experience, are
one-dimensional extended objects. They have only length. Strings in string
theory move through a background spacetime. Ripples on the string are
interpreted as particles.
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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