Page 90 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 11
observe the different number of effective dimensions.

Another problem is that there are at least four different string theories (open strings and three different closed
string theories) and millions of ways in which the extra dimensions predicted by string theory could be curled
up. Why should just one string theory and one kind of curling up be picked out? For a time there seemed no
answer, and progress got bogged down. Then, from about 1994, people started discovering what are called
dualities: different string theories and different ways of curling up the extra dimensions could lead to the same
results in four dimensions. Moreover, as well as particles, which occupy a single point of space, and strings,
which are lines, there were found to be other objects called p-branes, which occupied two-dimensional or
higher-dimensional volumes in space. (A particle can be regarded as a 0-brane and a string as a 1-brane but
there were also p-branes for p=2 to p=9.) What this seems to indicate is that there is a sort of democracy
among supergravity, string, and p-brane theories: they seem to fit together but none can be said to be more
fundamental than the others. They appear to be different approximations to some fundamental theory that are
valid in different situations.

People have searched for this underlying theory, but without any success so far. However, I believe there may
not be any single formulation of the fundamental theory any more than, as Godel showed, one could formulate
arithmetic in terms of a single set of axioms. Instead it may be like maps – you can’t use a single map to
describe the surface of the earth or an anchor ring: you need at least two maps in the case of the earth and four
for the anchor ring to cover every point. Each map is valid only in a limited region, but different maps will have a
region of overlap. The collection of maps provides a complete description of the surface. Similarly, in physics it
may be necessary to use different formulations in different situations, but two different formulations would agree
in situations where they can both be applied. The whole collection of different formulations could be regarded
as a complete unified theory, though one that could not be expressed in terms of a single set of postulates.

But can there really be such a unified theory? Or are we perhaps just chasing a mirage? There seem to be
three possibilities:

1. There really is a complete unified theory (or a collection of overlapping formulations), which we will someday
discover if we are smart enough.

2. There is no ultimate theory of the universe, just an infinite sequence of theories that describe the universe
more and more accurately.

3. There is no theory of the universe: events cannot be predicted beyond a certain extent but occur in a random
and arbitrary manner.

Some would argue for the third possibility on the grounds that if there were a complete set of laws, that would
infringe God’s freedom to change his mind and intervene in the world. It’s a bit like the old paradox: can God
make a stone so heavy that he can’t lift it? But the idea that God might want to change his mind is an example
of the fallacy, pointed out by St. Augustine, of imagining God as a being existing in time: time is a property only
of the universe that God created. Presumably, he knew what he intended when he set it up!

With the advent of quantum mechanics, we have come to recognize that events cannot be predicted with
complete accuracy but that there is always a degree of uncertainty. If one likes, one could ascribe this
randomness to the intervention of God, but it would be a very strange kind of intervention: there is no evidence
that it is directed toward any purpose. Indeed, if it were, it would by definition not be random. In modern times,
we have effectively removed the third possibility above by redefining the goal of science: our aim is to formulate
a set of laws that enables us to predict events only up to the limit set by the uncertainty principle.

The second possibility, that there is an infinite sequence of more and more refined theories, is in agreement
with all our experience so far. On many occasions we have increased the sensitivity of our measurements or
made a new class of observations, only to discover new phenomena that were not predicted by the existing
theory, and to account for these we have had to develop a more advanced theory. It would therefore not be
very surprising if the present generation of grand unified theories was wrong in claiming that nothing essentially
new will happen between the electroweak unification energy of about 100 GeV and the grand unification energy
of about a thousand million million GeV. We might indeed expect to find several new layers of structure more

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