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
basic than the quarks and electrons that we now regard as “elementary” particles.
However, it seems that gravity may provide a limit to this sequence of “boxes within boxes.” If one had a
particle with an energy above what is called the Planck energy, ten million million million GeV (1 followed by
nineteen zeros), its mass would be so concentrated that it would cut itself off from the rest of the universe and
form a little black hole. Thus it does seem that the sequence of more and more refined theories should have
some limit as we go to higher and higher energies, so that there should be some ultimate theory of the
universe. Of course, the Planck energy is a very long way from the energies of around a hundred GeV, which
are the most that we can produce in the laboratory at the present time. We shall not bridge that gap with
particle accelerators in the foreseeable future! The very early stages of the universe, however, are an arena
where such energies must have occurred. I think that there is a good chance that the study of the early
universe and the requirements of mathematical consistency will lead us to a complete unified theory within the
lifetime of some of us who are around today, always presuming we don’t blow ourselves up first.
What would it mean if we actually did discover the ultimate theory of the universe? As was explained in Chapter
1, we could never be quite sure that we had indeed found the correct theory, since theories can’t be proved.
But if the theory was mathematically consistent and always gave predictions that agreed with observations, we
could be reasonably confident that it was the right one. It would bring to an end a long and glorious chapter in
the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionize the
ordinary person’s understanding of the laws that govern the universe. In Newton’s time it was possible for an
educated person to have a grasp of the whole of human knowledge, at least in outline. But since then, the pace
of the development of science has made this impossible. Because theories are always being changed to
account for new observations, they are never properly digested or simplified so that ordinary people can
understand them. You have to be a specialist, and even then you can only hope to have a proper grasp of a
small proportion of the scientific theories. Further, the rate of progress is so rapid that what one learns at school
or university is always a bit out of date. Only a few people can keep up with the rapidly advancing frontier of
knowledge, and they have to devote their whole time to it and specialize in a small area. The rest of the
population has little idea of the advances that are being made or the excitement they are generating. Seventy
years ago, if Eddington is to be believed, only two people understood the general theory of relativity. Nowadays
tens of thousands of university graduates do, and many millions of people are at least familiar with the idea. If a
complete unified theory was discovered, it would only be a matter of time before it was digested and simplified
in the same way and taught in schools, at least in outline. We would then all be able to have some
understanding of the laws that govern the universe and are responsible for our existence.
Even if we do discover a complete unified theory, it would not mean that we would be able to predict events in
general, for two reasons. The first is the limitation that the uncertainty principle of quantum mechanics sets on
our powers of prediction. There is nothing we can do to get around that. In practice, however, this first limitation
is less restrictive than the second one. It arises from the fact that we could not solve the equations of the theory
exactly, except in very simple situations. (We cannot even solve exactly for the motion of three bodies in
Newton’s theory of gravity, and the difficulty increases with the number of bodies and the complexity of the
theory.) We already know the laws that govern the behavior of matter under all but the most extreme
conditions. In particular, we know the basic laws that underlie all of chemistry and biology. Yet we have
certainly not reduced these subjects to the status of solved problems: we have, as yet, had little success in
predicting human behavior from mathematical equations! So even if we do find a complete set of basic laws,
there will still be in the years ahead the intellectually challenging task of developing better approximation
methods, so that we can make useful predictions of the probable outcomes in complicated and realistic
situations. A complete, consistent, unified theory is only the first step: our goal is a complete understanding of
the events around us, and of our own existence.
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PREVIOUS NEXT
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CHAPTER 12
CONCLUSION
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We find ourselves in a bewildering world. We want to make sense of what we see around us and to ask: What
is the nature of the universe? What is our place in it and where did it and we come from? Why is it the way it is?
To try to answer these questions we adopt some “world picture.” Just as an infinite tower of tortoises supporting
the fiat earth is such a picture, so is the theory of superstrings. Both are theories of the universe, though the
latter is much more mathematical and precise than the former. Both theories lack observational evidence: no
one has ever seen a giant tortoise with the earth on its back, but then, no one has seen a superstring either.
However, the tortoise theory fails to be a good scientific theory because it predicts that people should be able to
fall off the edge of the world. This has not been found to agree with experience, unless that turns out to be the
explanation for the people who are supposed to have disappeared in the Bermuda Triangle!
The earliest theoretical attempts to describe and explain the universe involved the idea that events and natural
phenomena were controlled by spirits with human emotions who acted in a very humanlike and unpredictable
manner. These spirits inhabited natural objects, like rivers and mountains, including celestial bodies, like the
sun and moon. They had to be placated and their favor sought in order to ensure the fertility of the soil and the
rotation of the seasons. Gradually, however, it must have been noticed that there were certain regularities: the
sun always rose in the east and set in the west, whether or not a sacrifice had been made to the sun god.
Further, the sun, the moon, and the planets followed precise paths across the sky that could be predicted in
advance with considerable accuracy. The sun and the moon might still be gods, but they were gods who
obeyed strict laws, apparently without any exceptions, if one discounts stories like that of the sun stopping for
Joshua.
At first, these regularities and laws were obvious only in astronomy and a few other situations. However, as
civilization developed, and particularly in the last 300 years, more and more regularities and laws were
discovered. The success of these laws led Laplace at the beginning of the nineteenth century to postulate
scientific determinism; that is, he suggested that there would be a set of laws that would determine the
evolution of the universe precisely, given its configuration at one time.
Laplace’s determinism was incomplete in two ways. It did not say how the laws should be chosen and it did not
specify the initial configuration of the universe. These were left to God. God would choose how the universe
began and what laws it obeyed, but he would not intervene in the universe once it had started. In effect, God
was confined to the areas that nineteenth-century science did not understand.
We now know that Laplace’s hopes of determinism cannot be realized, at least in the terms he had in mind.
The uncertainty principle of quantum mechanics implies that certain pairs of quantities, such as the position and
velocity of a particle, cannot both be predicted with complete accuracy. Quantum mechanics deals with this
situation via a class of quantum theories in which particles don’t have well-defined positions and velocities but
are represented by a wave. These quantum theories are deterministic in the sense that they give laws for the
evolution of the wave with time. Thus if one knows the wave at one time, one can calculate it at any other time.
The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions
and velocities of particles. But maybe that is our mistake: maybe there are no particle positions and velocities,
but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. The
resulting mismatch is the cause of the apparent unpredictability.
In effect, we have redefined the task of science to be the discovery of laws that will enable us to predict events
up to the limits set by the uncertainty principle. The question remains, however: how or why were the laws and
the initial state of the universe chosen?
In this book I have given special prominence to the laws that govern gravity, because it is gravity that shapes
the large-scale structure of the universe, even though it is the weakest of the four categories of forces. The
laws of gravity were incompatible with the view held until quite recently that the universe is unchanging in time:
the fact that gravity is always attractive implies that the universe must be either expanding or contracting.
According to the general theory of relativity, there must have been a state of infinite density in the past, the big
bang, which would have been an effective beginning of time. Similarly, if the whole universe recollapsed, there
must be another state of infinite density in the future, the big crunch, which would be an end of time. Even if the
whole universe did not recollapse, there would be singularities in any localized regions that collapsed to form
black holes. These singularities would be an end of time for anyone who fell into the black hole. At the big bang
and other singularities, all the laws would have broken down, so God would still have had complete freedom to
choose what happened and how the universe began.
When we combine quantum mechanics with general relativity, there seems to be a new possibility that did not
