Page 82 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 11
CHAPTER 11

THE UNIFICATION OF PHYSICS

As was explained in the first chapter, it would be very difficult to construct a complete unified theory of
everything in the universe all at one go. So instead we have made progress by finding partial theories that
describe a limited range of happenings and by neglecting other effects or approximating them by certain
numbers. (Chemistry, for example, allows us to calculate the interactions of atoms, without knowing the internal
structure of an atom’s nucleus.) Ultimately, however, one would hope to find a complete, consistent, unified
theory that would include all these partial theories as approximations, and that did not need to be adjusted to fit
the facts by picking the values of certain arbitrary numbers in the theory. The quest for such a theory is known
as “the unification of physics.” Einstein spent most of his later years unsuccessfully searching for a unified
theory, but the time was not ripe: there were partial theories for gravity and the electromagnetic force, but very
little was known about the nuclear forces. Moreover, Einstein refused to believe in the reality of quantum
mechanics, despite the important role he had played in its development. Yet it seems that the uncertainty
principle is a fundamental feature of the universe we live in. A successful unified theory must, therefore,
necessarily incorporate this principle.

As I shall describe, the prospects for finding such a theory seem to be much better now because we know so
much more about the universe. But we must beware of overconfidence – we have had false dawns before! At
the beginning of this century, for example, it was thought that everything could be explained in terms of the
properties of continuous matter, such as elasticity and heat conduction. The discovery of atomic structure and
the uncertainty principle put an emphatic end to that. Then again, in 1928, physicist and Nobel Prize winner
Max Born told a group of visitors to Gottingen University, “Physics, as we know it, will be over in six months.”
His confidence was based on the recent discovery by Dirac of the equation that governed the electron. It was
thought that a similar equation would govern the proton, which was the only other particle known at the time,
and that would be the end of theoretical physics. However, the discovery of the neutron and of nuclear forces
knocked that one on the head too. Having said this, I still believe there are grounds for cautious optimism that
we may now be near the end of the search for the ultimate laws of nature.

In previous chapters I have described general relativity, the partial theory of gravity, and the partial theories that
govern the weak, the strong, and the electromagnetic forces. The last three may be combined in so-called
grand unified theories, or GUTs, which are not very satisfactory because they do not include gravity and
because they contain a number of quantities, like the relative masses of different particles, that cannot be
predicted from the theory but have to be chosen to fit observations. The main difficulty in finding a theory that
unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate
the uncertainty principle of quantum mechanics. On the other hand, the other partial theories depend on
quantum mechanics in an essential way. A necessary first step, therefore, is to combine general relativity with
the uncertainty principle. As we have seen, this can produce some remarkable consequences, such as black
holes not being black, and the universe not having any singularities but being completely self-contained and
without a boundary. The trouble is, as explained in Chapter 7, that the uncertainty principle means that even
“empty” space is filled with pairs of virtual particles and antiparticles. These pairs would have an infinite amount
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of energy and, therefore, by Einstein’s famous equation E = mc , they would have an infinite amount of mass.
Their gravitational attraction would thus curve up the universe to infinitely small size.

Rather similar, seemingly absurd infinities occur in the other partial theories, but in all these cases the infinities
can be canceled out by a process called renormalization. This involves canceling the infinities by introducing
other infinities. Although this technique is rather dubious mathematically, it does seem to work in practice, and
has been used with these theories to make predictions that agree with observations to an extraordinary degree
of accuracy. Renormalization, however, does have a serious drawback from the point of view of trying to find a
complete theory, because it means that the actual values of the masses and the strengths of the forces cannot
be predicted from the theory, but have to be chosen to fit the observations.

In attempting to incorporate the uncertainty principle into general relativity, one has only two quantities that can
be adjusted: the strength of gravity and the value of the cosmological constant. But adjusting these is not

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