Quantum Field Theory
The next contradiction that physicists faced was between quantum mechanics
(which had been developed over the thirty years following Planck's seminal insight)
and the special theory of relativity. Most of the work in quantum mechanics
was in the Galilean (or non-relativistic) approximation.
To be sure, Dirac
had developed a relativistic wave equation for the electron, which was an important
advance, but there was still a basic contradiction that needed to be resolved.
The new feature that is required in a successful union of quantum mechanics
and special relativity is the possibility of the creation and annihilation of
quanta (or `particles'). The non-relativistic theory does not have this feature.
The framework in which quantum mechanics and special relativity are
successfully reconciled
is called quantum field theory. It is based on three basic principles: two of them, of
course, are quantum mechanics and special relativity. The third one, which I wish to
emphasize, is the postulate that elementary particles are point-like objects of
zero intrinsic size. In practice, they are smeared over a region of space due to quantum
effects, but their descripton in the basic equations is as mathematical points.
Now the general principles on which quantum field theory are based actually allow
for many different consistent theories to be constructed. (The consistency has
not been established with mathematical rigour, but this is not a concern for most
physicists.)
Among these various possible theories there is a class of theories,
called `gauge theories' or `Yang-Mills theories' that turn out to be especially
interesting and important. These are characterized by a symmetry structure (called a
Lie group) and the assignment of various matter particles to particular symmetry
patterns (called group representations). There is an infinite set of possibilities
for the choice of the symmetry group, and for each group there are many possible
choices of group representations for the matter particles.
One of this infinite array
of theories has been experimentally singled out. It is called the ``standard model''.
It is based on a Lie group called SU(3) X SU(2) X U(1). The matter
particles consist of three families of quarks and leptons. (I will not describe the
representations that they are assigned to here.) There are also addition matter
particles called ``Higgs particles'', which are required to account for the fact that
part of the symmetry is spontaneously broken.
The standard model contains some
20 adjustable parameters, whose values are determined experimentally.
Still, there are many
more things that can be measured than that, and the standard model is
amazingly successful in accounting for a wide range of experiments to very
high precision. Indeed, at the time this is written, there is only
one clear-cut piece of experimental
evidence that the standard model is not an exactly correct theory.
This evidence is the fact that the
standard model does not contain gravity!
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