The Standard Model
When I studied physics in high school and college, atoms were portrayed
as consisting of a nucleus of protons and neutrons, with electrons orbit-
ing around the nucleus in a manner akin to planets orbiting a star (al-
though some of my teachers did mention that this was not a totally
accurate depiction). There were four forces—gravity, electromagnetism,
the weak force (which governed radioactivity), and the strong force (which
held nuclei together against the mutual repulsion of the positively charged
protons in the nucleus). There were a few leftover particles, such as neu-
trinos and muons, and although it was understood that electromagnet-
ism was the result of movement of electrons, the jury was still out on how
the other forces worked.
Half a century later, much of this has been augmented and unified as the
Standard Model.^7 It is now known that there are three families of particles
that admit a very attractive classification scheme, and that forces are con-
veyed through the interchange of various particles. However, even if the
Standard Model is the last word, there are still numerous questions, such
as “What causes mass?” (the current leading contender is something called
the Higgs particle, which no one has yet seen and which always seems to
be one generation of particle accelerators away) and “Why is electromagnet-
ism stronger than gravity by a factor of 1 followed by 39 zeroes?”
One of the attractive features of a theory of quantum gravity is that it
should allow for unification of the four forces. Nearly thirty years ago,
Sheldon Glashow, Steven Weinberg, and Abdus Salam won the Nobel
Prize for a theory^8 that unified the electromagnetic force and the weak
force into the electroweak force, which was present only at the ultrahigh
temperatures that occurred immediately after the big bang. A number of
physicists believe that there is a theory in which all the forces will coa-
lesce into a single force at an almost inconceivably high temperature, and
then the various individual forces will separate as the temperature falls,
somewhat as various components of a mixture will separate from the
mixture as it cools.
I’d love to see such a theory. I’m sure it would take me years of study
before I had a hope in hell of comprehending it, for such a theory would
undoubtedly be vastly different from any branch of mathematics I’ve ever
studied. Most mathematical theories begin with a very general structure
that has a relatively small set of axioms and definitions—such as the
structure known as an algebra. A good example of an algebra is the col-
lection of all polynomials—you can add and subtract polynomials and
multiply them by constants or other polynomials, and the result is still a
36 How Math Explains the World