Grand Unified Theory

Theory of Everything

Fig 21.23.

Unification of the forces.As we go from left to right in the figure, we see how, at higher energies, the forces become more unified.

In the electroweak force, the photon and the W (or Z) are essentially the same. You might wonder how two particles can be the same if one is very massive and the other is massless. The answer to this question tells us what we really mean by unification. In this case, the electromagnetic and weak forces appear to be the same when we deal with particles whose energies are much greater than the difference between the mass of the W and the mass of the photon (zero). At these high energies, the W mass arises from a small spontaneous symmetry breaking. However, we don't really notice the difference until the energy is so low that the mass of the W can no longer be ignored. This is another case of our maxim that nature is symmetric as long as there is enough energy.

The masses of the W and Z are about 80 GeV (being expressed as equivalent energy, where the proton mass is about 1 GeV). These masses are barely accessible in today's best particle accelerators. Therefore, we cannot even approach the range where particles will have energies much greater than this in order to see a world in which the electromagnetic and weak forces are the same. However, there must have been a brief instant in the early universe when the temperature was high enough for this symmetry to be present. This is one of the important connections between particle physics and cosmology, and we will explore it further in the next section.

The next step has been to unify the color (strong) force with the electroweak force, using the same mathematical tools. Theories that do this are called grand unified theories, or GUTs. These are still in the developmental stage. The carriers of this force are designated the X and Y particles. There masses are estimated to be about 1014 GeV, or 1012 times the mass of the W. This means that the differences between the color force and the electroweak force disappear when the energies are much greater than 1014 GeV. These energies are clearly beyond the range of accelerators that we could contemplate on the Earth. However, these conditions existed, ever so briefly, in the big bang.

One prediction of these GUTs is that the proton is not stable. Our normal understanding of the apparent stability of the proton is that it is the lowest mass baryon. The electroweak and color forces obey a conservation of baryons. Since a decay must always be to a lower mass particle, if a proton decayed the result would not be a baryon. Hence the stability of the proton. However, GUTs say that, at high enough energies, there is no difference between the electroweak and color forces. This means that the differences between hadrons and leptons should be lost. According to these theories, the proton would decay into a positron and a pion, with a half-life of about 1031 years. This doesn't mean that half of the protons wait this long, and then decay all at once. There should be a steady trickle of decays. The probability of any proton decaying in a given year is small, but there are many protons on the Earth, so we could actually hope to catch some decaying. So far, no such decays have been detected, indicating that the proton probably lives about ten times as long as the theory predicts. This means that there will have to be some modification of the theory.

Another prediction of the GUTs is the existence of magnetic monopoles. These are particles that would serve as the source of magnetic fields that are not due to the motions of charges. The magnetic field around a magnetic monopole would look like the electric field around a proton. The simplest GUT theory predicts that there should have been a large number of magnetic monopoles made in the big bang, and they should be as numerous as baryons. However, none have been detected. Again, some modification of the theory is required.

Even though there are still problems with GUTs, some theoreticians are forging ahead with the final step, the inclusion of gravity in the unified forces. These theories have been called super GUTs, or supergravity, or theories of everything (TOE). Needless to say, they are still in the very speculative stages.

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