Grand Unification of Forces

If we are in a situation where symmetry is broken, we may not recognize that there even is a symmetry lurking somewhere in the background. If we lived, for example, at the bottom of a valley with circular symmetry, similar to the shape of the potential for the Higgs field similar to the shape of the ridged bowl (as in Fig. 26 ), we may not appreciate the existence of a circular symmetry. This happens to be the case in our thinking about the forces around us as well. In addition to gravity, there are three other known forces: the electromagnetic, strong and weak forces. Electromagnetic forces are familiar. The strong forces, which bind the quarks to make protons and neutrons, are not so readily discerned. Weak forces–which are responsible for the radioactivity seen, for example, in \beta decays–are also largely concealed in everyday life. A quark, however, experiences all the known forces. These forces have different strengths, which can be assessed as follows: We fix a small distance, say 10^{-16}cm , which is equivalent to the energy of 100 GeV for a photon of that wavelength, and then compute the ratio of the different forces that a quark exerts on another quark, 10^{-16} cm away. The ratio of these forces is given by the ratio of the square of the corresponding charges g_i^2 . It turns out that in such a scale: g^2_{strong}>g^2_{weak}>g^2_{electromagnetic} The g_{electromagnetic}=e the familiar electric charge. So these forces certainly appear to be very different, at least in terms of their relative strengths. However, if we continue to ask that question at shorter and shorter distances, the corresponding charges of the three forces change. The charges, moreover, seem to become the same at a distance scale of about 10^{-30}cm (corresponding to an energy scale of 10^{16} GeV=M_{GUT} ). See Fig. 34 .