Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature

by Steven Weinberg

The value of the Planck energy confronts us with a formidable new problem. It is not that this energy is so large—it arises in physics at such a deep level that we can suppose that the Planck energy is simply the fundamental unit of energy that appears in the equations of the final theory. The mystery is why are all the other energies so small? In particular, in the original version of the standard model the masses of the electron and the W and Z particles and all the quarks are proportional to the one mass that appears in the equations of the model, the mass of the Higgs particle. From what we know of the masses of the W and Z particles, we can infer that the energy in a Higgs particle mass could not be greater than about a trillion volts. But this is at least a hundred million million times smaller than the Planck energy. This also means that there is a hierarchy of symmetries: whatever symmetry unites the gravitational and strong nuclear forces with the electroweak forces is broken roughly a hundred million million times more strongly than the symmetry that unifies the weak and electromagnetic interactions. The puzzle of explaining this enormous difference in fundamental energies is therefore known in elementary particle physics today as the hierarchy problem.