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

by Steven Weinberg

The problem of infinities could have been solved by brute force, by simply decreeing that electrons can emit and absorb photons only with energies below some limiting value. All the successes scored in the 1930s by quantum electrodynamics in explaining the interactions of electrons and photons involved low-energy photons, so these successes could be preserved by supposing that this limiting value of photon energies is sufficiently high, for example, 10 million volts. With this sort of limit on virtual photon energies, quantum electrodynamics would predict a very small energy shift of atoms. No one at this time had measured the energies of atoms with enough precision to tell whether or not this tiny energy shift was actually present, so there was no question of any disagreement with experiment. (In fact, quantum electrodynamics was regarded with such pessimism that no one even tried to calculate just what the energy shift would be.) The trouble with this solution to the problem of infinities was not that it was in conflict with experiment but that it was too arbitrary and ugly to contemplate.