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

by Steven Weinberg

Quantum electrodynamics had almost been killed off by the problem of infinities but had been saved by the idea of canceling the infinities in a redefinition or renormalization of the electron mass and charge. But in order for the problem of infinities to be solved in this way, it is necessary that the infinities occur in calculations in only certain very limited ways, which is the case only for a limited class of specially simple quantum field theories. Such theories are called renormalizable. The simplest version of quantum electrodynamics is renormalizable in this sense, but any sort of small change in this theory would spoil this property and lead to a theory with infinities that could not be canceled by a redefinition of the constants of the theory. Thus this theory was not only mathematically satisfactory and in agreement with experiment, but it seemed to contain within itself an explanation of why it was the way it was; any small change in the theory would lead not only to a disagreement with experiment but to results that were totally absurd—infinite answers to perfectly sensible questions.