Dashen-Frautschi Fiasco and Historical Roadmap for Strings

Abstract

In 1964, Dashen and Frautschi published two papers in the Physical Review claiming that they calculated the neutron-proton mass difference. It was once regarded as a history-making calculation, in view of the fact that the proton and neutron had been and still are regarded as the same particle with different electromagnetic properties. However, their calculation was shown to be based on a bound-state wave function which violates the localization condition in quantum mechanics. There is one important lesson to be learned from the mistake made by Dashen and Frautschi. They did not pay much attention to the fact that there are running waves and standing waves in quantum mechanics. The S-matrix formalism is based on running waves, while bound-state problem are based on normalizable wave functions which are standing waves. Wave functions contained in the S matrix are analytic continuations of running waves, and they do not in general satisfy the localization condition for bound states. These days, there are very serious questions raised against string theory. Is string theory a form of quantum field theory? Is it a physical theory or only a mathematical exercise. Is a new new Einstein going to emerge from string theory? It is pointed out that, if the distinction is recognized between running and standing waves, string theory has its place in the historical roadmap land-marked by Einstein, Heisenberg, Schrödinger, Dirac, Wigner, and Feynman.