Paradoxes in the Theory of Relativity

That Einstein's insight was profound goes without saying. A strildng indication of its depth is the abundance of unexpected riches that others have found in his work - riches reserved for those daring to give serious attention to implications that at first sight seem unphysical. A famous instance is that of the de Broglie waves. If, in ac- cordance with Fermat's principle, a photon followed the path of least time, de Broglie felt that the photon should have some phys- ical means of exploring alternative paths to determine which of them would in fact require the least time. For this and other rea- sons, he assumed that the photon had a nonvanishing rest mass, and, in accordance with Einstein's E = h v, he endowed the photon with a spread-out pulsation of the form A Sin(27TEt/h) in the photon's rest frame. According to the theory of relativity such a pulsation, every- where simultaneous in a given frame, seemed absurd as a physical entity. Nevertheless de Broglie took it seriously, applied a Lorentz transformation in the orthodox relativistic tradition, and found that the simultaneous pulsation was transformed into a wave whose phase velocity was finite but greater than c while its group velocity was that of the particle. By thus pursuing Einsteinian concepts into thickets that others had not dared to penetrate, de Broglie laid the brilliant foundations of wave mechanics.