Square root of minus one, complex phases and Erwin Schrödinger
Chen Ning Yang · Cambridge University Press eBooks · 1987
Introduction In a lecture in April 1970 Dirac talked about the early days of quantum mechanics (Dirac, 1972). Among other topics he discussed noncommutative algebra, and added The question arises whether the noncommutation is really the main new idea of quantum mechanics. Previously I always thought it was but recently I have begun to doubt it and to think that maybe from the physical point of view, the noncommutation is not the only important idea and there is perhaps some deeper idea, some deeper change in our ordinary concepts which is brought about by quantum mechanics. He then expanded on this subject and concluded So if one asks what is the main feature of quantum mechanics, I feel inclined now to say that it is not noncommutative algebra. It is the existence of probability amplitudes which underlie all atomic processes. Now a probability amplitude is related to experiment but only partially. The square of its modulus is something that we can observe. That is the probability which the experimental people get. But besides that there is a phase, a number of modulus unity which can modify without affecting the square of the modulus. And this phase is all important because it is the source of all interference phenomena but its physical significance is obscure. […]