What Interpretation for Probability in Physics?

Abstract

Probability enters into modern science in three ways. (1) Measurement errors. This regards all of science; in physics, probability associated with errors of measurement enters—implicitly or explicitly—into all of its branches. In this sense, one can say that a probabilistic aspect is already present in classical mechanics. Indeed, the theory of errors came to completion around the end of the 18th Century,when Newtonian mechanics was at its peak. (2) The analysis of mass phenomena, like gas particles. In physics, this use of probability is linked to statistical mechanics. Here probability makes it possible to describe through mean values the behaviour of phenomena that are too complex to allow finer descriptions. In principle, these probabilities are not essential to the theory, they are needed because of the complexity of the phenomena under study, which makes a fully detailed analysis impossible. (3) Quantum mechanics. Here probability acquires a peculiar character in view of the fact of being ‘primary’ (to use an expression of Hermann Weyl),or ‘intrinsic’ to the theory (as Harold Jeffreys used to say). This is because the measurements realized on physical systems in quantum mechanics are genuinely random. On the assumption that the theory is complete, there is no way, not even in principle, of getting rid of probability.