The paradox of probability in physics

Abstract

Probability is a controversial subject whether or not we consider it in relation to fundamental issues in physics, but most of the general controversy centres on its alternative interpretations in (i) statistical, or (ii) subjective, terms; and this problem is not in my opinion immediately relevant to the present discussion, for which I shall always use the first meaning. Moreover, at a meeting in 1956 of the Philosophy of Science Group of the British Society for the History of Science, I discussed (see Bartlett, 1962) the three classical paradoxes — Loschmidt’s reversibility paradox, Zermelo’s recurrence paradox and the paradox of Maxwell’s demon — therefore I do not want to consider these in detail now. They all relate to the Second Law of Thermodynamics. Loschmidt’s and Zermelo’s were formulated in terms of deterministic laws, but they are not removed either by the introduction of quantum mechanics or by statistics. In fact, while Loschmidt’s is partly resolved by the distinction between conditional and absolute probabilities, both paradoxes emphasize the limitations of the Second Law, which is not infallible for all sizes of physical system. Maxwell’s paradox is, I believe, even more subtle, for Szilard showed that it could only be resolved by ascribing to observations an inevitable interference with the system leading to entropy increase at least as great as the reduction intended (cf. Brillouin, 1962. §13.6).