Abstract

``Quantum phenomena are more truly random than any other phenomena one can imagine” (R. Gill, 1997). Do they follow Kolmogorov probability?

This talk has two parts. After a very brief review of Kolmogorov probability, we summarize Feynman’s 1951 talk to the 2nd Berkeley symposium on mathematical statistics and probability in which he discussed applying Young’s two-slit experiment to electrons. While his main point was to develop a new calculus of probabilities for the quantum world, he claimed that the two-slit experment gave empirical refutation to Kolmogorov’s axiom of the additivity of probability of disjoint events. We discuss some of the more cogent and interesting critiques of this work.

In the second part, we describe basic aspects of the mathematical field of quantum probability in which events are subspaces of a Hilbert space rather than subsets of a sigma-field and random variables are observables, represented by Hermitian operators rather than measurable functions. Exploring these distinctions gives rise to a bestiary of differences from Kolmogorov probability. Conditional quantum probability allows us to view the two-slit experiment from a different perspective.