A Bayesian Examination of Time-Symmetry in the Process of Measurement

Abstract

We investigate the thesis of Aharonov, Bergmann, and Lebowitz that time-symmetry holds in ensembles defined by both an initial and a final condition, called “pre- and postselected ensembles”. We distinguish two senses of time symmetry and show that the first one, concerning forward directed and time reversed measurements, holds if the measurement process is ideal, but fails if the measurement process is non-ideal, i.e., violates Lüders’s rule. The second kind of time symmetry, concerning the interchange of initial and final conditions, fails even in the case of ideal measurements. Bayes’s theorem is used as a primary tool for calculating the relevant probabilities. We are critical of the concept that a pair of vectors in Hubert space, characterizing the initial and final conditions, can be considered to constitute a generalized quantum state.

Dedicated to Richard Jeffrey in honor of his fine work and in celebration of nearly half a century of friendship.