Reply to Fleming: Symmetries, observables, and the occurrence of events

Abstract

First I want to thank Prof. Fleming for his detailed, thoughtful, and thought-provoking remarks, and particularly for his generous advice on how to improve successive versions of the conference paper presented here in its final form. While our continuing correspondence has led to something of a convergence of views, there are several differences of opinion that resist this reconciliation. In this reply I will present my side of two of these remaining disputes, which are particularly relevant for understanding how accepting my account of event time observables (sketched in the final section of the paper) leads to a distinctive view of quantum theory. The core of what is distinctive about my view is that it restores a certain symmetry between time and space with respect to what is observable according to the theory. The empirical motivation for this view is that often the outcomes of an experiment may be located in time as well as in space. The theoretical consequence of this view is that time covariant POVMs must be provided which have this specific empirical interpretation.

Understanding quantum mechanics: a review and synthesis in precise language

“…-Time can either be measured by a clock external to the relevant systems, or it can be defined through the dynamical behaviour of those systems. -Time can also be considered as an observable (although views differ on this [97][98][99][100][101]).…”