Quantum Measure Theory and Ontology

Abstract

Since noncommutative measure theory plays a central role in the quantum theory, one might say that quantum mechanics is a new generalized theory of probability. That assertion, however, raises many problems with interpreting quantum probabilities and quantum events. Although one can take a radically instrumentalist or pragmatist approach toward this question, it is much more interesting, both theoretically and heuristically, to adopt a realistic or ontological strategy that treats the quantum measure as an effective parameter of an underlying time-symmetric regime of physical dynamics, which only generates the classical events and probabilities at its limit. It is argued that time-symmetric relativistic reformulations of the quantum theory with time-like nonseparability have important advantages over space-like nonlocal hidden-variable Bohmian-type models, which have Aristotelian spacetime as their natural environment.