Quantum Measure Theory and its Interpretation

TL;DR

This paper introduces a spacetime-based interpretation of quantum theory using a quantum measure that predicts a single, definite history of the universe, providing an objective account of measurements without relying on observers.

Contribution

It proposes a novel quantum measure framework that generalizes classical probability, offering a realistic interpretation with definite histories and objective predictions in quantum physics.

Findings

Quantum measure fulfills a sum rule extending classical probability.

Application to electron-electron scattering yields definite trajectories.

Provides an objective, measurement-independent account of quantum phenomena.

Abstract

We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| fulfills a sum rule generalizing that of classical probability theory. We interpret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve *conditonal* preclusion (which apparently requires a notion of coarse-graining for its formulation) and the need to "locate spacetime regions in advance" without the aid of a fixed background metric (which can be achieved in the context of conditional preclusion via a construction which makes sense both in continuum gravity and in the discrete setting of causal set theory).