Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History

TL;DR

This paper reformulates decoherent histories quantum theory by assuming a single real fine-grained history within an ensemble, introducing extended probabilities and exploring implications for observability and classical interpretation.

Contribution

It introduces a new formulation of decoherent histories quantum mechanics with a single real history and extended probabilities, linking quantum and classical descriptions.

Findings

Real history is embedded in an ensemble of histories.

Extended probabilities can be negative or greater than one.

Coarse-grained histories yield standard probabilities compatible with observations.

Abstract

Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational discovery. However, sufficiently and appropriately coarse-grained sets of alternative histories have standard probabilities providing information about the real fine-grained history that can be compared with observation. We recover the probabilities of decoherent histories quantum mechanics for sets of histories that are recorded and therefore decohere. Quantum mechanics can be viewed as a classical stochastic theory of histories with extended probabilities and a well-defined notion of reality common to all decoherent sets of alternative coarse-grained histories.