Dynamics and statistics in the operator algebra of quantum mechanics

TL;DR

This paper explores the relationship between statistics and dynamics in quantum mechanics, proposing that the Hilbert space formalism can be viewed as a theory of ergodic randomization linking deterministic laws to probabilistic outcomes.

Contribution

It offers a novel interpretation of quantum formalism as an ergodic randomization process, connecting the deterministic dynamics with statistical descriptions.

Findings

Hilbert space formalism as ergodic randomization

Quantum dynamics linked to probabilistic state preparation and measurement

Provides new insights into the statistical nature of quantum observables

Abstract

Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the unobservable time evolution by introducing mathematical objects that are only loosely connected to the actual physics by statistical concepts and cannot be explained by any conventional sets of events. Here, I examine the relation between statistics and dynamics in quantum theory and point out that the Hilbert space formalism can be understood as a theory of ergodic randomization, where the deterministic laws of motion define probabilities according to a randomization of the dynamics that occurs in the processes of state preparation and measurement.