Probabilistic observables, conditional correlations, and quantum physics

TL;DR

This paper demonstrates that quantum mechanics can be derived from classical statistical models with many micro-states, using probabilistic observables and conditional correlations, providing a classical foundation for quantum phenomena.

Contribution

It introduces a classical statistical framework that reproduces quantum laws for two-state systems and entanglement, emphasizing probabilistic observables and conditional correlations.

Findings

Quantum laws follow from classical statistics with conserved purity.

Non-commutative quantum correlations correspond to classical conditional correlations.

Classical models can realize quantum entanglement with four-state systems.

Abstract

We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The "coarse graining of the information" to micro-states implies probabilistic observables. For two-level probabilistic observables only a probability for finding the values one or minus one can be given for any micro-state, while such observables can be realized as classical observables with sharp values on a substate level. For a continuous family of micro-states parameterized by a sphere all the quantum mechanical laws for a two-state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The non-commutative correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four-state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro-states.