Emergence of quantum mechanics from classical statistics

TL;DR

This paper demonstrates that quantum mechanics can emerge from classical statistical systems, showing how quantum properties like non-commutativity and unitary evolution arise from classical probabilistic frameworks.

Contribution

It provides a framework where quantum mechanics is derived from classical statistics, clarifying the classical origins of quantum phenomena.

Findings

Quantum systems are subsystems of classical statistical systems with infinitely many states.

Quantum operators' non-commutativity relates to conditional probabilities in classical systems.

Unitary evolution reflects the isolation of quantum subsystems within classical systems.

Abstract

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables "measure" properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.