Quantum mechanics from classical statistics

TL;DR

This paper demonstrates that quantum mechanics can be derived from classical statistical systems, showing that quantum phenomena like entanglement and uncertainty emerge naturally without additional concepts.

Contribution

It provides a framework where quantum mechanics arises from classical statistics, including derivations of key quantum principles from classical probabilistic concepts.

Findings

Quantum states correspond to probabilistic observables in classical ensembles.

Quantum laws like Heisenberg's uncertainty and Bell inequality violations follow from classical probability.

A classical model of a quantum computer is discussed.

Abstract

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a "purity constraint". Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. 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. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. 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. As an illustration, we discuss a classical statistical implementation of a quantum computer.