Derivation of quantum probabilities from deterministic evolution

TL;DR

This paper demonstrates that the Born rule in quantum mechanics can be derived from deterministic Bohmian dynamics without statistical assumptions, suggesting quantum probabilities emerge from underlying deterministic laws.

Contribution

It provides a derivation of the Born rule within Bohmian mechanics, eliminating the need for statistical postulates and addressing the measurement problem.

Findings

Measurement outcomes match Born-rule probabilities

Quantum probabilities emerge from deterministic evolution

Supports the view of underlying determinism in quantum phenomena

Abstract

The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to justify the Born rule from other physical principles, and thus elucidate the measurement process, have involved lengthy statistical or information-theoretic arguments. Here we show that Bohm's deterministic formulation of quantum mechanics allows the Born rule for measurements on a single system to be derived, without any statistical assumptions. We solve a simple example where the creation of an ensemble of identical quantum states, together with position measurements on those states, are described by Bohm's quantum dynamics. The calculated measurement outcomes agree with the Born-rule probabilities, which are thus a consequence of deterministic evolution. Our results demonstrate that quantum probabilities can emerge from simple dynamical laws alone, and they support the view that there is no underlying indeterminism in quantum phenomena.