Deterministic Quantum Mechanics

TL;DR

This paper introduces a deterministic quantum theory that predicts a positive joint probability distribution for position and momentum, aligning with standard quantum results but providing new insights into their correlations.

Contribution

It proposes a novel deterministic framework for quantum mechanics with a positive joint distribution, differing from traditional noncommutative approaches.

Findings

Predicts a positive joint probability distribution for position and momentum.

Aligns with standard quantum theory for separate distributions.

Suggests correlations between position and momentum in individual events.

Abstract

Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability distribution such that the separate probability distributions for position and momentum agree with usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive definite. The theory predicts a correlation between position and momentum in individual events.