Stochastic bra-ket interpretation of quantum mechanics

TL;DR

This paper introduces a bilinear stochastic interpretation of quantum mechanics using two Markovian processes, offering a new perspective on entanglement and interference that emphasizes the stochastic nature of density matrices.

Contribution

It proposes a novel bilinear two-process framework for density matrices, providing a stochastic, ontological interpretation of quantum phenomena distinct from traditional wave function superpositions.

Findings

Entanglement arises from bilinear density matrix structure, not superpositions.

Quantum interference is explained as a multiplicative effect.

Illustrations include EPR and double-slit experiments.

Abstract

The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.