Weak valued statistics as fundamental explanation of quantum physics

TL;DR

This paper proposes that the fundamental structure of quantum mechanics can be understood through complex conditional probabilities derived from weak measurements, revealing that non-commutativity stems from imaginary correlations between physical properties.

Contribution

It introduces a new perspective linking operator algebra to complex probabilities, explaining quantum non-commutativity as arising from fundamental imaginary correlations.

Findings

Complex conditional probabilities underpin operator relations.

Non-commutativity reflects imaginary correlations in physical properties.

Weak measurement statistics reveal fundamental quantum relations.

Abstract

Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued statistics observed in weak measurements relate to the operator algebra of the conventional Hilbert space formalism and show that the algebra of operators originates from more fundamental relations between the physical properties of a quantum system that can be expressed in terms of complex conditional probabilities. In particular, commutation relations can be identified with fundamental imaginary correlations that characterize the relations between physical properties in terms of their transformation dynamics. Non-commutativity thus originates from a definition of relations between physical properties that replaces the assumption of joint reality with a complex-valued probability reflecting the dynamical response of the system to external forces, e.g. in measurement interactions.