Contextual viewpoint to quantum stochastics

TL;DR

This paper explores how contextual dependence in physical experiments can explain quantum interference and noncommutativity without relying on wave functions or Hilbert spaces, using elementary geometric and algebraic principles.

Contribution

It introduces a novel approach to quantum probabilities based on context, deriving quantum rules and noncommutativity from elementary geometric and algebraic facts.

Findings

Derived quantum probability addition rule from contextual dependence.

Obtained Hilbert space representation via the cosine theorem.

Identified the contextual origin of noncommutativity of observables.

Abstract

We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the addition of probabilities of alternatives. Thus we obtain quantum interference without applying to wave or Hilbert space approach. The Hilbert space representation of contextual probabilities is obtained as a consequence of the elementary geometric fact: $\cos$-theorem. By using another fact from elementary algebra we obtain complex-amplitude representation of probabilities. Finally, we found contextual origin of noncommutativity of incompatible observables.