Contextual unification of classical and quantum physics

TL;DR

This paper proposes a unified framework for classical and quantum physics based on the mathematical implications of infinite tensor products, addressing the limitations of traditional quantum formalism at infinite degrees of freedom.

Contribution

It introduces a novel interpretation of the loss of unitary equivalence in infinite tensor products as a natural way to unify classical and quantum physics.

Findings

Provides a mathematical model for the Heisenberg cut

Shows how classical and quantum physics emerge as different sectors

Addresses the limitations of quantum formalism at infinite degrees of freedom

Abstract

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of particles (or degrees of freedom) are encountered. This is because the dimension of the corresponding Hilbert space becomes uncountably infinite, leading to the loss of unitary equivalence, and to sectorization. By interpreting physically this mathematical fact, we show that it provides a natural way to describe the "Heisenberg cut", as well as a unified mathematical model including both quantum and classical physics, appearing as required incommensurable facets in the description of nature.