An unexpected theoretical structure that could explain quantum-mechanics postulates like the Born rule and the wave-function reduction

TL;DR

This paper proposes a novel theoretical framework based on nonlinear gauge transformations that underpins quantum mechanics, offering insights into the wave-function collapse and quantum measurement phenomena through a classical-to-quantum derivation.

Contribution

It introduces a unique postulate involving invariance under nonlinear gauge transformations that derives quantum mechanics from classical mechanics, including a new explanation for wave-function collapse.

Findings

Derives quantum mechanics from classical mechanics using a new invariance principle.

Proposes a Schrödinger-bridge process explaining wave-function collapse.

Identifies non-causal, non-quantum phenomena in a new space-like dimension.

Abstract

A unique postulate is shown to underly the whole quantum mechanics theory: the invariance of the Heisenberg uncertainty inequality under a group of special nonlinear gauge transformations (NLGT). With this postulate, the quantum mechanics of a free particle is derived from classical mechanics, including the statements of the postulates of quantum mechanics, except for the wave-function-collapse postulate. An explanatory mechanism for the latter postulate is derived by performing an analytical continuation of the NLGTs. This extension results in a Schr\"odinger-bridge process, intertwined under the NLGT with the standard unitary quantum evolution, and revealing non-quantum (or beyond-quantum) phenomena. Mechanisms of that latter kind, like the ones associated to the quantum measurement process, occur in a new space-like dimension and hence are non causal in nature, in opposition to a time evolution. The present exercice focusses on the free particle in order to highlight the features of the performed derivation in the simplest possible way. Work is in progress to extend the performed derivation beyond that simple case.