Is quantum mechanics based on an invariance principle?

TL;DR

This paper demonstrates that non-relativistic quantum mechanics can be derived from classical mechanics by applying an invariance principle related to space dilations, leading to the emergence of the Schrödinger equation and wave function collapse.

Contribution

It introduces a novel invariance principle based on space dilation transformations that derive quantum mechanics from classical mechanics, including both unitary and non-unitary evolutions.

Findings

Quantum mechanics emerges from classical mechanics via invariance principles.

The Schrödinger equation is derived alongside a nonlinear equation for non-unitary processes.

Solutions suggest a mechanism for wave function collapse.

Abstract

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are induced by isotropic space dilations. This invariance imposes a change in the laws of classical mechanics that exactly corresponds to the transition to quantum mechanics. The Schroedinger equation appears jointly with a second nonlinear equation describing non-unitary processes. Unitary and non-unitary evolutions are exclusive and appear sequentially in time. The non-unitary equation admits solutions that seem to correspond to the collapse of the wave function.