The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion

TL;DR

This paper derives the Born Rule from the time-reversal symmetry of quantum equations of motion, providing a foundational basis and identifying limits to its applicability.

Contribution

It presents a novel derivation of the Born Rule based on time-reversal symmetry, linking fundamental quantum principles.

Findings

Born Rule derived from time-reversal symmetry

Identifies limits to the applicability of the Born Rule

Provides a new foundational perspective on quantum probabilities

Abstract

It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the time-reversal symmetry of quantum equations of motion. The derivation is based on a simple functional equation that takes into account properties of probability, as well as the linearity and time-reversal symmetry of quantum equations of motion. The derivation presented in this work also allows to determine certain limits to applicability of the Born Rule.