The Born rule for quantum probabilities from Newton's third law

TL;DR

This paper presents a novel derivation of the Born rule in quantum mechanics by linking it to Newton's third law, using a physical model involving a particle's interaction with a measuring apparatus.

Contribution

It introduces a new physical scheme where the Born rule naturally emerges from the interaction dynamics and Newton's third law, providing a conceptual foundation for quantum probabilities.

Findings

Derivation of the Born rule from Newton's third law.

A physical model involving particle and apparatus interaction.

Phase reversal leading to probability interpretation.

Abstract

According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is constructed within which the Born rule arises in a natural way. In the proposed scheme, the interaction of a particle with a measuring apparatus is equivalent to creation of a "mirror image" of particle wave function in the space region of interaction. The observable quantity is the product of the particle wave function and its "image". The phase of the latter is reversed due to Newton's third law, thus leading to the Born rule.