Where does the Born Rule come from? Superposition

TL;DR

This paper demonstrates that the Born Rule naturally emerges from extending classical probability theory with superposition events, providing a mathematical basis for its origin without relying on physical assumptions.

Contribution

It shows that the Born Rule arises solely from adding superposition events to finite probability theory, offering a purely mathematical explanation.

Findings

Born Rule appears by extending probability theory with superposition events

The approach does not require physics-based derivation of the Born Rule

Superposition events mathematically explain the probability rule in quantum mechanics

Abstract

The Born Rule plays a critical role in quantum mechanics (QM) since it supplies the link between the mathematical formalism and experimental results in terms of probabilities. The Born Rule does not occur in ordinary probability theory. Where then does it come from? This has been a topic of considerable controversy in the literature. We take the approach of asking what is the simplest extension of ordinary probability theory where the Born rule appears. This is answered by showing that the Born Rule appears by adding the notion of superposition events (in addition to the ordinary discrete events) to finite probability theory. Hence the rule does not need any physics-based derivation. It is simply a feature of the mathematics of superposition when only superposition events are added to ordinary probability theory.