The Born rule

TL;DR

This paper derives the Born rule using basic quantum mathematics and empirical concepts, avoiding reliance on quantum postulates, and discusses the implications of this approach for quantum foundations.

Contribution

It presents a derivation of the Born rule solely from elementary quantum mathematics and empirical notions, challenging traditional reliance on quantum axioms.

Findings

The Born rule can be derived without quantum postulates.

Empirical detector-clicks are formalized into quantum micro-events.

Quantum axioms may be inconsistent with the derivation approach.

Abstract

We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature comes from the experimental detector-clicks being formalized into the abstract quantum micro-events. We also comment on that it is not only that the use has not been made of some quantum axioms when deriving the rule but, in a sense, their invoking would be inconsistent.