Quantum probabilities and the Born rule in the intuitionistic interpretation of quantum mechanics

TL;DR

This paper offers a new explanation for quantum probabilities and the Born rule within the framework of intuitionistic logic, replacing classical truth with constructive probability to avoid the law of excluded middle.

Contribution

It introduces an interpretation of quantum mechanics where constructive logic explains quantum probabilities, providing a novel foundation for the Born rule.

Findings

Quantum probabilities derived from constructive logic

Abandonment of the law of excluded middle in quantum interpretation

Reconceptualization of truth as constructive probability

Abstract

This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of constructive logic makes it possible (through a replacement of the concept of truth with the concept of constructive probability) to abandon the law of excluded middle in the intuitionistic interpretation.