Relational Quantum Mechanics

TL;DR

This paper proposes that the core structure of Quantum Mechanics is based on relational logic, connecting it to category theory, and explores its implications for quantum probability, phase space granularity, and philosophical understanding.

Contribution

It introduces relational logic as the foundational syntax of Quantum Mechanics, linking it to category theory and deriving quantum probability rules from this framework.

Findings

Relational logic models quantum relations as category theory arrows.

Quantum probability emerges from the composition law of relations.

Phase space granularity is determined by Planck's constant h.

Abstract

We suggest that the inner syntax of Quantum Mechanics is relational logic, a form of logic developed by C. S. Peirce during the years 1870 - 1880. The Peircean logic has the structure of category theory, with relation serving as an arrow (or morphism). At the core of the relational logical system is the law of composition of relations. This law leads to the fundamental quantum rule of probability as the square of an amplitude. Our study of a simple discrete model, extended to the continuum, indicates that a finite number of degrees of freedom can live in phase space. This "granularity" of phase space is determined by Planck's constant h. We indicate also the broader philosophical ramifications of a relational quantum mechanics.