Propositional Quantum Mechanics

TL;DR

This paper reformulates quantum mechanics using propositional calculus and Hartle's state definition, deriving key formulas and probability distributions for individual systems and ensembles.

Contribution

It introduces a propositional calculus framework for quantum mechanics based on Hartle's state definition, deriving fundamental formulas from elementary postulates.

Findings

Derives canonical commutation relations and Schrödinger's equation from propositional calculus.

Shows the expected frequency of events matches the expected value of a state operator.

Produces a binomial probability distribution for indefinite propositions.

Abstract

Quantum mechanics is reformulated using Hartle's definition of the state of an individual physical system and a variant of von Neumann's propositional calculus. An elementary set of quantum postulates lead inductively to the familiar formulas of quantum theory, including the canonical commutation relation and Schr\"odinger's equation. The expected value of the frequency of events for an ideal ensemble is equal to the expected value of a state operator for an individual system, producing a binomial probability distribution for the determination of indefinite experimental propositions.