A Reconstruction of Quantum Mechanics

TL;DR

This paper reconstructs quantum mechanics by replacing classical property structures with a union of property sets, deriving standard quantum concepts and addressing interpretational dilemmas.

Contribution

It introduces a novel principle replacing Boolean algebras with ta-complexes, deriving quantum formalism from interaction-based extrinsic properties.

Findings

Derives Schrödinger equation from the new framework

Provides a consistent interpretation of quantum measurement

Reconciles quantum mechanics with classical concepts

Abstract

We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by interactions with other systems. We apply the canonical definitions of the concepts of classical physics of observables, states, combined systems, symmetries, and dynamics to derive the standard quantum characterizations, including the Schr\"odinger equation and the von Neumann-L\"uder's Projection Rule. This manifestly consistent reconstruction of quantum mechanics is then used to discuss and resolve the dilemmas of the orthodox interpretation.