A Stepwise Planned Approach to the Solution of Hilbert's Sixth Problem. III : Measurements and von Neumann Projection/Collapse Rule

TL;DR

This paper presents a physics-based justification for the von Neumann collapse rule within the supmech framework, showing how decoherence from observational constraints suppresses superpositions in quantum measurements.

Contribution

It introduces a unified mechanics framework that naturally explains the collapse process without traditional decoherence objections.

Findings

Superpositions are suppressed after measurement interactions.

Decoherence arises from observational constraints on pointer readings.

Collapse is justified as a physical process within supmech.

Abstract

Supmech, the universal mechanics developed in the previous two papers, accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmech based treatment of quantum measurements, an unambiguous treatment of the apparatus as a quantum system approximated well by a classical one. Taking explicitly into consideration the fact that observations on the apparatus are made when it has `settled down after the measurement interaction' and are restricted to macroscopically distinguishable pointer readings, the unwanted superpositions of (system + apparatus) states are shown to be suppressed; this provides a genuinely physics based justification for the (traditionally \emph{postulated}) von Neumann projection/collapse rule. The decoherence mechanism brought into play by the stated observational constraints is free from the objections against the traditional decoherence program.