"Almost" Quotient Space, Non-dynamical Decoherence and Quantum Measurement

TL;DR

This paper introduces non-dynamical decoherence via 'almost' quotient spaces to address the quantum measurement problem, providing a new perspective on how classical outcomes emerge from quantum systems.

Contribution

It develops a novel non-dynamical decoherence framework using quotient Hilbert spaces and random phase operators to explain measurement outcomes.

Findings

Constructs an 'almost' quotient space to model open quantum systems.

Derives Born's rule within the quotient space framework.

Explains classical properties and measurement outcomes through the quotient space concept.

Abstract

An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added environment) in a quantum measurement process. We show that this open system can be well described by an "almost" quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a density matrix can be constructed to give the Born's probability rule, realizing a (non-dynamical) decoherence. The concept of the ("almost") quotient space can also be used to explain the classical properties of a macroscopic system. We show further that the definite outcomes in a quantum measurement are mainly caused by the "almost" quotient space of the macroscopic apparatus.