Classical-Quantum Coexistence: a `Free Will' Test

TL;DR

This paper explores the coexistence of classical and quantum variables over time, applying a 'free will' test to distinguish useful classical variables for causal control from those that are not.

Contribution

It introduces a 'free will' test to evaluate classical variables within various theories of classical-quantum coexistence, aiding in identifying those useful for causal control.

Findings

The 'free will' test can differentiate useful classical variables from useless ones.

Application to multiple theories shows varying degrees of classical-quantum coexistence.

Provides a framework for understanding classical variables' role in quantum systems.

Abstract

Von Neumann's statistical theory of quantum measurement interprets the instantaneous quantum state and derives instantaneous classical variables. In realty, quantum states and classical variables coexist and can influence each other in a time-continuous way. This has been motivating investigations since longtime in quite different fields from quantum cosmology to optics as well as in foundations. Different theories (mean-field, Bohm, decoherence, dynamical collapse, continuous measurement, hybrid dynamics, e.t.c.) emerged for what I call `coexistence of classical continuum with quantum'. I apply to these theories a sort of `free will' test to distinguish `tangible' classical variables useful for causal control from useless ones.