Bell's Conspiracy, Schr\"odinger's Black Cat and Global Invariant Sets

TL;DR

This paper proposes a locally causal hidden-variable theory based on a cosmological invariant set that can violate Bell inequalities without conspiratorial assumptions, offering a new perspective on quantum nonlocality and free will.

Contribution

It introduces the Cosmological Invariant Set Postulate, a novel physically plausible explanation for measurement correlations that avoids conspiracy and superdeterminism in quantum theory.

Findings

The theory can violate the CHSH inequality without conspiratorial assumptions.

It accommodates classical notions of free will within a quantum framework.

The invariant set concept provides a new way to understand quantum correlations.

Abstract

A locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory also partially violates the measurement independence condition. However, such violation can appear unphysical, implying implausible conspiratorial correlations between the hidden-variables of particles being measured and earlier determinants of instrumental settings. A novel physically plausible explanation for such correlations is proposed, based on the hypothesis that states of physical reality lie precisely on a non-computational measure-zero dynamically invariant set in the state space of the universe: the Cosmological Invariant Set Postulate. To illustrate the relevance of the concept of a global invariant set, a simple analogy is considered where a massive object is propelled into a black hole depending on the decay of a radioactive atom. It is claimed that a locally causal hidden-variable theory constrained by the Cosmological Invariant Set Postulate can violate the CHSH inequality without being conspiratorial, superdeterministic, fine-tuned or retrocausal, and the theory readily accommodates the classical compatibilist notion of (experimenter) free will.