Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting

TL;DR

This paper constructs a hidden-variable model based on Invariant-set theory to critically evaluate its claims, revealing issues with nonlocality, measurement independence, and superdeterminism in explaining quantum correlations.

Contribution

It develops a concrete hidden-variable model for Invariant-set theory and analyzes its implications, challenging its claims about superdeterminism and quantum foundations.

Findings

Model is superdeterministic and nonlocal with an ontic quantum state.

Arguments about counter-factuals and nonlocality fail in the model.

Supports the view that superdeterminism unlikely explains Bell correlations.

Abstract

A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However, a clear cut hidden-variable model has not been developed, which makes it difficult to assess the proposal from a quantum foundational perspective. In this article, we first build a hidden-variable model based on the proposal, and then critically analyse several aspects of the proposal using the model. We show that several arguments related to counter-factual measurements, nonlocality, non-commutativity of quantum observables, measurement independence etcetera that appear to work in the proposal fail when considered in our model. We further show that our model is not only superdeterministic but also nonlocal, with an ontic quantum state. We argue that the bit string defined in the model is a hidden variable and that it contains redundant information. Lastly, we apply the analysis developed in a previous work (Proc. R. Soc. A, 476(2243):20200214, 2020) to illustrate the issue of superdeterministic conspiracy in the model. Our results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.