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

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 (Sen I, Valentini A, 2020 Proc. R. Soc. A, 476, 20200214) 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.

Automated summary

This article analyzes the recent proposal of the Invariant-set theory, which suggests a superdeterministic account of quantum mechanics. The authors first develop a hidden-variable model based on the proposal and then critically examine various aspects of the proposal using this model. Their analysis demonstrates that certain arguments in the proposal fail when considered in their model. Furthermore, they show that their model is not only superdeterministic but also nonlocal, with an ontic quantum state. The authors argue that the bit string defined in their model is a hidden variable and contains redundant information. Lastly, they apply previous work to illustrate the issue of superdeterministic conspiracy in the model, further supporting the conclusion that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.