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arXiv:2109.11109

Reply to superdeterminists on the hidden-variable formulation of Invariant-set theory

Indrajit Sen

Published Sep 23, 2021• 0 citations
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Abstract

In a recent article (arXiv:2108.08144), Hance, Hossenfelder and Palmer have advanced arguments claiming to show that the analysis of Invariant-set theory in a hidden-variable setting (arXiv:2107.04761) is wrong. We explain here why these arguments are incorrect, and involve misunderstandings of the hidden-variable model in question and Bell's notion of local causality.

DOI
10.48550/arxiv.2109.11109

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Comment on "Analysis of the superdeterministic invariant-set theory in a hidden-variable setting"

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In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor $\psi$-epistemic. We here detail multiple problems with Sen's argument.

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In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor $ψ$-epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.

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Reply to "Comment on 'Experimentally adjudicating between different causal accounts of Bell-inequality violations via statistical model selection'"

Daley, Patrick, Kevin J. Resch, Robert W. Spekkens

Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative, of which a class of superdeterministic models are an example, overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modelling. In their comment (arXiv:2206.10619), Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavoured by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modelling framework and from the fact that we referred to this framework as "classical" in order to contrast it with an intrinsically quantum alternative. In this reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist heirarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.

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Reply to “Comment on ‘Experimentally adjudicating between different causal accounts of Bell-inequality violations via statistical model selection' ”

Patrick J. Daley, Kevin J. Resch, Robert W. Spekkens

Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative---of which a class of superdeterministic models are an example---overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modeling. In their comment [Phys. Rev. A 109, 026201 (2024)], Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavored by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modeling framework and from the fact that we referred to this framework as ``classical'' in order to contrast it with an intrinsically quantum alternative. In this Reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist hierarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.

Physical Review A•Jan 16, 2025•0 citations

Reply to "Comment on 'Why interference phenomena do not capture the essence of quantum theory' "

Lorenzo Catani, Matthew Leifer, David Schmid +1 more

Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.

arXiv:2207.11791•Jul 24, 2022•1 citation
In a recent article (arXiv:2108.08144), Hance, Hossenfelder and Palmer have advanced arguments claiming to show that the analysis of Invariant-set theory in a hidden-variable setting (arXiv:2107.04761) is wrong. We explain here why these arguments are incorrect, and involve misunderstandings of the hidden-variable model in question and Bell's notion of local causality.
In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor ψ\psiψ-epistemic. We here detail multiple problems with Sen's argument.
In a recent paper (arXiv:2107.04761), Sen critiques a superdeterministic model of quantum physics, Invariant Set Theory, proposed by one of the authors. He concludes that superdeterminism is `unlikely to solve the puzzle posed by the Bell correlations'. He also claims that the model is neither local nor ψψψ-epistemic. We here detail multiple inaccuracies with Sen's arguments - notably that the hidden-variable model of quantum physics he uses to critique Invariant Set Theory bares no relation to Invariant Set Theory - and use this opportunity to lay out the properties of Invariant Set Theory as clearly as possible.
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.
Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative, of which a class of superdeterministic models are an example, overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modelling. In their comment (arXiv:2206.10619), Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavoured by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modelling framework and from the fact that we referred to this framework as "classical" in order to contrast it with an intrinsically quantum alternative. In this reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist heirarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.
Our article described an experiment that adjudicates between different causal accounts of Bell inequality violations by a comparison of their predictive power, finding that certain types of models that are structurally radical but parametrically conservative---of which a class of superdeterministic models are an example---overfit the data relative to models that are structurally conservative but parametrically radical in the sense of endorsing an intrinsically quantum generalization of the framework of causal modeling. In their comment [Phys. Rev. A 109, 026201 (2024)], Hance and Hossenfelder argue that we have misrepresented the purpose of superdeterministic models. We here dispute this claim by recalling the different classes of superdeterministic models we defined in our article and our conclusions regarding which of these are disfavored by our experimental results. Their confusion on this point seems to have arisen in part from the fact that we characterized superdeterministic models within a causal modeling framework and from the fact that we referred to this framework as ``classical'' in order to contrast it with an intrinsically quantum alternative. In this Reply, therefore, we take the opportunity to clarify these points. They also claim that if one is adjudicating between a pair of models, where one model can account for strictly more operational statistics than the other, the first model will tend to overfit the data relative to the second. Because this model inclusion relation can arise for pairs of models in a reductionist hierarchy, they conclude that overfitting should not be taken as evidence against the first model. We point out here that, contrary to this claim, one does not expect overfitting to arise generically in cases of model inclusion, so that it is indeed sometimes appropriate to consider overfitting as a criterion for adjudicating between such models.
Our article [arXiv:2111.13727(2021)] argues that the phenomenology of interference that is traditionally regarded as problematic does not, in fact, capture the essence of quantum theory -- contrary to the claims of Feynman and many others. It does so by demonstrating the existence of a physical theory, which we term the "toy field theory", that reproduces this phenomenology but which does not sacrifice the classical worldview. In their Comment [arXiv:2204.01768(2022)], Hance and Hossenfelder dispute our claim. Correcting mistaken claims found therein and responding to their criticisms provides us with an opportunity to further clarify some of the ideas in our article.