Superdeterministic hidden-variables models II: conspiracy

Sen, Indrajit; Valentini, Antony

doi:10.1098/rspa.2020.0214

Cited by 13 publications

(29 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Without this assumption, called ‘measurement-independence’ [3–6] in recent literature, local hidden-variables models of quantum mechanics cannot be ruled out via Bell’s theorem. The subject of this paper, and a subsequent one denoted by B [7], is superdeterminism. Superdeterministic models (e.g.…”

Section: Introductionmentioning

confidence: 99%

Superdeterministic hidden-variables models I: non-equilibrium and signalling

Sen

Valentini

2020

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

This is the first of two papers that attempt to comprehensively analyse superdeterministic hidden-variables models of Bell correlations. We first give an overview of superdeterminism and discuss various criticisms of it raised in the literature. We argue that the most common criticism, the violation of ‘free-will’, is incorrect. We take up Bell’s intuitive criticism that these models are ‘conspiratorial’. To develop this further, we introduce non-equilibrium extensions of superdeterministic models. We show that the measurement statistics of these extended models depend on the physical system used to determine the measurement settings. This suggests a fine-tuning in order to eliminate this dependence from experimental observation. We also study the signalling properties of these extended models. We show that although they generally violate the formal no-signalling constraints, this violation cannot be equated to an actual signal. We therefore suggest that the so-called no-signalling constraints be more appropriately named the marginal-independence constraints. We discuss the mechanism by which marginal-independence is violated in superdeterministic models. Lastly, we consider a hypothetical scenario where two experimenters use the apparent-signalling of a superdeterministic model to communicate with each other. This scenario suggests another conspiratorial feature peculiar to superdeterminism. These suggestions are quantitatively developed in the second paper.

show abstract

Section: Introductionmentioning

confidence: 99%

Superdeterministic hidden-variables models I: non-equilibrium and signalling

Sen

Valentini

2020

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Bell-scenario model of the Proposal illustrates a key conspiratorial feature of superdeterminism discussed in [27,28]. In the aforementioned references, the conspiratorial character of superdeterministic models is quantified in two separate ways.…”

Section: (C) Superdeterministic Conspiracymentioning

confidence: 99%

“…Intuitively, one can identify this as a conspiratorial feature of the model: the experimenter does not know beforehand which apparatus will be subject to the constraint for any given run, but the initial conditions ensure that the experimenter unconsciously makes the correct choice for each run. The correlation required for this 'mimicking of causation' grows with N [28]. Therefore, the initial conditions in the model…”

Section: (C) Superdeterministic Conspiracymentioning

confidence: 99%

“…How to justify such initial conditions is a major conceptual question for this approach. It has been argued in [27,28] that any such justification would necessarily be conspiratorial in a quantitative sense.…”

Section: Introductionmentioning

confidence: 99%

“…We also show how several arguments made in the Proposal fail when considered in the model. Lastly, we use our model and recent results about superdeterministic conspiracy [27,28] to discuss the conspiratorial nature of superdeterminism in the Proposal.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Sen

2022

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Indeterminism and Undecidability

Landsman

2021

Undecidability, Uncomputability, and Unpredictability

View full text Add to dashboard Cite

The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Gödel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e. almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories. Contents 1 Introduction: Gödel and Bell 2 Randomness and its unprovability 3 Rethinking Bell's theorem 4 Are deterministic hidden variable theories deterministic? 5 Conclusion and discussion A The Born rule B 1-Randomness C Bell's theorem and free will theorem References

show abstract

Superdeterministic hidden-variables models II: conspiracy

Cited by 13 publications

References 20 publications

Superdeterministic hidden-variables models I: non-equilibrium and signalling

Superdeterministic hidden-variables models I: non-equilibrium and signalling

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

Indeterminism and Undecidability

Contact Info

Product

Resources

About