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REVIEW 3 major objections 4 minor 46 references

The paper claims that violations of measurement independence can be made testable by turning them into signalling in principle, and proves a version of the nonlocality theorem without that assumption.

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2026-08-03 00:11 UTC pith:4M3Q4X3R

load-bearing objection A serious, mostly sound paper that reclassifies measurement-independence violations as operationally testable nonlocality, but the advertised no-signalling Bell theorem overstates what is proven and Theorem 2 needs a small but real repair. the 3 major comments →

arxiv 2602.11300 v2 pith:4M3Q4X3R submitted 2026-02-11 quant-ph

Extending Bell's Theorem: Nonlocality via Measurement Dependence

G. Bacciagaluppi , R. Hermens , G. Leegwater This is my paper
classification quant-ph MSC 81P1381P05
keywords measurement independencehidden variablesnonlocalitysignalling in principleequiprobability theoremretrocausalitysuperdeterminismquantum foundations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that violating the assumption that hidden variables are independent of measurement settings—often dismissed as a 'conspiracy loophole'—need not be a dead end for testing quantum nonlocality. It shows that certain violations of this assumption can be re-expressed as signalling in principle: if Charlie can prepare appropriate sub-ensembles, Alice or Bob can send a message. The main theorem derives a nonlocality inequality from no-signalling plus Outcome Independence, without assuming Measurement Independence. A sympathetic reader should care because this converts a philosophical loophole into an operationally meaningful distinction between forms of nonlocality.

Core claim

The central claim is Theorem 2: in a hidden-variable model that satisfies Outcome Independence and reproduces high (anti)correlations along four chains of nearby spin directions, any violation of the four-term correlation inequality beyond 4ε guarantees that there exists a sub-distribution deviating from equiprobability. If that sub-distribution can be operationally prepared by Charlie as a sub-ensemble, then at least one of Alice or Bob can signal. The proof pieces together the equiprobability theorem—which bounds hidden-level marginals by chain correlations—with a lemma showing that a Bell-inequality violation forces a large marginal deviation in some sub-distribution. Thus, under the stat

What carries the argument

The load-bearing object is the equiprobability theorem: for a hidden-variable model reproducing near-perfect (anti)correlations along a chain of alternating spin directions, each hidden variable's local outcomes must be equiprobable unless parameter or measurement independence fails. The paper converts this into a quantitative statement: a chain of 2n directions at angle π/2n bounds the marginal deviation by 2nδ. Combining this with the fact that a Bell-inequality violation larger than 4ε forces a sub-distribution with marginal deviation larger than ε yields the extended theorem. The second essential ingredient is the operational notion of a sub-ensemble: a sub-distribution that Charlie can

Load-bearing premise

The load-bearing premise is that Charlie can in principle reliably prepare the non-quantum sub-ensembles that Theorem 2 needs; the proof shows such sub-distributions exist mathematically, but existence in the formalism does not guarantee operational preparability, and the paper itself (Section 7) notes that some MI-violating descriptions—contextual and divergent-worlds pictures—do not allow preparation of any ensembles beyond the quantum ones.

What would settle it

A concrete check is to construct an explicit hidden-variable model satisfying Outcome Independence, high chain correlations, and a four-term inequality violation larger than 4ε, and then test whether any protocol can prepare the guaranteed sub-ensemble with weight at least 1/2 uniformly across all settings; if no such protocol exists, the signalling conclusion does not follow. The paper's own Section 7 examples—contextual and branching-world descriptions—would also falsify the general claim if they reproduce the Bell violation yet provably cannot prepare non-quantum ensembles.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If a hidden-variable model satisfies Outcome Independence and reproduces quantum-like chain correlations, then any Bell-inequality violation above 4ε makes the model signalling-capable whenever Charlie can prepare the relevant sub-ensemble.
  • No-signalling alone, without Measurement Independence, suffices to derive a nonlocality theorem under the stated chain-correlation and sub-ensemble assumptions.
  • A concrete retrocausal model discussed in the paper reproduces the quantum correlations but underdetermines the hidden distribution; certain allowed non-quantum distributions violate equiprobability and permit signalling in principle.
  • In principle, action-at-a-distance (Parameter Independence failure) can be operationally distinguished from measurement-dependence signalling: the latter requires no preferred time ordering between Alice's and Bob's measurements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Going beyond the paper: if the sub-ensemble preparation condition is dropped, Theorem 2 collapses; the decisive physical question is whether any genuine, non-formal violation of Measurement Independence must allow reliable non-quantum sources.
  • Editorial extension: the paper's contrast between formal and causal violations suggests a testable hierarchy—an MI-violating theory that can signal in principle is one in which the settings influence the hidden distribution through an actual mechanism, not merely through a re-description of the same quantum state.
  • The quantitative threshold ε ≥ 4nγ could be turned into a concrete experimental programme: measure chain correlations and the four-term inequality on the same ensemble to determine the maximum chain length n for which no-signalling still forces signalling.
  • The authors' own limitation examples imply that any attempt to prepare the sub-ensemble must be checked for uniformity across all settings; a model satisfying Theorem 2's premises but lacking such a uniform preparation protocol would be a counterexample to the theorem's applicability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper examines the assumption of Measurement Independence (MI) in Bell's theorem and proposes that certain violations of MI can be understood as 'signalling in principle', making them operationally testable. The authors prove equiprobability theorems (Theorems 0 and 0'), then show that operational violations of equiprobability imply signalling (Theorems 1 and 1'). They introduce Lemmas 1 and 2 connecting CHSH violations to sub-distribution deviations and chain-correlation bounds, leading to Theorem 2/2' as an apparent extension of Bell's theorem without MI, conditional on Outcome Independence, finite chain-correlation bounds, and Charlie's ability to prepare 'appropriate sub-ensembles'. Section 6 applies the framework to the Schulman/Wharton model; Section 7 discusses limitations, including Bohr-style contextualism and Everett 'divergent worlds', where the required ensembles cannot be prepared.

Significance. The paper's novelty is to convert a standard loophole—Measurement Independence—into a potential operational resource with quantitative thresholds. The direct proofs of Theorems 0/0' and 1/1' in Appendices A and B are clear, self-contained, and do not involve parameter fitting. The chain-correlation framework gives robust, experimentally checkable conditions. The authors are also unusually candid about the scope and limitations of their claims, particularly in Section 7. If the main theorem can be made fully rigorous, the paper would be a meaningful contribution to the foundations of quantum mechanics and to 'experimental metaphysics'.

major comments (3)
  1. [§5, Theorem 2 proof] The proof of Theorem 2 contains a quantifier shift. Lemma 1 guarantees only a sub-distribution σ_0^{IJ} of the single context distribution σ_K^{IJ} with weight ≥1/2 and |⟨A⟩_0^{IJ}| > ε. But a sub-ensemble, as defined in Eq. (17), is a collection of distributions for all I,J. The proof states: 'By Lemma 2, any sub-ensemble with weight 1/2≤α≤1... By Lemma 1, one of these sub-ensembles also satisfies (19)...' No construction of such a global K1 is given. A repair would define K1 by setting its IJ component to the sub-distribution from Lemma 1 and all other components equal to K, but this requires Charlie to prepare an ensemble whose distributions differ only at one future setting pair—an extra, non-trivial operational assumption that is not stated in Theorem 2. The authors acknowledge the general difficulty in footnote 28 and Section 7, but the theorem as stated and proved is incomplete.
  2. [Abstract and §5 (first paragraph)] The Abstract claims: 'by imposing no-signalling one can prove a version of Bell's theorem that does not require the assumption of Measurement Independence.' Section 5's opening paragraph similarly says: 'imposing no-signalling allows one to derive the Bell inequalities.' However, Theorem 2 assumes Outcome Independence (Eq. (3)), finite chain-correlation bounds (21)–(22), and the additional premise 'If Charlie can prepare appropriate sub-ensembles of K'. Outcome Independence is not a no-signalling condition, and the theorem does not follow from no-signalling alone. The advertised conclusion is therefore stronger than what is proven. The Abstract and Section 5 should be rephrased to say that, under OI, finite chain-correlation bounds, and preparability of sub-ensembles, violations of MI become signalling in principle.
  3. [Appendix C, Lemma 1 proof] The proof of Lemma 1 contains an unjustified equivalence claim. It reads: 'Now assume that |⟨A⟩_1^{IJ}|, |⟨A⟩_2^{IJ}| ≤ ε. This is equivalent to assuming the bound in (59) for all possible sub-distributions, since for any other sub-distribution there will be partial cancellations.' This equivalence is false: a sub-distribution can select a subset of σ_1 with a larger mean than the mean over all of σ_1. Moreover, the contrapositive of Lemma 1 only bounds sub-distributions with weight ≥1/2; it does not bound the lighter of σ_1 and σ_2. Yet the chain of inequalities (60) uses bounds on both parts regardless of their weights. Since Lemma 1 is used in the proof of Theorem 2, a correct proof or a modified lemma is needed.
minor comments (4)
  1. [§2, near Eq. (2)] The text says 'returns the expectation values ... (as defined in (4))', but Eq. (4) defines Parameter Independence, not expectation values. The reference should be to Eq. (2).
  2. [§5, after Lemma 1] The sentence 'Setting ε=1/2 and contraposing yields the Bell inequalities' could be expanded to show explicitly that this gives the CHSH bound |CHSH| ≤ 2.
  3. [§6, Eq. (32)] The coefficients α, β, γ, δ in (32) reuse letters that earlier denote mixture weights (α) and error parameters (γ). Consider using different symbols to avoid confusion.
  4. [§5, Theorem 2'] The claim that 'this single chain contains all the measurements we need' is terse. A short explanation of how the 12 chain directions include the four Bell-correlation directions would improve readability.

Circularity Check

0 steps flagged

No load-bearing circularity: the derivation chain is self-contained; the main caveat is a non-circular quantifier-shift gap in Theorem 2.

full rationale

The derivation chain is self-contained. Theorems 0 and 0' are proved in Appendix A from PI/MI and chain-correlation inequalities; Theorems 1 and 1' follow by contraposition using the trivial hidden-variable model (lambda = K), where no-signalling makes PI true by definition and MI is trivially true. This is a legitimate reduction, not a circular one. Lemmas 1 and 2 are elementary averaging/contraposition arguments, and Theorem 2 composes them with Theorem 1' under explicit premises (OI, chain correlations, CHSH violation > 4 epsilon, epsilon >= 4n gamma, and preparable sub-ensembles). The only concerns are non-circular: (i) the proof of Theorem 2 silently promotes Lemma 1's single-context sub-distribution to a global operational sub-ensemble (Section 5, Eq. (17) vs Lemma 1), a quantifier-shift gap; and (ii) the preparability assumption is physically contingent, as Section 7 concedes for Bohr-style and Everett-style models. Neither step makes the conclusion equivalent to the premises or to a fitted input. Self-citations (e.g., Leegwater 2016 for proof technique, footnote 24) are not load-bearing because the relevant proofs are reproduced in the paper. No parameter is fitted and no prediction is renamed from an input.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

No new physical entities (particles, forces, dimensions) are introduced. 'Non-quantum ensembles' and the 'trivial hidden-variable model' are mathematical constructions, not physical entities. The quoted free parameters and axioms are the only extra assumptions the central theorems depend on.

free parameters (2)
  • Schulman/Wharton model parameter γ = very small (unspecified)
    Used in the illustrative Schulman ansatz w(α)=1/(α²+γ²). It is a free parameter of the example model, not of the paper's central theorems.
  • Wharton hidden-spin coefficients α, β, γ, δ = constrained by lines (34)–(35), e.g. α=γ=β=δ=1/4
    The retrocausal model underdetermines the distribution over hidden spin pairs; the Born rule is recovered only under (35). These are free in the example, not in the main proofs.
axioms (4)
  • domain assumption Operational well-definedness of mixtures when MI is violated (Equation 17): mixing ensembles uniformly across all Alice/Bob contexts
    Needed to define sub-ensembles, which are central to Theorem 2. The authors themselves note (Section 5) that this must be established explicitly in any concrete MI-violating theory.
  • domain assumption Charlie can prepare appropriate non-quantum sub-ensembles of the ensemble K
    The conclusion of Theorem 2/2' is conditional on this. The paper's own Section 7 admits that Bohr-style and Everett-divergence interpretations violate MI only formally and do not allow such preparation.
  • domain assumption Settings are treated as parameters, not random variables
    Footnote 11 (Section 2) explains this modeling choice; it is needed to make sense of 'genuine' violations of MI as law-like rather than merely statistical.
  • standard math Standard probability and spin-½ quantum formalism, including the CHSH framework
    The paper's inequalities and equiprobability theorems are derived within this framework; no new quantum formalism is introduced.

pith-pipeline@v1.3.0-alltime-deepseek · 25223 in / 22042 out tokens · 230985 ms · 2026-08-03T00:11:10.119253+00:00 · methodology

0 comments
read the original abstract

Besides well-known conditions of locality or factorisability, deriving the Bell inequalities requires assuming that the distribution of hidden variables and Alice's and Bob's measurement settings be independent of each other. We show that (analogously to violations of locality due to action at a distance) certain violations of this Measurement Independence assumption can be associated with a notion of signalling in principle, thus making them also testable in principle, and spell out the appropriate conditions. Accordingly, we show that by imposing no-signalling one can prove a version of Bell's theorem that does not require the assumption of Measurement Independence. We discuss the "Schulman model" as an example, as well as lessons for "experimental metaphysics".

Figures

Figures reproduced from arXiv: 2602.11300 by G. Bacciagaluppi, G. Leegwater, R. Hermens.

Figure 1
Figure 1. Figure 1: Action at a distance in pilot-wave theory: spin measurement with two choices of polarity for the field. One usually says that in this scenario there is ‘signalling in principle’. This is not to suggest one should analyse anthropocentrically the notion of action at a distance (which, as emphasised, occurs independently of whether Alice knows the position of her particle), rather it invites us to consider a … view at source ↗
Figure 2
Figure 2. Figure 2: Spin directions for the proof of the equiprobability theorem. The main idea behind the proof is that, considering a chain of coplanar spin measurements Ai and Bj alternating between Alice’s and Bob’s side (see [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

46 extracted references · 1 canonical work pages

  1. [1]

    (2016), ‘Are retrocausal accounts of entanglement unnaturally fine-tuned?’,International Journal of Quantum Foundations2, 1–16.https://arxiv.org/pdf/1510.03706

    Almada, D., Ch’ng, K., Kintner, S., Morrison, B., and Wharton, K. (2016), ‘Are retrocausal accounts of entanglement unnaturally fine-tuned?’,International Journal of Quantum Foundations2, 1–16.https://arxiv.org/pdf/1510.03706

    Pith/arXiv arXiv 2016

  2. [2]

    (2012), ‘Non-equilibrium in stochastic mechanics’,Journal of Physics: Conference Series361, 012017/1– 12.http://philsci-archive.pitt.edu/9120/

    Bacciagaluppi, G. (2012), ‘Non-equilibrium in stochastic mechanics’,Journal of Physics: Conference Series361, 012017/1– 12.http://philsci-archive.pitt.edu/9120/

    2012

  3. [3]

    (2026), ‘The relativity of branching’, in A

    Bacciagaluppi, G. (2026), ‘The relativity of branching’, in A. Ney (ed.),Local Quantum Mechanics: Everett, Many Worlds, and Reality(Oxford: OUP), in press.https://philsci-archive.pitt.edu/25071/

    2026

  4. [4]

    local causality

    Bacciagaluppi, G. (in preparation), ‘Against “local causality”’.https://www.dpg-verhandlungen.de/year/2025/conference/ bonn/static/syqt1.pdf

    2025

  5. [5]

    Barrett, J[eff] (1999),The Quantum Mechanics of Minds and Worlds(Oxford: OUP).https://sites.socsci.uci.edu/ ~jabarret/bio/publications/bookpdf.pdf

    1999

  6. [6]

    (2011), ‘How much measurement independence is needed to demonstrate nonlocality?’, Physical Review Letters106, 100406/1–4.https://arxiv.org/pdf/1008.3612

    Barrett, J[on], and Gisin, N. (2011), ‘How much measurement independence is needed to demonstrate nonlocality?’, Physical Review Letters106, 100406/1–4.https://arxiv.org/pdf/1008.3612

    Pith/arXiv arXiv 2011

  7. [7]

    (2006), ‘Maximally nonlocal and monogamous quantum correlations’,Physical Review Letters97, 170409/1–4.https://arxiv.org/pdf/quant-ph/0605182

    Barrett, J[on], Kent, A., and Pironio, S. (2006), ‘Maximally nonlocal and monogamous quantum correlations’,Physical Review Letters97, 170409/1–4.https://arxiv.org/pdf/quant-ph/0605182

    Pith/arXiv arXiv 2006

  8. [8]

    Bell, J. S. (1981), ‘Bertlmann’s socks and the nature of reality’,Journal de Physique42, C2/41–61. Repr. as Chap. 16 inSpeakable and Unspeakable in Quantum Mechanics(Cambridge: CUP, 1987), pp. 139–158.https://hal.science/ jpa-00220688/document 19

    1981

  9. [9]

    (1935), ‘Can quantum-mechanical description of physical reality be considered complete?’,Physical Review 48(8), 696–702.https://journals.aps.org/pr/pdf/10.1103/PhysRev.48.696

    Bohr, N. (1935), ‘Can quantum-mechanical description of physical reality be considered complete?’,Physical Review 48(8), 696–702.https://journals.aps.org/pr/pdf/10.1103/PhysRev.48.696

    doi:10.1103/physrev.48.696 1935

  10. [10]

    (1992), ‘Bell’s theorem: What it takes’,The British Journal for the Philosophy of Science43(1), 41–83

    Butterfield, J. (1992), ‘Bell’s theorem: What it takes’,The British Journal for the Philosophy of Science43(1), 41–83. https://www.researchgate.net/publication/245583158_Bell’s_Theorem_What_it_Takes

    arXiv 1992

  11. [11]

    (2011), ‘No extension of quantum theory can have improved predictive power’,Nature Communications2(1), 411/1–5.https://www.nature.com/articles/ncomms1416.pdf

    Colbeck, R., and Renner, R. (2011), ‘No extension of quantum theory can have improved predictive power’,Nature Communications2(1), 411/1–5.https://www.nature.com/articles/ncomms1416.pdf

    2011

  12. [12]

    (2016), ‘The completeness of quantum theory for predicting measurement outcomes’, in G

    Colbeck, R., and Renner, R. (2016), ‘The completeness of quantum theory for predicting measurement outcomes’, in G. Chiribella and R. Spekkens (eds),Quantum Theory: Informational Foundations and Foils(Dordrecht: Springer), pp. 497–528.https://arxiv.org/pdf/1208.4123 D¨ urr, D., Goldstein, S., and Zangh ` ı, N. (1992), ‘Quantum equilibrium and the origin o...

    Pith/arXiv arXiv 2016

  13. [13]

    (1998), ‘Exorcist XIV: The wrath of Maxwell’s demon

    Earman, J., and Norton, J. (1998), ‘Exorcist XIV: The wrath of Maxwell’s demon. Part I. From Maxwell to Szilard’, Studies in History and Philosophy of Modern Physics29(4), 435–471.https://sites.pitt.edu/ ~jdnorton/papers/ ExorcistXIV/Exorcist1.pdf

    1998

  14. [14]

    (1999), ‘Exorcist XIV: The wrath of Maxwell’s demon

    Earman, J., and Norton, J. (1999), ‘Exorcist XIV: The wrath of Maxwell’s demon. Part II. From Szilard to Landauer and beyond’,Studies in History and Philosophy of Modern Physics30(1), 1–40.https://sites.pitt.edu/~jdnorton/ papers/ExorcistXIV/Exorcist2.pdf

    1999

  15. [15]

    (2019), ‘Relaxed Bell inequalities with arbitrary mea- surement dependence for each observer’,Physical Review A99, 012121/1–23.https://arxiv.org/pdf/1809.01307

    Friedman, A., Guth, A., Hall, M., Kaiser, D., and Gallicchio, J. (2019), ‘Relaxed Bell inequalities with arbitrary mea- surement dependence for each observer’,Physical Review A99, 012121/1–23.https://arxiv.org/pdf/1809.01307

    Pith/arXiv arXiv 2019

  16. [16]

    (2024), ‘The consistent histories approach to quantum mechanics’, in E

    Griffiths, R. (2024), ‘The consistent histories approach to quantum mechanics’, in E. Zalta and U. Nodelman (eds), The Stanford Encyclopedia of Philosophy (Summer 2024 Edition).https://plato.stanford.edu/archives/sum2024/ entries/qm-consistent-histories/

    2024

  17. [17]

    (2011), ‘Relaxed Bell inequalities and Kochen-Specker theorems’,Physical Review A84, 022102/1–16.https: //arxiv.org/pdf/1102.4467

    Hall, M. (2011), ‘Relaxed Bell inequalities and Kochen-Specker theorems’,Physical Review A84, 022102/1–16.https: //arxiv.org/pdf/1102.4467

    Pith/arXiv arXiv 2011

  18. [18]

    (1935), ‘Die naturphilosophischen Grundlagen der Quantenmechanik’,Abhandlungen der Fries’schen Schule (Neue Folge),6(2), 69–152

    Hermann, G. (1935), ‘Die naturphilosophischen Grundlagen der Quantenmechanik’,Abhandlungen der Fries’schen Schule (Neue Folge),6(2), 69–152. Translated as ‘The natural-philosophical foundations of quantum mechanics’, in E. Crull and G. Bacciagaluppi (eds),Grete Hermann: Between Physics and Philosophy(Dordrecht: Springer), pp. 239–278

    1935

  19. [19]

    (2019), ‘An operationalist perspective on setting dependence’,Foundations of Physics49(3), 260–282

    Hermens, R. (2019), ‘An operationalist perspective on setting dependence’,Foundations of Physics49(3), 260–282. https://link.springer.com/article/10.1007/s10701-019-00243-5

    work page doi:10.1007/s10701-019-00243-5 2019

  20. [20]

    Hermens, R. (2020), ‘Completely real? A critical note on the claims by Colbeck and Renner’,Studies in History and Philosophy of Modern Physics72, 121–137.https://arxiv.org/pdf/2008.01444 ’t Hooft, G. (2016),The Cellular Automaton Interpretation of Quantum Mechanics(Cham: Springer).https://link. springer.com/book/10.1007/978-3-319-41285-6

    Pith/arXiv arXiv 2020

  21. [21]

    (2020), ‘Rethinking superdeterminism’,Frontiers in Physics8, 139/1–13.https: //www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00139/full

    Hossenfelder, S., and Palmer, T. (2020), ‘Rethinking superdeterminism’,Frontiers in Physics8, 139/1–13.https: //www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00139/full

    arXiv 2020

  22. [22]

    (1993), ‘Against experimental metaphysics’,Midwest Studies in Philosophy18, 295–316

    Jones, M., and Clifton, R. (1993), ‘Against experimental metaphysics’,Midwest Studies in Philosophy18, 295–316. https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1475-4975.1993.tb00269.x

    arXiv 1993

  23. [23]

    (2022), ‘Tackling loopholes in experimental tests of Bell’s inequality’, in O

    Kaiser, D. (2022), ‘Tackling loopholes in experimental tests of Bell’s inequality’, in O. Freire, G. Bacciagaluppi, O. Dar- rigol, T. Hartz, C. Joas, A. Kojevnikov, and O. Pessoa (eds),The Oxford Handbook of the History of Quantum Interpre- tations(Oxford: OUP), pp. 339–370.https://arxiv.org/pdf/2011.09296

    Pith/arXiv arXiv 2022

  24. [24]

    Leegwater, G. (2016), ‘An impossibility theorem for parameter independent hidden variable theories’,Studies in History and Philosophy of Modern Physics54, 18–34.https://philsci-archive.pitt.edu/12067/1/CR_Phil-Sci.pdf

    2016

  25. [25]

    (2014), ‘Is the quantum state real? An extended review ofψ-ontology theorems’,Quanta3(1), 67–155

    Leifer, M. (2014), ‘Is the quantum state real? An extended review ofψ-ontology theorems’,Quanta3(1), 67–155. https://arxiv.org/pdf/1409.1570 20

    Pith/arXiv arXiv 2014

  26. [26]

    (1994),Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics(Oxford: Black- well; 3rd ed., Malden: Wiley-Blackwell, 2011)

    Maudlin, T. (1994),Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics(Oxford: Black- well; 3rd ed., Malden: Wiley-Blackwell, 2011)

    1994

  27. [27]

    (2006), ‘Bell inequalities for random fields’,Journal of Physics A: Mathematical and General39(23), 7441–7456.https://arxiv.org/pdf/cond-mat/0403692

    Morgan, P. (2006), ‘Bell inequalities for random fields’,Journal of Physics A: Mathematical and General39(23), 7441–7456.https://arxiv.org/pdf/cond-mat/0403692

    Pith/arXiv arXiv 2006

  28. [28]

    (2016), ‘Lessons of Bell’s theorem: Nonlocality, yes; action at a distance, not necessarily’, in M

    Myrvold, W. (2016), ‘Lessons of Bell’s theorem: Nonlocality, yes; action at a distance, not necessarily’, in M. Bell and S. Gao (eds),Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem(Cambridge: CUP), pp. 238–260. https://philsci-archive.pitt.edu/12382/1/MyrvoldBellCurrentVersionPhilSci.pdf

    2016

  29. [29]

    (2009), ‘Local causality and completeness: Bell vs

    Norsen, T. (2009), ‘Local causality and completeness: Bell vs. Jarrett’,Foundations of Physics39(3), 273–294.https: //arxiv.org/pdf/0808.2178

    Pith/arXiv arXiv 2009

  30. [30]

    (2021), ‘Lapsing quickly into fatalism: Bell on backward causation’,Entropy23(2), 251/1–29

    Norsen, T., and Price, H. (2021), ‘Lapsing quickly into fatalism: Bell on backward causation’,Entropy23(2), 251/1–29. https://www.mdpi.com/1099-4300/23/2/251

    2021

  31. [31]

    Palmer, T. (2020), ‘Discretization of the Bloch sphere, fractal invariant sets and Bell’s theorem’,Proceedings of the Royal Society A476(2236), 20190350/1–24.https://royalsocietypublishing.org/rspa/article/476/2236/20190350/80682 de la Pe˜ na, L., and Cetto, A. M. (1996),The Quantum Dice: An Introduction to Stochastic Electrodynamics(Dordrecht: Springer)....

    arXiv 2020

  32. [32]

    (1996),Time’s Arrow & Archimedes’ Point: New Directions for the Physics of Time(Oxford: OUP)

    Price, H. (1996),Time’s Arrow & Archimedes’ Point: New Directions for the Physics of Time(Oxford: OUP)

    1996

  33. [33]

    special state

    Schulman, L. (2012), ‘Experimental test of the “special state” theory of quantum measurement’,Entropy14, 665–686. https://www.mdpi.com/1099-4300/14/4/665

    2012

  34. [34]

    (1986), ‘Events and processes in the quantum world’, in R

    Shimony, A. (1986), ‘Events and processes in the quantum world’, in R. Penrose and C. Isham (eds),Quantum Concepts in Space and Time(Oxford: OUP), pp. 182–203

    1986

  35. [35]

    (1989), ‘Search for a worldview which can accommodate our knowledge of microphysics’, in J

    Shimony, A. (1989), ‘Search for a worldview which can accommodate our knowledge of microphysics’, in J. Cushing and E. McMullin (eds),Philosophical Consequences of Quantum Theory(Notre Dame: University of Notre Dame Press), pp. 25–37

    1989

  36. [36]

    (1994), ‘Non-locality from an analogue of the quantum Zeno effect’,Studies in History and Philosophy of Science25(3), 425–435

    Squires, E., Hardy, L., and Brown, H. (1994), ‘Non-locality from an analogue of the quantum Zeno effect’,Studies in History and Philosophy of Science25(3), 425–435

    1994

  37. [37]

    (2012), ‘An experimental test of all theories with predictive power beyond quantum theory’,Physical Review Letters109, 020402/1–5.https://arxiv.org/pdf/1105.0133

    Stuart, T., Slater, J., Colbeck, R., Renner, R., and Tittel, W. (2012), ‘An experimental test of all theories with predictive power beyond quantum theory’,Physical Review Letters109, 020402/1–5.https://arxiv.org/pdf/1105.0133

    Pith/arXiv arXiv 2012

  38. [38]

    Valentini, A., (1992), ‘On the pilot-wave theory of classical, quantum and subquantum physics’, PhD thesis, SISSA, Trieste.https://iris.sissa.it/handle/20.500.11767/4334

    1992

  39. [39]

    (2002), ‘Signal-locality in hidden-variables theories’,Physics Letters A297(5–6), 273–278.https://arxiv

    Valentini, A. (2002), ‘Signal-locality in hidden-variables theories’,Physics Letters A297(5–6), 273–278.https://arxiv. org/pdf/quant-ph/0106098 21

    Pith/arXiv arXiv 2002

  40. [40]

    (2024), ‘Pilot-wave theory and the search for new physics’.https://arxiv.org/pdf/2411.10782

    Valentini, A. (2024), ‘Pilot-wave theory and the search for new physics’.https://arxiv.org/pdf/2411.10782

    Pith/arXiv arXiv 2024

  41. [41]

    (2005), ‘Dynamical origin of quantum probabilities’,Proceedings of the Royal Society A 461(2053), 253–272.https://arxiv.org/pdf/quant-ph/0403034

    Valentini, A., and Westman, H. (2005), ‘Dynamical origin of quantum probabilities’,Proceedings of the Royal Society A 461(2053), 253–272.https://arxiv.org/pdf/quant-ph/0403034

    Pith/arXiv arXiv 2005

  42. [42]

    (2013), ‘Bell’s theorem: Two neglected solutions’,Foundations of Physics43(6), 769–791.https://arxiv

    Vervoort, L. (2013), ‘Bell’s theorem: Two neglected solutions’,Foundations of Physics43(6), 769–791.https://arxiv. org/pdf/1203.6587

    Pith/arXiv arXiv 2013

  43. [43]

    (2025), ‘Test of the physical significance of Bell non-locality’,Nature Communications16(1), 4390/1–7.https://www.nature.com/articles/s41467-025-59247-7.pdf

    Vieira, C., Ramanathan, R., and Cabello, A. (2025), ‘Test of the physical significance of Bell non-locality’,Nature Communications16(1), 4390/1–7.https://www.nature.com/articles/s41467-025-59247-7.pdf

    2025

  44. [44]

    (2014), ‘Quantum states as ordinary information’,Information5(1), 190–208.https://www.mdpi.com/ 2078-2489/5/1/190

    Wharton, K. (2014), ‘Quantum states as ordinary information’,Information5(1), 190–208.https://www.mdpi.com/ 2078-2489/5/1/190

    2014

  45. [45]

    (2024), ‘A localized reality appears to underpin quantum circuits’.https://arxiv.org/pdf/2412.05456

    Wharton, K., Sutherland, R., Amza, T., Liu, R., and Saslow, J. (2024), ‘A localized reality appears to underpin quantum circuits’.https://arxiv.org/pdf/2412.05456

    Pith/arXiv arXiv 2024

  46. [46]

    (2020),The Nature of Contingency: Quantum Physics as Modal Realism(Oxford: OUP)

    Wilson, A. (2020),The Nature of Contingency: Quantum Physics as Modal Realism(Oxford: OUP). 22

    2020