Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 79 tok/s
Gemini 2.5 Pro 41 tok/s Pro
GPT-5 Medium 25 tok/s Pro
GPT-5 High 23 tok/s Pro
GPT-4o 99 tok/s Pro
Kimi K2 199 tok/s Pro
GPT OSS 120B 444 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Counterfactual restrictions and Bell's theorem (1909.06608v6)

Published 14 Sep 2019 in quant-ph and physics.hist-ph

Abstract: We show that the ability to consider counterfactual situations is a necessary assumption of Bell's theorem, and that, to allow Bell inequality violations while maintaining all other assumptions, we just require certain measurement choices be counterfactually restricted, rather than the full removal of counterfactual definiteness. We illustrate how the counterfactual definiteness assumption formally arises from the statistical independence assumption. Counterfactual restriction therefore provides a way to interpret statistical independence violation different to what is typically assumed (i.e. that statistical independence violation means either retrocausality or superdeterminism). We tie counterfactual restriction to contextuality, and show the similarities to that approach.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (67)
  1. Quantum information and relativity theory. Rev. Mod. Phys., 76:93–123, 1 2004. doi:10.1103/RevModPhys.76.93.
  2. John S Bell. Introduction to the hidden-variable question. Technical report, CM-P00058691, 1971.
  3. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47:777–780, May 1935. doi:10.1103/PhysRev.47.777.
  4. Experimental test of local hidden-variable theories. Phys. Rev. Lett., 28:938–941, Apr 1972. doi:10.1103/PhysRevLett.28.938.
  5. Experimental tests of realistic local theories via bell’s theorem. Phys. Rev. Lett., 47:460–463, 8 1981. doi:10.1103/PhysRevLett.47.460.
  6. Experimental realization of einstein-podolsky-rosen-bohm gedankenexperiment: A new violation of bell’s inequalities. Phys. Rev. Lett., 49:91–94, Jul 1982. doi:10.1103/PhysRevLett.49.91.
  7. D. Bohm. Quantum Theory. Dover Books on Physics Series. Dover Publications, 1951. URL: https://books.google.co.uk/books?id=9DWim3RhymsC.
  8. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23:880–884, Oct 1969. doi:10.1103/PhysRevLett.23.880.
  9. Paul Adrien Maurice Dirac. A new notation for quantum mechanics. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 35, pages 416–418. Cambridge University Press, 1939. doi:10.1017/S0305004100021162.
  10. Albert Einstein. Letter from einstein to max born, 3 march 1947. In Max Born and Irene Born, editors, The Born-Einstein Letters; Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955, pages 157–158. Macmillan, London, 1971.
  11. Taxonomy for physics beyond quantum mechanics. arXiv preprint arXiv:2309.12293, 2023. doi:10.48550/arXiv.2309.12293.
  12. J. S. Bell. On the einstein podolsky rosen paradox. Physics Physique Fizika, 1:195–200, Nov 1964. doi:10.1103/PhysicsPhysiqueFizika.1.195.
  13. Eugene P. Wigner. On hidden variables and quantum mechanical probabilities. American Journal of Physics, 38(8):1005–1009, 1970. doi:10.1119/1.1976526.
  14. Michael Redhead. Incompleteness, nonlocality, and realism: a prolegomenon to the philosophy of quantum mechanics. Oxford University Press, 1987.
  15. Boris S Cirel’son. Quantum generalizations of bell’s inequality. Letters in Mathematical Physics, 4(2):93–100, 1980. doi:10.1007/BF00417500.
  16. Quantum nonlocality as an axiom. Foundations of Physics, 24(3):379–385, 3 1994. doi:10.1007/BF02058098.
  17. Relativistic independence bounds nonlocality. Science Advances, 5(4):eaav8370, 2019. doi:10.1126/sciadv.aav8370.
  18. Jan-Åke Larsson. Loopholes in bell inequality tests of local realism. Journal of Physics A: Mathematical and Theoretical, 47(42):424003, 2014. doi:10.1088/1751-8113/47/42/424003.
  19. The violation of bell inequalities in the macroworld. Foundations of Physics, 30(9):1387–1414, Sep 2000. doi:10.1023/A:1026449716544.
  20. Alain Aspect. Proposed experiment to test the nonseparability of quantum mechanics. Phys. Rev. D, 14:1944–1951, 10 1976. doi:10.1103/PhysRevD.14.1944.
  21. Violation of bell’s inequality under strict einstein locality conditions. Physical Review Letters, 81(23):5039, 1998. doi:10.1103/PhysRevLett.81.5039.
  22. Experimental violation of a bell’s inequality with efficient detection. Nature, 409(6822):791–794, 2 2001. doi:10.1038/35057215.
  23. Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526(7575):682–686, 10 2015. doi:10.1038/nature15759.
  24. Significant-loophole-free test of bell’s theorem with entangled photons. Phys. Rev. Lett., 115:250401, Dec 2015. doi:10.1103/PhysRevLett.115.250401.
  25. Bell’s inequality and the coincidence-time loophole. EPL (Europhysics Letters), 67(5):707, 2004. doi:10.1209/epl/i2004-10124-7.
  26. Bell-inequality violation with entangled photons, free of the coincidence-time loophole. Phys. Rev. A, 90:032107, 9 2014. doi:10.1103/PhysRevA.90.032107.
  27. Causarum investigatio and the two bell’s theorems of john bell. In Quantum [Un] Speakables II, pages 119–142. Springer, 2017. doi:10.1007/978-3-319-38987-5_6.
  28. What does it take to solve the measurement problem? Journal of Physics Communications, 6(10):102001, 2022. doi:10.1088/2399-6528/ac96cf.
  29. Abner Shimony. Controllable and uncontrollable non-locality, volume 2, page 130–139. Cambridge University Press, 1993. doi:10.1017/CBO9781139172196.010.
  30. A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere al Nuovo Cimento, 27(10):293–298, 1980. doi:10.1007/BF02817189.
  31. Nature Physics Editorial Team. Survey the foundations. Nature Physics, 18(9):961–961, 9 2022. doi:10.1038/s41567-022-01766-x.
  32. Sandu Popescu. Nonlocality beyond quantum mechanics. Nature Physics, 10(4):264–270, 4 2014. doi:10.1038/nphys2916.
  33. Bell nonlocality. Reviews of Modern Physics, 86(2):419, 2014. doi:10.1103/RevModPhys.86.419.
  34. A snapshot of foundational attitudes toward quantum mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 44(3):222–230, 2013. doi:10.1016/j.shpsb.2013.04.004.
  35. Surveying the attitudes of physicists concerning foundational issues of surveym mechanics. arXiv preprint arXiv:1612.00676, 2016. URL: https://arxiv.org/abs/1612.00676.
  36. Eddy Keming Chen. Bell’s theorem, quantum probabilities, and superdeterminism. In The Routledge Companion to Philosophy of Physics, pages 184–199. Routledge, 2021.
  37. Bell’s theorem allows local theories of quantum mechanics. Nature Physics, 18(12):1382–1382, 12 2022. doi:10.1038/s41567-022-01831-5.
  38. Michael J. W. Hall. Relaxed bell inequalities and kochen-specker theorems. Phys. Rev. A, 84:022102, Aug 2011. doi:10.1103/PhysRevA.84.022102.
  39. Relaxed bell inequality as a trade-off relation between measurement dependence and hiddenness. Physical Review A, 108(2):022214, 2023. doi:10.1103/PhysRevA.108.022214.
  40. Rethinking superdeterminism. Frontiers in Physics, 8:139, 2020. doi:10.3389/fphy.2020.00139.
  41. Sabine Hossenfelder. Superdeterminism: A guide for the perplexed. arXiv preprint arXiv:2010.01324, 2020. URL: https://arxiv.org/abs/2010.01324.
  42. Supermeasured: Violating bell-statistical independence without violating physical statistical independence. Foundations of Physics, 52(4):81, Jul 2022. doi:10.1007/s10701-022-00602-9.
  43. K. B. Wharton and N. Argaman. Colloquium: Bell’s theorem and locally mediated reformulations of quantum mechanics. Rev. Mod. Phys., 92:021002, 5 2020. doi:10.1103/RevModPhys.92.021002.
  44. Superdeterministic hidden-variables models i: non-equilibrium and signalling. Proceedings of the Royal Society A, 476(2243):20200212, 2020. doi:10.1098/rspa.2020.0212.
  45. Superdeterministic hidden-variables models ii: conspiracy. Proceedings of the Royal Society A, 476(2243):20200214, 2020. doi:10.1098/rspa.2020.0214.
  46. Carl H. Brans. Bell’s theorem does not eliminate fully causal hidden variables. International Journal of Theoretical Physics, 27(2):219–226, 2 1988. doi:10.1007/BF00670750.
  47. Gerard t Hooft. The cellular automaton interpretation of quantum mechanics. Springer Nature, 2016. doi:10.1007/978-3-319-41285-6.
  48. On superdeterministic rejections of settings independence. British Journal for the Philosophy of Science, 2020. doi:10.1086/714819.
  49. Toy model for local and deterministic wave-function collapse. Phys. Rev. A, 106:022212, Aug 2022. doi:10.1103/PhysRevA.106.022212.
  50. TN Palmer. Discretization of the bloch sphere, fractal invariant sets and bell’s theorem. Proceedings of the Royal Society A, 476(2236):20190350, 2020. doi:10.1098/rspa.2019.0350.
  51. Experimentally adjudicating between different causal accounts of Bell-inequality violations via statistical model selection. Phys. Rev. A, 105:042220, 4 2022. doi:10.1103/PhysRevA.105.042220.
  52. Comment on” experimentally adjudicating between different causal accounts of bell-inequality violations via statistical model selection”. arXiv preprint arXiv:2206.10619, 2022. doi:10.48550/arXiv.2206.10619.
  53. TN Palmer. A local deterministic model of quantum spin measurement. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 451(1943):585–608, 1995. doi:10.1098/rspa.1995.0145.
  54. TN Palmer. The invariant set postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465(2110):3165–3185, 2009. doi:10.1098/rspa.2009.0080.
  55. TN Palmer. Invariant set theory. arXiv preprint arXiv:1605.01051, 2016. URL: https://arxiv.org/abs/1605.01051.
  56. Foundations of the theory of probability: Second English Edition. Courier Dover Publications, 2018.
  57. Tim Maudlin. What bell proved: A reply to blaylock. American Journal of Physics, 78(1):121–125, 2010. doi:10.1119/1.3243280.
  58. Boris Kment. Varieties of Modality. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Spring 2021 edition, 2021.
  59. Robert W. Spekkens. Evidence for the epistemic view of quantum states: A toy theory. Phys. Rev. A, 75:032110, Mar 2007. doi:10.1103/PhysRevA.75.032110.
  60. S. J. van Enk. A toy model for quantum mechanics. Foundations of Physics, 37(10):1447–1460, Oct 2007. doi:10.1007/s10701-007-9171-3.
  61. Theories of systems with limited information content. New Journal of Physics, 12(5):053037, may 2010. doi:10.1088/1367-2630/12/5/053037.
  62. Toy quantum categories (extended abstract). Electronic Notes in Theoretical Computer Science, 270(1):29–40, 2011. Proceedings of the Joint 5th International Workshop on Quantum Physics and Logic and 4th Workshop on Developments in Computational Models (QPL/DCM 2008). doi:10.1016/j.entcs.2011.01.004.
  63. Reconstruction of gaussian quantum mechanics from liouville mechanics with an epistemic restriction. Phys. Rev. A, 86:012103, Jul 2012. doi:10.1103/PhysRevA.86.012103.
  64. Robert W. Spekkens. Quasi-Quantization: Classical Statistical Theories with an Epistemic Restriction, pages 83–135. Springer Netherlands, Dordrecht, 2016. doi:10.1007/978-94-017-7303-4_4.
  65. Kochen-specker contextuality. Rev. Mod. Phys., 94:045007, Dec 2022. doi:10.1103/RevModPhys.94.045007.
  66. Contextuality in three types of quantum-mechanical systems. Foundations of Physics, 45(7):762–782, Jul 2015. doi:10.1007/s10701-015-9882-9.
  67. Contextuality-by-default: A brief overview of ideas, concepts, and terminology. In Harald Atmanspacher, Thomas Filk, and Emmanuel Pothos, editors, Quantum Interaction, pages 12–23, Cham, 2016. Springer International Publishing. doi:10.1007/978-3-319-28675-4_2.
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (1)

  1. Jonte R. Hance
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Don't miss out on important new AI/ML research

See which papers are being discussed right now on X, Reddit, and more:

Explore Trending Papers

“Emergent Mind helps me see which AI papers have caught fire online.”

Philip

Philip

Creator, AI Explained on YouTube