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Aspects of Superdeterminism Made Intuitive

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Abstract

We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial ‘bang’ correlates all events, just as in the superdeterministic universe. We introduce the notions of ‘strong’ and ‘soft’ superdeterminism, in order to clarify debates in the literature. Based on the analogy with billiards, we show that superdeterministic correlations may exist as a matter of principle, but be undetectable for all practical purposes. Even if inaccessible, such strong-superdeterministic correlations can explain why soft-, or effective, superdeterministic theories can be built. We counter classic objections to superdeterminism such as the claim that it would be at odds with the scientific method, and with the construction of new theories. Finally, we show that probability theory, as a physical theory, indicates that superdeterminism has a greater explanatory power than its competitors: it can coherently answer questions from probability theory for which other positions remain powerless. Since probability theory is, in a sense, the most unifying physics theory (all physical systems comply with it), this argument confers considerable weight.

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Notes

  1. Parts of this Section were elaborated in greater detail in [27].

  2. Indeed, a relativistic version of Bohmian mechanics is lacking (see [29], § 14).

  3. Equations (2–3) are probabilistic assumptions that are surely intuitive, but there is no proof within an accepted physics theory that they necessarily apply to a given physical system.

  4. Hossenfelder and Palmer do not consider future input dependence and retrocausality as different from SD; they state in a ‘disambiguation’ section: “But some authors […] distinguish Superdeterminism from retrocausality (or Future Input Dependence, respectively)” [11]. Does this mean that retrocausality is (a form of) SD? Our main point is that relying on unusual types of causality (as mentioned in [12], p. 8) is not necessary: future input dependence, we believe, is nothing else than an effective type of SD, which can safely be justified by the classic SD relying on the classic causality and the usual causal arrow of time, as argued in the next section.

  5. The model of [12] is in any case a soft-superdeterministic model in the sense that (a, b) refer to angles, not angle choices.

  6. A possible reason why one can measure this quantum correlation, in contrast to many of the correlations between macroscopic variables, is that x and y refer to 1-particle variables of a fundamental theory, quantum mechanics. Usual classical systems have too many degrees of freedom and too many interactions between them, so they appear uncorrelated (unless a strong enough cause correlates them). This is a possible answer to questions asked in [19,20,21].

  7. In quantum experiments decoherence is ubiquitous and one needs to fix not only a and b but a whole series of other variables; a specific well-controlled quantum set-up is needed to detect correlations.

  8. Such a view immediately begs the question: what is the entity that materializes, or is responsible for, such an absolutely independent free will? An immaterial mind? A homunculus in the brain? There is no evidence for these in neuroscience.

  9. This has non-trivial consequences also for deterministic theories: it implies for instance that two statistically independent stochastic variables x and y with an underlying deterministic (relativistic) dynamics must be functions x = fx(λx), y = fy(λy), where the sets of variables λx and λy share no variables.

  10. If one finds our answer too speculative, note that to come to our final conclusion it is enough that the first two questions are answered.

References

  1. Shimony, A., Horne, M.A., Clauser, J.F.: Comment on ‘The theory of local beables.’ Epistemol. Lett. 13(1), (1976); reprinted as “An exchange on local beables,” Dialectica 39, 97–101 (1985)

  2. Bell, J.: Bertlmann’s socks and the nature of reality. J. de Physique (Colloques) 42(C2), 41–62 (1981)

    MathSciNet  Google Scholar 

  3. Brans, C.H.: Bell’s theorem does not eliminate fully causal hidden variables. Int. J. Theor. Phys. 27, 219 (1988)

    Article  Google Scholar 

  4. ’t Hooft, G.: Physics on the boundary between classical and quantum mechanics. J. Phys: Conf. Ser. 504, 012003 (2014)

    Google Scholar 

  5. ’t Hooft, G.: The Cellular Automaton Interpretation of Quantum Mechanics (Fundamental Theories of Physics, 185). Springer Open (2016)

    Book  MATH  Google Scholar 

  6. ’t Hooft, G.: Free will in the theory of everything. https://arxiv.org/1709.02874 (2017)

  7. ’t Hooft, G.: The ontology conservation law as an alternative to the many world interpretation of quantum mechanics. In: Proceedings of the Current Problems in Theoretical Physics, at the Conference PAFT2019, Vietri sul Mare, Salerno, Italy, 13–17 April 2019. https://arxiv.org/1904.12364 (2019)

  8. ’t Hooft, G.: Fast vacuum fluctuations and the emergence of quantum mechanics. https://arxiv.org/2010.02019 (2021)

  9. Hossenfelder, S.: Testing super-deterministic hidden variables theories. Found. Phys. 41, 1521 (2011)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  10. Hossenfelder, S.: Superdeterminism: A Guide for the perplexed. https://arxiv.org/2010.01324 (2011)

  11. Hossenfelder, S., Palmer, T.: Rethinking superdeterminism. Front. Phys. 8, 139 (2020)

    Article  Google Scholar 

  12. Donadi, S., Hossenfelder, S.: A toy model for local and deterministic wave-function collapse. https://arxiv.org/2010.01327 (2021)

  13. Elze, H.-T.: Are quantum spins but small perturbations of ontological Ising spins? Found. Phys. 50(12), 1875–1893 (2020)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. Elze, H.T.: Quantum features of natural cellular automata. J. Phys: Conf. Ser. 701, 01201 (2016)

    Google Scholar 

  15. Elze, H.T.: Are nonlinear discrete cellular automata compatible with quantum mechanics? J. Phys.: Conf. Ser. (2015). https://doi.org/10.1088/1742-6596/631/1/012069

    Article  Google Scholar 

  16. Elze, H.-T.: Action principle for cellular automata and the linearity of quantum mechanics. Phys. Rev. A 89, 012111 (2014)

    Article  ADS  Google Scholar 

  17. Wood, C.J., Spekkens, R.W.: The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning. New J. Phys. 17, 033002 (2015)

    Article  MATH  ADS  Google Scholar 

  18. Bendersky, A., Senno, G., de la Torre, G., Figueira, S., Acin, A.: Non-signaling deterministic models for non-local correlations have to be uncomputable. Phys. Rev. Lett. 118, 130401 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  19. Ciepielewski, G.S., Okon, E., Sudarsky, D.: On superdeterministic rejections of settings independence. https://arxiv.org/2008.00631 (2020) (accepted by Brit. J. Phil. of Science)

  20. Chen, E.K.: Bell’s theorem, quantum probabilities, and superdeterminism. In: Knox, E., Wilson, A. (eds.) The Routledge Companion to Philosophy of Physics. Routledge, London (2021)

    Google Scholar 

  21. Baas, A., Le Bihan, B.: What does the world look like according to superdeterminism. British J. Philos of Sci. (2021). https://doi.org/10.1086/714815

    Article  Google Scholar 

  22. Khrennikov, A.: Interpretations of Probability. de Gruyter, Berlin (2008)

    MATH  Google Scholar 

  23. Khrennikov, A.: Bell's inequality: Physics meets probability. https://arxiv.org/abs/0709.3909 (2007)

  24. Nieuwenhuizen, T.M.: Is the contextuality loophole fatal for the derivation of Bell Inequalities? Found. Phys. 41, 580 (2011)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  25. Cetto, A.M., Valdés-Hernández, A., de la Peña, L.: On the spin projection operator and the probabilistic meaning of the bipartite correlation function. Found. Phys. 50, 27–39 (2020)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  26. Vervoort, L.: Bell’s theorem: two neglected solutions. Found. Phys. 43, 769–791 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  27. Vervoort, L.: Probability theory as a physical theory points to superdeterminism. Entropy 21(9), 848 (2019)

    Article  ADS  Google Scholar 

  28. Bell, J.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)

    Article  MathSciNet  Google Scholar 

  29. Goldstein, S.: Bohmian mechanics. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), https://plato.stanford.edu/archives/fall2021/entries/qm-bohm/ (2021)

  30. Vervoort, L.: Are hidden-variable theories for pilot-wave systems possible? Found. Phys. 48(7), 803–826 (2018)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  31. Hall, M.J.W.: The significance of measurement independence for Bell inequalities and locality. In: At the Frontier of Spacetime, pp. 189–204. https://arxiv.org/1511.00729 (2016)

  32. Scheidl, T., Ursin, R., Kofler, J., Ramelow, S., Ma, X., Herbst, T., Ratschbacher, L., Fedrizzi, A., Langford, N., Jennewein, T., Zeilinger, A.: Violation of local realism with freedom of choice. PNAS 107, 19708 (2010)

    Article  MATH  ADS  Google Scholar 

  33. Bell, J., Clauser, J.F., Horne, M.A., Shimony, A.: An exchange on local beables. Dialectica 39, 85–110 (1985)

    Article  MathSciNet  Google Scholar 

  34. Von Mises, R.: Probability, Statistics and Truth, 2nd edn. Dover Publications, New York (1981)

    MATH  Google Scholar 

  35. Von Mises, R.: Mathematical Theory of Probability and Statistics. Academic Press, New York (1964)

    MATH  Google Scholar 

  36. Vervoort, L.: A detailed interpretation of probability, and its link with quantum mechanics. https://arxiv.org/1011.6331 (2010)

  37. Vervoort, L.: The instrumentalist aspects of quantum mechanics stem from probability theory. In: AIP Conference Proceedings, American Institute of Physics, College Park, MD. USA, vol. 1424, pp. 348–354 (2012)

  38. Libet, B.: Unconscious cerebral initiative and the role of conscious will in voluntary action. Behav. Brain Sci. 8, 529–566 (1985)

    Article  Google Scholar 

  39. Soon, C.S., Brass, M., Heinze, H.-J., Haynes, J.D.: Unconscious determinants of free decisions in the human brain. Nat. Neurosci. 11, 543–545 (2008)

    Article  Google Scholar 

  40. Pereboom, D. (ed.): Free Will. Hackett Publishing, Indianapolis (1997)

    Google Scholar 

  41. Vervoort, L., Blusiewicz, T.: The CMT model of free will. Dialogue, the Canadian. Philos. Rev. 59(3), 415–435 (2020)

    Article  Google Scholar 

  42. Vervoort, L., Blusiewicz, T.: Free will and (In)determinism in the brain: a case for naturalized philosophy. Theoria 35(3), 345–364 (2020)

    Article  Google Scholar 

  43. Kolmogorov, A.N.: Foundations of the Theory of Probability, 2nd edn. Chelsea Publishing Company, New York (1956)

    MATH  Google Scholar 

  44. Pearl, J.: Causality: Models, Reasoning, and Inference, 2nd edn. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  45. Spirtes, P., Glymour, C.N., Scheines, R.: Causation, Prediction, and Search. MIT Press (2001)

    Book  MATH  Google Scholar 

  46. Tijms, H.: Understanding Probability: Chance Rules in Everyday Life. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

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Acknowledgements

We would like to thank the participants to the conference “Superdeterminism and Retrocausality”, and especially the organizers, Sabine Hossenfelder, Huw Price and Tim Palmer, for helpful discussions.

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Authors and Affiliations

  1. School of Advanced Studies, University of Tyumen, Tyumen, Russia

    Vitaly Nikolaev

  2. Higher School of Economics, Moscow, Russia

    Louis Vervoort

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Appendix. Numerical Data for the Billiard Simulations

Appendix. Numerical Data for the Billiard Simulations

Here we provide the numerical data for the billiard simulations presented in Sect. 4. Figure 2 is an on-scale drawing of the billiard table at simulation time t = 0, containing 11 balls at rest with radius 20 (all parameters are in arbitrary units). Other parameters of the experiment:

  • Dimensions of the table: 600 × 300

  • Length of a time tick: 0.1 (experiments can run till t = 250, 500, 1000 etc., cf. text)

  • Initial positions of the balls (given as (x, y) coordinates of the balls’ centers assuming that (0, 0) is the lower left corner of the table):

    • green cue ball: (200, 155 ± ε), ε = 3 (uniform distribution, cf. text)

    • other balls: (300, 150), (340, 120), (340, 180), (380, 210), (380, 150), (380, 90), (420, 240) [red ball], (420, 180), (420, 120), (420, 60)

  • Initial velocity of the green ball: (vx, vy) = (20, 0)

  • Positions of the test squares (given as (x1, y1) – upper left corner, and (x2, y2) – lower right corner):

    • (150, 270), (240, 180)

    • (430, 120), (520, 30)

For the experiment of Fig. 4 (Brownian motion), all the positions of all balls are uniformly distributed with x ∈ [20, 580] and y ∈ [20, 280] (intersections of the balls are not allowed). The initial velocities are distributed uniformly such that vx ∈ [−20, 20] and vy ∈ [−20, 20].

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Nikolaev, V., Vervoort, L. Aspects of Superdeterminism Made Intuitive. Found Phys 53, 17 (2023). https://doi.org/10.1007/s10701-022-00648-9

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