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In quantum mechanics, superdeterminism is a loophole in Bell's theorem. By postulating that all systems being measured are correlated with the choices of which measurements to make on them, the assumptions of the theorem are no longer fulfilled. A hidden variables theory which is superdeterministic can thus fulfill Bell's notion of local causality and still violate the inequalities derived from Bell's theorem.^[1] This makes it possible to construct a local hidden-variable theory that reproduces the predictions of quantum mechanics, for which a few toy models have been proposed.^[2]^[3]^[4] In addition to being deterministic, superdeterministic models also postulate correlations between the state that is measured and the measurement setting.

Overview

Bell's theorem assumes that the measurements performed at each detector can be chosen independently of each other and of the hidden variables that determine the measurement outcome. This relation is often referred to as measurement independence or statistical independence. In a superdeterministic theory this relation is not fulfilled; the hidden variables are necessarily correlated with the measurement setting. Since the choice of measurements and the hidden variable are predetermined, the results at one detector can depend on which measurement is done at the other without any need for information to travel faster than the speed of light. The assumption of statistical independence is sometimes referred to as the free choice or free will assumption, since its negation implies that human experimentalists are not free to choose which measurement to perform.

It is possible to test restricted versions of superdeterminism that posit that the correlations between the hidden variables and the choice of measurement have been established in the recent past.^[5] In general, though, superdeterminism is fundamentally untestable, as the correlations can be postulated to exist since the Big Bang, making the loophole impossible to eliminate.^[6]

In the 1980s, John Stewart Bell discussed superdeterminism in a BBC interview:^[7]^[8]

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be.

Although he acknowledged the loophole, he also argued that it was implausible. Even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be "effectively free for the purpose at hand," because the machine's choice is altered by a large number of very small effects. It is unlikely for the hidden variable to be sensitive to all of the same small influences that the random number generator was.^[9]

Nobel Prize in Physics winner Gerard 't Hooft discussed this loophole with John Bell in the early 1980s:

I raised the question: Suppose that also Alice's and Bob's decisions have to be seen as not coming out of free will, but being determined by everything in the theory. John said, well, you know, that I have to exclude. If it's possible, then what I said doesn't apply. I said, Alice and Bob are making a decision out of a cause. A cause lies in their past and has to be included in the picture".^[10]

According to the physicist Anton Zeilinger, if superdeterminism is true, some of its implications would bring into question the value of science itself by destroying falsifiability:

[W]e always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature.^[11]

Physicists Sabine Hossenfelder and Tim Palmer have argued that superdeterminism "is a promising approach not only to solve the measurement problem, but also to understand the apparent non-locality of quantum physics".^[12]

Howard M. Wiseman and Eric Cavalcanti argue that any hypothetical superdeterministic theory "would be about as plausible, and appealing, as belief in ubiquitous alien mind-control".^[13]

Examples

The first superdeterministic hidden variables model was put forward by Carl H. Brans in 1988.^[2] Other models were proposed in 2010 by Michael Hall,^[3] and in 2022 by Donadi and Hossenfelder.^[4] Gerard 't Hooft has referred to his cellular automaton model of quantum mechanics as superdeterministic^[14] though it has remained unclear whether it fulfills the definition.

Some authors consider retrocausality in quantum mechanics to be an example of superdeterminism, whereas other authors treat the two cases as distinct.^[15] No agreed-upon definition for distinguishing them exists.

References

^ Larsson, Jan-Åke (2014). "Loopholes in Bell inequality tests of local realism". Journal of Physics A: Mathematical and Theoretical. 47 (42): 16. arXiv:1407.0363. Bibcode:2014JPhA...47P4003L. doi:10.1088/1751-8113/47/42/424003. S2CID 40332044.
^ ^a ^b Brans, Carl H. (1988-02-01). "Bell's theorem does not eliminate fully causal hidden variables". International Journal of Theoretical Physics. 27 (2): 219–226. Bibcode:1988IJTP...27..219B. doi:10.1007/BF00670750. ISSN 1572-9575. S2CID 121627152.
^ ^a ^b Hall, Michael J. W. (2010-12-16). "Local Deterministic Model of Singlet State Correlations Based on Relaxing Measurement Independence". Physical Review Letters. 105 (25): 250404. arXiv:1007.5518. Bibcode:2010PhRvL.105y0404H. doi:10.1103/PhysRevLett.105.250404. hdl:10072/42810. PMID 21231566. S2CID 45436471.
^ ^a ^b Donadi, Sandro; Hossenfelder, Sabine (2022-08-19). "Toy model for local and deterministic wave-function collapse". Physical Review A. 106 (2): 022212. arXiv:2010.01327. Bibcode:2022PhRvA.106b2212D. doi:10.1103/PhysRevA.106.022212. S2CID 237260229.
^ Thomas Scheidl; Rupert Ursin; Johannes Kofler; Sven Ramelow; Xiao-Song Ma; Thomas Herbst; Lothar Ratschbacher; Alessandro Fedrizzi; Nathan K. Langford; Thomas Jennewein; Anton Zeilinger; et al. (2010). "Violation of local realism with freedom of choice". Proc. Natl. Acad. Sci. 107 (46): 19708–19713. arXiv:0811.3129. Bibcode:2010PNAS..10719708S. doi:10.1073/pnas.1002780107. PMC 2993398. PMID 21041665.
^ Wolchover, Natalie. "The Universe Is as Spooky as Einstein Thought". The Atlantic. Retrieved 2017-02-20.
^ BBC Radio interview with Paul Davies, 1985
^ The quotation is an adaptation from the edited transcript of the radio interview with John Bell of 1985. See The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics, by Paul C. W. Davies and Julian R. Brown, 1986/1993, pp. 45-46
^ J. S. Bell, Free variables and local causality, Epistemological Letters, Feb. 1977. Reprinted as Chapter 12 of J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press 1987)
^ Musser, George (7 October 2013). "Does Some Deeper Level of Physics Underlie Quantum Mechanics? An Interview with Nobelist Gerard 't Hooft".
^ A. Zeilinger, Dance of the Photons, Farrar, Straus and Giroux, New York, 2010, p. 266. Abner Shimony, Michael Horne and John Clauser made a similar comment in replying to John Bell in their discussions in the Epistemological Letters: "In any scientific experiment in which two or more variables are supposed to be randomly selected, one can always conjecture that some factor in the overlap of the backward light cones has controlled the presumably random choices. But, we maintain, skepticism of this sort will essentially dismiss all results of scientific experimentation. Unless we proceed under the assumption that hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation." (Shimony A, Horne M A and Clauser J F, "Comment on the theory of local beables", Epistemological Letters, 13 1 (1976), as quoted in Jan-Åke Larsson, "Loopholes in Bell inequality tests of local realism", J. Phys. A: Math. Theor. 47 (2014))
^ Hossenfelder, Sabine; Palmer, Tim (2020). "Rethinking Superdeterminism". Frontiers in Physics. 8: 139. arXiv:1912.06462. Bibcode:2020FrP.....8..139P. doi:10.3389/fphy.2020.00139. ISSN 2296-424X.
^ Wiseman, Howard; Cavalcanti, Eric (2016). "Causarum Investigatio and the Two Bell's Theorems of John Bell". In R. Bertlmann; A. Zeilinger (eds.). Quantum [Un]Speakables II. The Frontiers Collection. Springer. pp. 119–142. arXiv:1503.06413. doi:10.1007/978-3-319-38987-5_6. ISBN 978-3-319-38985-1.
^ 't Hooft, Gerard (2016). The Cellular Automaton Interpretation of Quantum Mechanics. Fundamental Theories of Physics. Vol. 185. doi:10.1007/978-3-319-41285-6. ISBN 978-3-319-41284-9. S2CID 7779840.
^ Wharton, K. B.; Argaman, N. (2020-05-18). "Colloquium: Bell's theorem and locally mediated reformulations of quantum mechanics". Reviews of Modern Physics. 92 (2): 021002. arXiv:1906.04313. Bibcode:2020RvMP...92b1002W. doi:10.1103/RevModPhys.92.021002. S2CID 184486977.

External links

Hall, Michael J. W. (2010). "Local Deterministic Model of Singlet State Correlations Based on Relaxing Measurement Independence". Physical Review Letters. 105 (25): 250404. arXiv:1007.5518. Bibcode:2010PhRvL.105y0404H. doi:10.1103/PhysRevLett.105.250404. PMID 21231566. S2CID 45436471. He [Michael J. W. Hall] shows that locality and reality can be retained with a 14% reduction of the experimenters' "free will".