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Superdeterminism: a reappraisal

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Abstract

This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death of the scientific methodology. In this paper, we offer a defense to these and other objections. To counter the conspiracy objection, we draw upon the philosophical literature on time travel, and conclude that the picture of the world offered by the superdeterminist does not need to be particularly surprising or conspiratorial. We then move on to other recent objections, in particular those that focus on the methodology of science and the nature of the physical laws compatible with superdeterminism. A key ingredient of our arguments is that the principle of statistical independence may be violated in theory, but valid for practical purposes. Our overarching goal is to offer a defense of superdeterminism with respect to its main objections, so that it can earn its keep as a legitimate contender among the possible interpretations of quantum mechanics.

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Notes

  1. Since there are no finalized superdeterministic theories (in the physical sense) yet, i.e. theories that are based on the statistical dependence expressed in Eq. (2), we will usually term superdeterminism an “interpretation” (or an assumption) rather than a “theory”. But as will become clear from this article, we do not exclude that full-blown physical theories based on this assumption could be constructed.

  2. One might note thatin two recent physics publications proposing first versions of superdeterministic theories (‘t Hooft, 2021; Donadi and Hossenfelder, 2021) the authors explicitly claim that those theories arenot conspiratorial.

  3. To be more precise, the consequent in (C) should be “b or a sub-collection of the same statistical profile as b would have been selected”. This is so because other sub-collections could be in accordance with actual observations and superdeterminism. For instance, in the case of set-up B, the following would do: The collection of photon pairs that goes through the B set-up (let us call this collection “b*”) is such that 25 pairs are of type 5 and 75 are of type 3. In the remainder of the paper we will ignore such complication, as the gist of our argument should remain clear without this specification.

  4. Lewis’s and Stalnaker’s accounts differ in details, and the definition used here is imprecise. However, it captures the spirit of their proposal and it is precise enough for our purposes here.

  5. There is actually nothing special about autoinfanticide. Time travelers can never change the past. They, for instance, cannot kill Baby Hitler, as Hitler did not die when he was a baby. This does not mean time travelers cannot affect the past (see Lewis 1976 for a distinction between changing and affecting the past).

  6. It should be noted this was not Horwich’s intent.

  7. Baas and Le Bihan raise other worries, but those we treat in this and the next section are considered the most pressing ones by these authors. Another worry is the a-typicality and/or fine-tuned nature of the cosmological initial conditions that superdeterministic theories would need (this problem is closely related to the conspiracy objection and the problem treated in the present section). In any case, we agree with Baas and Le Bihan that fine-tuning is not specific to superdeterminism and seems not an ultimate objection. We believe the same holds for a-typicality. Any deterministic physical theory that makes a prediction “at token level”, i.e. about detailed facts of the world, needs to use unique initial values (in such deterministic “initial value problems” unique initial values are mapped on unique solutions). Finally, in (Donadi and Hossenfelder 2021) counterarguments against the charge of a-typicality / fine-tuning are given by explicit construction of a superdeterministic toy model that is, according to the authors, neither fine-tuned nor conspiratorial.

  8. See (‘t Hooft, 2021), Eq. (14) and accompanying text.

  9. Cf. e.g. (Donadi and Hossenfelder 2021) p. 8.

  10. Indeed, from Eq. (3) follows that \(P(x = + 1,y = + 1\left| {\theta_{1} ,\theta_{1} )} \right.\) = \(P( + , + )\) = ½ = \(P( - , - )\); and \(P( + , - )\) = \(P( - , + )\) = 0, corresponding to perfect correlation.

  11. This is especially the case when the two correlated events are in an indirect, distant causal relation, e.g. when they are widely separated in time and/or space and when they are causally connected via many intermediate events/causes. This would clearly apply to the correlations in (Eq. 2).

  12. “since their birth at the Big Bang, or closely afterwards”, one might add, somewhat metaphorically. Note that the idea of universal correlation is very natural in quantum field theories, supposedly already valid shortly after the Big Bang.

  13. The exception being macroscopic events that have a recent or strong causal link, say between throwing a rock and the window breaking, or between the positions of earth and moon.

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Acknowledgements

Giacomo Andreoletti thanks the project PID2019-­108762GB-­I00 of the Spanish Ministry of Science and Innovation. Louis Vervoort would like to thank the participants of the conference “Superdeterminism and Retrocausality” (Bonn 2022), and especially the organizers, Sabine Hossenfelder, Huw Price and Tim Palmer, for helpful discussions.

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Andreoletti, G., Vervoort, L. Superdeterminism: a reappraisal. Synthese 200, 361 (2022). https://doi.org/10.1007/s11229-022-03832-6

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