Hance JR

Hossenfelder S

English

Newcastle University E-Prints

Bell’s theorem allows local theories of quantum mechanicsJonte R. Hance1, ∗ and Sabine Hossenfelder21Quantum Engineering Technology Laboratories, Department of Electrical and Electronic Engineering,University of Bristol, Woodland Road, Bristol, BS8 1US, UK2Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main, GermanyA recent Nature Physics editorial (Nat. Phys. (2022) 18, 961) falsely claims “any theory thatuses hidden variables still requires non-local physics.” We correct this claim and explain why it isimportant to get this right.A recent Editorial in Nature Physics makes the valu-able point that with so much of modern science and tech-nology dependent on quantum mechanics, trying to un-derstand its foundations is time well spent [1]. However,we see the need to correct an unfortunate mistake in theEditorial, which is the statement:“One route out of this paradox could be an un-detected, so-called hidden variable associatedwith both particles that underlies the corre-lated behaviour. However, John Stewart Bellproved that such an approach cannot explainthe quantum mechanical outcomes. Any the-ory that uses hidden variables still requiresnon-local physics.”This passage reflects a common misconception [2, 3] thatBell’s theorem proves that hidden variable theories thatreproduce quantum mechanics require nonlocal physics.In fact, locally causal completions of quantum mechanicsare possible, if they violate the assumption that the hid-den variables do not in any way depend on measurementsettings.There is no independent evidence that thisassumption—commonly known as statisticalindependence—is fulfilled for quantum systems. Asa consequence, the observed violations of Bell’s in-equality can be said to show that maintaining localcausality requires violating statistical independence.We wish to stress that this is not merely an issue ofinterpretation. The statistical independence assumptionis mathematically necessary for the formulation ofBell-type inequalities [4–6].Types of hidden variables theories which violate sta-tistical independence include those which are superdeter-ministic [7], retrocausal [8], and supermeasured [9]. Somehave dismissed them on metaphysical grounds, by asso-ciating a violation of statistical independence with theexistence of “free will” or “free choice” and then arguingthat these are not assumptions we should give up.It is, in hindsight, difficult to understand how this as-sociation came about. We believe it originated in theidea that a correlation between the hidden variables andthe measurement setting would somehow prevent the ex-perimentalist from choosing the setting to their liking.However, this is mistaking a correlation with a causa-tion. And any serious philosophical discussion of freewill acknowledges that human agency is of course con-strained by the laws of nature anyway. For this reason,the mathematical assumption of statistical independencebears no relevance to the philosophical discussion of freewill.In our view, this oversight and the unwillingness toconsider theories without statistical independence maybe the reason we do not yet have a locally causal theoryfor the foundations of physics that is consistent with gen-eral relativity. Understanding the implications is evenmore important now that the experimentally observedviolations of Bell’s inequality have been awarded the2022 Nobel Prize in Physics. Contrary to what is of-ten stated, these observations do not demonstrate that“spooky action at a distance” is real and nature thereforenon-local. Rather, the observations show that if natureis local, then statistical independence must be violated.We should therefore look for independent experimentalevidence that can distinguish the two different options:non-locality and statistical independence, or locality andviolations of statistical independence.Acknowledgements - JRH acknowledges support by theUniversity of York’s EPSRC DTP grant EP/R513386/1,and the Quantum Communications Hub funded by EP-SRC grants EP/M013472/1 and EP/T001011/1. SH ac-knowledges support by the Deutsche Forschungsgemein-schaft (DFG, German Research Foundation) under grantnumber HO 2601/8-1.[1] Survey the foundations. Nature Physics, 18(9):961–961,Sep 2022. doi:10.1038/s41567-022-01766-x.∗ jonte.hance@bristol.ac.uk[2] Maximilian Schlosshauer, Johannes Kofler, and AntonZeilinger. A snapshot of foundational attitudes towardquantum mechanics. Studies in History and Philosophy ofScience Part B: Studies in History and Philosophy of Mod-ern Physics, 44(3):222–230, 2013. doi:10.1016/j.shpsb.2013.04.004.2[3] Sujeevan Sivasundaram and Kristian Hvidtfelt Nielsen.Surveying the attitudes of physicists concerning foun-dational issues of quantum mechanics. arXiv preprintarXiv:1612.00676, 2016. URL: https://arxiv.org/abs/1612.00676.[4] Michael L. G. Redhead. Incompleteness, Nonlocality, andRealism, chapter 4. Nonlocality and the Bell Inequality.Clarendon Press, Oxford, UK, 1987.[5] Louis Vervoort. Bell’s theorem: Two neglected solutions.Foundations of Physics, 43(6):769–791, Jun 2013. doi:10.1007/s10701-013-9715-7.[6] Eddy Keming Chen. Bell’s theorem, quantum probabili-ties, and superdeterminism. In The Routledge Companionto Philosophy of Physics, pages 184–199. Routledge, 2021.[7] Sabine Hossenfelder and Tim Palmer. Rethinking su-perdeterminism. Frontiers in Physics, 8:139, 2020. doi:10.3389/fphy.2020.00139.[8] K. B. Wharton and N. Argaman. Colloquium: Bell’stheorem and locally mediated reformulations of quan-tum mechanics. Rev. Mod. Phys., 92:021002, May 2020.doi:10.1103/RevModPhys.92.021002.[9] Jonte R. Hance, Sabine Hossenfelder, and Tim N. Palmer.Supermeasured: Violating Bell-statistical independencewithout violating physical statistical independence. Foun-dations of Physics, 52(4):81, Jul 2022. doi:10.1007/s10701-022-00602-9.

Bell\u27s theorem allows local theories of quantum mechanics

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Bell\u27s theorem allows local theories of quantum mechanics

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