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Counterfactual Reasoning, Realism and Quantum Mechanics: Much Ado About Nothing?

Abstract

I show why old and new claims on the role of counterfactual reasoning for the EPR argument and Bell’s theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, after emphasizing the role of incompleteness arguments that Einstein developed before the EPR paper, I critically review more recent claims that equate the use of counterfactual reasoning with the assumption of a strong form of realism and argue that such claims are untenable.

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Fig. 1

Notes

  1. A side remark. Given a thesis X, it is quite peculiar to say that a certain argument both ‘assumes’ and ‘concludes’ X: the logical status of X within the argument—hence, the argument itself—changes dramatically if X is an assumption or the outcome of a derivation! As we will see later, this is exactly the heart of the matter with counterfactual definiteness in EPR-Bell kind of arguments.

  2. This is one of the episodes in the history of contemporary physics where the received view of Einstein as a reactionary scientist, unable to follow the more promising lines of development of the new physics in the second half of his life, proves so dramatically inadequate. As an instance of this inadequacy, let me recall what Werner Heisenberg said in his introduction to The Born–Einstein Letters, commenting on the Einstein’s attitude toward quantum mechanics: “Most scientists are willing to accept new empirical data and to recognize new results, provided they fit into their philosophical framework. But in the course of scientific progress it can happen that a new range of empirical data can be completely understood only when the enormous effort is made to enlarge this framework and to change the very structure of the thought processes. In the case of quantum mechanics, Einstein was apparently no longer willing to take this step, or perhaps no longer able to do so” (Born 2005, xxxvii).

  3. This theory is downgraded by Arthur Fine to the status of a ‘semantic’ theory of disturbance (Fine 1986, 35).

  4. See the deep analysis of this point in the chapter 3 of Fine (1986); see also Maudlin (2014, 424010-12, 13).

  5. A further, simplified version of the Einstein 1927 thought experiment is due to Hardy (1995). A slightly different formulation, inspired by the argument that Einstein proposed in 1927, is known as the Einstein boxes experiment and supposed to emphasize even more dramatically the dilemma between locality and completeness. This kind of thought experiment is reformulated by Einstein in the letter to Schrödinger of June 19th, 1935, in which he complains about the published version of the EPR argument: see the discussion of it in Fine (1986, 35–38), and Norsen (2005) for a thorough and more recent analysis.

  6. On the nature of Einstein’s realism, see e.g. Howard (1993) and Home and Whitaker (2007, ch. 8).

  7. It should be pointed out that λ can just be ψ.

  8. The standard reference for all arguments relying on the equivalence between factorizability and existence of a joint probability distribution is Fine (1982): see also Mermin (1992), where the author writes: “Bell’s theorem, although it does rely on the properties of a particular state, proves the non-existence of a joint distribution for a set of observables required to have one by an apparently common-sense notion of physical locality” (27, my emphasis). In addition to the argument defended above in the main text, it can be shown that the Fine deterministic hidden variable model implicitly assumes locality anyway (Shimony 1984; Laudisa 1996).

  9. A remark in sociology of science: since the American Journal of Physics is the intended journal of US physics teachers, it is an revealing sign that in two issues of the journal in two different years readers are pedagogically taught that a ghostly assumption like counterfactual definiteness does play an essential role in the EPR argument and in the ensuing Bell theorem!

  10. For older, notable statements in the same direction see e.g. Unruh (1999, 2001). It should be noted that, historically, there is an interesting antecedent to the discussion in the text, namely the debate surrounding the counterfactual formulation of the Bell theorem proposed especially by Eberhard (1977, 1978), Stapp (1985a, b) and Kraus (1989). In 1990, Butterfield et al. by applying the very conceptual resources of the Lewisian theory of counterfactual conditionals to the Eberhard–Stapp–Kraus formulation, could show that such formulation in fact embodied an implicit assumption of determinism: in that context such assumption is de facto equivalent to counterfactual definiteness, which in turn leads us back to the issue that I discuss in the text.

  11. Maudlin goes as far as claiming that the EPR criterion—what I call here Reality—is an analytic criterion, namely a criterion that simply follows from the very meanings of the words that compose it (Maudlin 2014, 424010-6).

  12. In the so-called consistent-histories approach, that Gell-Mann, Hartle, Griffiths, Omnes (and others) have developed in detail, it is also claimed that locality can be preserved for quantum mechanics: see for instance Griffiths (2011). Arguments that show this claim to be far from convincing can be found in Goldstein et al. (2011) and Maudlin (2011).

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Laudisa, F. Counterfactual Reasoning, Realism and Quantum Mechanics: Much Ado About Nothing?. Erkenn 84, 1103–1118 (2019). https://doi.org/10.1007/s10670-018-9997-4

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