Abstract
Quantum mechanics portrays the universe as involving non-local influences that are difficult to reconcile with relativity theory. By postulating backward causation, retro-causal interpretations of quantum mechanics could circumvent such influences and, accordingly, increase the prospects of reconciling these theories. The postulation of backward causation poses various challenges for retro-causal interpretations of quantum mechanics and for the existing conceptual frameworks for analyzing counterfactual dependence, causation and causal explanation, which are important for studying these interpretations. In this chapter, we consider the nature of time, causation and explanation in a local, deterministic retro-causal interpretation of quantum mechanics that is inspired by Bohmian mechanics. This interpretation, the ‘causally symmetric Bohmian model’, offers a deterministic, local ‘hidden-variables’ model of the Einstein-Podolsky-Rosen/Bohm experiment that presents a new challenge for Reichenbach ’s principle of the common cause. In this model, the common cause – the ‘complete’ state of the particles at the emission from the source – screens off the correlation between its effects – the distant measurement outcomes – but nevertheless fails to explain it.
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Notes
- 1.
Cover (1997, p. 306) thinks that it is “not unreasonable to read Kant ’s Second Analogy as expressing a causal theory of time.”
- 2.
- 3.
To simplify things, in what follows in Sects. 8.1–8.8 we shall not discuss the exact characterization of probabilistic causation, though the approximate contours of the concept of causation we have in mind will become clearer as we go. In Sect. 8.9, we shall characterize Reichenbach's concept of probabilistic causation more precisely and discuss it in the context of a deterministic , retro-causal interpretation of QM.
- 4.
See, for example, Costa de Beauregard (1953, 1977, 1979, 1985), Cramer (1980, 1983, 1986, 1988), Sutherland (1983, 1998, 2008), Price (1984, 1994, 1996, 2008, 2012), Reznik and Aharonov (1995), Miller (1996, 2008), Berkovitz (2002a, 2008, 2011), Gruss (2000), Aharonov and Gruss (2005), Aharonov and Tollaksen (2007), Kastner (2012), and Price and Wharton (Chap. 7 in this volume).
- 5.
In the philosophical literature, the nature of causation is controversial. It is common to think of causation as a relation, though different accounts explicate causation in terms of different relations, and there is a controversy about whether the relata are events or facts. There are also theories of causation that explicate causation in terms of processes (see Sect. 8.5). For a review of the metaphysics of causation, see Schaffer (2003/2016) and references therein; and for a discussion of whether causation is a relation, see Hausman (1998, Sect. 2.3).
- 6.
- 7.
In Dirac’s notation, the singlet state for spin is expressed as follows: \( \left|\psi \right\rangle =\frac{1}{\sqrt{2}}\left({\left| n+\right\rangle}_1{\left| n-\right\rangle}_2-{\left| n-\right\rangle}_1{\left| n+\right\rangle}_2\right) \), where the indexes ‘1’ and ‘2’ denote the first and the second particle respectively, and \( {\left| n+\right\rangle}_1\left({\left| n+\right\rangle}_2\right) \) and \( {\left| n-\right\rangle}_1\left({\left| n-\right\rangle}_2\right) \) are the states of the first (second) particle having respectively spin ‘up’ and spin ‘down’ along the direction n.
- 8.
Some hidden-variables interpretations of QM, like Bohmian mechanics , postulate the existence of ‘parameter dependence’, i.e. the dependence of the probability of the distant measurement outcome on the setting of the nearby measurement apparatus in the EPR/B experiment. But, as Berkovitz (1998, Sections 2.3–2.4, 2007/2016, Section 8.4) argues, Bohmian mechanics involves ‘specific’ outcome dependence, and parameter dependence is the result of this outcome dependence. For the characterization of ‘specific measurement outcomes’ in this experiment, see Fnt. 16.
- 9.
- 10.
More precisely, it is common to assume that (the probability of) an effect is counterfactually dependent on its cause, or that there is a chain of counterfactual dependencies that connect the effect to the cause (see, for example, Lewis 1986, Chap. 21).
- 11.
In this analysis, in resolving the vagueness of ‘non-backtracking’ counterfactuals , we typically hold the past fixed until the time in which the antecedent of the counterfactual is supposed to obtain.
- 12.
The time asymmetry of counterfactual dependence is the same as the asymmetry of counterfactual dependence in forward causation. But in a universe with backward causation the asymmetry of counterfactual dependence may obtain while the time asymmetry of counterfactual dependence is violated.
- 13.
- 14.
Two comments: (i) Lewis talks about ‘worlds’ but really mean universes. (ii) In fact, the above definition is a slight modification of Lewis’ account, as Lewis (1986, pp. 176–177) requires that the objective single-case probability that the effect has with the cause be much higher than it would have been without the cause; where ‘much higher’ means by a large factor, though not necessarily by a large difference.
- 15.
Here for the sake of simplicity, we suppose that S is compatible with both loops.
- 16.
In the EPR/B experiment, the measurements are of spin quantities. Unless said otherwise, by ‘spin measurement outcomes’, we shall mean ‘specific’ outcomes, e.g. spin ‘up’ in the direction m (rather than the ‘non-specific’ outcome spin ‘up’, which appears in various discussions of quantum non-locality ). In RCIQM of the second kind, models of the EPR/B experiments postulate that specific measurement outcomes influence the complete pair-state at the emission, and so the backward influences of the measurement outcomes also embody information about the apparatus settings.
- 17.
To simplify things, we ignore the question of backward influences on the QM preparation of the particle pair.
- 18.
For a review of interpretations of probabilities, see Hájek (2002/2012).
- 19.
- 20.
- 21.
That is, the values of the N j are such that \( \underset{-\infty }{\overset{+\infty }{\int }}{\psi}_i^{\ast}\left({x}_j\right){\psi}_i\left({x}_j\right){d}^3{x}_j=1 \).
- 22.
The same is true for other local retro-causal interpretations of QM.
- 23.
The QM preparation of the particle pair and the particles’ final wavefunctions jointly determine the measurement outcomes, independently of the specific position configuration of the particles. Thus, the position configuration does not play any explicit role in the analysis of Loop 3.
- 24.
The question whether indeterministic RCIQM in which the complete pair-state is determined by events/states that correspond to the measurement outcomes (but are not the outcomes themselves) could overcome these challenges, is beyond the scope this chapter.
- 25.
- 26.
- 27.
That is, in the local ‘hidden-variables ’ models of the EPR/B experiment that Bell considered there are generally many different possible complete pair-states (which are compatible with the QM wavefunction of the particle pair), and Bell's generalized principle applies to all of them.
- 28.
Sober and Eells give as an example a case where an event C is a probabilistic cause of an event D which is a common cause of events A and B.
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Acknowledgment
For comments on earlier versions of this chapter, I am very grateful to the audience at the Bordeaux conference “The Time of Nature, the Nature of Time”, the editors Christophe Bouton and Philippe Huneman, and Aaron Kenna and Noah Stemeroff. The research for this paper was supported by a SSHRC Insight Grant.
List of Acronyms
- BM ::
-
Bohmian mechanics
- CSBM ::
-
causally symmetric Bohmian model
- EPR/B::
-
Einstein-Podolsky-Rosen/Bohm
- PCC ::
-
Reichenbach’s principle of the common cause
- RCIQM ::
-
retro-causal interpretations of quantum mechanics
- QM::
-
quantum mechanics
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Berkovitz, J. (2017). On Time, Causation and Explanation in the Causally Symmetric Bohmian Model of Quantum Mechanics. In: Bouton, C., Huneman, P. (eds) Time of Nature and the Nature of Time. Boston Studies in the Philosophy and History of Science, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-53725-2_8
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