Abstract
The curious correlations between distant events in quantum phenomena suggest the existence of non-local influences. Indeed, as John Bell demonstrated in his celebrated theorem, granted some plausible premises any quantum theory will predict the existence of such non-local influences. One of the theorem’s premises is that the probability distribution of the states that systems may assume is independent of the measurements that they undergo at a later time. Retro-causal interpretations of quantum mechanics postulate backward influences from measurement events to the state of systems at an earlier time, and accordingly violate this premise. We argue that retro-causal interpretations predict the existence of closed causal loops, and consider the challenges that these loops for the explanatory power of these interpretations.
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Notes
- 1.
There are some dissenting views. In particular, Fine (1981, 1986, 59–60, 1989) denies that non-accidental correlations must have causal explanation, and Cartwright (1989, Chapters 3 and 6) and Chang and Cartwright (1993) challenge the assumption that common causes render their joint effects probabilistically independent.
- 2.
Recall that an event C screens off event E from event F if given C the probability of E is independent of F: \(P\left( {E/C\; \& \;F} \right) = P\left( {E/C} \right)\).
- 3.
There are different ways to interpret the meaning of conditional probability. The common way is along Kolmogorov’s axiomatization, where the probability of B given A is defined as the ratio of unconditional probabilities: \(P\left( {B/A} \right) \equiv {{P\left( {B\;\&\; A} \right)} \mathord{\left/ {\vphantom {{P\left( {B\& A} \right)} {P\left( A \right)}}} \right. \kern-\nulldelimiterspace} {P\left( A \right)}}\). A different approach is to interpret conditional probability as a ‘primitive’, \(P_A \left( B \right)\), so that the conditioning events A are outside the probability space. On this alternative approach, conditional probability could be understood as a conditional with a probabilistic consequent, so that \(P_A \left( B \right) = p\) denotes the conditional “if A, then the probability of B is p” or “if A had been the case, then the probability of B would have been p”. For ease of presentation, we shall follow the first approach. For a general discussion of the second approach and its relation to the first approach, see Hajek (2003) and Berkovitz (2009a,2009b), and for a discussion of the advantages of the second approach in the context of Bell’s theorem, see Butterfield (1992) and Berkovitz (2002).
- 4.
Although Bell’s conclusion is widely accepted, there are some dissenting views. In particular, Fine (1981, 1986, pp. 59–60, 1989), Cartwright (1989, Chapters 3 and 6) and Chang & Cartwright (1993) deny that the failure of Factorizability entails non-locality, and Fine (1982a, p. 294) argues that what the Bell inequalities are all about is the dubious requirement of making “well defined precisely those probability distributions for non-commuting observables whose rejection is the very essence of quantum mechanics” (cf. Berkovitz 1995, 2009a, Sections 1–2).
- 5.
- 6.
In more general models, the complete pair-state at the emission may also be influenced by other factors, such as other final boundary conditions of the experiment. But while these models will substantially complicate our analysis, they will not alter significantly its main conclusions.
- 7.
The main arguments to follow will hold even if we assume that complete pair-states are only compatible with certain apparatus settings, and accordingly prescribe outcomes just for the corresponding measurements.
- 8.
I am grateful to Mauricio Suarez for pointing out to me the importance of emphasizing here the distinction between deterministic causal connections and indeterministic causal connections with propensity one.
- 9.
The constraints of causal loops with two indeterministic causes may, however, limit the range of the possible long-run frequencies of effects in the reference class of their indeterministic causes. For an example, see Berkovitz (2002, Section 4).
- 10.
The same is true for the complete pair-state, i.e. the state that is constituted by the initial and final wavefunctions of the particles and their position configuration; for the initial and final wavefunctions of the particles determine the measurement outcomes.
- 11.
In Loop I, the differences between Model DS and Model IS are suppressed. Model DS predict Loop I with all the causal connections being deterministic, whereas Model IS predict Loop I with the causal connections between the complete pair-state and the R-outcome and between the L-setting and the complete pair-state being indeterministic.
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Acknowledgements
The work on this paper was prompted by an invitation to contribute to this volume. I am very grateful to the editor, Mauricio Suarez. Parts of this paper were presented at the Time-Symmetric Interpretations of Quantum Mechanics Workshop and the Summer Foundations Conference 2006, Centre for Time, Department of Philosophy, University of Sydney; CREA, Polytechnique, Paris; the Department of Philosophy, Universidad de Barcelona; the Department of Philosophy, Universidad Complutense de Madrid; and the Sigma Club, Centre for the Philosophy of Natural and Social Sciences, London School of Economics. These conferences and colloquia were instrumental in the development of the paper, and I thank the organizers, audiences, and in particular Rod Sutherland, Mauricio Suarez, Huw Price, David Miller, Carl Hoefer, Roman Frigg and Guido Bacciagaluppi. For support, I am very grateful to the Department of Philosophy, University of Sydney, and the Institute for History and Philosophy of Science and Technology, University of Toronto.
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Berkovitz, J. (2011). On Explanation in Retro-causal Interpretations of Quantum Mechanics. In: Suárez, M. (eds) Probabilities, Causes and Propensities in Physics. Synthese Library, vol 347. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9904-5_6
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