Abstract
In this paper I assess the adequacy of no-conspiracy conditions employed in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these cannot be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. In the right circumstances then, violations of measurement independence need not entail any kind of conspiracy (nor backwards in time causation). To the contrary, if measurement operations in the EPR context are taken to be causally relevant in a specific way to the experiment outcomes, their explicit causal role provides the grounds for a common cause explanation of the corresponding correlations.
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Notes
This definition is of positive correlation. A completely symmetrical definition may be given for negative correlations. Distinguishing between positive and negative correlations will not be important for the argument here. Thus, if not stated otherwise, positive correlations will be assumed throughout the paper.
I point the reader to San Pedro and Suárez (2009) for a recent assessment the significance of common cause completability, possible criticisms to it and the strategies to avoid these.
This is indeed standard and, as pointed out by p. 4 Szabó (2000), taking quantum probabilities as classical conditional probabilities is crucial for the whole issue regarding Reichenbachian common cause explanations of EPR correlations to be meaningful. As an alternative we would need to redefine RPCC to fit the non-classical probabilistic framework of quantum mechanics. This option is explored for instance in Henson (2005).
What it is exactly meant by ‘physical locality’ and whether such concept may be appropriately captured in terms of probabilistic relations, though, is far from settled. I shall not discuss these issues in detail here and just point the reader to Butterfield (2007), Fine (1981, 1986), Maudlin (1994), Wessels (1985) or Suárez (2000) for further reference.
In fact, I think this is why discussions about free will and backwards in time causation are so much entangled. For those defending backwards causation still assume (temporal) priority of common causes in relation to measurement operations. (Only, in those cases, time order and causal order are not assumed to coincide.) See, for instance, Berkovitz (2002) or Price (1994).
I am following here basically the same notation to that in the rest of the paper. Only I shall denote the common cause of the classical correlations with a serif font \(\mathsf{C_{ij}^{ab}}\) instead of the usual italic \(C_{ij}^{ab}\) used in standard treatments of the problem in order to stress their exclusively classical origin.
In the context of EPR correlations it is indeed standard to assume measurement operations not to be causally relevant for common causes—this is in fact why ‘no-conspiracy’-type conditions are required. Note moreover that the expression ‘measurement operations’ here include not only the experimenter’s act of setting-up the apparatus but also the actual interaction between the particle and the apparatus when measurement is preformed.
Why \(\mathsf{C_{ij}^{ab}}\) is defined as a subset of the conjunction \(L_i \land R_j \land \Lambda\), and not as identical to it, will become clear in a moment.
This characterisation of Λ reminds somehow to the kind of events Cartwright considers the right common cause events for EPR. That the similarity is quite so it will become clear in a moment, since I will be requiring (or at least allowing) that the Λ be non-screening-off events, just like in Cartwright’s common cause account of EPR (Cartwright 1987; Cartwright and Jones 1991; Chang and Cartwright 1993).
This view hinges on the claim that, because of the spherical symmetry of the spin-singlet state, quantum mechanics violates outcome independence, while it is compatible with parameter independence.
The idea of common causes taking place after measurement can also be found in Martel (2008). However, Martel’s proposal does not have the same aims and scope than mine here. In particular, Martel discusses specific issues as regards the philosophical status of the so-called causal Markov condition—a generalisation of RPCC—, and does not pay attention to the consequences of the actual violation of measurement independence, when it comes to locality, for instance.
I should note that the model is flexible enough not to commit to any particular account of causation even if, I have to admit, some idea of temporal order needs to be implemented if one is to challenge the requirement of measurement independence.
As Suárez (2007) points out, although the model was initially presented as a common cause model (containing backwards in time causal influences), Price seemed later to retract from interpreting it as causal. In particular, Price (1996b) seems to suggest that the backwards in time influences of the model be of no causal origin. Suárez (2007) also provides an explicit causal interpretation of Price’s model, which I endorse here.
Note that the probabilistic event structure of Price’s model and my own is exactly the same. Only, the interpretation of the events is different.
Of course, if the my conjecture turns out to be true, parameter independence would be violated in all cases where measurement independence would fail to hold. In other words, we could not have a model satisfying parameter independence while measurement independence was violated in it. But, on the other hand, because of the logical structure of the conjecture we could have models satisfying measurement independence, where parameter independence was nevertheless violated. This is the case in Bohm’s quantum mechanics, for instance.
This diagnosis is not free of controversies, however. Several authors in fact cast doubts as to whether factorizability indeed reflects the idea of physical locality—especially if locality is merely associated with the requirement that there not be superluminal signalling between the two wings of the EPR experiment. See for instance, Wessels (1985), Fine (1986) or Maudlin (1994).
Recall that because of its logic asymmetry, Conjecture 1 can accommodate violations of parameter independence in cases measurement independence holds.
Not even at the ontological level can they be compared, I think. For while Bohm’s quantum mechanics provides a definite ontological picture for quantum mechanics, the ontology associated to the common causes in the model is not to be taken as the quantum ontology—again, it is key to bear in mind that the common causes are not to be seen as hidden variables as such. This is not to say, of course, that the possible ontologies we might want to provide the model with will not ‘inherit’ somehow, or reflect, some quantum features, such as non-locality.
References
Bell, J. S. (1964). On the Einstein–Podolsky–Rosen paradox. Physics, 1, 195–200. Reprinted in J. S. Bell, Speakable and unspeakable in quantum mechanics (pp. 14–21). Cambridge University Press, 1987.
Bell, J. S. (1975). The theory of local beables. TH-2053-CERN, presented at the Sixth GIFT Seminar, June 1975. Reproduced in Epistemological Letters, March 1976, and reprinted in J. S. Bell, Speakable and unspeakable in quantum mechanics. Cambridge University Press, 1987, pp. 52–62.
Berkovitz, J. (2002). On causal loops in the quantum realm. In T. Placek, & J. Butterfield (Eds.), Non-locality and modality: Proceedings of the NATO advanced research workshop on modality, probability and Bell’s theorems (pp. 235–257). Dordrecht: Kluwer.
Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of ‘hidden’ variables, I and II. Physical Review, 85, 166–193.
Butterfield, J. (1989). A space-time approach to the Bell inequality. In J. Cushing, & E. McMullin (Eds.), Philosophical consequences of quantum theory (pp. 114–144). Notre Dame: University of Notre Dame Press.
Butterfield, J. (2007). Stochastic Einstein’s locality revisited. British Journal for the Philosophy of Science, 58, 805–867.
Cartwright, N. (1987). How to tell a common cause: Generalizations of the conjunctive fork criterion. In J. H. Fetzer (Ed.), Probability and causality (pp. 181–188). Dordrecht: Reidel.
Cartwright, N., & Jones, M. (1991). How to hunt quantum causes. Erkenntnis, 35, 205–231.
Chang, H., & Cartwright, N. (1993). Causality and realism in the EPR experiment. Erkenntnis, 38, 169–190.
Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47, 777–780.
Fine, A. (1981). Correlations and physical locality. In P. Asquith, & R. Giere (Eds.), Proceedings of the 1980 biennial meeting of the Philosophy of Science Association (Vol. 2, pp. 535–556). Lansing.
Fine, A. (1986). The shaky game. Einstein realism and the quantum theory. Chicago: The University of Chicago Press. 2nd edition, 1996.
Graßhoff, G., Portman, S., & Wüthrich, A. (2005). Minimal assumption derivation of a Bell-type inequality. The British Journal for the Philosophy of Science, 56, 663–680.
Healey, R. (1992). Chasing quantum causes: How wild is the goose? Philosophical Topics, 20, 181–204.
Henson, J. (2005). Comparing causality principles. Studies in the History and Philosophy of Modern Physics, 36, 519–543.
Hofer-Szabó, G., Rédei, M., & Szabó, L. E. (1999). On Reichenbach’s common cause principle and Reichenbach’s notion of common cause. The British Journal for the Philosophy of Science, 50, 377–399.
Hofer-Szabó, G., Rédei, M., & Szabó, L. E. (2000). Common cause completability of classical and quantum probability spaces. International Journal of Theoretical Physics, 39, 913–919.
Hofer-Szabó, G., Rédei, M., & Szabó, L. E. (2002). Common causes are not common-common causes. Philosophy of Science, 69, 623–636.
Martel, I. (2008). The principle of the common cause, the Causal Markov condition, and quantum mechanics: Comments on Cartwright. In S. Hartmann, C. Hoefer, & L. Bovens (Eds.), Nancy Cartwright’s philosophy of science (pp. 242–262). London: Routledge.
Maudlin, T. (1994). Quantum non-locality and relativity. Oxford: Blackwell. 2nd edition, 2002.
Price, H. (1994). A neglected route to realism about quantum mechanics. Mind, 103, 303–336.
Price, H. (1996a). Locality, independence and the pro-liberty Bell. arXiv:quant-ph/9602020v1.
Price, H. (1996b). Time’s arrow and Archimedes’ point. Oxford: Oxford University Press.
Reichenbach, H. (1956). The direction of time. Edited by Maria Reichenbach. Unabridged Dover, 1999 (republication of the original University of California Press, 1956).
San Pedro, I., & Suárez, M. (2009). Reichenbach’s principle of the common cause and indeterminism: A review. In J. L. González Recio (Ed.), Philosophical essays in physics and biology (pp. 223–250). Georg Olms.
Suárez, M. (2000). The many faces of non-locality: Dickson on the quantum correlations. British Journal for the Philosophy of Science, 51, 882–892.
Suárez, M. (2007). Causal inference in quantum mechanics: A reassessment. In F. Russo, & J. Williamson (Eds.), Causality and probability in the sciences (pp. 65–106). London College.
Szabó, L. E. (2000). On an attempt to resolve the EPR-Bell paradox via Reichenbachian concept of common cause. International Journal of Theoretical Physics, 39, 911–926.
Szabó, L. E. (2008). The Einstein–Podolsky–Rosen argument and the Bell inequalities. The Internet Encyclopaedia of Philosophy. http://www.iep.utm.edu/.
van Fraassen, B C. (1982). The charybdis of realism: Epistemological implications of Bell’s Inequality. Synthese, 52, 25–38. Reprinted with corrections in J. Cushing and E. McMullin (Eds.), Philosophical consequences of quantum theory. University of Notre Dame Press, 1989, pp. 97–113.
Wessels, L. (1985). Locality, factorability and the Bell inequalities. Noûs, 19, 481–519.
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Support from the Spanish Ministry of Science and Innovation (FFI2008-06418-C01-03), and the Department of Education of Madrid’s Regional Government (S2007-HUM/0501) is gratefully acknowledged.
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San Pedro, I. Causation, measurement relevance and no-conspiracy in EPR. Euro Jnl Phil Sci 2, 137–156 (2012). https://doi.org/10.1007/s13194-011-0037-3
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DOI: https://doi.org/10.1007/s13194-011-0037-3