On EPR, Counterfactuals, and Relation Between Quantum Mechanics and Relativity

It is a widely acknowledged fact that the relations between standard quantum mechanics and special theory of relativity are quite tense. In its very foundation quantum mechanics contains concepts and postulates, like for example the postulate of the collapse of the wave function, that are hard to interpret in a relativistically invariant way. One of the prime examples of the apparent incompatibility between quantum-mechanical description and some requirements of special relativity is the notorious Einstein-Podolsky-Rosen argument. The EPR argument aims at showing that the relativistic principle of locality, prohibiting the existence of superluminal interactions between separate parts of an entangled quantum system, leads to the conclusion that the standard quantum-mechanical formalism is incomplete. Surprisingly, the original EPR argument has been presented in a non-relativistic framework, with an explicit reference to the absolute notion of simultaneity defined for two spatially separated measuring apparatuses. Only recently attempts have been made to reformulate this argument in a fully relativistic way (Ghirardi, Grassi 1994), (Pagonis, Redhead, La Rivière 1996), (Redhead, La Rivière 1997), (Shimony 2001). Beside their commitment to the accurate relativistic description of the EPR situation, these approaches (with the exception of Shimony’s article) display another interesting trait: they namely rely on the logic of counterfactual conditionals. In this paper I would like to follow this lead and propose yet another counterfactual and relativistically invariant explication of the EPR argument. I claim that the EPR argument in the proposed interpretation does not reach its intended goal, as it fails to establish that quantum-mechanical formalism implies the existence of measurement-induced non-local interactions between distant parts of the entangled system. The only residual form of non-locality that the EPR argument leaves us with is the outcome-induced non-locality, often accepted as being weaker than the previous one.

The proposed counterfactual analysis is based on several precisely stated premises and principles. Its main starting point is the adoption of a particular relativistically invariant semantics for spatiotemporal counterfactuals. In the simplest case when the antecedent of a given counterfactual refers to a free-choice point-event, this semantics boils down to the requirement that for such a counterfactual to be true, its consequent has to be true in all antecedent-worlds which are identical with the actual world everywhere outside the antecedent-event’s forward light cone. In other cases the evaluation of counterfactuals has to be done with the help of the appropriately defined comparative relation between possible worlds with respect to their similarity to the actual world (see Lewis 1973, Finkelstein 1999, and Bigaj 2004). The next crucial element of the counterfactual reconstruction of the EPR argument is the locality condition. The general semantic locality condition (referred to as SLOC) adopted for the sake of the analysis stipulates that for every possible event e there is a possible world in which e holds and which differs from the actual world within the forward light cone of e only (hence e has no effects in areas space-like separated from it). And finally, in place of Einstein’s famous criterion of physical reality, the counterfactual interpretation of property attributions is put forward. According to this interpretation, a statement announcing that one particle possesses a definitive value of a given measurable property (typically, spin-component in a given direction) when the other particle undergoes a measurement of the same property, is replaced with a counterfactual: “If the appropriate measurement were performed, the outcome would be as predicted on the basis of the perfect correlation with the distant outcome”. It is stressed that we have no sufficient grounds for believing that such a counterfactual statement refers to an objective and categorical property that the system in question possesses at a given time; rather, it expresses certain disposition of the system to act in a particular way when the conditions are satisfied. When we reject the supposition that there is an “objective element of reality” corresponding to a counterfactual property attribution derived from the outcome of the distant measurement, then the counterfactual semantics that we have adopted allows for a situation in which under an alternative measurement selection of the distant particle the local property attribution “disappears” without actually violating the locality principle (SLOC) as applied to the measurement selection. In other words, no measurement-induced non-locality follows when one assumes that quantum-mechanical formalism offers a complete description of the physical situation. However, it can be showed that the EPR situation forces us to accept a different form of non-locality: the non-locality induced by the outcome revealed in measurement. In the paper I explain precisely under what circumstances the semantic locality requirement (SLOC) can be applied to the outcomes of measurements, and why it is so that the EPR situation does not satisfy this version of the locality condition.

Selected bibliography

Bigaj, T.: 2004, “Counterfactuals and Spatiotemporal Events”, Synthese, 142, 1, pp. 1-20.

Clifton, R., C. Pagonis, and I. Pitowsky: 1992, “Relativity, Quantum Mechanics and EPR’, in: D. Hull, M. Forbes and K. Okruhlik (eds.), PSA 1992, Vol. 1, East Lansing, Michigan, 114-128.

Einstein, A., Podolsky, B., and Rosen, N.: 1935, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review 48, 696-702.

Finkelstein, J.: 1999, ‘Space-time Counterfactuals’, Synthese 119, 287-298.

Ghirardi, G. and Grassi, R: 1994, “Outcome Predictions and Property Attribution: the EPR Argument Reconsidered”, Studies in the History and Philosophy of Science, 25 (3), 397-423.

Lewis, D.: 1973, Counterfactuals, Harvard Univ. Press, Cambridge (Mass.)

Myrvold, W.C.: 2002, ‘On Peaceful Coexistence: Is the Collapse Postulate Incompatible with Relativity?’, Studies in History and Philosophy of Modern Physics 33, 435-466.

Pagonis, P., M. Redhead and P. La Rivière: 1996, “EPR, Relativity and the GHZ Experiment”, in: R. Clifton (ed.) Perspectives on Quantum Reality, Kluwer, 43-55.

Redhead, M. and P. La Rivière: 1997, “The Relativistic EPR Argument” in R.S. Cohen, M. Horne and J. Stachel (eds.), Potentiality, Entanglement and Passion-at-a-Distance, Dordrecht.

Shimony, A.: 2001, “The Logic of EPR”, Annales de la Fondation Louis de Broglie, vol. 26, 399-410.