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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, spincomponent 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 nonlocality: 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.