Abstract
Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. I find that a sufficient condition for the existence of elements of reality, introduced in these proofs, seems to be used also as a necessary condition. I argue that Lorentz-invariant elements of reality can be defined but, as Vaidman pointed out, they won’t satisfy the so-called product rule. In so doing I obtain algebraic constraints on elements of reality associated with a maximal set of commuting Hermitian operators.
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Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Bohr, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696–702 (1935)
Redhead, M.: Incompleteness, Nonlocality, and Realism. Clarendon, Oxford (1987)
Bohm, D.: A suggested interpretation of the quantum theory in terms of ‘hidden’ variables (I and II). Phys. Rev. 85, 166–193 (1952)
Vermaas, P.E.: A Philosopher’s Understanding of Quantum Mechanics. Possibilities and Impossibilities of a Modal Interpretation. Cambridge University Press, Cambridge (1999)
Hardy, L.: Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Phys. Rev. Lett. 68, 2981–2984 (1992)
Clifton, R., Niemann, P.: Locality, Lorentz invariance, and linear algebra: Hardy’s theorem for two entangled spin-s particles. Phys. Lett. A 166, 177–184 (1992)
Clifton, R., Pagonis, C., Pitowsky, I.: Relativity, quantum mechanics and EPR. In: Proceedings of the Biennial Meeting of the PSA, vol. 1, pp. 114–128. Philosophy of Science Association (1992)
Vaidman, L.: Lorentz-invariant ‘elements of reality’ and the joint measurability of commuting observables. Phys. Rev. Lett. 70, 3369–3372 (1993)
Vaidman, L.: The analysis of Hardy’s experiment revisited. quant-ph/9703018
Hellwig, K.E., Kraus, K.: Formal description of measurements in local quantum field theory. Phys. Rev. D 1, 566–571 (1970)
Berndl, K., Goldstein, S.: Comment on ‘Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories’. Phys. Rev. Lett. 72, 780 (1994)
Hardy, L.: Hardy replies. Phys. Rev. Lett. 72, 781 (1994)
Cohen, O., Hiley, B.J.: Reexamining the assumption that elements of reality can be Lorentz invariant. Phys. Rev. A 52, 76–81 (1995)
Dewdney, C., Horton, G.: Relativistically-invariant extension of the de Broglie-Bohm theory of quantum mechanics. J. Phys. A 35, 10117–10127 (2002)
Tumulka, R.: A relativistic version of the Ghirardi-Rimini-Weber model. J. Stat. Phys. 125, 825–844 (2006)
Aharonov, Y., Bergmann, P.G., Lebowitz, J.L.: Time symmetry in the quantum process of measurement. Phys. Rev. 134, B1410–B1416 (1964)
Cohen, O., Hiley, B.J.: Elements of reality, Lorentz invariance, and the product rule. Found. Phys. 26, 1–15 (1996)
Aharonov, Y., Botero, A., Popescu, S., Reznik, B., Tollaksen, J.: Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values. Phys. Lett. A 301, 130–138 (2002)
Marchildon, L.: The counterfactual meaning of the ABL rule. In: Khrennikov, A. (ed.) Proceedings of the International Conference on Quantum Theory: Reconsideration of Foundations—2, pp. 403–412. Växjö University Press, Växjö (2004). quant-ph/0307082
Aharonov, A., Albert, D.Z.: Can we make sense out of the measurement process in relativistic quantum mechanics? Phys. Rev. D 24, 359–370 (1981)
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Marchildon, L. On Relativistic Elements of Reality. Found Phys 38, 804–817 (2008). https://doi.org/10.1007/s10701-008-9238-9
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DOI: https://doi.org/10.1007/s10701-008-9238-9