Is quantum theory compatible with special relativity?
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c Indian Academy of Sciences
— journal of physics
Vol. 80, No. 3 March 2013 pp. 429–437
Is quantum theory compatible with special relativity? M BAHRAMI1 , A SHAFIEE2,∗ , M SARAVANI3 and M GOLSHANI4 1 Condense
Matter and Statistical Physics, The Abdul Salam ICTP, Trieste, Italy Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran 3 Perimeter Institute for Theoretical Physics, Waterloo, Canada; Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada 4 Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran; Institutes for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5531, Tehran, Iran ∗ Corresponding author. E-mail: [email protected] 2 Research
MS received 19 July 2011; revised 26 September 2012; accepted 8 October 2012 Abstract. How a proposed quantum nonlocal phenomenon could be incompatible with the requirements of special relativity is studied. To show this, the least set of assumptions about the formalism and the interpretation of non-relativistic quantum theory is considered. Then, without any reference to the collapse assumption or any other stochastic processes, an experiment is proposed, involving two quantum systems, that interacted at an arbitrary time, with results which seem to be in conflict with requirements of special relativity. Keywords. Quantum non-locality; no-signalling theorems. PACS Nos 03.30.+p; 03.65.−w; 03.65.Ta
1. Introduction Although the Schrödinger equation is characteristically non-relativistic, the nonrelativistic quantum theory instrumentally complies with the requirement of special relativity (SR) in very peculiar ways. That is, those counterintuitive non-local phenomena predicted by non-relativistic quantum mechanics (e.g., collapse of wave function [1,2], non-local quantum correlations [3–15], the instantaneous spreading of a compact wave function [16], Aharonov–Bohm effect [17], and protective measurements [17]) do not imply the practical possibility of sending a true signal faster than the speed of light in vacuum. However, it is not trivial to show where those non-local proposals for the superluminal communication fail. In general, different arguments have been presented for each distinctive case. In the following, we review this issue in detail. Briefly, the superluminal communication schemes break down either due to the violation of rules of non-relativistic dynamics (in particular due to no-signalling theorems [3–15]), or because DOI: 10.1007/s12043-012-0487-y; ePublication: 7 March 2013
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M Bahrami et al they include arbitrary energies greater than the relativistic limit (e.g., see [17]), or because of the unavoidable stochastic noise processes [18]. Following the celebrated Bell’s theorem [19], there is also a conceptually different approach to investigate the compatibility of a non-local theory (including quantum theory) with SR, which would not be pursued in this paper. In this approach, the
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