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Reconstructing Bohr’s Reply to EPR in Algebraic Quantum Theory

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Abstract

Halvorson and Clifton have given a mathematical reconstruction of Bohr’s reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr’s reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr’s requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.

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Notes

  1. The reason for their rejection of Howard’s contextualized version of the EPR reality criterion is obscure. They argued that the EPR reality criterion is best construed as a version of ‘inference to the best explanation’ following Redhead [18, p. 72] and that we cannot expect Bohr to be persuaded by such inference to the best explanation since he is not a classical scientific realist [10, p. 11]. This is plausible, and yet it is not clear whether Bohr would contend against the contextualized version either.

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Acknowledgements

The authors thank Jeremy Butterfield for helpful comments and suggestions for an earlier version of this paper. M.O. thanks Andreas Doering for his warm hospitality at the Department of Computer Science, Oxford University, where the final part of this work has been done. M.O. is supported in part by the JSPS KAKENHI, No. 21244007 and No. 22654013. Y.K. is supported by the JSPS KAKENHI, No. 23701009.

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  1. Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya, 464-8601, Japan

    Masanao Ozawa

  2. College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba, 275-8576, Japan

    Yuichiro Kitajima

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  1. Masanao Ozawa
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  2. Yuichiro Kitajima
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Correspondence to Masanao Ozawa.

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Ozawa, M., Kitajima, Y. Reconstructing Bohr’s Reply to EPR in Algebraic Quantum Theory. Found Phys 42, 475–487 (2012). https://doi.org/10.1007/s10701-011-9615-7

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