Foundations of Physics

, Volume 42, Issue 4, pp 475–487 | Cite as

Reconstructing Bohr’s Reply to EPR in Algebraic Quantum Theory

  • Masanao OzawaEmail author
  • Yuichiro Kitajima


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.


Bohr EPR Algebraic quantum theory Modal interpretation 



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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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Graduate School of Information ScienceNagoya UniversityNagoyaJapan
  2. 2.College of Industrial TechnologyNihon UniversityNarashinoJapan

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