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Zimba, J.R. and Clifton, R.K. (1998) Valuations on Functionally Closed Sets of Quantum Mechanical Observables and von Neumann’s “No-Hidden-Variables” Theorem. In: Dieks, D. and Vermaas, P., Eds., The Modal Interpretation of Quantum Mechanics, Kluwer Academic Publishers, Dordrecht, 69-101.

has been cited by the following article:

  • TITLE: Whether the CPT Symmetry Can Be Almighty Even in a Photon

    AUTHORS: Koji Nagata, Tadao Nakamura

    KEYWORDS: Quantum Measurement Theory, Formalism, Quantum Nonlocality, Quantum Computer

    JOURNAL NAME: Open Access Library Journal, Vol.2 No.8, August 25, 2015

    ABSTRACT: As a trial, though thinking of general concepts, of our scientific challenge, we consider whether the Charge-Parity-Time (CPT) symmetry can be almighty even in a photon. This is the main aim of this paper. In what follows, we discuss our argumentations dividing the conjecture into two parts. Rotational invariance of physical laws is an accepted principle in Newton’s theory. We show that it leads to an additional constraint on local realistic theories with mixture of ten-particle Greenberger-Horne-Zeilinger state. This new constraint rules out such theories even in some situations in which standard Bell inequalities allow for explicit construction of such theories. This says new hypothesis to the number of ten. Next, it turns out Zermelo-Fraenkel set theory has contradictions. Further, the von Neumann’s theory has a contradiction by using ±1/. We solve the problem of von Neumann’s theory while escaping from all contradictions made by Zermelo-Fraenkel set theory, simultaneously. We assume that the results of measurements are . We assume that only and are possible. This situation meets a structure made by Zermelo-Fraenkel set theory with the axiom of choice. We result in the fact that it may be kept to perform the Deutsch-Jozsa algorithm even in the macroscopic scale because zero does not exist in this case. Our analysis agrees with recent experimental report.