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-Fra- enkel 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.
Cite this paper
Nagata, K. and Nakamura, T. (2015). Whether the CPT Symmetry Can Be Almighty Even in a Photon. Open Access Library Journal, 2, e1806. doi: http://dx.doi.org/10.4236/oalib.1101806.
Yokota, K., Yamamoto, T., Koashi, M. and Imoto, N. (2009) Direct Observation of Hardy’s Paradox by Joint
Weak Measurement with an Entangled Photon Pair. New Journal of Physics, 11, Article
ID: 033011. http://dx.doi.org/10.1088/1367-2630/11/3/033011
Nagata, K., Laskowski, W., Wiesniak, M. and Zukowski, M. (2004) RotationalInvariance as an Additional Constraint on Local Realism. Physical Review Letters, 93, Article
ID: 230403. http://dx.doi.org/10.1103/PhysRevLett.93.230403
Nagata, K. and Ahn, J. (2008) Violation of Rotational Invariance of Local Realistic Models with Two
Settings. Journal of the Korean Physical Society, 53, 2216.
Nagata, K. and Ahn, J. (2008) The Conflict between Bell-Zukowski Inequality and Bell-Mermin
Inequality. Modern Physics Letters A, 23, 2967. http://dx.doi.org/10.1142/S0217732308028727
Greenberger, D.M., Horne, M.A. and Zeilinger, A. (1989) Going Beyond Bell’s Theorem. In:Kafatos, M., Ed., Bell’s Theorem, Quantum Theory and Conceptions of the
Universe, Kluwer Academic, Dordrecht, 69-72. http://dx.doi.org/10.1007/978-94-017-0849-4_10
Nagata, K. (2007) Multipartite
Omnidirectional Generalized Bell Inequality. Journal
of Physics A: Mathematical
and Theoretical, 40, 13101. http://dx.doi.org/10.1088/1751-8113/40/43/017
Einstein, A.,
Podolsky, B. and Rosen, N. (1935) Can
Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777. http://dx.doi.org/10.1103/PhysRev.47.777
Groblacher, S., Paterek, T., Kaltenbaek, R., Brukner, C.,
Zukowski, M., Aspelmeyer,
M. and Zeilinger, A.
(2007) An Experimental Test of Non-Local Realism. Nature, 446,
871-875. http://dx.doi.org/10.1038/nature05677
Paterek, T.,
Fedrizzi, A.,
Groblacher, S.,
Jennewein, T., Zukowski, M.,
Aspelmeyer, M. and Zeilinger, A.
(2007) Experimental Test of Nonlocal Realistic Theories without the Rotational
Symmetry Assumption. Physical Review Letters, 99, Article ID: 210406. http://dx.doi.org/10.1103/PhysRevLett.99.210406
Scarani, V. and Gisin, N. (2001) Quantum Communication between N Partners and Bell’s Inequalities. Physical
Review Letters, 87, Article ID: 117901. http://dx.doi.org/10.1103/PhysRevLett.87.117901
Brukner, C., Zukowski, M., Pan, J.-W.
and Zeilinger, A.
(2004) Bell’s Inequalities and Quantum Communication Complexity. Physical
Review Letters, 92, Article ID: 127901. http://dx.doi.org/10.1103/PhysRevLett.92.127901
Mermin, N.D. (1990) Extreme Quantum Entanglement in a Superposition of Macroscopically
Distinct States. Physical Review Letters, 65, 1838-1840. http://dx.doi.org/10.1103/PhysRevLett.65.1838
Roy,
S.M. and Singh, V. (1991) Tests of
Signal Locality and Einstein-Bell Locality for Multiparticle Systems. Physical
Review Letters, 67, 2761-2764. http://dx.doi.org/10.1103/PhysRevLett.67.2761
Ardehali, M. (1992) Bell Inequalities with a Magnitude of Violation That Grows
Exponentially with the Number of Particles. Physical Review A, 46,
5375-5378. http://dx.doi.org/10.1103/PhysRevA.46.5375
Werner, R.F. and Wolf, M.M. (2001) All-Multipartite Bell-Correlation Inequalities for Two
Dichotomic Observables per Site. Physical Review A, 64, Article ID: 032112. http://dx.doi.org/10.1103/PhysRevA.64.032112
Abian, A. and LaMacchia, S. (1978) On the Consistency and Independence of Some
Set-Theoretical Axioms. Notre
Dame Journal of Formal Logic, 19, 155-158. http://dx.doi.org/10.1305/ndjfl/1093888220
Suppes, P. (1972) Axiomatic Set Theory. Dover Reprint. Perhaps the
Best Exposition of ZFC before the Independence of AC and the Continuum
Hypothesis, and the Emergence of Large Cardinals. Includes Many Theorems.
van Heijenoort, J. (1967) Investigations in the Foundations of Set
Theory. In: van Heijenoort, J.,
Ed., From Frege to Godel: A Source Book in Mathematical Logic,
1879-1931, Harvard University Press, Cambridge, MA, 199-215.
Nagata, K.
and Nakamura, T. (2011) Does
Singleton Set Meet Zermelo-Fraenkel Set Theory with the Axiom of Choice? Advanced
Studies in Theoretical Physics, 5, 57.
Nagata, K. and Nakamura, T. (2010) Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm? International
Journal of Theoretical Physics, 49, 162-170. http://dx.doi.org/10.1007/s10773-009-0189-5
Gudder, S.P. (1980) Proposed Test for a Hidden Variables Theory. International Journal of
Theoretical Physics, 19, 163-168. http://dx.doi.org/10.1007/BF00669767
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.
Aspect, A.,
Dalibard, J. and Roger, G.
(1982) Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers. Physical
Review Letters, 49, 1804-1807. http://dx.doi.org/10.1103/PhysRevLett.49.1804
Hellmuth, T., Walther, H., Zajonc, A. and Schleich, W. (1987) Delayed-Choice Experiments in Quantum
Interference. Physical
Review A, 35, 2532-2541. http://dx.doi.org/10.1103/PhysRevA.35.2532