Bell’s inequality itself is usually considered to belong to mathematics and not quantum mechanics. We think that this is making our understanding of Bell’ theory be confused. Thus in this paper, contrary to Bell’s spirit (which inherits Einstein’s spirit), we try to discuss Bell’s inequality in the framework of quantum theory with the linguistic Copenhagen interpretation. And we clarify that the violation of Bell’s inequality (i.e., whether or not Bell’s inequality holds) does not depend on whether classical systems or quantum systems, but depend on whether a combined measurement exists or not. And further we conclude that our argument (based on the linguistic Copenhagen interpretation) should be regarded as a scientific representation of Bell’s philosophical argument (based on Einstein’s spirit).
References
[1]
Ishikawa, S. (2006) Mathematical Foundations of Measurement Theory. Keio University Press Inc. Tokyo, 335 p. http://www.keio-up.co.jp/kup/mfomt/
[2]
Ishikawa, S. (2011) A New Interpretation of Quantum Mechanics. Journal of Quantum Information Science, 1, 35-42. http://www.scirp.org/journal/PaperInformation.aspx?paperID=7610 https://doi.org/10.4236/jqis.2011.12005
[3]
Ishikawa, S. (2012) Quantum Mechanics and the Philosophy of Language: Reconsideration of Traditional Philosophies. Journal of Quantum Information Science, 2, 2-9. http://www.scirp.org/journal/PaperInformation.aspx?paperID=18194 https://doi.org/10.4236/jqis.2012.21002
[4]
Ishikawa, S. (2012) A Measurement Theoretical Foundation of Statistics. Applied Mathematics, 3, 283-292. http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=18109 https://doi.org/10.4236/am.2012.33044
[5]
Ishikawa, S. (2012) Monty Hall Problem and the Principle of Equal Probability in Measurement Theory. Applied Mathematics, 3, 788-794. http://www.scirp.org/journal/PaperInformation.aspx?PaperID=19884 https://doi.org/10.4236/am.2012.37117
[6]
Ishikawa, S. (2012) Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View. World Journal of Mechanics, 2, 125-130. http://www.scirp.org/journal/PaperInformation.aspx?PaperID=18861 https://doi.org/10.4236/wjm.2012.22014
[7]
Ishikawa, S. (2015) Linguistic Interpretation of Quantum Mechanics; Projection Postulate. Journal of Quantum Information Science, 5, 150-155. http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=62464 https://doi.org/10.4236/jqis.2015.54017
[8]
Ishikawa, S. (2016) Linguistic Interpretation of Quantum Mechanics: Towards World-Description in Quantum Language. Shiho-Shuppan Publisher, Tsukuba, 416 p. http://www.math.keio.ac.jp/academic/research_pdf/report/2016/16001.pdf
[9]
Ishikawa, S. (2017) A Final Solution to Mind-Body Problem by Quantum Language. Journal of Quantum Information Science, 7, 48-56. http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=76391 https://doi.org/10.4236/jqis.2017.72005
[10]
Ishikawa, S. (2017) Bell’s Inequality Is Violated in Classical Systems as Well as Quantum Systems. The W*-Algebraic Version of This Paper, Research Report, Keio University, Yokohama, 10 p. http://www.math.keio.ac.jp/academic/research_pdf/report/2017/17006.pdf
[11]
Ishikawa, S. (1991) Uncertainty Relation in Simultaneous Measurements for Arbitrary Observables. Reports on Mathematical Physics, 9, 257-273. http://www.sciencedirect.com/science/article/pii/003448779190046P https://doi.org/10.1016/0034-4877(91)90046-P
[12]
Ishikawa, S. (1997) Fuzzy Inferences by Algebraic Method. Fuzzy Sets and Systems, 87, 181-200. http://www.sciencedirect.com/science/article/pii/S0165011496000358 https://doi.org/10.1016/S0165-0114(96)00035-8
[13]
Einstein, A., Podolosky, B. and Rosen, N. (1935) Can Quantum-Mechanical Description of Reality Be Considered Completely? Physical Review, 47, 777-780. https://doi.org/10.1103/PhysRev.47.777
[14]
Bohr, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 48, 696-702. https://doi.org/10.1103/PhysRev.48.696
[15]
Bell, J.S. (1964) On the Einstein-Podolosky-Rosen Paradox. Physics, 1, 195-200.
[16]
Clauser, J.F., Horne, M.A., Shimony, A. and Holt, R.A. (1969) Proposed Experiment to Test Local Hidden Variable Theories. Physical Review Letters, 23, 880-884. https://doi.org/10.1103/PhysRevLett.23.880
[17]
Redhead, M. (1987) Incompleteness, Non-Locality, and Realism. Oxford University Press, Oxford.
[18]
Selleri, F. (1983) Die Debatte um die Quantentheorie, Friedr. Vieweg & Sohn Verlagsgesellscvhaft MBH, Braunschweig.
[19]
Sakai, S. (1971) C*-Algebras and W*-Algebras. Springer-Verlag, Berlin Heidelberg.
[20]
Yosida, K. (1980) Functional Analysis. Springer-Verlag, 6th Edition, Berlin Heidelberg New York.
[21]
Davies, E.B. (1976) Quantum Theory of Open Systems. Academic Press, London, New York.
[22]
Born, M. (1926) Zur Quantenmechanik der Stoßprozesse (Vorläufige Mitteilung). Zeitschrift für Physik, 37, 863-867.
