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Foundational Problems of Quantum Mechanics

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Quantum Adaptivity in Biology: From Genetics to Cognition

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Abstract

In this chapter, we briefly discuss the main foundational problems of quantum mechanics, especially the problem of hidden variables—variables which might provide finer description of quantum phenomena than given by quantum states.

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Notes

  1. 1.

    These statements are not really theorems in the rigorous mathematical sense. They are statements of the physical nature. Apart from mathematical assumptions (which are typically vaguely formulated), they contain a list of physical assumptions.

  2. 2.

    However clear philosophical understanding of the process of transition from individual nonobjectivity to statistical objectivity is still absent, cf. [5, 32, 33].

  3. 3.

    For the latter, we have already pointed out, Chap. 1, that, opposite to quantum physics, in quantum(-like) biology it is impossible to draw a sharp distinction between an observer and a system. Self-observation is an important component of state-monitoring performed by bio-systems.

References

  1. Feynman, R., Hibbs, A.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965)

    Google Scholar 

  2. Bell, J.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  3. Khrennikov, A.: Växjö interpretation-2003: realism of contexts. In: Khrennikov, A.Yu. (ed.) Quantum Theory: Reconsideration of Foundations-2. Series Mathematical Modeling, vol. 10, pp. 323–338. Växjö University Press, Växjö (2004)

    Google Scholar 

  4. Khrennikov, A.: Contextual Approach to Quantum Formalism. Springer, Berlin (2009)

    Book  Google Scholar 

  5. Khrennikov, A.: Interpretations of Probability, 2nd edn. De Gruyter, Berlin (2009). (completed)

    Book  Google Scholar 

  6. Fuchs, C.A.: Quantum mechanics as quantum information (and only a little more). In: Khrennikov, A. (ed.) Quantum Theory: Reconsideration of Foundations. Series Mathematical Modeling, vol. 2, pp. 463–543. Växjö University Press, Växjö (2002)

    Google Scholar 

  7. Fuchs, C.: Delirium quantum (or, where I will take quantum mechanics if it will let me). In: Adenier, G., Fuchs, C., Khrennikov, A.Yu. (eds.) Foundations of Probability and Physics-3. Series Conference Proceedings, vol. 889, pp. 438–462. American Institute of Physics, Melville (2007)

    Google Scholar 

  8. Garola, C., Khrennikov, A.: Dialog on beyond quantum. In: Khrennikov, A. (ed.) Quantum Theory: Reconsideration of Foundations-5. Series Conference Proceedings, vol. 1232, pp. 355–359. American Institute of Physics, Melville (2010)

    Google Scholar 

  9. Boole, G.: An Investigation of the Laws of Thought. Dover Edition, New York (1958)

    Google Scholar 

  10. Vorob’ev, N.N.: Consistent Families of Measures and Their Extensions. Theory Probab. Appl. 7, 147–162 (1962)

    Article  Google Scholar 

  11. Conte, E., Khrennikov, A., Todarello, O., Federici, A., Zbilut, J.P.: A preliminary experimental verification on the possibility of Bell inequality violation in mental states. Neuroquantology 6, 214–221 (2008)

    Google Scholar 

  12. Bruza, P., Kitto, K., Ramm, B., Sitbon, L., Blomberg, S., Song, D.: Quantum-like non-separability of concept combinations, emergent associates and abduction. Log. J. IGPL 20(2), 455–457 (2010)

    Google Scholar 

  13. Busemeyer, J., Bruza, P.D.: Quantum Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  14. Dzhafarov, E.N., Kujala, J.V.: Quantum entanglement and the issue of selective influences in psychology: an overview. Lect. Notes Comput. Sci. 7620, 184–195 (2012)

    Article  Google Scholar 

  15. Von Neuman, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)

    Google Scholar 

  16. Kochen, S., Specker, E.: The problem of hidden variables in quantum mechanical systems. J. Math. Mech. 17, 59–87 (1967)

    Google Scholar 

  17. Khrennikov, A.Yu., Volovich, I.V.: Local realism, contextualism and loopholes in Bell’s experiments. In: Khrennikov, A.Yu. (ed.) Foundations of Probability and Physics-2. Series Mathematical Modeling, vol. 5, pp. 325–344. Växjö University Press, Växjö (2002)

    Google Scholar 

  18. Adenier, G., Khrennikov, A.Yu.: Is the fair sampling assumption supported by EPR experiments? Phys. B: At., Mol. Opt. Phys. 40(1), 131–141 (2007)

    Article  CAS  Google Scholar 

  19. Acacio de Barros, J.: Quantum-like model of behavioral response computation using neural oscillators. Biosystems 110, 171–182 (2012)

    Article  PubMed  Google Scholar 

  20. Acacio de Barros, J.: Joint probabilities and quantum cognition. In: Proceedings of the International Conference on Quantum Theory: Reconsiderations of Foundations-6. Växjö, Sweden, 11–14 June (2012)

    Google Scholar 

  21. Khrennikov, A.: Detection model based on representation of quantum particles by classical random fields: Born’s rule and beyond. Found. Phys. 39, 997–1022 (2009)

    Article  Google Scholar 

  22. Khrennikov, A., Ohya, M., Watanabe, N.: Classical signal model for quantum channels. J. Russ. Laser Res. 31, 462–468 (2010)

    Article  Google Scholar 

  23. Khrennikov, A.: Prequantum classical statistical field theory: Schrödinger dynamics of entangled systems as a classical stochastic process. Found. Phys. 41, 317–329 (2011)

    Article  Google Scholar 

  24. Khrennikov, A.: Description of composite quantum systems by means of classical random fields. Found. Phys. 40, 1051–1064 (2010)

    Article  Google Scholar 

  25. Khrennikov, A., Ohya, M., Watanabe, N.: Quantum probability from classical signal theory. Int. J. Quantum Inf. 9, 281–292 (2011)

    Article  Google Scholar 

  26. Ohya, M., Watanabe, N.: A new treatment of communication processes with Gaussian channels. Jpn. J. Ind. Appl. Math. 3, 197–206 (1986)

    Article  Google Scholar 

  27. Khrennikov, A.: Role of detectors and their proper calibration in inter-relation between classical and quantum optics. Opt. Eng. 51, Article number 069001 (2012)

    Google Scholar 

  28. Acacio de Barros, J., Suppes, P.: Quantum mechanics, interference, and the brain. Math. Psychol. 53, 306–313 (2009)

    Article  Google Scholar 

  29. Khrennikov, A.: On the physical basis of theory of “mental waves”. Neuroquantology 8, S71–S80 (2010)

    Article  Google Scholar 

  30. Khrennikov, A.: Quantum-like model of processing of information in the brain based on classical electromagnetic field. Biosystems 105(3), 250–262 (2011)

    Article  PubMed  Google Scholar 

  31. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge Press, Cambridge (2012)

    Google Scholar 

  32. Plotnitsky, A.: Reading Bohr: Physics and Philosophy. Springer, Heidelberg (2006)

    Google Scholar 

  33. Plotnitsky, A.: On the reasonable and unreasonable effectiveness of mathematics in classical and quantum Physics. Found. Phys. 41, 466–491 (2011)

    Article  Google Scholar 

  34. Khrennikov, A.: Towards a resolution of dilemma: nonlocality or nonobjectivity? Int. J. Theor. Phys. 51, 2488–2502 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Liberal Arts Division, Tokuyama College of Technology, Tokuyama, Japan

    Masanari Asano

  2. International Center for Mathematical Modeling in Physics and Cognitive Science, Linnaeus University, Växjö, Sweden

    Andrei Khrennikov

  3. Information Science, Tokyo University of Science, Tokyo, Japan

    Masanori Ohya & Yoshiharu Tanaka

  4. Department of Biological Science and Technology, Tokyo University of Science, Tokyo, Japan

    Ichiro Yamato

Authors
  1. Masanari Asano
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  2. Andrei Khrennikov
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  3. Masanori Ohya
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  4. Yoshiharu Tanaka
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  5. Ichiro Yamato
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Correspondence to Masanari Asano .

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Asano, M., Khrennikov, A., Ohya, M., Tanaka, Y., Yamato, I. (2015). Foundational Problems of Quantum Mechanics. In: Quantum Adaptivity in Biology: From Genetics to Cognition. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9819-8_9

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