Skip to main content
SpringerLink
Log in

View of bunching and antibunching from the standpoint of classical signals

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

The similarity between classical wave mechanics and quantum mechanics was noted in the works of De Broglie, Schrödinger, “late” Einstein, Lamb, Lande, Mandel, Marshall, Santos, Boyer, and many others. We present a new wave model of quantum mechanics, the so-called prequantum classical statistical field theory, in which an analogy between some quantum phenomena and the classical theory of random fields is investigated. Quantum systems are interpreted as symbolic representations of such fields (not only for photons, cf. Lande and Lamb, but even for massive particles). All quantum averages and correlations (including composite systems in entangled states) can be represented as averages and correlations for classical random fields. We use the prequantum classical statistical field theory to obtain bunching and antibunching in the framework of classical signal theory. We note that antibunching at least is typically considered an essentially quantum (nonclassical) phenomenon.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Plotnitsky, J. Modern Optics, 54, 2393–2402 (2007).

    Article  Google Scholar 

  2. A. Plotnitsky, Epistemology and Probability: Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking (Fund. Theories Phys., Vol. 161), Springer, Berlin (2009).

    Google Scholar 

  3. W. H. Louisell, Quantum Statistical Properties of Radiation, Wiley, New York (1990).

    MATH  Google Scholar 

  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge Univ. Press, Cambridge (1995).

    Google Scholar 

  5. M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge Univ. Press, Cambridge (1997).

    Google Scholar 

  6. L. de la Pea and A. Cetto, The Quantum Dice: An Introduction to Stochastic Electrodynamics (Fund. Theories Phys., Vol. 75), Kluwer, Dordrecht (1996).

    Google Scholar 

  7. A. Casado, T. Marshall, and E. Santos, J. Opt. Soc. Am. B, 14, 494–502 (1997).

    Article  ADS  Google Scholar 

  8. G. Brida, M. Genovese, M. Gramegna, C. Novero, and E. Predazzi, Phys. Lett. A, 299, 121–124 (2002); arXiv:quant-ph/0203048v1 (2002).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. T. H. Boyer, “A brief survey of stochastic electrodynamics,” in: Foundations of Radiation Theory and Quantum Electrodynamics (A. Barut, ed.), Plenum, New York (1980), p. 49–63.

    Google Scholar 

  10. D. C. Cole, A. Rueda, and K. Danley, Phys. Rev. A, 63, 054101 (2001).

    Article  ADS  Google Scholar 

  11. Th. M. Nieuwenhuizen, “Classical phase space density for the relativistic hydrogen atom,” in: Quantum Theory: Reconsideration of Foundations (AIP Conf. Proc., Vol. 810, G. Adenier, A. Yu. Khrennikov, and Th. M. Nieuwenhuizen, eds.), AIP, Melville, N. Y., p. 198–210; arXiv:quant-ph/0511144v1 (2005).

    Google Scholar 

  12. E. Nelson, Quantum Fluctuation, Princeton Univ. Press, Princeton, N. J. (1985).

    Google Scholar 

  13. M. Davidson, J. Math. Phys., 20 (1865–1869).

  14. M. Davidson, “Stochastic models of quantum mechanics — a perspective,” in: Foundations of Probability and Physics — 4 (AIP Conf. Proc., Vol. 889, G. Adenier, A. Yu. Khrennikov, and C. A. Fuchs, eds.), AIP, Melville, N. Y. (2007), p. 106–119; arXiv:quant-ph/0610046v1 (2006).

    Google Scholar 

  15. A. Bach, J. Math. Phys., 14, 125–132 (1981).

    Article  MathSciNet  Google Scholar 

  16. A. Bach, Phys. Lett. A, 73, 287–288 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  17. V. I. Man’ko, J. Russian Laser Research, 17, 579–584 (1996).

    Article  Google Scholar 

  18. V. I. Man’ko and E. V. Shchukin, J. Russian Laser Research, 22, 545–560 (2001).

    Article  Google Scholar 

  19. Yu. M. Belousov and V.I. Man’ko, Density Matrix: Representations and Applications in Statistical Physics [in Russian], Moscow Inst. Phys. Tech., Moscow (2004).

    Google Scholar 

  20. M. A. Manko, V. I. Manko, and R. V. Mendes, J. Russian Laser Research, 27, 507–532 (2006).

    Article  Google Scholar 

  21. S. De Nicola, R. Fedele, M. A. Manko, and V. I. Manko, J. Russian Laser Research, 25, 1–29 (2004).

    Article  Google Scholar 

  22. G. ’t Hooft, “Quantum mechanics and determinism,” arXiv:hep-th/0105105v1 (2001).

  23. G. ’t Hooft, “The free-will postulate in quantum mechanics,” arXiv:quant-ph/0701097v1 (2007).

  24. H.-T. Elze, J. Phys. Conf. Ser., 174, 012009 (2009); arXiv:0906.1101v1 [quant-ph] (2009).

    Article  ADS  Google Scholar 

  25. H.-T. Elze, J. Phys. Conf. Ser., 67, 012016 (2007); arXiv:0704.2559v1 [quant-ph] (2007).

    Article  ADS  Google Scholar 

  26. V. V. Kisil, Europhys. Lett., 72, 873–879 (2005); arXiv:quant-ph/0506122v4 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  27. A. Einstein and L. Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta, Cambridge Univ. Press, Cambridge (1961).

    Google Scholar 

  28. A. Khrennikov, J. Phys. A, 38, 9051–9073 (2005); arXiv:quant-ph/0505228v4 (2005).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. A. Khrennikov, Found. Phys. Lett., 18, 637–650 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Khrennikov, Phys. Lett. A, 357, 171–176 (2006); arXiv:quant-ph/0602210v2 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. A. Khrennikov, Found. Phys. Lett., 19, 299–319 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  32. A. Khrennikov, Nuovo Cimento B, 121, 505–521 (2006); arXiv:hep-th/0604163v1 (2006).

    MathSciNet  ADS  Google Scholar 

  33. A. Khrennikov, Phys. E, 42, 287–292 (2010).

    Article  Google Scholar 

  34. A. Yu. Khrennikov, Theor. Math. Phys., 164, 1156–1162 (2010).

    Article  Google Scholar 

  35. A. Khrennikov, Nuovo Cimento B, 121, 1005–1021 (2006).

    MathSciNet  ADS  Google Scholar 

  36. M. Ohya and N. Watanabe, Japan. J. Appl. Math., 3, 197–206 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  37. A. Khrennikov, J. Modern Opt., 55, 2257–2267 (2008).

    Article  MATH  Google Scholar 

  38. A. Khrennikov, Europhys. Lett., 88, 40005 (2009).

    Article  ADS  Google Scholar 

  39. A. Khrennikov, Europhys. Lett., 90, 40004 (2010).

    Article  ADS  Google Scholar 

  40. A. Khrennikov, J. Russian Laser Research, 31, 191–200 (2010).

    Article  Google Scholar 

  41. I. V. Volovich, “Photon antibunching, sub-Poisson statistics, and Cauchy-Bunyakovsky and Bell’s inequalities,” arXiv:1106.1892v1 [quant-ph] (2011).

  42. I. Volovich, “Quantum cryptography in space and Bell’s theorem,” in: Foundations of Probability and Physics (Quantum Prob. White Noise Anal., Vol. 13, A. Khrennikov, ed.), World Scientific, River Edge, N. J. (2001), p. 364–372.

    Chapter  Google Scholar 

  43. M. Ohya and I. Volovich, Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems, Springer, New York (2011).

    Book  MATH  Google Scholar 

  44. A. Khrennikov, Contextual Approach to Quantum Formalism (Fund. Theories Phys., Vol. 160), Springer, Dordrecht (2009).

  45. A. Khrennikov, “Born’s rule from measurements of classical signals by threshold detectors which are properly calibrated,” arXiv:1105.4269v2 [quant-ph] (2011).

  46. A. Khrennikov, M. Ohya, and N. Watanabe, J. Russian Laser Research, 31, 462–468 (2010).

    Article  Google Scholar 

  47. Y.I. Ozhigov, Russian Microelectronics, 35, 53–65 (2006).

    Article  Google Scholar 

  48. Y. I. Ozhigov, “Dynamical diffusion as the approximation of one quantum particle dynamics,” arXiv:quant-ph/0702237v2 (2007).

  49. Y. I. Ozhigov, “Simulation of quantum dynamics via classical collective behavior,” arXiv:quant-ph/0602155v1 (2006).

  50. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, N. J. (1955).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Växjö, Sweden

    A. Yu. Khrennikov

Authors
  1. A. Yu. Khrennikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Khrennikov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 1, pp. 155–176, July, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khrennikov, A.Y. View of bunching and antibunching from the standpoint of classical signals. Theor Math Phys 172, 1017–1034 (2012). https://doi.org/10.1007/s11232-012-0092-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-012-0092-8

Keywords

Search

Navigation