Skip to main content
SpringerLink
Log in

Towards a Field Model of Prequantum Reality

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We start with an extended review of classical field approaches to quantum mechanics (QM). In particular, we present Einstein’s dream to exclude particles totally from quantum physics. We also describe the evolution of Einstein’s views: from the invention of the light quantum to a purely classical field picture of quantum reality. Then we present briefly a new field-type model, prequantum classical statistical field theory (PCSFT), which was recently developed in a series of the author’s papers. PCSFT reproduces basic predictions of QM, including correlations for entangled systems. Finally, we present a mathematical model which justifies the usage of Gaussian random fields in PCSFT. Such fields provide an approximative description of extremely dense trains of wave pulses. Possible physical sources of such pulses are discussed.

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

Notes

  1. This interpretation was later elaborated by Leslie Ballentine [18, 19] who used the term statistical interpretation.

  2. Originally the concept of photon was invented by physical chemist G.N. Lewis who really considered photons as light particles that transmit radiation from one atom to another. Wave-like properties of photon were attributed to guiding ghost field. See Lamb’s “Anti-photon” [22, pp. 201–211], for more details.

  3. The semiclassical approach can describe a number of quantum effects, e.g., the photoelectric effect (G. Wentzel and G. Beck, 1926; see W.E. Lamb and M.O. Scully [24] for more detailed calculations).

  4. Unfortunately, I was not able to find in Schrödinger’s papers any explanation of the impossibility to divide this cloud into a few smaller clouds, i.e., no attempt to explain the fundamental discreteness of the electric charge.

  5. The account of this evolution sketched here is courtesy of Arkady Plotnitsky (private communication, see also [28]). For Einstein’s later views, see especially both of his contributions to the Schilpp volume [29].

  6. For example, the Schrödinger dynamics is performed on this time scale.

References

  1. Mie, G.: Grundlagen einer Theorie der Materie. Zweite Mittelung. Ann. Phys. 39, 1–40 (1912)

    Article  Google Scholar 

  2. Mie, G.: Grundlagen einer Theorie der Materie. Dritte Mittelung. Ann. Phys. 40, 1–66 (1913)

    Article  MATH  Google Scholar 

  3. Bohr, N., Kramers, H.A., Slater, J.C.: Über die Quantentheorie der Strahlung. Z. Phys. 24, 69–87 (1920)

    ADS  Google Scholar 

  4. Einstein, A., Infeld, L.: Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta. Simon & Schuster, New York (1961)

    MATH  Google Scholar 

  5. Boyer, T.H.: A brief survey of stochastic electrodynamics. In: Barut, A.O. (ed.) Foundations of Radiation Theory and Quantum Electrodynamics, pp. 141–162. Plenum, New York (1980)

    Google Scholar 

  6. De la Pena, L., Cetto, A.M.: The Quantum Dice: An Introduction to Stochastic Electrodynamics. Kluwer Academic, Dordrecht (1996)

    Google Scholar 

  7. Cole, D.: Simulation results related to stochastic electrodynamics. In: Adenier, G., Khrennikov, A.Yu., Nieuwenhuizen, Th.M. (eds.) Quantum Theory: Reconsideration of Foundations-3. Conference Proceedings, Melville, NY, vol. 810, pp. 99–113 Am. Inst. Phys., New York (2006)

    Google Scholar 

  8. Nieuwenhuizen, Th.M.: Classical phase space density for relativistic electron. In: Adenier, G., Khrennikov, A.Yu., Nieuwenhuizen, Th.M. (eds.) Quantum Theory: Reconsideration of Foundations-3. Conference Proceedings, Melville, NY, vol. 810, pp. 198–210. Am. Inst. Phys., New York (2006)

    Google Scholar 

  9. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  10. Louisell, H.H.: Quantum Statistical Properties of Radiation. Wiley, New York (1973)

    Google Scholar 

  11. Mandel, L., Wolf, E.: Optical Coherence and Quantum Optics. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  12. Khrennikov, A.: A pre-quantum classical statistical model with infinite-dimensional phase space. J. Phys. A, Math. Gen. 38, 9051–9073 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Khrennikov, A.: Prequantum classical statistical field theory: time scale of fluctuations. Dokl. Math. 75, 456–459 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Khrennikov, A.: Subquantum detection theory. Physica E Low-Dimens. Syst. Nanostruct. 42, 287–292 (2010)

    Article  ADS  Google Scholar 

  15. Khrennikov, A.: An analogue of the Heisenberg uncertainty relation in prequantum classical field theory. Phys. Scr. 81(6), 065001 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  16. Khrennikov, A.: Pairwise correlations in a three-partite quantum system from a prequantum random field. J. Russ. Laser Res. 31(2), 191–200 (2010)

    Article  Google Scholar 

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

    Google Scholar 

  18. Ballentine, L.E.: The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42, 358–381 (1989)

    Article  ADS  Google Scholar 

  19. Ballentine, L.E.: Quantum Mechanics. Prentice Hall, Englewood Cliffs (1989)

    Google Scholar 

  20. Lande, A.: Foundations of Quantum Theory. Yale University Press, New Haven (1955)

    MATH  Google Scholar 

  21. Lande, A.: New Foundations of Quantum Mechanics. Cambridge University Press, Cambridge (1965)

    MATH  Google Scholar 

  22. Lamb, W.E.: The Interpretation of Quantum Mechanics. Rinton Press, Princeton (2001). (Edited and annotated by Mehra, Ja).

    MATH  Google Scholar 

  23. Einstein, A.: On the theory of light quanta and the question of localization of electromagnetic energy. Arch. Sci. Phys. Nat. 29, 525–528 (1910). In: Howard, D. (ed.) The Collected Papers of Albert Einstein. The Swiss Years: Writings, 1909–1911, pp. 207–208. Princeton University Press, Princeton (1993)

    Google Scholar 

  24. Lamb, W.E., Scully, M.O.: The photoelectric effect without photons. In: Polarization, Matter and Radiation. Jubilee Volume in Honour of Alfred Kasiler, pp. 363–369. Press of University de France, Paris (1969)

    Google Scholar 

  25. Mukunda, N.: The story of the photon. Resonance 5, 35–51 (2000)

    Article  Google Scholar 

  26. Hofmann, H.F.: Quantum noise and spontaneous emission in semiconductor laser devices. Institut für Technische Physik, Deutsches Zentrum für Luft und Raumfahrt, Stuttgard (1999)

  27. Lockwood, M.: What Schrödinger have learned from his cat. In: Bitbol, M., Darrigol, O., Schrödinger, E. (eds.) Philosophy and the Birth of Quantum Mechanics, pp. 380–390. Editions Frontieres, Gif-sur-Yvette (1992)

    Google Scholar 

  28. Plotnitsky, A.: Epistemology and Probability: Bohr, Heisenberg, Schrödinger, and the Nature of Quantum-Theoretical Thinking. Springer, Heidelberg (2009)

    Google Scholar 

  29. Schilpp, P.A.: Albert Einstein: Autobiographical Notes. Open Court Publ. Company, Chicago (1979)

    Book  Google Scholar 

  30. Ritov, S.M.: Introduction to Statistical Radiophysics. Nauka, Fizmatlit, Moscow (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, Växjö, 35195, Sweden

    Andrei Khrennikov

Authors
  1. Andrei Khrennikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrei Khrennikov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khrennikov, A. Towards a Field Model of Prequantum Reality. Found Phys 42, 725–741 (2012). https://doi.org/10.1007/s10701-011-9611-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9611-y

Keywords

Search

Navigation