Abstract
In this paper, I argue that light is a continuous classical electromagnetic wave, while the observed so-called quantum nature of the interaction of light with matter is connected to the discrete (atomic) structure of matter and to the specific nature of the light–atom interaction. From this point of view, the Born rule for light is derived, and the double-slit experiment is analysed in detail. I show that the double-slit experiment can be explained without using the concept of a “photon”, solely on the basis of classical electrodynamics. I show that within this framework, the Heisenberg uncertainty principle for a “photon” has a simple physical meaning not related to the fundamental limitations in accuracy of the simultaneous measurement of position and momentum or time and energy.
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References
Taylor, G.I.: Interference fringes with feeble light. Proc. Camb. Philos. Soc. 15(1), 114–115 (1909)
Dimitrova, T.L., Weis, A.: The wave-particle duality of light: a demonstration experiment. Am. J. Phys. 76(2), 137–142 (2008)
Rashkovskiy, S.A.: A rational explanation of wave-particle duality of light. In: SPIE Optical Engineering \(+\) Applications, pp. 88321O–88321O. International Society for Optics and Photonics (2013)
Holland, P.R.: The Quantum Theory of Motion: An Account of the De Broglie–Bohm Causal Interpretation of Quantum Mechanics. Cambridge university press, Cambridge (1995)
Auletta, G.: Foundations and Interpretation of Quantum Mechanics. World Scientific, Singapore (2000)
Bacciagaluppi, G.: The Modal Interpretation of Quantum Mechanics. Cambridge University Press, Cambridge (2006)
Bohm, D., Hiley, B.J.: The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge, London (2006)
Ballentine, L.E.: The statistical interpretation of quantum mechanics. Rev. Mod. Phys. 42(4), 358 (1970)
Cramer, J.G.: The transactional interpretation of quantum mechanics. Rev. Mod. Phys. 58(3), 647 (1986)
Omnès, R.: Consistent interpretations of quantum mechanics. Rev. Mod. Phys. 64(2), 339 (1992)
Schlosshauer, M.: Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76(4), 1267 (2005)
Tegmark, M.: The interpretation of quantum mechanics: many worlds or many words? Fortschr. der Phys. 46, 855–862 (1998)
Einstein, A.: Zum gegenwärtigen Stande des Strahlungsproblems. Phys. Z. 10, 185–193 (1909)
Einstein, A.: Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung. Phys. Z. 10, 817–825 (1909)
Pais, A.: Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press, Oxford (1986). (Specifically, Born mentioned about Einstein’s never-published attempts to develop a “ghost-field” theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell’s equations)
Messiah, A.: Quantum Mechanics. Dover Publications Inc., New York (1999)
Bohr, N., Kramers, H.A., Slater, J.C.: LXXVI. The quantum theory of radiation. Lond. Edinb. Dublin Philos. Mag. J. Sci. 47(281), 785–802 (1924)
Lamb Jr, W.E.: Anti-photon. Appl. Phys. B 60, 77–84 (1995)
Lamb, W.E.: The Interpretation of Quantum Mechanics. Rinton Press, Inc., Princeton (2001). (Edited and annotated by Mehra, Ja.)
Lande, A.: New Foundations of Quantum Mechanics. Cambridge Univ. Press, Cambridge (1965)
Muthukrishnan, A., Scully, M.O., Zubairy, M.S.: The concept of the photon-revisited. OPN Trends Suppl. Opt. Photonics News 14(10), 18–27 (2003)
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)
Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)
Dirac, P.A.M.: Relativity quantum mechanics with an application to Compton scattering. Proc. R. Soc. Lond. A 111, 405-423 (1926)
Dirac, P.A.M.: The Compton effect in wave mechanics. Proc. Camb. Philos. Soc. 23, 500–507 (1926)
Gordon, W.: Der Comptoneffekt nach der Schrödingerschen Theorie. Zeit. f. Phys. 40, 117–133 (1926)
Klein, O., Nishina, Y.: Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac. Z. Phys. 52(11–12), 853–869 (1929)
Klein, O., Nishina, Y.: On the scattering of radiation by free electrons according to Dirac’s new relativistic quantum dynamics. In: The Oskar Klein Memorial Lectures: 1988–1999, vol. 1, pp. 253-272 (2014)
Barut, A.O., Van Huele, J.F.: Quantum electrodynamics based on self-energy: lamb shift and spontaneous emission without field quantization. Phys. Rev. A 32(6), 3187–3195 (1985)
Stroud, C.R. Jr., Jaynes, E.T.: Long-term solutions in semiclassical radiation theory. Phys. Rev. A 1(1), 106-121 (1970)
Crisp, M.D., Jaynes, E.T.: Radiative effects in semiclassical theory. Phys. Rev. 179(5), 1253–1261 (1969)
Barut, A.O., Dowling, J.P.: Self-field quantum electrodynamics: the two-level atom. Phys. Rev. A 41(5), 2284–2294 (1990)
Nesbet, R.K.: Spontaneous emission in semiclassical radiation theory. Phys. Rev. A 4(1), 259–264 (1971)
Hanbury Brown, R., Twiss, R.Q.: Correlation between photons in two coherent beams of light. Nature (London) 177, 27–29 (1956)
Brown, R.H., Twiss, R.Q.: A test of a new type of stellar interferometer on Sirius. Nature (London) 178, 1046–1048 (1956)
Kracklauer, A.F.: What do correlations tell us about photons? In.: Roychoudhuri C., Kracklauer A.F., Creath K. (eds.) The Nature of Light: What Are Photons? Art-Number 66640H, Proc. SPIE 6664 (2007)
Kracklauer, A.F., Rangacharyulu, C., Roychoudhuri, C., Brooks, H.J., Carroll, J., Khrennikov, A.: Is indivisible single photon really essential for quantum communications, computing and encryption? In.: Roychoudhuri, C., Kracklauer, A.F., Khrennikov, A.Y. (eds.) The Nature of Light: What are Photons? III, Art.-Number 74210Y, Proc. SPIE 7421 (2009)
Roychoudhuri, C., Kracklauer, A.F., Creath, K. (eds.): The Nature of Light: What Are Photons? Proc. SPIE 6664 (2007)
Roychoudhuri, C., Kracklauer, A.F., Khrennikov, A.Y. (eds.): The Nature of Light: What are Photons? III, Proc. SPIE 7421 (2009)
Khrennikov, A.: Nonlinear Schrödinger equations from prequantum classical statistical field theory. Phys. Lett. A 357, 171–176 (2006)
Khrennikov, A.: Quantum probabilities and violation of CHSH-inequality from classical random signals and threshold type detection scheme. Prog. Theor. Phys. 128(1), 31–58 (2012)
Purcell, E.M.: The question of correlation between photons in coherent light rays. Nature (London) 178, 1449–1450 (1956)
Mandel, L.: Fluctuations of photon beams and their correlations. Proc. Phys. Soc. 72(6), 1037 (1958)
Mandel, L.: V fluctuations of light beams. Prog. Opt. 2, 181–248 (1963)
Mandel, L.: Intensity fluctuations of partially polarized light. Proc. Phys. Soc. 81(6), 1104 (1963)
Mandel, L., Sudarshan, E.G., Wolf, E.: Theory of photoelectric detection of light fluctuations. Proc. Phys. Soc. 84(3), 435 (1964)
Landau, L.D., Lifshitz, E.M.: Quantum Mechanics: Non-Relativistic Theory, vol. 3, 3rd edn. Pergamon Press, USA (1977)
Wiener, O.: Stehende Lichtwellen und die Schwingungsrichtung polarisirten Lichtes. Ann. Phys. Chem. 40, 203–243 (1890)
Drude, P., Nernst, W.: Wiedem. Ann 45, 460 (1892)
Ives, H.E., Fry, T.C.: J. Opt. Soc. Am. 23, 73 (1933)
Born, M., Wolf, E.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, Cambridge (1999)
Schrödinger, E.: Uber den Comptoneffekt. Ann. Phys. 82, 257–264 (1927)
Sommerfeld, A.: Wave-Mechanics: Supplementary Volume to Atomic Structure and Spectral Lines. Dutton, New York (1934)
Berestetskii, V.B., Lifshitz, E.M., Pitaevskii, L.P.: Quantum Electrodynamics, vol. 4, 2nd edn. Butterworth-Heinemann, London (1982)
Keldysh, L.V.: Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307 (1965)
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, vol. 2, 4th edn. Butterworth-Heinemann, London (1975)
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Funding was provided by Tomsk State University competitiveness improvement program.
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Rashkovskiy, S.A. Quantum mechanics without quanta: the nature of the wave–particle duality of light. Quantum Stud.: Math. Found. 3, 147–160 (2016). https://doi.org/10.1007/s40509-015-0063-5
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DOI: https://doi.org/10.1007/s40509-015-0063-5
Keywords
- Wave–particle duality of light
- Classical electrodynamics
- Double-slit experiment
- Born rule
- Heisenberg uncertainty principle