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Journal of Optics

A semi-classical theory for matter-ray interaction

Jacques Moret‐Bailly, J -L Monnot

Published Mar 1, 1994• 1 citation
Publisher

Abstract

The stochastic electrodynamics (SED) or neoclassical electrodynamics (NED) explains a lot of optical experiments from the hypothesis that a stochastic electromagnetic field exists, equivalent to the half quantum per mode of quantum electrodynamics; we show that, in a semi-classical theory, this field must be introduced for coherence; we propose a non-linear classical model of the interaction between an atom and an electromagnetic field, to build a semi-classical theory.

DOI
10.1088/0150-536x/25/2/003

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The stochastic electrodynamics (SED) or neoclassical electrodynamics (NED) explains a lot of optical experiments from the hypothesis that a stochastic electromagnetic field exists, equivalent to the half quantum per mode of quantum electrodynamics; we show that, in a semi-classical theory, this field must be introduced for coherence; we propose a non-linear classical model of the interaction between an atom and an electromagnetic field, to build a semi-classical theory.
I propose that quantum mechanics is a stochastic theory and quantum phenomena derive from the existence of real vacuum stochastic fields filling space. I revisit stochastic electrodynamics (SED), a theory that studies classical systems of electrically charged particles immersed in an electromagnetic (zeropoint) radiation field with spectral density proportional to the cube of the frequency, Planck's constant appearing as the parameter fixing the scale. Asides from briefly reviewing known results, I make a detailed comparison between SED and quantum mechanics. Both theories make the same predictions when the stochastic equations of motion are of first order in Planck constant, but not in general. I propose that SED provides a clue for a realistic interpretation of quantum theory.
Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many “paradoxes” and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random “zero point radiation” is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, “self field” electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can “interact with themselves” in a non-linear fashion, and may thereby explain many quantum phenomena from a semi-classical viewpoint. Referred to as self fields, they have gone by other names in the literature: “evanesccent radiation”, “virtual photons”, and “vacuum fluctuations”. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the black-body radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.
The article “Insights from the classical atom,” by Petar Grujić and Nenad Simonović (Physics Today, May 2012, page 41), was interesting but incomplete. It left out stochastic electrodynamics (SED), an approach to classical mechanics that includes the effects of a proposed zero-point radiation background.The zero-point radiation is a Lorentz-invariant random distribution of energy into different modes of electromagnetic radiation. Quantum electrodynamics (QED) uses the hypothesis that the amplitudes of the Lorentz-invariant radiation are quantized, whereas SED uses the hypothesis that they are continuous.The motions of electric charges in SED are modeled using the equations of motion for a particle, often associated with a concrete visualization. SED is considered part of classical physics because of the continuous distribution of amplitudes. However, discrete values for energy and momentum emerge from SED without the ad hoc quantization conditions of QED.Stochastic electrodynamics has been investigated as a classical physics explanation for quantum phenomena. For instance, the blackbody radiation spectrum has been derived without quantum assumptions.11. T. H. Boyer, Phys. Rev. 182, 1374 (1969). https://doi.org/10.1103/PhysRev.182.1374 Lorentz-invariant radiation provides perturbations that mimic quantum phenomena such as the Casimir force, the van der Waals force, the Lamb shift, and the radius of the Bohr atom.22. M. Ibison, B. Haisch, Phys. Rev. A 54, 2737 (1996). https://doi.org/10.1103/PhysRevA.54.2737Physical chemistry provides many mathematical expressions that are often thought to be fundamentally quantum in nature. However, some of those expressions have been shown to emerge from both QED and SED. For example, the Schrödinger equation has been derived from SED,33. G. H. Goedecke, Found. Phys. 13, 1101 (1983); https://doi.org/10.1007/BF00728139 G. H. Goedecke, Found. Phys. 13, 1195 (1983). https://doi.org/10.1007/BF00727993 and the wavefunction in the SED Schrödinger equation is shown to have the a priori significance of position probability amplitude. A physical model based on SED has been developed to increase our understanding of both the diffraction of particle beams and the Pauli exclusion principle.44. A. F. Kracklauer, Found. Phys. Lett. 12, 441 (1999). https://doi.org/10.1023/A:1021629310707Quantum mechanics is often cited to justify chemical bonding on an elementary level. However, the visualizations used for chemical bonding are often based on mathematical expressions that can be derived from either QED or SED. Regardless of which turns out to be more accurate in physics experiments or more complete in mathematical description, the two theories overlap with regard to physical chemistry. Therefore, I propose that introductory chemistry taught in secondary schools can be rationalized as easily by references to SED as to QED.Either theory produces identical predictions for many experiments involving second-order correlations, squeezing (quadrature noise reduction), and the original Einstein-Podolsky-Rosen proposal.55. S. Chaturvedi, P. D. Drummond, Phys. Rev. A 55, 912 (1997). https://doi.org/10.1103/PhysRevA.55.912 However, SED is not completely equivalent to QED on a mathematical or physical level. The SED Schrödinger equation is incomplete, because there is a companion equation that has no counterpart in ordinary quantum mechanics and restricts initial conditions.33. G. H. Goedecke, Found. Phys. 13, 1101 (1983); https://doi.org/10.1007/BF00728139 G. H. Goedecke, Found. Phys. 13, 1195 (1983). https://doi.org/10.1007/BF00727993 Furthermore, the predictions of QED and SED are different with regard to high-order correlations in nonlinear optics.I agree fully with Grujić and Simonović that the classical atom is alive and well. Models of the atom based on SED are sufficiently accurate for many technological and most pedagogical applications. Even if the classical atom isn’t the most fundamental description of the physical world, it is still an important one.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. T. H. Boyer, Phys. Rev. 182, 1374 (1969). https://doi.org/10.1103/PhysRev.182.1374, Google ScholarCrossref, ISI2. M. Ibison, B. Haisch, Phys. Rev. A 54, 2737 (1996). https://doi.org/10.1103/PhysRevA.54.2737, Google ScholarCrossref, ISI3. G. H. Goedecke, Found. Phys. 13, 1101 (1983); https://doi.org/10.1007/BF00728139 , Google ScholarCrossref, ISIG. H. Goedecke, Found. Phys. 13, 1195 (1983). https://doi.org/10.1007/BF00727993, , Google ScholarCrossref, ISI4. A. F. Kracklauer, Found. Phys. Lett. 12, 441 (1999). https://doi.org/10.1023/A:1021629310707, Google ScholarCrossref, ISI5. S. Chaturvedi, P. D. Drummond, Phys. Rev. A 55, 912 (1997). https://doi.org/10.1103/PhysRevA.55.912, Google ScholarCrossref, ISI© 2013 American Institute of Physics.
During the last decades there has been a relatively extensive attempt to develop the theory of stochastic electrodynamics (SED) with a view to establishing it as the foundation for quantum mechanics. The theory had several important successes, but failed when applied to the study of particles subject to nonlinear forces. An analysis of the failure showed that its reasons are not to be ascribed to the principles of SED, but to the methods used to construct the theory, particularly the use of a Fokker-Planck approximation and perturbation theory. A new, non perturbative approach has been developed, called linear stochastic electrodynamics (LSED), of which a clean form is presented here. After introducing the fundamentals of SED, we discuss in detail the principles on which LSED is constructed. We pay attention to the fundamental issue of the mechanism that leads to the quantum behaviour of field and matter, and demonstrate that indeed LSED is a natural way to the quantum formalism by demanding its solutions to comply with a limited number of principles, each one with a clear physical meaning. As a further application of the principles of LSED we derive also the Planck distribution. In a final section we revisit some of the most tantalizing quandaries of quantum mechanics from the point of view offered by the present theory, and show that it offers a clear physical answer to them.
The Jaynes-Cummings paper treats the problem of one-atom interacting with one cavity mode with two alternative theories: quantum electrodynamics and semiclassical theory, and compares the predictions. The semiclassical theory was later extended to treat a single atom in free space interacting with a classical field including radiation reaction. The resulting theory was called Neoclassical theory, and is described by nonlinear optical Bloch equations. These nonlinear equations have shown up in a number of physical systems and were the subject of the famous Jaynes-Franken bet that was a prominent feature of the early Rochester Coherence and Quantum Optics Conferences. We will touch on all of these topics in a historical review.
We investigate in this chapter the general problem of the interaction of an atom (or a molecule) and a classical electromagnetic field. Its importance derives firstly from the fact that a large part of our knowledge of atoms is obtained from a study of the radiation they absorb or emit (we shall consider equally visible radiation and radio-frequency and X-rays) and, secondly, that the interaction with matter modifies the propagation of the electromagnetic field itself, notably through absorption, refraction or scattering. The interactions of atoms with light therefore encompass a vast range of physical effects that we could not hope to cover adequately in a single chapter. In this chapter we shall therefore present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell's equations. A rigorous description of the atom–light interaction would have to take into account the quantum nature of light. This we shall leave to Chapter 6. It turns out, nevertheless, that many important results can be obtained from the semi-classical viewpoint adopted here (although it is perhaps more appropriate to refer to this treatment as ‘semi-quantized’).