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AIP conference proceedings

Simulation Results Related to Stochastic Electrodynamics

Daniel C. Cole

Published Jan 1, 2006• 12 citations
Publisher

Abstract

Stochastic electrodynamics (SED) is a classical theory of nature advanced significantly in the 1960s by Trevor Marshall and Timothy Boyer. Since then, SED has continued to be investigated by a very small group of physicists. Early investigations seemed promising, as SED was shown to agree with quantum mechanics (QM) and quantum electrodynamics (QED) for a few linear systems. In particular, agreement was found for the simple harmonic electric dipole oscillator, physical systems composed of such oscillators and interacting electromagnetically, and free electromagnetic fields with boundary conditions imposed such as would enter into Casimir‐type force calculations. These results were found to hold for both zero‐point and non‐zero temperature conditions. However, by the late 1970s and then into the early 1980s, researchers found that when investigating nonlinear systems, SED did not appear to provide agreement with the predictions of QM and QED. A proposed reason for this disagreement was advocated by Boyer and Cole that such nonlinear systems are not sufficiently realistic for describing atomic and molecular physical systems, which should be fundamentally based on the Coulombic binding potential. Analytic attempts on these systems have proven to be most difficult. Consequently, in recent years more attention has been placed on numerically simulating the interaction of a classical electron in a Coulombic binding potential, with classical electromagnetic radiation acting on the classical electron. Good agreement was found for this numerical simulation work as compared with predictions from QM. Here this worked is reviewed and possible directions are discussed. Recent simulation work involving subharmonic resonances for the classical hydrogen atom is also discussed; some of the properties of these subharmonic resonances seem quite interesting and unusual.

DOI
10.1063/1.2158714

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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.

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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.

Physics Today•Apr 30, 2013•2 citations

Stochastic electrodynamics and the interpretation of quantum theory

Emilio Santos

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.

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Wayne Huang, Herman Batelaan

Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.

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Theo M. Nieuwenhuizen, Matthew Liska

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Aloysius F. Kracklauer

Abstract An extended version of Stochastic Electrodynamics (SED) which provides an interpretation of Quantum Mechanics free of its preternatural aspects is reviewed briefly. In addition, recent simulations of the hydrogen ground state based on SED which have been inconclusive are criticized for having employed only a restricted understating of the physical consequences of the hypothetical underpinning of SED.

Journal of Physics Conference Series•Jun 1, 2019•0 citations
Stochastic electrodynamics (SED) is a classical theory of nature advanced significantly in the 1960s by Trevor Marshall and Timothy Boyer. Since then, SED has continued to be investigated by a very small group of physicists. Early investigations seemed promising, as SED was shown to agree with quantum mechanics (QM) and quantum electrodynamics (QED) for a few linear systems. In particular, agreement was found for the simple harmonic electric dipole oscillator, physical systems composed of such oscillators and interacting electromagnetically, and free electromagnetic fields with boundary conditions imposed such as would enter into Casimir‐type force calculations. These results were found to hold for both zero‐point and non‐zero temperature conditions. However, by the late 1970s and then into the early 1980s, researchers found that when investigating nonlinear systems, SED did not appear to provide agreement with the predictions of QM and QED. A proposed reason for this disagreement was advocated by Boyer and Cole that such nonlinear systems are not sufficiently realistic for describing atomic and molecular physical systems, which should be fundamentally based on the Coulombic binding potential. Analytic attempts on these systems have proven to be most difficult. Consequently, in recent years more attention has been placed on numerically simulating the interaction of a classical electron in a Coulombic binding potential, with classical electromagnetic radiation acting on the classical electron. Good agreement was found for this numerical simulation work as compared with predictions from QM. Here this worked is reviewed and possible directions are discussed. Recent simulation work involving subharmonic resonances for the classical hydrogen atom is also discussed; some of the properties of these subharmonic resonances seem quite interesting and unusual.
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 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.
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.
Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy 1 2 ℏ ω in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham–Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full 3 d problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modellings the atom ionises at longer times.