Classical Electromagnetic Zero-point Radiation Research Articles

Disguised electromagnetic connections in classical electron theory

In the first quarter of the 20th century, physicists were not aware of the existence of classical electromagnetic zero-point radiation nor of the importance of special relativity. Inclusion of these aspects allows classical electron theory to be extended beyond its 19th century successes. Here we review spherical electromagnetic radiation modes in a conducting-walled spherical cavity and connect these modes to classical electromagnetic zero-point radiation and to electromagnetic scale invariance. Then we turn to the scattering of radiation in classical electron theory within a simple approximation. We emphasize that, in steady-state, the interaction between matter and radiation is disguised so that the mechanical motion appears to occur without the emission of radiation, even though the particle motion is actually driven by classical electromagnetic radiation. It is pointed out that, for nonrelativistic particles, only the harmonic oscillator potential taken in the low-velocity limit allows a consistent equilibrium with classical electromagnetic zero-point radiation. For relativistic particles, only the Coulomb potential is consistent with electrodynamics. The classical analysis places restrictions on the value of e 2/ℏc.

Thermal radiation equilibrium: (nonrelativistic) classical mechanics versus (relativistic) classical electrodynamics

Physics students continue to be taught the erroneous idea that classical physics leads inevitably to energy equipartition, and hence to the Rayleigh–Jeans law for thermal radiation equilibrium. Actually, energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal equilibrium from three different perspectives. First, we contrast the thermal equilibrium of nonrelativistic mechanical oscillators (where point collisions are allowed and frequency is irrelevant) with the equilibrium of relativistic radiation modes (where frequency is crucial). The Rayleigh–Jeans law appears from applying a dipole-radiation approximation to impose the nonrelativistic mechanical equilibrium on the radiation spectrum. In this discussion, we note the possibility of zero-point energy for relativistic radiation, which possibility does not arise for nonrelativistic classical-mechanical systems. Second, we turn to a simple electromagnetic model of a harmonic oscillator and show that the oscillator is fully in radiation equilibrium (which involves all radiation multipoles, dipole, quadrupole, etc) with classical electromagnetic zero-point radiation, but is not in equilibrium with the Rayleigh–Jeans spectrum. Finally, we discuss the contrast between the flexibility of nonrelativistic mechanics with its arbitrary potential functions allowing separate scalings for length, time, and energy, with the sharply-controlled behavior of relativistic classical electrodynamics with its single scaling connecting together the scales for length, time, and energy. It is emphasized that within classical physics, energy-sharing, velocity-dependent damping is associated with the low-frequency, nonrelativistic part of the Planck thermal radiation spectrum, whereas acceleration-dependent radiation damping is associated with the high-frequency adiabatically-invariant and Lorentz-invariant part of the spectrum corresponding to zero-point radiation.

Relativity and radiation balance for the classical hydrogen atom in classical electromagnetic zero-point radiation

When teaching modern physics, every instructor must deal with the apparent failure of classical physics to prevent the radiation collapse of the nuclear atom. Here we review the understanding of the classical hydrogen atom in classical electromagnetic zero-point radiation, and emphasize the importance of special relativity. The crucial missing ingredient in earlier calculational attempts (both numerical and analytic) is the use of valid approximations to the full relativistic analysis. It is pointed out that the nonrelativistic time Fourier expansion coefficients given by Landau and Lifshitz are in error as the electromagnetic description of a charged particle in a Coulomb potential, and, because of this error, Marshall and Claverie’s conclusion regarding the failure of radiation balance is invalid. Rather, using Marshall and Claverie’s calculations, but restricted to lowest nonvanishing order in the orbital eccentricity (where the nonrelativistic orbit is a valid approximation to the fully relativistic electromagnetic orbit) radiation balance for classical electromagnetic zero-point radiation is shown to hold at the fundamental frequencies and associated first overtones.

Particle Brownian motion due to random classical radiation: superfluid-like behavior in the presence of classical zero-point radiation

Nonrelativistic classical mechanics allows no fundamental transition between low-velocity and high-velocity forms of behavior, nor between low-temperature and high-temperature forms. In contrast, classical electrodynamics, which is a relativistic theory, allows fundamental transitions in velocity. Furthermore, the inclusion within the classical theory of Lorentz-invariant classical zero-point radiation allows classical electrodynamics to distinguish high-temperature and low-temperature forms of behavior. Because electromagnetism is a relativistic theory, it may provide a thermal radiation bath which gives rise to phenomena in Brownian motion which are not included in a model with a thermal bath based upon nonrelativistic particles. Here we explore the Brownian motion of a classical electric-dipole particle in random classical radiation, making use of the calculations of Einstein and Hopf. The Brownian motion as a function of temperature is analyzed in terms of the mean-square velocity and the diffusion constant for four different classical radiation spectra: the Rayleigh–Jeans spectrum, the Planck spectrum without zero-point radiation, the zero-point radiation spectrum, and the Planck spectrum including zero-point radiation. We illustrate how the inclusion of classical electromagnetic zero-point radiation alters Brownian motion behavior between high-temperature and low-temperature forms. For the Planck spectrum with zero-point radiation, the high-temperature Brownian motion agrees with some aspects found from nonrelativistic mechanics, while the low-temperature behavior includes some aspects analogous to superfluid behavior. At sufficiently low temperatures, the Brownian particle has an increasing mean-square velocity and more rapid diffusion with decreasing temperature due to the increasing dominance of the classical electromagnetic zero-point radiation.

Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. The first part of this article addresses the concern by some about the related disturbing concept of “extracting energy” from this formally, enormous source of energy. The second part of this article introduces a new method for calculating probabilities of fields in SED, which can be extended to linear oscillators in SED.

Equilibrium for classical zero-point radiation: detailed balance under scattering by a classical charged harmonic oscillator

It has been shown repeatedly over a period of 50 years that the use of relativistic classical physics and the inclusion of classical electromagnetic zero-point radiation leads to the Planck blackbody spectrum for classical radiation equilibrium. However, none of this work involves scattering calculations. In contrast to this work, currently accepted physical theory connects classical physics to only the Rayleigh-Jeans spectrum. Indeed, in the past, it has been shown that a nonlinear classical oscillator (which is necessarily a nonrelativistic scattering system) achieves equilibrium only for the Rayleigh-Jeans spectrum where the random radiation present at the frequency of the second harmonic of the oscillator motion has the same energy per normal mode as the radiation present at the fundamental frequency. Here we continue work emphasizing the importance of relativistic versus nonrelativistic analysis. We consider the scattering of random classical radiation by a charged harmonic oscillator of small but non-zero oscillatory amplitude (which can be considered as a relativistic scattering system) and show that detailed radiation balance holds not only at the fundamental frequency of the oscillator but through the first harmonic corresponding to quadrupole scattering, provided that the radiation energy per normal mode at the first harmonic is double the radiation energy per normal mode at the fundamental frequency. This condition corresponds exactly to the zero-point radiation spectrum which is linear in frequency. It is suggested that for this relativistic scattering system, the detailed balance for zero-point radiation holds not only for the fundamental and first harmonic but extends to all harmonics. Here we have the first example of an explicit relativistic classical scattering calculation; equilibrium corresponds not to the Rayleigh-Jeans spectrum, but rather corresponds to the Lorentz-invariant zero-point radiation spectrum.

Blackbody radiation in classical physics: A historical perspective

We point out that current textbooks of modern physics are a century out-of-date in their treatment of blackbody radiation within classical physics. Relativistic classical electrodynamics including classical electromagnetic zero-point radiation gives the Planck spectrum with zero-point radiation as the blackbody radiation spectrum. In contrast, nonrelativistic mechanics cannot support the idea of zero-point energy; therefore, if nonrelativistic classical statistical mechanics or nonrelativistic mechanical scatterers are invoked for radiation equilibrium, one arrives at only the low-frequency Rayleigh-Jeans part of the spectrum, which involves no zero-point energy, and does not include the high-frequency part of the spectrum involving relativistically invariant classical zero-point radiation. Here, we first discuss the correct understanding of blackbody radiation within relativistic classical physics, and then we review the historical treatment. Finally, we point out how the presence of Lorentz-invariant classical zero-point radiation and the use of relativistic particle interactions transform the previous historical arguments, so as now to give the Planck spectrum including classical zero-point radiation. Within relativistic classical electromagnetic theory, Planck's constant ℏ appears as the scale of source-free zero-point radiation.

Understanding the Planck blackbody spectrum and Landau diamagnetism within classical electromagnetism

Electromagnetism is a relativistic theory, and one must exercise care in coupling this theory with nonrelativistic classical mechanics and with nonrelativistic classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: (1) the neglect of classical electromagnetic zero-point radiation, and (2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we review the treatment of classical blackbody radiation, and show that the presence of Lorentz-invariant classical electromagnetic zero-point radiation can explain both the Planck blackbody spectrum and Landau diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statistical mechanics is applied only in the low-frequency limit when zero-point energy makes no contribution.

Classical Zero-Point Radiation and Relativity: The Problem of Atomic Collapse Revisited

The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point radiation, and 2) the importance of special relativity. In classes in modern physics today, the problem of atomic collapse is still mentioned in the historical context of the early 20th century. However, the classical problem of atomic collapse is currently being treated in the presence of classical zero-point radiation where the problem has been transformed. The presence of classical zero-point radiation indeed keeps the electron from falling into the Coulomb potential center. However, the old collapse problem has been replaced by a new problem where the zero-point radiation may give too much energy to the electron so as to cause self-ionization. Special relativity may play a role in understanding this modern variation on the atomic collapse problem, just as relativity has proved crucial for a classical understanding of blackbody radiation.

Discrete Excitation Spectrum of a Classical Harmonic Oscillator in Zero-Point Radiation

We report that upon excitation by a single pulse, a classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation exhibits a discrete harmonic spectrum in agreement with that of its quantum counterpart. This result is interesting in view of the fact that the vacuum field is needed in the classical calculation to obtain the agreement.

Contrasting Classical and Quantum Vacuum States in Non-inertial Frames

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. Based upon the classical analysis, it is suggested that the claimed heating effects of acceleration through the vacuum may not exist in nature.

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell’s equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.

Any classical description of nature requires classical electromagnetic zero-point radiation

Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation to account for the Casimir forces between parallel conducting plates at low temperatures. This zero-point radiation leads to classical explanations for several phenomena that are usually regarded as requiring quantum physics. We provide a brief overview of classical electromagnetic theory including classical zero-point radiation and note the areas of agreement and disagreement between the classical and quantum theories, both of which contain Planck’s constant.

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example.

Connecting Blackbody Radiation, Relativity, and Discrete Charge in Classical Electrodynamics

It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the scales of length, time, and energy. Indeed, there are analogies between the electrostatic forces for groups of particles of discrete charge and the van der Waals forces in equilibrium thermal radiation. The differing Lorentz- or Galilean-transformation properties of the zero-point radiation spectrum and the Rayleigh-Jeans spectrum are noted in connection with their scaling properties. Also, the thermal effects of acceleration within classical electromagnetism are related to the existence of thermal equilibrium within a gravitational field. The unique scaling and phase-space properties of a discrete charge in the Coulomb potential suggest the possibility of an equilibrium between the zero-point radiation spectrum and matter which is universal (independent of the particle mass), and an equilibrium between a universal thermal radiation spectrum and matter where the matter phase space depends only upon the ratio mc^2/kT. The observations and qualitative suggestions made here run counter to the ideas of currently accepted quantum physics.

Comments on Cole and Zou's Calculation of the Hydrogen Ground State in Classical Physics

Cole and Zou's computer-simulation calculation of the hydrogen ground state in classical electrodynamics with classical electromagnetic zero-point point radiation suggests that the problem of atomic collapse in atomic physics amy have been solved. Analytic calculations of the early 1980s do not contradict the new results.

Quantum mechanical ground state of hydrogen obtained from classical electrodynamics

The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to agree closely with the probability density distribution of Schrödinger's wave equation for the ground state of hydrogen. These results again raise the possibility that the main tenets of stochastic electrodynamics (SED) are correct.

Thermodynamics of Blackbody Radiation Via Classical Physics for Arbitrarily Shaped Cavities with Perfectly Conducting Walls

An analysis is carried out involving reversible thermodynamic operations on arbitrarily shaped small cavities in perfectly conducting material. These operations consist of quasistatic deformations and displacements of cavity walls and objects within the cavity. This analysis necessarily involves the consideration of Casimir-like forces. Typically, even for the simplest of geometrical structures, such calculations become quite complex, as they need to take into account changes in singular quantities. Much of this complexity is reduced significantly here by working directly with the change in electromagnetic fields as a result of the deformation and displacement changes. A key result of this work is the derivation that for such cavity structures, classical electromagnetic zero-point radiation is the appropriate spectrum at a temperature of absolute zero to ensure that the reversible deformation operations obey both isothermal and adiabatic conditions. In addition, a generalized Wien displacement law is obtained from the demand that the change in entropy of the radiation in these arbitrarily shaped structures must be a state function of temperature and frequency.

Reinvestigation of the thermodynamics of blackbody radiation via classical physics.

A key part of the early thermodynamic work on blackbody radiation by Wien, St\'efan, Boltzmann, Planck, and others involved the thermodynamic behavior of a movable piston sliding in a cylinder containing classical electromagnetic thermal radiation. This early work used only classical physics concepts. Here, this analysis is reinvestigated with the change that the implicit assumption is not made that the thermal radiation spectrum reduces to zero at the temperature T=0. Previous work has shown that this consideration may be an important one to yield agreement, or at least better agreement, between classical physical theory and the actual physical behavior of molecular, atomic, and subatomic systems in nature. Indeed, the present analysis on ``cavity thermodynamics'' accounts for the thermodynamic behavior of Casimir forces between the walls of the cavity. Using only the traditional thermodynamic definition of T=0, the form of the classical electromagnetic zero-point (ZP) radiation spectrum is deduced. From the second law of thermodynamics, two forms of Wien's displacement law are obtained and generalized to include the possibility of ZP radiation. The entropy is then explicitly calculated for the parallel-plate case. Also, the limiting situation of high-temperature radiation between the plates and low temperature outside is examined to recover the early analysis by Wien, Planck, and others. Most of the analysis is carried out for two parallel conducting plates bathed in thermal radiation; the Appendix extends this analysis to a rectangular conducting box with a movable interior wall.

Connection of the classical electromagnetic zero-point radiation spectrum to quantum mechanics for dipole harmonic oscillators.

Recently the classical electrodynamic zero-point spectrum was derived as being the appropriate spectrum for the thermodynamic definition of absolute-zero temperature to hold for classical, electric dipole harmonic oscillators [Cole, Phys. Rev. A 42, 1847 (1990)]. This analysis involved the lengthy calculation of nonperturbative, retarded van der Waals thermodynamic functions. Here this derivation is shown to hold for the much simpler unretarded, resonance situation. The connection to quantum mechanics is then more immediate.