Electromagnetic Zero-point Field Research Articles

Stochastic electrodynamics. I. On the stochastic zero-point field

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrodinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrodinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrodinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned.

Exploration of a possible cumulative action of the zero-point field on intergalactic particles and implications for cosmic rays and a X-ray background from the intergalactic medium

The intergalactic space (IGS) has ideal conditions to test the weak but cumulative action that the electromagnetic (EM) zero-point field (ZPF) of ordinary quantum theory (QT), if conceived as a real field, may have on EM interacting particles. Recent results (classical stochastic and quantum) indicate that if the EM ZPF of ordinary QT is conceptually assimilated to a real random field, electrically polarizable particles perform a random walk in velocity space to ever-increasing translational kinetic energies. As the ZPF has a Lorentz-invariant energy density spectrum, statistically it keeps the same form and is homogeneous and isotropic in all inertial frames of reference. No velocity-dependent forces can hence appear on particles moving through the ZPF. Acceleration is thus possible in a high vacuum. The hierarchy of dissipation mechanisms for the accelerated ultrarelativistic protons in the IGS is established in detail. In the IGS outside superclusters cosmic expansion is the most significant dissipation mechanism. The previously derivedE −η particle energy spectrum is obtained except for a cut-off: cosmic expansion puts a drastic cut-off to the energy spectrum of ZPF accelerated particles in the IGS out-side clusters or superclusters. This cut-off does not appear for CR primaries confined to the magnetic cavities of clusters or superclusters. When this confinement is effective, the ZPF acceleration may still be as relevant a CR acceleration mechanism as previously contended. The possible relevance of the ZPF in energizing the intergalactic medium (IGM) is briefly discussed. As it has recently been shown that electrons are not accelerated by the ZPF, electrons can only receive energy from the proton component of the IGM plasma and should display an approximately Maxwellian distribution. This could not occur, would electrons absorb energy directly from the ZPF. In that case they would display the Lorentz-invariant distribution. The electron component loses energy mainly by thermal bremsstrahlung or by inverse Compton collisions with the 2.7 K photons depending on the assumed number density of IGS electrons. The X-ray emission of the proton component can be dismissed in comparison with that of the electrons, despite the usual higher energies of protons in their distribution which is not Maxwellian. The relevance of the ZPF acceleration model for explaining the observed X-ray background is preliminarily discussed. The inherent thermodynamic limitations of the model are also briefly outlined.

Zitterbewegung in stochastic electrodynamics and implications on a zero-point field acceleration mechanism

According to the current general ideas on the zitterbewegung and if we assume the existence of a universal classical electromagnetic zeropoint field (CEMZPF) in the manner of stochastic electrodynamics (SED), it can be shown that the recently predicted growing trend of the translational kinetic energy for monopolar classical particles immersed in the CEMZPF should be quenched, when ZPF-induced relativistic oscillations of the centre of charge with respect to the centre of mass of classical monopolar particles are considered. This should occur in such a way that, if proper values of the parameters are assumed, absolutely no translational kineticenergy growth occurs. This is consistent with the fact that protons and other composite particles (nuclei) are found at very high energies (up to 1021 eV and beyond), while primary cosmic-ray electrons do not show up beyond (1012÷1013) eV and only in a e/p=1/100 ratio. That no total quenching occurs for polarizable particles,e.g. protons, is consistent with expectations in astrophysics for a highly excited X-ray-emitting and very rarefied intergalactic neutral plasma. Previous astrophysical speculations on a CR ZPF acceleration mechanism and on the associated very hot intergalactic gas are briefly looked at from this perspective. It is finally conjectured that this concept of a CEMZPF-induced zitterbewegung may be relevant for making further progress in well-known unsolved problems in SED (hydrogen atom, anharmonic oscillator, etc.).

Brownian motion of a mirror

Einstein's analysis of the Brownian motion of a mirror in a field of natural radiation played a crucial role, in the first decade of quantum theory, in persuading physicists that the Maxwell description of the electromagnetic field was inadequate, and that light quanta, with discrete momentum as well as energy, have a real existence. Here an alternative analysis is given of this motion. We see that, if the spectral density of the radiation field is given by the Planck spectrum plus the zero-point electromagnetic field, that is, by the spectral density of Planck's second theory, then the motion is correctly described in terms of the Maxwell theory, without any need for a quantum hypothesis. An essential step in this analysis is to include Boyer's correction to the Einstein model, whereby account is taken of the radiative energy loss each time the mirror collides with the walls of the cavity.

Behavior of classical particles immersed in the classical electromagnetic zero-point field

This article presents a general analysis of some aspects of the interaction of classical particles with the classical electromagnetic zero-point field (cemzpf). The analysis provides a possible observational test for stochastic electrodynamics (SED). A convergence form factor derived semiclassically supports the narrow linewidth and related approximations of SED by introducing a typically sharp frequency cutoff. An extended classical charge monopole can then be shown to perform a simple jiggling motion under the influence of the cemzpf. Besides this motion (same as polarizable particles), monopolar particles also display a random walk in velocity space which leads them to ever-increasing translational kinetic energies. Hence, classical particles under the influence of the cemzpf display a conspicuous behavior because of the following well-known interrelated results: First, no velocity-dependent forces exist for classical particles moving exclusively through the cemzpf. Second, both monopolar and polarizable particles in SED are predicted to perform a random walk in velocity space due to the action of this field. Only collisions may provide a stopping mechanism. An analysis of the work of Boyer and others concerning particle collisions with walls, suggests the idea that collisions transfer energy from an unconfined gas of mutually colliding particles to the random field. Using this, a Fokker-Planck model for an unconfined gas of mutually colliding classical particles is constructed. It displays a universal equilibrium energy spectrum ${E}^{\ensuremath{-}\mathrm{const}}$ for the gas particles under the cemzpf as seen from any point fixed to co-moving coordinates. Primary cosmic rays have such an energy distribution. This motivated the proposal of a zero-point field (zpf) cosmic-ray acceleration mechanism in a previous work. Such a proposal requires a careful examination. However, methodologically speaking, one should first examine the alternative possibility that the behavior predicted in SED for classical particles does not occur in nature. If that would happen to be the case, then SED and the cemzpf concept should be critically revised. That the cemzpf concept may apparently lead to difficulties, is seen by presenting a paradoxical example where a monopolar particle moving through the cemzpf is predicted to suffer an enormous frictional force due to the surrounding zpf. The prediction obviously violates the Lorentz invariance of the cemzpf energy density spectrum. But the paradox is easily resolved by realizing the improper ultrarelativistic behavior of the Lorentz-Dirac equation which is used in the example. Extreme care must then be exerted in the use of the equations of motion of classical charged particles when moving under the influence of a zpf. The search for internal contradictions in SED, not related with the well-known renormalization and other difficulties of classical electrodynamics, has so far been unsuccessful. This and several points of rigor here and elsewhere included, are enough to indicate that the conspicuous behavior of classical particles discussed here is correctly predicted from the assumptions of SED. It is therefore proposed that this predicted behavior may serve as an observational test for the validity of SED.

Quantum mechanics of the Einstein–Hopf model

The Einstein–Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Essential to the consistency of the theory is the fluctuation–dissipation theorem connecting the radiation reaction with the zero-point electromagnetic field. The well-known ’’particle’’ term in the Einstein fluctuation formula is shown to be aconsequence of the quantum-mechanical zero-point oscillations of the field and the dipole radiators. Both the wave and particle aspects of the fluctuation formula are interpreted in terms of the fundamental absorption and emission processes.

The propagator of stochastic electrodynamics

The "elementary propagator" for the position of a free charged particle subject to the zero-point electromagnetic field with Lorentz-invariant spectral density $\ensuremath{\propto}{\ensuremath{\omega}}^{3}$ is obtained. The nonstationary process for the position is solved by the stationary process for the acceleration. The dispersion of the position elementary propagator is compared with that of quantum electrodynamics. Finally, the evolution of the probability density is obtained starting from an initial distribution confined in a small volume and with a Gaussian distribution in the velocities. The resulting probability density for the position turns out to be equal, to within radiative corrections, to $\ensuremath{\psi}{\ensuremath{\psi}}^{*}$ where $\ensuremath{\psi}$ is the Kennard wave packet. If the radiative corrections are retained, the present result is new since the corresponding expression in quantum electrodynamics has not yet been found. Besides preceding quantum electrodynamics for this problem, no renormalization is required in stochastic electrodynamics.

Can stochastic physics be a complete theory of nature?

The prospects for a complete stochastic theory of microscopic phenomena are considered. The two traditional schools of stochastic physics, the diffusion process school and the zero-point electromagnetic field school, are reviewed. A completely relativistic theory, stochastic field theory, is proposed as an extension of the ideas of these two schools. Within the context of stochastic field theory we present the following new results: an elementary stochastization scheme which produces the zero-point electromagnetic field; a physical interpretation of the mathematical methods developed by Lukosz for calculating zero-point energies; a calculation of the first-order Lamb shift which generalizes that of Welton; a new setting for a finite-temperature theory; and comments on the bag model for quark confinement.