Classical Stochastic Electrodynamics Research Articles

Stochastic methods for light propagation and recurrent scattering in saturated and nonsaturated atomic ensembles

We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low light intensity limit we illustrate the simulations in a system of atoms in a Mott-insulator state in a 2D optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.

Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics

Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentally classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell’s equations for fluctuations of the electromagnetic field

The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture.Based on this parallelism between QED and CSED, it is natural to expect validity of the Lorentz condition and Maxwell’s equations for the time-normal averages of the potential and current. Things however turn out to be more complicated. Maxwell’s equations under the time-normal ordering can only be demonstrated subject to cancellation of the so-called Schwinger terms by gauge-invariant regularisations. We presume this pattern to be general, formulating this as “commutativity conjecture”. Consistency of the latter with the Heisenberg uncertainty principle is discussed.

A stochastic electrodynamics interpretation of spontaneous transitions in the hydrogen atom

Seidl and Lipas have calculated the lifetime of the excited states of the hydrogen atom within an entirely classical framework and obtained good agreement with the corresponding quantum results. Here we propose an explanation for this good agreement and show that the agreement can be significantly improved by including in their classical model the effects of the random zero-point electromagnetic fields postulated by the classical stochastic electrodynamics. Moreover, we show that the zero-point electromagnetic radiation provides a physical mechanism for the atomic stability on classical grounds.

Maxwell electromagnetic theory, Planck's radiation law, and Bose—Einstein statistics

We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of chargedmatter oscillators with the thermal and zeropoint electromagnetic fields characteristic of quantum electrodynamics and classical stochastic electrodynamics. Planck's formula for the spectral distribution and the elements of energy hw are interpreted without resorting to discontinuities. We also show the aspects in which our model calculation complement other derivations of blackbody radiation spectrum without quantum assumptions.

Einstein-Ehrenfest's radiation theory and Compton-Debye's kinematics

Einstein and Ehrenfest's radiation theory is modified in order to take into account the effects of the random zero-point fields, characteristic of classical stochastic electrodynamics, in a system of classical molecules interacting with thermal radiation. This is done by replacing the Einstein concept of “random spontaneous emission” by the concept of stimulated emission by the random zero-point fields. As a result, Compton and Debye's kinematic relations are obtained within the realm of a completely classical theory, that is, without having to consider the wave-particle duality for the molecules or the radiation.

Spin and paramagnetism in classical stochastic electrodynamics.

Etude des proprietes statistiques du spin S et du dipole magnetique pr d'une particule a 2 constituants lies par une force harmonique. On determine la relation entre S et μ et conclut que ∼h 2 . Le systeme contient des forces paramagnetiques et une comparaison avec l'experience montre un excellent accord avec l'electrodynamique stochastique

Electron spin in classical stochastic electrodynamics

Electron spin in classical stochastic electrodynamics

The relation between stochastic mechanics and classical stochastic electrodynamics

The relation between stochastic mechanics and classical stochastic electrodynamics

The harmonic and anharmonic oscillator in classical stochastic electrodynamics

The sensitivity of the spectral density and the correlation of the harmonic oscillator to the charge distribution is examined in the context of classical stochastic electrodynamics. While the first exhibits some degree of sensitivity, the second exhibits none in the limit of zero charge. Thus a comparison can be made with nonrelativistic quantum mechanics independent of the charge distribution. In the same spirit, the anharmonic oscillator is examined. In the limit of zero charge, it is shown that classical stochastic electrodynamics qualitatively agrees with quantum mechanics, but ambiguities make a quantitative comparison difficult. In an appendix, the oscillator approximation to the hydrogen atom is briefly discussed.

Suppression of runaway effect in classical stochastic electrodynamics

Suppression of runaway effect in classical stochastic electrodynamics