Quantum and classical statistics of the electromagnetic zero-point field

Abstract

A classical electromagnetic zero-point field (ZPF) analogue of the vacuum of quantum field theory has formed the basis for theoretical investigations in the discipline known as random or stochastic electrodynamics (SED) wherein quantum measurements are imitated by the introduction of a stochastic classical background EM field. Random EM fluctuations are assumed to provide perturbations which can mimic some quantum phenomena while retaining a purely classical basis, e.g. the Casimir force, the Van-der-Waals force, the Lamb shift, spontaneous emission, the RMS radius of the harmonic oscillator, and the radius of the Bohr atom. This classical ZPF is represented as a homogeneous, isotropic ensemble of plane waves with fixed amplitudes and random phases. Averaging over the random phases is assumed to be equivalent to taking the ground-state expectation values of the corresponding quantum operator. We demonstrate that this is not precisely correct by examining the statistics of the classical ZPF in contrast to that of the EM quantum vacuum. We derive the distribution for the individual mode amplitudes in the ground-state as predicted by quantum field theory (QFT) and then carry out the same calculation for the classical ZPF analogue, showing that the distributions are only in approximate agreement, diverging as the density of k states decreases. We introduce an alternative classical ZPF with a different stochastic character, and demonstrate that it can exactly reproduce the statistics of the EM vacuum of QED. Incorporated into SED, this new field is shown to give the correct (QM) distribution for the amplitude of the ground-state of a harmonic oscillator, suggesting the possibility of developing further successful correspondences between SED and QED.Comment: 18 page

Gravity and the quantum vacuum inertia hypothesis

“…For simplicity and to facilitate comparison with much previous SED work, we omit the Ibison and Haisch modification of Eqs. (3) in which the amplitudes are also randomized in such a way as to bring the quantum and classical statistics of the electromagnetic zero-point field into exact agreement [13].…”

Semiclassical random electrodynamics: spontaneous emission and the Lamb shift

“…Note that this expression for the ZPF is equivalent to that recently discussed by Ibison and Haisch. 25 To explore the interaction of the ZPF with a quantum 4. PERTURBATION THEORY system we consider an atom conveniently placed at the A E vo i ut j on 0 f the Wave Function origin of the coordinate system and make the dipole ap-We nQW cons i,j er the Schrödinger equation for an atom in proximation (i.e., for the modes of interest, k s ■ r <S 1).…”

Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

“…The vacuum field used in Boyer's work arises from the homogeneous solution of Maxwell's equations, which is assumed to be zero in classical electrodynamics [4]. In an unbounded (free) space, the vacuum field has an integral form (a detailed account of the vacuum field in unbounded space is given in Appendix A.1) [26]:…”