  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.
