Trevor W. Marshall

Local realism has not been refuted by atomic cascade experiments

Abstract We obtain a local realistic model, involving just one angular hidden variable, giving predictions, for the coincidence counts in atomic cascade experiments, which come extremely close to those of the quantum-mechanical model, and which fit the experimental data as closely as do the predictions of that model.

A drop of ink falls from my pen...It comes to earth, I know not when

The authors obtain, for a Brownian particle in a uniform force field, the mean and asymptotic first-passage times as functions of the particles initial position and velocity, with the recurrence times given as a special case. They discuss the region of phase space for which the diffusion model of Brownian motion provides an adequate approximation, and conclude that there is no possibility of obtaining the recurrence times within that model. They find that the nature of the boundary-value problem is profoundly altered when the motion is treated as a process in phase rather than configuration space, because the time-development operator is then parabolic rather than elliptic. They argue that such a change in the treatment of Brownian motion places it within the sphere of transport theory rather than diffusion theory, and that, consequently, results such as ours have relevance to the study of phenomena such as radiative transfer and neutron transport.

Collective effects in the atomic-cascade experimental tests of Bell inequalities

On etudie les effets collectifs dans les excitations et desexcitations atomiques comme moyens de verification experimentale des inegalites de Bell

The analytic solutions of some boundary layer problems in the theory of Brownian motion

The authors give analytic solutions of the generalised albedo and Milne problems for the Uhlenbeck-Ornstein process, and discuss the relation between these and the original Wang-Uhlenbeck (1945) problem of determining the distribution of first-passage times.

A stochastic local realist model for the EPR atomic-cascade experiment which reproduces the quantum-mechanical coincidence rates

Abstract We show that a recent model of Barut and Meystre is not local realist, but that by suitable modification it besomes one for the particular case of EPR atomic-cascade experiments, using either one-channel or two-channel analyzers. It exhibits clearly the enhancement property necessary for a model violating the second Clauser-Horne inequality. It satisfies the Bell inequality, and it may be used to understand more clearly that the quantum model for real analyzers also satisfies this inequality.

The distance separating quantum theory from reality

Abstract A local realistic model of optical cascades, involving just one angular hidden variable, is found to give a coincidence curve which differs from the quantum-theoretic curve by an average of 1.5% for currently realizable experiments. The results indicates that it is extremely difficult, though not impossible, to use such experiments to discriminate between quantum theory and local realistic theories. However, in no experiment performed to date has sufficient accuracy been achieved to make such a discrimination.

Type II parametric downconversion in the Wigner-function formalism: entanglement and Bell’s inequalities

We continue the analysis of our previous papers that were devoted to type I parametric downconversion, the extension to type II being straightforward. We show that entanglement, in the Wigner representation, is merely a correlation that involves both signals and vacuum fluctuations. An analysis of the detection process opens the way to a complete description of parametric downconversion in terms of pure Maxwell electromagnetic waves.

Local realist model for the coincidence rates in atomic-cascade experiments

Abstract We assume that the two photons emerging from an atomic cascade process are classical wave-packets with well defined intensities and states of elliptical polarization. Such weak light signals, when interacting with optical devices such as linear polarizers and quarter-wave plates, are assumed to undergo stochastic changes of intensity in addition to the change in polarization experienced by macroscopic signals. We show how such assumptions can lead, in a natural way, to an enhancement in the detection probability of certain signals, and hence to a family of models which fit the observed counting rates in all atomic-cascade experiments so far performed, including those which investigate the circular polarizations of the photons.

Parametric Down-Conversion Experiments in the Wigner Representation

The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.

Parametric down and up conversion in the Wigner representation of quantum optics

Abstract We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.