Nelson's stochastic formulation of quantum theory is briefly surveyed and put in relation to the classical stochastic formalisms. The approach is investigated comparatively with the Bohm-Vigier model of stochastic fluctuations. Parallels to the causal interpretation of de Broglie-Bohm are drawn.

Starting from a classical Hamilton-Jacobi theory the Schrödinger equation of non-relativistic quantum mechanics is derived by introducing an averaging procedure over the free parameters of the classical formalism. The conceptual implications, the relation to the causal interpretation and possible extensions of the formalism are discussed.

Using the example of a harmonic oscillator and nondispersive wave packets, we derive, in the frame of the causal interpretation, the equations of motion and particle trajectories in one- and two-particle systems. The role of the symmetry or antisymmetry of the wave function is analyzed as it manifests itself in the specific types of corelated trajectories. This simple example shows that the concepts of the quantum potential and the quantum forces prove to be essential for the specification of the dynamics of a microsystem and the resulting statistical behavior.

We discuss generally and with reference to typical examples the classical limit of quantum mechanics, including equations of motion and the uncertainty relations, from the point of view of the causal interpretation. We show how universal criteria may be formulated in terms of sufficient conditions to be satisfied by the wavefunction in order that the classical results are recovered. These overcome the problems associated with limiting procedures such as ħ←0 or high quantum numbers On discute de facon generale et exemples a l'appui la limite classique de la mecanique quantique, y compris les equations du mouvement et les relations d'incertitude, dans l'optique de l'interpretation causale. On montre comment des criteres universels peuvent etre formules en termes de conditions suffisantes que la fonction d'onde doit satisfaire avant de retrouver les resultats classiques. Ces criteres surmontent les problemes associes aux passages a la limite tels que ħ→0 ou celle des grands nombres quantiques

Spin superposition in neutron interferometry, spin measurement, and non–local Einstein-Podolsky-Rosen spin correlations can be understood in terms of well–defined individual particle trajectories with continuously variable spin vectors.

On the basis of our assumption that the Tersoff-Bayer averaging is a consequence of the nonlocal correlations inherent in the quantum potential model of Bohm we describe a situation where this potential can be "switched" on and off giving rise to Bose-Einstein and Boltzmann statistics, respectively. This would imply a change in the fringe visibility in interference experiments.

We analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, we discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. We then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.

Assuming that future experiments confirm Aspect's discovery of nonlocal interactions between quantum pairs of correlated particles, we analyze the constraints imposed by the EPR reasoning on the said interactions. It is then shown that the nonlocal relativistic quantum potential approach plainly satisfies the Einstein causality criteria as well as the energy-momentum conservation in individual microprocesses. Furthermore, this approach bypasses a new causal paradox for timelike separated EPR measurements deduced by Sutherland in the frame of an approach by means of space-time zigzags with advanced potentials. It is finally demonstrated that this inherent quantum causal direct interaction establishes permanent EPR correlations which are always restricted to spacelike separations and are instantaneous only in the center-of-mass rest frame of the two-particle system.

The authors give a causal interpretation of a double Stern-Gerlach experiment on the basis of spacetime solutions to the Pauli equation. For an initial singlet state, they determine the continuous particle trajectories and spin vector orientations. The graphical results exemplify how non-local actions of the quantum potential and quantum torque give rise to a correlated evolution of dynamical variables.

Contrary to a recent formulation of classical and quantum statistics in terms of indistinguishable particles it is claimed that the notion of distinguishability can account for classical as well as for quantum statistics. The resulting non-local correlations are a manifestation of a fluctuating stochastic metric which has been shown to produce the quantum potential.

In a set of older and recent experiments1–4 extremely high intensity laser beams are focused onto metals or gases and anomalous photoelectric emission and gas photo-ionization is observed. The anomalous character of the effect consists of the fact that outcoming photoelectrons are observed although the single photon energy is lower than the work function of the material. The first attempt to interpret this effect was based on a light intensity dependent approach, the multiphoton theory5. This theory makes a definite prediction for the photoelectron current i as a function of the light intensity I, namely i ∝ In where n is the integer part of W/h v + 1,W being the work function of the material. This was however disprooved by experiment6 since the latter showed a linear relation between the current and the light intensity thus discarding the multiphoton hypothesis.

We investigate the implications of a manifestly covariant formulation of relativistic quantum mechanics by using a relativistic version of Schrödinger's equation with an independent scalar evolution parameter canonically conjugated to the variable mass. This approach, which yields ordinary relativistic Klein-Gordon quantum mechanics as an evolution-time stationary solution, can be shown to lead to an alternative quantum field theoretical formulation which could be devoid of the divergency problems of the standard quantum field theory. This covariant Schrödinger formalism as derived from a stochastic variational principle is shown to yield a natural Hilbert space construction in direct analogy with non-relativistic quantum mechanics. It is then demonstrated that this theory can be interpreted as a consequence of a space-time metric fluctuation and that it can be related to mass ensemble theories. Furthermore a Lagrangian formulation of the theory is presented and the relation between the field Hamiltonian and the components of the energy-momentum tensor is established. Some interesting conclusions can be drawn by requiring the local U(1) invariance of the theory, as e.g. the emergence of an additional scalar potential V related to the variable mass and the corresponding field equations. A possible generalization of the theory is finally presented by introducing Clebsch parameters which generalize the quantum motions without introducing new forces.

Based on a recent association of quantum observable algebra with stochastic processes in the frame of the causal stochastic interpretation of quantum mechanics, a relativistic Hilbert space is defined for the Klein-Gordon case. It is demonstrated that unitary transformations in Hilbert space reflect canonical transformations in the associated phase space, manifesting thus an underlying symplectic structure.

One of the models proposed in order to account for nonlocal correlations emerging in EPR-singlet states of spinning particles is based on a “retroaction in time” mechanism.’ This model proposes a time-arrowless microcausality, a transition between the prepared and measured state instead of a retarded unitary evolution, an explicit use of acausal Pauli-Jordan rather than Feynman propagators, a combination of wave function collapse and retrocollapse, and, finally, a time zigzagging of positive energies as a manifestation of psychokinetic effects. Apart from general objections and criticism resting essentially on the fact that CPT-invariance only manifests the existence of antiparticles (along with Feynman zigzags preserving the time-arrow and irreversibility), a powerful objection has been formulated recently by Sutherland’ for the case of two EPR-singlet particles on which a spin-measurement is performed at M ; and M2, with M ; M 2 being a timelike interval (FIGURE 1): Because the “retroaction” mechanism is insensitive to the interval character between measurements and the M 2 result depends on the M; instrument setting, we can modulate the original M ; setting after the M2 measurement by a timelike signal and produce a paradox. We can do this because for certain configurations of settings, no spin-measurement outcome is consistent. Sutherland suggests that a correct model should imply that MI must affect M 2 when M , is outside the forward light cone of M,, but not when it is inside. This is exactly the constraint satisfied by the nonlocal quantum potential model that obeys Einstein causality and individual conservation laws. This model, treated for simplicity for scalar particles, results out of a Madelung-type decomposition of the Klein-Gordon equation, ( + $) # = 0 (where J. = ep“s/”),

A Wigner-Moyal phase-space approach is developed for the Dirac and Feynman-Gell-Mann equations. The role of spinors as primitive elements of the spacetime and phase-space Clifford algebras is emphasized. A conserved phase-space current is constructed.

We generalize to a Lorentz covariant formalism (with proper-time dependence) the non-negative phase-space distribution proposed by Kuryshkin and make a specific proposal to define the corresponding correspondence rule between functions of phase-space and quantum operators on the basis of the introduction of a non-dispersive soliton wave surrounding particles in space-time.