George Horton

Bohm particles and their detection in the light of neutron interferometry

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories

We demonstrate how to construct a Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. The covariant theory that we propose employs a multi-time formalism and a Lorentz-invariant rule for the coordination of the spacetime points on the individual particle trajectories. In this way we show that there is no contradiction between non-locality and Lorentz-invariance in quantum mechanics. The approach is illustrated for relativistic bosons, using a simple model to discuss the individual non-locally correlated particle motion which ensues when the wavefunction is entangled. A simple example of measurement is described.

Wave-particle dualism and the interpretation of quantum mechanics

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.

A relativistically covariant version of Bohm's quantum field theory for the scalar field

We give a relativistically covariant, wave-functional formulation of Bohms quantum field theory for the scalar field based on a general foliation of spacetime by space-like hypersurfaces. The wave functional, which guides the evolution of the field, is spacetime-foliation independent but the field itself is not. Hence, in order to have a theory in which the field may be considered a beable, some extra rule must be given to determine the foliation. We suggest one such rule based on the eigenvectors of the energy–momentum tensor of the field itself.

Relativistically invariant extension of the de Broglie–Bohm theory of quantum mechanics

We show that quantum mechanics can be given a Lorentz-invariant realistic interpretation by applying our recently proposed relativistic extension of the de Broglie–Bohm theory to deduce non-locally correlated, Lorentz-invariant individual particle motions for the Einstein–Podolsky–Rosen experiment and the double-interferometer experiment proposed by Horne, Shimony and Zeilinger.

Time-like flows of energy momentum and particle trajectories for the Klein-Gordon equation

The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a single-particle relativistic quantum mechanical equation that defines unique time-like particle trajectories. The particle trajectories are determined by the conserved flow of the intrinsic energy density, which can be derived from the specification of the Klein-Gordon energy-momentum tensor in an Einstein-Riemann space. The approach is illustrated by application to the simple single-particle phenomena associated with square potentials.

Reply to 'Comment on ''Timelike flows of energy momentum and particle trajectories for the Klein?Gordon equation'''

We demonstrate that a straightforward limiting process can be used to continue trajectories in spacetime through exceptional regions in the velocity field (identified by Tumulka (2000 J. Phys. A: Math. Gen. 35 7691)) using the formalism we previously proposed (Horton G, Dewdney C and Nesteruk A 2000 J. Phys. A: Math. Gen. 33 7337).

de Broglie's pilot-wave theory for the Klein–Gordon equation and its space-time pathologies

We illustrate, using a simple model, that in the usual formulation the time-component of the Klein–Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de Broglies theory of particle trajectories the particle follows the current this leads to difficulties of interpretation, with the appearance of trajectories which are closed loops in space-time and velocities not limited from above. We show that at least this pathology can be avoided if one adapts in a covariant form the formulation of relativistic point particle dynamics proposed by Gitman and Tyutin.

De Broglie, Bohm and the Boson

Until recently most of the discussion concerning the interpretation of quantum theory has been carried out in the context of phenomena that can be adequately treated using the non-relativistic Schrodinger equation. In this context the interpretations of quantum mechanics proposed by de Broglie (1926; 1927) and by Bohm (1952a,b; Bohm and Vigier 1954) formally overlap in the one-particle case in what de Broglie called the “pilot-wave” theory and Bell called the de Broglie—Bohm interpretation.1 Both Bohm’s and de Broglie’s approach yield the same guidance condition for the “particle”, but they differ in what the particle is. For Bohm the particles are point-like whilst their guiding ψ-field exists in configuration space, whereas in de Broglie’s theory the particle is considered to be a solitonlike structure in its own ψ-field, consequently the field of each particle must exist in real space (and not the abstract configuration-space of the many-particle non-relativistic Schrodinger equation). The latter idea presented grave difficulties for de Broglie, which were never satisfactorily solved and we do not consider the soliton solutions in this paper.