About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm Theory of Pilot Wave

The standard relativistic de-Broglie--Bohm theory has the problems of tacyonic solutions and the incorrect non-relativistic limit. In this paper we obtain a relativistic theory, not decomposing the relativistic wave equations but looking for a generalization of non-relativistic Bohmian theory in such a way that the correct non-relativistic limit emerges. In this way we are able to construct a relativistic de-Broglie--Bohm theory both for a single particle and for a many-particle system. At the end, the theory is extended to the curved space-time and the connection with quantum gravity is discussed.Comment: 13 pages, RevTeX. To appear in Physica Scripta, 200

Photon mass and quantum effects of the Aharonov-Bohm type

The magnetic field due to the photon rest mass $m_{ph}$ modifies the standard results of the Aharonov-Bohm effect for electrons, and of other recent quantum effects. For the effect involving a coherent superposition of beams of particles with opposite electromagnetic properties, by means of a table-top experiment, the limit $m_{ph}x10^{-51}g$ is achievable, improving by 6 orders of magnitude that derived by Boulware and Deser for the Aharonov-Bohm effect.Comment: 5 page

Relaxation to quantum equilibrium for Dirac fermions in the de Broglie-Bohm pilot-wave theory

Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but arises dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave-function obeys the non-relativistic Schroedinger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave-function which act as vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie-Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the 2D Dirac oscillator and the Dirac particle in a spherical 2D box).Comment: 11 pages, 9 figure

Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy

We consider spatially two dimensional Madelung fluid whose irrotational motion reduces into the Schr\"odinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a rotational quantum flow. We then ask for the most likely wave function possessing a given average energy by maximizing the Shannon information entropy over the quantum probability density. We show that there exists a class of solutions in which the wave function is self-trapped, rotationally symmetric, spatially localized with finite support, and spinning around its center, yet stationary. The stationarity comes from the balance between the attractive quantum force field of a trapping quantum potential generated by quantum probability density and the repulsive centrifugal force of a rotating velocity vector field. We further show that there is a limiting case where the wave function is non-spinning and yet still stationary. This special state turns out to be the lowest stationary state of the ordinary Schr\"odinger equation for a particle in a cylindrical tube classical potential.Comment: 19 page

Conformal Invariance and Wave-Particle Duality

We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical variables. This leads to the geometrization of the quantum aspects of matter.Comment: 5 page

On the influence of resonance photon scattering on atom interference

Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d_p/\lambda_i = y'_{12} (2\pi/kd\lambda_i), where y'_{12} is distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic center-of-mass motion, $d$ is the grating constant and \lambda_i is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of "which-way" information for the interference visibility.Comment: 9 pages, 1 figur

Might EPR particles communicate through a wormhole?

We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.Comment: Corrected version, to appears in EP

Self Interference of Single Electrodynamic Particle in Double Slit

It is by the long established fact in experiment and theory that electromagnetic waves, here as one component of an IED particle, passing a double slit will undergo self inference each, producing at a detector plane fringed intensities. The wave generating point charge of a zero rest mass, as the other component of the particle, is maintained a constant energy and speed by a repeated radiation reabsorption/reemission scheme, and in turn steered in direction in its linear motion by the reflected radiation field, and will thereby travel to the detector along (one of) the optical path(s) of the waves leading to a bright interference fringe. We elucidate the process formally based on first principles solutions for the IED particle and known principles for wave-matter interaction.Comment: Presentation at The 6th Int. Symp. Quantum Theory and Symmetries, Univ. Kent, 2009

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.Comment: 14 pages, 11 figure

Quantum Mechanical Properties of Bessel Beams

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physical consequences of these results are examined.Comment: 17 pages, no figures. New versio