Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure

Soil availability, plant uptake and soil to plant transfer of 99Tc - A review

The fission yield of 99Tc from 239Pu and 235U is similar to that of 137Cs or 90Sr and it is therefore an important component of nuclear weapons fall-out, nuclear waste and releases from nuclear facilities. There is particular current interest in 99Tc transfer from soil to plants for: (a) environmental impact assessments for terrestrial nuclear waste repositories, and (b) assessments of the potential for phytoextraction of radionuclides from contaminated effluent and soil. Vascular plants have a high 99Tc uptake capacity, a strong tendency to transport it to shoot material and accumulate it in vegetative rather than reproductive structures. The mechanisms that control 99Tc entry to plants have not been identified and there has been little discussion of the potential for phytoextraction of 99Tc contaminated effluents or soil. Here we review soil availability, plant uptake mechanisms and soil to plant transfer of 99Tc in the light of recent advances in soil science, plant molecular biology and phytoextraction technologies. We conclude that 99Tc might not be highly available in the long term from up to 50% of soils worldwide, and that no single mechanism that might be easily targeted by recombinant DNA technologies controls 99Tc uptake by plants. Overall, we suggest that Tc might be less available in terrestrial ecosystems than is often assumed but that nevertheless the potential of phytoextraction as a decontamination strategy is probably greater for 99Tc than for any other nuclide of radioecological interest. © 2002 Elsevier Science Ltd. All rights reserved

Nodal points and the transition from ordered to chaotic Bohmian trajectories

We explore the transition from order to chaos for the Bohmian trajectories of a simple quantum system corresponding to the superposition of three stationary states in a 2D harmonic well with incommensurable frequencies. We study in particular the role of nodal points in the transition to chaos. Our main findings are: a) A proof of the existence of bounded domains in configuration space which are devoid of nodal points, b) An analytical construction of formal series representing regular orbits in the central domain as well as a numerical investigation of its limits of applicability. c) A detailed exploration of the phase-space structure near the nodal point. In this exploration we use an adiabatic approximation and we draw the flow chart in a moving frame of reference centered at the nodal point. We demonstrate the existence of a saddle point (called X-point) in the vicinity of the nodal point which plays a key role in the manifestation of exponential sensitivity of the orbits. One of the invariant manifolds of the X-point continues as a spiral terminating at the nodal point. We find cases of Hopf bifurcation at the nodal point and explore the associated phase space structure of the nodal point - X-point complex. We finally demonstrate the mechanism by which this complex generates chaos. Numerical examples of this mechanism are given for particular chaotic orbits, and a comparison is made with previous related works in the literature.Comment: 32 pages, 13 figures, Accepted for publication in Journal of Physics

Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen

The Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semi-classical) radiation. The transition between the 1s ground state and the 2p0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R^3. The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.Comment: 18 pages, 8 figure

Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment

The double slit problem is idealized by simplifying each slit by a point source. A composite reduced action for the two correlated point sources is developed. Contours of the reduced action, trajectories and loci of transit times are developed in the region near the two point sources. The trajectory through any point in Euclidian 3-space also passes simultaneously through both point sources.Comment: 12 pages LaTeX2e, 9 figures. Typos corrected. Author's final submission. A companion paper to "Interference, reduced action, and trajectories", quant-ph/0605120. Keywords: interference, Young's experiment, entanglement, nonlocality, trajectory representation, determinis

A Critical Evaluation of Structural Analysis Tools used for the Design of Large Composite Wind Turbine Rotor Blades under Ultimate and Cycle Loading

Rotor blades for 10-20MW wind turbines may exceed 120m. To meet the demanding requirements of the blade design, structural analysis tools have been developed individually and combined with commercial available ones by blade designers. Due to the various available codes, understanding and estimating the uncertainty introduced in the design calculations by using these tools is needed to allow assessment of the effectiveness of any future design modification. For quantifying the introduced uncertainty a reference base was established within INNWIND.EU in which the several structural analysis concepts are evaluated. This paper shows the major findings of the comparative work performed by six organizations (universities and research institutes) participating in the benchmark exercise. The case concerns a 90m Glass/Epoxy blade of a horizontal axis 10MW wind turbine. The detailed blade geometry, the material properties of the constitutive layers and the aero-elastic loads formed the base by which global and local blade stiffness and strength are evaluated and compared. Static, modal, buckling and fatigue analysis of the blade were performed by each partner using their own tools; fully in-house developed or combined with commercially available ones, with its specific structural analysis approach (thin wall theory and finite element models using beam, shell or solid elements) and their preferable analysis type (linear or geometrical non-linear). Along with sectional mass and stiffness properties, the outcome is compared in terms of displacements, stresses, strains and failure indices at the ply level of the blade structure, eigen-frequencies and eigen-modes, critical buckling loads and Palmgren-Miner damage indices due to cycle loading. Results indicate that differences between estimations range from 0.5% to even 40%, depending on the property compared. Modelling details, e.g. load application on the numerical models and assumptions, e.g. type of analysis, lead to these differences. The paper covers these subjects, presenting the modelling uncertainty derived

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure

Understanding quantization: a hidden variable model

We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by stochastically-parameterized c-numbers. Unlike canonical quantization, the method is free from operator ordering ambiguity and the resulting quantum system has a straightforward interpretation as statistical modification of ensemble of classical trajectories. We then develop measurement without wave function collapse \`a la pilot-wave theory and point out new testable predictions.Comment: 16 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz von Foerster Conference 2011)", see http://iopscience.iop.org/1742-6596/361/

Grounding Bohmian Mechanics in Weak Values and Bayesianism

Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability density P(x). However, this ``standard'' j is in fact only one of infinitely many that transform correctly and satisfy \dot P + \del . j=0. In this article I show that there is a unique j that can be determined experimentally as a weak value using techniques that would make sense to a classical physicist. Moreover, this operationally defined j equals the standard j, so, assuming \dot x = j/P, the possible Bohmian paths can also be determined experimentally from a large enough ensemble. Furthermore, this approach to deriving BM singles out x as the hidden variable, because (for example) the operationally defined momentum current is in general incompatible with the evolution of the momentum distribution. Finally I discuss how, in this setting, the usual quantum probabilities can be derived from a Bayesian standpoint, via the principle of indifference.Comment: 11 page