APL And The Numerical Solution Of High-Order Linear Differential Equations

An Nth‐order linear ordinary differential equation is rewritten as a first‐order equation in an N×N matrix. Taking advantage of the matrix manipulation strength of the APL language this equation is then solved directly, yielding a great simplification over the standard procedure of solving N coupled first‐order scalar equations. This eases programming and results in a more intuitive algorithm. Example applications of a program using the technique are given from quantum mechanics and control theory

Gravitational and electromagnetic fields of a charged tachyon

An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the uncharged tachyon which was earlier obtained by Vaidya. The null surfaces for the charged tachyon are discussed.Comment: 8 pages, LaTex, To appear in Pramana- J. Physic

On the Foundation of the Relativistic Dynamics with the Tachyon

The theoretical foundation of the object moving faster than light in vacuum ({\it tachyon}) is still missing or incomplete. Here we present the classical foundation of the relativistic dynamics including the tachyon. An anomalous sign-factor extracted from the transformation of ${ \sqrt{1-u^{2}/c^{2} } }$ under the Lorentz transformation, which has been always missed in the usual formulation of the tachyon, has a crucial role in the dynamics of the tachyon. Due to this factor the mass of the tachyon transforms in the unusual way although the energy and momentum, which are defined as the conserved quantities in all uniformly moving systems, transform in the usual way as in the case of the object moving slower than light ({\it bradyon}). We show that this result can be also obtained from the least action approach. On the other hand, we show that the ambiguities for the description of the dynamics for the object moving with the velocity of light ({\it luxon}) can be consistently removed only by introducing a new dynamical variable. Furthermore, by using the fundamental definition of the momentum and energy we show that the zero-point energy for any kind of the objects, {\it i.e.}, the tachyon, bradyon, and luxon, which has been known as the undetermined constant, should satisfy some constraints for consistency, and we note that this is essentially another novel relativistic effect. Finally, we remark about the several unsolved problems.Comment: 39 pages, latex, 15 figures avaliable upon reques

Causal paradoxes: a conflict between relativity and the arrow of time

It is often argued that superluminal velocities and nontrivial spacetime topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA) that points from the past to the future, the apparent paradoxes appear to be an artefact of the wrong tacit assumption that the relativistic coordinate TA coincides with the physical TA. The latter should be identified with the thermodynamic TA, which, by being absolute and irrotational, does not lead to paradoxes.Comment: 7 pages, revised, new references, to appear in Found. Phys. Let

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Tachyonic Field Theory and Neutrino Mass Running

In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.Comment: 13 pages; RevTeX; to appear in Cent. Eur. J. Phy

Magnetic Resonance Thermometry at 7T for Real-Time Monitoring and Correction of Ultrasound Induced Mild Hyperthermia

While Magnetic Resonance Thermometry (MRT) has been extensively utilized for non-invasive temperature measurement, there is limited data on the use of high field (≥7T) scanners for this purpose. MR-guided Focused Ultrasound (MRgFUS) is a promising non-invasive method for localized hyperthermia and drug delivery. MRT based on the temperature sensitivity of the proton resonance frequency (PRF) has been implemented in both a tissue phantom and in vivo in a mouse Met-1 tumor model, using partial parallel imaging (PPI) to speed acquisition. An MRgFUS system capable of delivering a controlled 3D acoustic dose during real time MRT with proportional, integral, and derivative (PID) feedback control was developed and validated. Real-time MRT was validated in a tofu phantom with fluoroptic temperature measurements, and acoustic heating simulations were in good agreement with MR temperature maps. In an in vivo Met-1 mouse tumor, the real-time PID feedback control is capable of maintaining the desired temperature with high accuracy. We found that real time MR control of hyperthermia is feasible at high field, and k-space based PPI techniques may be implemented for increasing temporal resolution while maintaining temperature accuracy on the order of 1°C

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference