The mathematical structure of Newtonian spacetime: Classical dynamics and gravitation

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are timelike vector fields on ) plays a fundamental role in our approach, and the classification of all possible reference frames on is investigated in detail. We succeed in identifying a Lorentzian structure on and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning.     

A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh

A conservative formulation of the Lorentz force is given here for magnetohydrodynamic (MHD) flows at a low magnetic Reynolds number with the current density calculated based on Ohm’s law and the electrical potential formula. This conservative formula shows that the total momentum contributed from the Lorentz force is conservative when the applied magnetic field is constant. For the case with a non-constant applied magnetic field, the Lorentz force has been divided into two parts: a strong globally conservative part and a weak locally conservative part.The conservative formula has been employed to develop a conservative scheme for the calculation of the Lorentz force on an unstructured collocated mesh. Only the current density fluxes on the cell faces, which are calculated using a consistent scheme with good conservation, are needed for the calculation of the Lorentz force. Meanwhile, a conservative interpolation technique is designed to get the current density at the cell center from the current density fluxes on the cell faces. This conservative interpolation can keep the current density at the cell center conservative, which can be used to calculate the Lorentz force at the cell center with good accuracy. The Lorentz force calculated from the conservative current at the cell center is equivalent to the Lorentz force from the conservative formula when the applied magnetic field is constant, which can conserve the total momentum. We will further prove that the simple interpolation scheme used in the Part I [M.-J. Ni, R. Munipalli, N.B. Morley, P.Y. Huang, M. Abdou, A current density conservative scheme for MHD flows at a low magnetic Reynolds number. Part I. On a rectangular collocated grid system, Journal of Computational Physics, in press, doi:10.1016/j.jcp.2007.07.025] of this series of papers is conservative on a rectangular grid and can keep the total momentum conservative in a rectangular grid.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

Spinor Matter in a Gravitational Field: Covariant Equations à la Heisenberg

A fundamental tenet of general relativity is geodesic motion of point particles. For extended objects, however, tidal forces make the trajectories deviate from geodesic form. In fact Mathisson, Papapetrou, and others have found that even in the limit of very small size there exists a residual curvature-spin force. Another important physical case is that of field theory. Here the ray (WKB) approximation may be used to obtain the equation of motion. In this article I consider an alternative procedure, the proper time translation operator formalism, to obtain the covariant Heisenberg equations for the quantum velocity, momentum, and angular momentum operators for the case of spinor fields. I review the flat spacetime results for Dirac particles in Yang-Mills fields, where we recover the Lorentz force. For curved spacetime I find that the geodesic equation is modified by an additional term involving the spin tensor, and the parallel transport equation for the momentum is modified by an additional term involving the curvature tensor. This curvature term is the Lorentz force of the gravitational field. The main result of this article is that these equations are exactly the (symmetrized) Mathisson-Papapetrou equations for the quantum operators. Extension of these results to the case of spin-one fields may be possible by use of the KDP formalism.     

Calculation of the electric potential and the Lorentz force in a transverse flow past a circular cylinder in a nonuniform magnetic field for various configurations of a locally ionized region at the cylinder surface

We obtain a solution to the equation for the electric potential in a locally ionized transverse magnetohydrodynamic flow past a circular cylinder in a nonuniform magnetic field produced by a linear conductor for various configurations of the ionization region. Analytical formulas are derived for the volume density of the Lorentz force acting on the flow in a locally ionized region. The effect of the Hall parameter and of the configuration of the region of the magnetohydrodynamic interaction on the Lorentz force is analyzed. It is shown that an increase in the Hall parameter leads to a decrease in the Lorentz force acting on the flow, and a change in the configuration of the locally ionized region makes it possible to suppress the effect of the Hall parameter on the Lorentz force.     

Non-minimal coupling to a Lorentz-violating background and topological implications

The non-minimal coupling of fermions to a background responsible for the breaking of Lorentz symmetry is introduced in Diracs equation; the non-relativistic regime is contemplated, and the Pauli equation is used to show how an Aharonov-Casher phase may appear as a natural consequence of the Lorentz violation, once the particle is placed in a region where there is an electric field. Different ways of implementing the Lorentz breaking are presented and, in each case, we show how to relate the Aharonov-Casher phase to the particular components of the background vector or tensor that realizes the violation of Lorentz symmetry.Received: 23 February 2005, Revised: 12 March 2005, Published online: 18 May 2005     

Some Logical Implications of the Two Einstein Assumptions Used in His Analysis of Geometry on a Relativistically Rotating Disc

We show that with the help of the two well known Einstein assumptions used by him in the treatment of geometry on relativistically rotating disc, and elementary logical analysis only, two different and opposite models of rotating discs can be constructed: In one of them the disc, set rotating from the stationary state, changes neither its radius nor circumference, as measured from stationary inertial frame; while in the other both the radius and the circumference contract by the same Lorentz factor. We also show that one can construct discs whose contraction factors vary continuously from unity (no contraction) to the full Lorentz factor.     

Performance Analysis of a Diagonal MHD Accelerator for Space Propulsion

The performance of a diagonal magnetohydrodynamic (MHD) accelerator has been numerically investigated. Studies were carried out using air plasma as a working gas in an equilibrium condition based on the MHD Augmented Propulsion Experiment channel designed by NASA. The MacCormack scheme is employed in order to solve the set of differential equations with MHD approximations. The fundamental performance of a diagonal MHD accelerator considering both flow performance along the channel and propulsion performance has been evaluated under various applied input currents and magnetic fields. The optimum performance is dominated by ${bf j} times {bf B}$ Lorentz body force acceleration, while it is increased with Joule heating and the ${bf u} times {bf B}$ term's contribution, which are detrimental to the propulsion performance. Moreover, friction forces resist the flow performance, particularly near the channel exit.      

The anomalous radiation force of light on a left-handed material

This paper derives the force of the electromagnetic radiation on left-handed materials (LHMs) by a direct applica-tion of the Lorentz law of classical electrodynamics.The expressions of radiation force are given for TE-polarised and TM-polarised fields.The numerical results demonstrate that electromagnetic waves exert an inverse lateral radiation force on each edge of the beams,that is,the lateral pressure is expansive for TE-polarised beams and compressive for TM-polarised beams.The investigation of the radiation force will provide insights into the fundamental properties of LHMs and will provide to better understanding of the interaction of light with LHMs.     

洛伦兹力公式是怎样给出的

在电子尚未发现,并无任何实验证据的1892年,洛伦兹力公式是怎样给出的?回顾了电磁学历史上超距作用和近距作用观点的长期论争以及"什么是电"的长期论争后指出,洛伦兹力公式是场观点和"电就是带电粒子"相结合的产物.一切磁作用力都应归结为磁场对运动带电粒子的作用力--洛伦兹力.     

Quantitative interpretation ofc-axis magnetoresistivity for fields parallel toc-axis in single crystalline La1.86Sr0.14CuO4

The magnetoresistivity, (T, B), of single crystalline La_1.86SrO_0.14CuO₄ as a function of temperature (T) and magnetic field (B) is experimentally studied in a typical Lorentz force free configuration ofB//I//C-axis. It is shown that the extended Josephson coupling model recently developed can quantitatively account for the variation in (T, B) in a wide transition region (five orders)     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

Computation of the electric potential and the Lorentz force in a locally ionized magnetohydrodynamic flow in a nonuniform magnetic field for a transverse flow past a circular cylinder

An analytical solution to electrodynamic equations is obtained for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow for a transverse flow past a circular cylinder in the non-uniform magnetic field of a rectilinear conductor. Analytical formulas for computing the volume density of the Lorentz force acting on the flow in a locally ionized MHD flow are obtained for the case of the conducting and nonconducting surfaces of the cylinder. The influence of the Hall parameter and width of the MHD interaction region on the value of the Lorentz force is analyzed. It is demonstrated that the Lorentz force, which accelerates and not decelerates the flow, appears under certain conditions near the surface of the cylinder in the neighborhood of the critical point.     

确定分布的展向Lorentz力调制下的槽道湍流涡结构

采用直接数值模拟方法,对槽道湍流中确定分布的Lorentz力的流动控制与减阻问题进行研究.讨论了Lorentz力作用于槽道湍流后,流场的特性和涡结构的特性,并对此类Lorentz力对槽道湍流的控制与减阻机理进行了讨论.研究发现:1)Lorentz力诱导的层流流场壁面附近存在梯度极大的展向速度剪切层,该剪切层容易形成流向涡结构;2)在给定合适参数的确定分布的Lorentz力作用下,湍流流场仅剩周期分布的准流向涡;3)与未控制流场相比,控制后的流场中,准流向涡的抬升高度大大降低,从而减小猝发强度,使壁面阻力下降.     

Invariant simultaneity

The concept of the relativity of simultaneity, as a consequence of the Lorentz transformations, is shown to be an unproven inference based on the implicit idea that simultaneity can be determined only on the basis of synchroneity. The Lorentz transformations do imply, by interpretive inference, a relativity of synchroneity whereby a moving system of synchronized clocks appears to be nonsynchronous, with constant nonzero time invariant phases among the clocks that depend only on their relative fixed distances from each other. It does not seem to have been recognized that such an array of uniformly running nonsynchronous clocks, described as isochronous, can also lead to the unambiguous determination of simultaneity. The important significance of the relative temporal phases, namely the relativity of synchroneity, entailed by the Lorentz transformations is that certain alleged logical inconsistencies, asserted by both proponents and opponents of the special theory of relativity, can be readily resolved. The relativity of synchroneity does, however, raise certain other consequences that merit attention and careful consideration.     

Light-induced drift of ions in a magnetic field

The effect of a magnetic field on the ion drift in a weakly ionized gas under the combined action of the light-induced drift and light pressure is studied theoretically. It is shown that, under the action of light, a component of ion drift velocity transverse to the direction of propagation of radiation may appear in a weakly ionized gas upon the application of an external magnetic field. It is shown that the Lorentz force acting on ions in the magnetic field radically changes the dependence of the ion drift velocity on the radiation frequency detuning. It is predicted that the ion drift velocity component along the direction of radiation must reverse its sign upon an increase in the magnetic field and an anomalous light-induced drift may be observed.     

Maxwell electrodynamics from a theory of macroscopically extended particles

It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential A—interpreted absolutely as a measure of the local shift of each particle off its mass shell—rather than theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance.     

Topologies for Lorentz manifolds: The space topology

The main result in this note states and proves that the space topology for Lorentz manifolds is 0-semimetrizable. This is in a certain sense the spacelike version of an analogous result for the Hawking-King-McCarthy path topology, which was published in [5]. But the proofs are completely different. The space topology is the finest topology on a Lorentz manifold, which induces the manifold topology on every spacelike hypersurface. Its geometric significance comes from the fact, that its full homeomorphismgroup is the group of all conformal diffeomorphisms. 0-semimetrics are very natural generalizations of metrics and have interesting interpretations as statistical metrics and as metrics with an elementary length.This paper is dedicated to Hans Vogler on the occasion of his fiftieth birthday.     

Flow pattern and lift evolution of hydrofoil with control of electro-magnetic forces

The initial responses and evolutions of the flow pattern and lift coefficient of a hydrofoil under the action of electro-magnetic (Lorentz) force have been studied experimentally and numerically, and trace particle methods are employed for them. With the introduction of BVF (boundary vortex flux), the quantitative relation among Lorentz forces, BVF and lifts is deduced. The influences of flow patterns on the hydrofoil lift coefficient have been discussed based on the BVF distribution, and the flow control mechanism of Lorentz force for a hydrofoil has been elucidated. Our results show that the flow pattern and lift of the hydrofoil vary periodically without any force. However, with the action of streamwise Lorentz forces, the separation point on the hydrofoil surface moves backward with a certain velocity, which makes the flow field steady finally. The streamwise Lorentz force raises the foil lift due to the increase of BVF intensity. On the other hand, Lorentz force also increases the hydrofoil surface pressure, which makes the lift decrease. However, the factor leading to the lift enhancement is determinant, therefore, the Lorentz force on the suction side can increase the lift, and the stronger the Lorentz force, the larger the lift enhancement. Our results also show that the localized Lorentz force can also both suppress the flow separation and increase the hydrofoil lift coefficient, furthermore, the Lorentz force located on the tail acts better than that located on the front.     

Energy-Momentum Properties and the Spin of Short-Lived Particles

The space–time translation property of a stable particle is characterized by a time-like Lorentz vector (E, _k ). We show in this contribution that unstable particles are, in addition, characterized by a space-like Lorentz 4-vector of uncertainties, or spreads, ( E, k). This is true for unstable states created in formation-, in production-, and in decay-experiments. The space-like nature of the spread vector causes a nonzero momentum spread to be present in all Lorentz frames so that there is no Lorentz frame in which the unstable particle is entirely at rest. With the space-like spreadvector ( E, k) in addition to the time-like (E, _k ), also the rotation property of an unstable particle is affected, and unstable states have an uncertainty in their spin. This means neighboring spin states are occupied in addition to the original spin. Experiments are discussed that show a principal limitation of the accuracy of spin measurement from finite lifetimes. Wave functions for unstable particles are discussed, and we show in the example of a short-lived spin-0 state that the appearance of a spin neighbor in the amplitude is proportional to the inverse lifetime.