Electrodynamics in accelerated frames revisited

Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space‐time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above.     

惯性系中直线运动的常加速度内禀刚性非惯性系

推导相对惯性系作直线运动的常加速度内禀刚性加速系的坐标变换关系式，并讨论该加速系的主要性质。     

Use of the Lorentz Transformations in Noninertial Reference Frames

The Lorentz transformations are used within the model of a noninertial reference frame without infinitely high accelerations arising at instantaneous jumps of an accelerated observer between different inertial reference frames. It is demonstrated that the twin paradox can be explained within this model with the help of the Lorentz transformations. Based on the model of a noninertial reference frame, the acceleration a measured in the noninertial reference frame is related to the acceleration a measured in an inertial reference frame.     

Application of the Lorentz transformations from an intrinsic reference frame of noninertial clocks

Accelerated motion is considered as a successive presence of an observer in accompanying inertial reference frames (AIRF) with jumps between them. A formula comprising two terms has already been derived to explain the twin paradox. The first term of this formula describes the time dilation in the reference frame associated with the twin at rest, while the moving twin is in the chosen AIRF. The second term describes a jump of readings of the clock of the twin at rest observed by the accelerated twin who jumps in the next AIRF. In the present study, this formula is used to derive the relative velocity and the distance passed by the accelerated twin by the scale associated with the twin at rest from a noninertial reference frame (NRF). Uniformly accelerated motion followed by uniformly decelerated motion to the stop in the initial inertial reference frame is examined. Readings of any clocks at rest, including clocks of the twin at rest, are derived from the NRF. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 59–64, December, 2005.     

Majorana,Pauling and the quantum theory of the chemical bond

Nonlocal electrodynamics is a formalism developed to include nonlocal effects in the measurement process in order to account for the impossibility of instantaneous measurement of physical fields. This theory modifies Maxwell's electrodynamics by eliminating the hypothesis of locality that assumes an accelerated observer simultaneously equivalent to a comoving inertial frame of reference. In this scenario, the transformation between an inertial and accelerated observer is generalized which affects the properties of physical fields. In particular, we analyze how an uniformly accelerated observer perceives a homogeneous and isotropic black body radiation. We show that all nonlocal effects are transient and most relevant in the first period of acceleration.     

Post-Newtonian approximation for a rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a rotating frame of reference. A new method of approximation is used based on a 3+1 decomposition of the equations. The results are expressed explicitly in terms of the gravitational potentials. The space-time is asymptotically flat but not locally flat. The space-time metric contains gravitational terms, inertial terms, and coupled gravitational-inertial terms. The inertial terms in the equation of motion are in agreement with terms obtained by other authors using kinematic methods. The metric and equation of motion reduce to those for an inertial frame of reference under a simple coordinate transformation. The total energy of a particle is given. For the restricted three-body problem this represents the relativistic extension of Jacobi's integral to post-Newtonian order.This article received an honorable mention from the Gravity Research Foundation for the year 1984—Ed.     

Post-Newtonian approximation for an accelerated,rotating frame of reference

The field equations of general relativity are solved to post-Newtonian order for a frame of reference having an arbitrary time-dependent, translational acceleration and an arbitrary time-dependent angular velocity. The derivation is based on a new 3+1 decomposition of the Einstein field equations and geodesic equation of motion. The resulting space-time metric and equation of motion contain gravitational terms, inertial terms, and coupled gravitational-inertial terms. These effects are expressed explicitly in terms of the Newtonian potential and standard post-Newtonian scalar and vector potentials. The physical meaning of the formulas derived is illustrated by application to a system of point-like gravitating masses. These results should be useful for the investigation of general relativistic effects in the analysis of real experimental measurements made with respect to a noninertial frame of reference, such as the surface of the rotating earth or an accelerated spacecraft.     

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame

The spatially one-dimensional relativistic Ornstein-Uhlenbeck process is studied in an arbitrary inertial reference frame. In particular, we derive directly from the stochastic equations of motion in an arbitrary inertial frame the transport equation for the distribution function of the diffusing particles in phase-space. We explain why this result is not trivial and has, at the very least, methodological interest. We also show that this result offers a conceptually new proof of the well-known fact that the relativistic one-particle distribution function in phase-space is a Lorentz scalar. Received 28 March 2000     

Electrodynamics of a continuous medium in a system with specified structure

It is shown that electrodynamics can be considered not only in Minkowski space but also in Riemannian space-time. The exact solutions for the electric field within and beyond a charged plate and a sphere and the space-time geometry are found without applying the Einstein equations. The space-time geometry of a Born-rigid noninertial frame of reference (NFR) with global linear acceleration in space-time having constant curvature is obtained on the basis of the structural equations (integrability conditions). A new Lorentz-covariant condition of stationarity for possible solutions to the Maxwell equations for the particles frozen in a Born-rigid NFR is formulated. In an inertial frame of reference this condition is equivalent to zero four-curl of the field of four-accelerations of particles. This condition provides zero relativistic generalized radiation friction force. The propagation of electromagnetic waves in this NFR and the Doppler effect are described. The limitations imposed on the energy-momentum tensor in the Einstein equations are derived.     

澄清对相对论性原理和协变性的误解

近来有些文章断言,在一个惯性参考系里能量守恒的物理系统,在别的参考系看来能量也一定守恒.实际上这些作者混淆了物理方程式的协变性和相对性原理.本文将澄清这一误解.     

Tomographic Description of a Quantum Wave Packet in an Accelerated Frame

The tomography of a single quantum particle (i.e., a quantum wave packet) in an accelerated frame is studied. We write the Schrödinger equation in a moving reference frame in which acceleration is uniform in space and an arbitrary function of time. Then, we reduce such a problem to the study of spatiotemporal evolution of the wave packet in an inertial frame in the presence of a homogeneous force field but with an arbitrary time dependence. We demonstrate the existence of a Gaussian wave packet solution, for which the position and momentum uncertainties are unaffected by the uniform force field. This implies that, similar to in the case of a force-free motion, the uncertainty product is unaffected by acceleration. In addition, according to the Ehrenfest theorem, the wave packet centroid moves according to classic Newton’s law of a particle experiencing the effects of uniform acceleration. Furthermore, as in free motion, the wave packet exhibits a diffraction spread in the configuration space but not in momentum space. Then, using Radon transform, we determine the quantum tomogram of the Gaussian state evolution in the accelerated frame. Finally, we characterize the wave packet evolution in the accelerated frame in terms of optical and simplectic tomogram evolution in the related tomographic space.     

Inertial spin Hall effect in non-commutative space

In the present Letter the study of inertial spin current (that appears in an accelerated frame of reference) is extended to Non-Commutative (NC) space. In the Hamiltonian framework, the Dirac Hamiltonian in an accelerating frame is computed in the low energy regime by exploiting the Foldy–Wouthuysen scheme. The NC θ-effect appears from the replacement of normal products and commutators by Moyal ?-products and ?-commutators. In particular, the commutator between the external magnetic vector potential and the potential induced by acceleration becomes non-trivial. Expressions for θ-corrected inertial spin current and conductivity are derived explicitly. We have provided yet another way of experimentally measuring θ. The θ bound is obtained from the out of plane spin polarization, which is experimentally observable.     

Use of Lorentz Transformations for Noninertial Frames of Reference

By analogy with the calculation of the path of a mass point in terms of the integral of the point velocity with respect to time, such that the point has a constant velocity V(t _i) within a time interval dt _i, then changes this velocity stepwise by V(t _i+1), moves with this velocity within a time interval dt _i+1, etc., an accelerated motion of an observer with a clock is represented by alternating states of rest in a sequence of inertial frames of reference and instantaneous jumps from one frame of reference into another. Lorentz transformations are used to calculate the readings of a resting clock observed from a noninertial frame of reference represented in this manner, during the rest of a noninertial observer in a next-in-turn inertial frame of reference belonging to the mentioned sequence, and upon a jump. For the observation from a noninertial frame of reference, the relation of the time interval counted by the resting clock to the time interval counted by the accelerated clock and to the acceleration has been obtained.     

探索惯性系

针对牛顿力学框架的两大疑难,结合朗格惯性系的定义,从理论上分析了星球参考系与质心参考系,并指出了在什么条件下它们可以充当惯性系.     

质心系中的基本形式的拉格朗日方程及其应用

推导了质心系中的基本形式的拉格朗日方程,并举例说明联合惯性系中的基本形式的拉格朗日方程可求解约束反力.     

The weight of extended bodies in a gravitational field with flat spacetime

Einstein's gravitational field equations in empty space outside a massive plane with infinite extension give a class of solutions describing a field with flat spacetime giving neutral, freely moving particles an acceleration. This points to the necessity of defining the concept gravitational field not simply by the nonvanishing of the Riemann curvature tensor, but by the nonvanishing of certain elements of the Christoffel symbols, called the physical elements, or the nonvanishing of the Riemann curvature tensor. The tidal component of a gravitational field is associated with a nonvanishing Riemann tensor, while the nontidal components are associated with nonvanishing physical elements of the Christoffel symbols. Spacetime in a nontidal gravitational field is flat. Such a field may be separated into a homogeneous and a rotational component. In order to exhibit the physical significance of these components in relation to their transformation properties, coordinate transformations inside a given reference frame are discussed. The mentioned solutions of Einstein's field equations lead to a metric identical to that obtained as a result of a transformation from an inertial frame to a uniformly accelerated frame. The validity of the strong principle of equivalence in extended regions for nontidal gravitational fields is made clear. An exact calculation of the weight of an extended body in a uniform gravitational field, from a global point of view, gives the result that its weight is independent of the position of the scale on the body.     

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E in a given reference frame were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We show that a tetrad field contains two informations about local rotation, which usually do not coincide. We compute the energy operator in the inertial and the rotating frame, using three different tetrad fields. We find that Mashhoon’s term is there if the spatial triad rotates as does the reference frame—but then it is also there in the energy operator for the inertial frame. In fact, if one uses the same given tetrad field, the Dirac Hamiltonian operators in two reference frames in relative rotation differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.     

Finslerian relativity theory. II

A scalar field and natural frame of reference are considered for a locally nontest inertial particle in a Finslerian space-time. The present paper is a direct continuation of the previous paper [1] of the author; it uses the same notation and continues the numeration of the equations and sections.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 25–28, May, 1980.     

On General Møller Transformation

We give a study on the general Møller transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of thegeodesic equations of motion, the differential form of the general Møller transformation at arbitrary direction is presented.