Electrodynamic equations in noninertial reference frames

The formalism for analysis of exterior spatial differential forms developed by the present author is used to study the equations of electrodynamics in noninertial reference frames. General covariant differential and integral relationships which generalize the corresponding laws of classical three-dimensional electrodynamics in inertial reference frames are obtained.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 7, pp. 97–104, July, 1978.The author expresses his sincere gratitude to V. I. Rodichev for his constant interest in the study and valuable advice.     

Analytical mechanics in noninertial reference frames

The fundamental equations of the relativistic analytical mechanics of N gravitating bodies in noninertial reference frames are obtained with the application of the apparatus of three-dimensional tensor analysis.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–39, September, 1981.     

Optical position meters in a noninertial frame of reference

The method of calculating simple optical position meters in the proper frames of reference of measuring devices is developed and applied to the analysis of two types of optical test-mass position meters, i.e., round trip and forward trip. It is shown that the results of calculation of the response in the laboratory frame of reference and in the proper frame of reference of the phase detector coincide for the meter of the first type but not for that of the second type. It is shown that only calculations in the proper frame of reference of the phase detector result in an experimentally measurable quantity.     

Formalism of exterior forms and noninertial reference frames

A general covariant theory of exterior spatial forms is proposed and the fundamental differential operations are defined in a formalism whose basic object is the congruence of timelike curves specified in a space-time manifold.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–97, July, 1978.The author is sincerely grateful to Professor V. I. Rodichev for his constant interest in the work.     

Quantum mechanics in noninertial reference frames: Relativistic accelerations and fictitious forces

One-particle systems in relativistically accelerating reference frames can be associated with a class of unitary representations of the group of arbitrary coordinate transformations, an extension of the Wigner–Bargmann definition of particles as the physical realization of unitary irreducible representations of the Poincaré group. Representations of the group of arbitrary coordinate transformations become necessary to define unitary operators implementing relativistic acceleration transformations in quantum theory because, unlike in the Galilean case, the relativistic acceleration transformations do not themselves form a group. The momentum operators that follow from these representations show how the fictitious forces in noninertial reference frames are generated in quantum theory.     

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration can equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle.     

光在激活光纤中的传输

本文推导了连续光及宽脉冲在激活光纤中的运动方程,采用激活物质极化的量子理论,在零级近似及一级近似情况下,对其运动方程进行了求解,并讨论了激活物质对脉冲群速度的影响,定量地描述了连续光及宽脉冲的振幅与位相及群速度在激活光纤中的变化行为。     

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.     

Light propagation in stratified anisotropic media

Light propagation in stratified anisotropic media with arbitrary orientation of optic axes smoothly varying from layer to layer is considered. In the WKB approximation, a general expression for the field is obtained. For the case of a uniaxial medium, the normal waves are found and specific features of the light propagation are analyzed. General conditions are obtained that determine the turning points and forbidden zones. It is shown that the developed approach allows one to find trajectories of rays in anisotropic media with arbitrary layered structure.     

Light propagation in twisted dielectric media

A periodically stratified medium is investigated. Especially, we use a dielectric tensor, which describes an optically uniaxial crystal, whose axis lies obliquely in space and rotates about thez-axis as function ofz. The interpretation of the results differs considerably from that for another often treated kind of anisotropy.     

Pseudo-entanglement evaluated in noninertial frames

We study quantum discord, in addition to entanglement, of bipartite pseudo-entanglement in noninertial frames. It is shown that the entanglement degrades from its maximum value in a stationary frame to a minimum value in an infinite accelerating frame. There is a critical region found in which, for particular cases, entanglement of states vanishes for certain accelerations. The quantum discord of pseudo-entanglement decreases by increasing the acceleration. Also, for a physically inaccessible region, entanglement and nonclassical correlation are evaluated and shown to match the corresponding values of the physically accessible region for an infinite acceleration.     

Rotational degeneracy breaking of atomic substates: A composite quantum system in a noninertial reference frame

The degenerate magnetic substates of a field-free atomic system are split in a rotating reference frame. The splitting and ordering of the states should be experimentally demonstrable by means of laser-induced quantum interference spectroscopy of hydrogenic Rydberg states. This would manifest dynamical consequences of a noninertial reference frame on theinternal structure of a composite quantum system-in contrast to the observed neutron Sagnac effect, which involves the relative phase of essentially point particles. The predicted level splitting is independent of constituent particle masses; a composite quantum system in a rotating reference frame exhibits effects inequivalent to those that would be engendered in an inertial frame by a gravitational field.The original essay upon which this article is based received honorable mention from the Gravity Research Foundation for 1988.     

Light propagation and light scattering

A self-consistent theory is given for the propagation and scattering of light in a material medium. A generalized statement for the extinction theorem is obtained. To first order Yvon's result is recovered for the intensity of polarized scattered light.