Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame

A discontinuity in the electromagnetic field of a uniformly accelerated charge

The electric field of a uniformly accelerated charge shows a plane of discontinuity, where the field extending only on one side of the plane, terminates abruptly on the plane with a finite value. This indicates a non-zero divergence of the electric field in a source-free region, implying a violation of Gauss law. In order to make the field compliant with Maxwell's equations everywhere, an additional field component, proportional to a $δ$-function at the plane of discontinuity, is required. Such a "$δ$-field" might be the electromagnetic field of the charge, moving with a uniform velocity appro…

匀加速运动物体追击曲线确定的数值方法

A Numerical Procedure for the Determination of the Pursuit Curve of Objects with Uniformly Accelerated Motion

本文针对不同加速度和初速度物体的追击问题，先分析直线逃逸情形，推导特殊初速下的解析解，再提出任意路径下的数值求解方法。

A new view on relativity: Part 1. Kinematic relations between inertial and relativistically accelerated systems based on symmetry

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation of the transformations between them. There are two consistent ways of defining the inputs and outputs to describe the transformations and relative motion between the systems. The standard approach uses a mixture of the two ways. By formulating the principle of special and general relativity as a symmetry principle we are able to specify these transformations …

Relativistic contraction of an accelerated rod

The relativistic motion of an arbitrary point of an accelerated rigid rod is discussed for the case when velocity and acceleration are directed along the rod's length. The discussion includes the case of a time-dependent force applied to a single point, as well as a time-independent force arbitrary distributed along the rod. The time dependence of the rod's relativistic length depends on the application point of the force, but after the termination of acceleration the final velocity and length do not depend on it. An observer on a uniformly accelerated rod feels an inertial force which decreas…

Einstein's accelerated reference systems and Fermi-Walker coordinates

We show that the uniformly accelerated reference systems proposed by Einstein when introducing acceleration in the theory of relativity are Fermi-Walker coordinate systems. We then consider more general accelerated motions and, on the one hand we obtain Thomas precession and, on the other, we prove that the only accelerated reference systems that at any time admit an instantaneously comoving inertial system belong necessarily to the Fermi-Walker class.

Radiation reaction and the acceleration-dependent mass increase of a charged sphere undergoing uniform acceleration

Photon emission from a uniformly accelerated charge is among the most mysterious physical phenomena. Theories based on the Lorentz-Abraham-Dirac equation mostly conclude that a uniformly accelerated point charge cannot feel radiation reaction. Such a conclusion suggests that the origin of the photon energy is unclear. In this paper, we determine the self-force of a uniformly accelerated charged sphere using the Lorentz force equation, with an assumption that the sphere is Lorentz-contracted during the acceleration. For large acceleration, the calculated self-force converges to the radiation re…

Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how…