Related papers: A Derivation of Three-Dimensional Inertial Transfo…
It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation…
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…
Ever since the work of von Ignatowsky circa 1910 it has been known (if not always widely appreciated) that the relativity principle, combined with the basic and fundamental physical assumptions of locality, linearity, and isotropy, leads…
In the standard formulation of the twin paradox an accelerated twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and…
A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
The equation of the Doppler shift of two bodies in inertial motion in a reference frame at rest (i.e., stationary reference frame) is derived. In this derivation, the wave-particle duality of photons in the theory of special relativity is…
A thought experiment first proposed by Sartori is analysed using the parallel velocity addition formula of special relativity. The distances and proper-time intervals between some similarly defined spatial coincidence events are found to be…
It is shown that the equations of gravitational waves and cosmological acceleration follow from the tensor of inertial forces. The possibility of the existence of three types of gravitational waves: transverse, potential and vortex waves…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical 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…
We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…
Basic for the definition of 'time' are clocks operating under stationary conditions. The periods of two clocks can be compared with each other via two return experiments. The central clock mediates between the rotating and the inertial…
Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of…
This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…
The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order…
In this paper we review two symmetry axioms of special relativity and their connections to each other together with their role in some famous predictions of relativity theory, such as time dilation, length contraction, and the twin paradox.…
The formulas for the 3-dimensional distance and the velocity modulus in the 4-dimensional linear space with the Berwald-Moor metrics are obtained. The used algorithm is applicable both for the Minkowski space and for the arbitrary…