Related papers: Explicit exact expression for the Thomas precessio…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
The paper proposes 4-dimensional equations for the proper characteristics of a rigid reference frame \[ {{{W}'}^{\gamma }}=\Lambda ^{0}_{\;\;i}\frac{d\Lambda ^{\gamma i}}{d{t}}\,\,,\] \[ {{{\Omega }'}^{\gamma }}=-\frac{1}{2}\,{{e}^{\alpha…
We define the notion of special Lagrangian curvature, showing how it may be interpreted as an alternative higher dimensional generalisation of two dimensional Gaussian curvature. We obtain first a local rigidity result for this curvature…
In this article, matrix and vector formalisms for Lorentz transformations in time ($t$) and two space dimensions ($x$ and $y$) are developed and discussed. Lorentz transformations conserve the squared interval $t^2 - x^2 - y^2$. Examples of…
It is well known that a sequence of two non-collinear pure Lorentz transformations (boosts) is not a boost again, but involves a spatial rotation, the Wigner or Thomas-Wigner rotation. The formation of this rotation is visually illustrated…
The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects…
This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $\Lambda$-term within gravito-electromagnetic formalism. It is shown that the presence of the $\Lambda$-term in the…
General relativity predicts that a rotating body produces a frame-dragging (or Lense-Thirring) effect: the orbital plane of a test particle in a non-equatorial orbit precesses about the body's symmetry axis. In this paper we compute the…
Gravitational Thomas Precession (GTP) is the name given to Thomas Precession when the acceleration is caused by a gravitational force field. The contributio n of the GTP to the the anomalous perihelion advance of the orbit of Mercury is…
We look afresh at the deduction of the "Lorentz contraction" of a "rod" from the Lorentz transformation equations of the special theory of relativity. We show that under special conditions, which include acceleration of the "rod", length…
We study a cosmological model based on the canonical Hamiltonian transformation theory. Using a linear-quadratic approach for the free gravitational De Donder-Weyl Hamiltonian $H_\mathrm{Gr}$, the model contains terms describing a…
For the Dirac particle in the rotational system, the rotation induced inertia effect is analogously treated as the modification of the "spin connection" on the Dirac equation in the flat spacetime, which is determined by the equivalent…
The Bargmann-Michel-Telegdi equation, which describes the precession of the spin of a charged Dirac particle moving in a homogeneous electromagnetic field, is generalized to include also other homogeneous background fields. The treatment…
The starting point of the theory of Special Relativity$^1$ is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity…
In a calculation that directly parallels the derivation of the Thomas precession, the first time derivative of the retarded potentials is derived. The solutions have to be integrated in time to obtain the potential solution. The Thomas…
We study the precession of an off-axis straight vortex in a rotating nonaxisymmetric harmonic trap in the Thomas-Fermi (TF) regime. A time-dependent variational Lagrangian analysis yields the dynamical equations of the vortex and the…
In this paper we study the orbits of massive bodies moving in the spacetime generated by a spherically symmetric and non-rotating distribution of mass. More specifically, our treatment discusses the more accurate calculation of the…