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A geometric diagram that allows one to visualize the Poincar\'e formula for relativistic addition of velocities in one dimension is presented. An analogous diagram representing the angle sum formula for trigonometric tangent is given.
Using spacetime algebra, the geometric algebra of spacetime, the general problem of relativistic addition of velocities is addressed. The successive application of non-collinear Lorentz boosts is then studied in Minkowski spacetime. Even…
Universal velocity addition formulas analogous to the well-known formula in special relativity are found for four geometrically defined relative velocities in a large class of Robertson-Walker spacetimes. Explicit examples are given. The…
In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
We reconsider velocity addition/subtraction in Special Relativity and re-derive its well-known non-commutative and non-associative algebraic properties in a self contained way, including various explicit expressions for the Thomas angle,…
The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this…
From the principle of relativity with two universal invariant parameters $c$ and $l$, 24 possible kinematical (including geometrical and static) algebras can be obtained. Each algebra is of 10 dimensional, generating the symmetry of a 4…
The book presents ideas by H. Poincare and H. Minkowski according to those the essence and the main content of the relativity theory are the following: the space and time form a unique four-dimensional continuum supplied by the…
We present a comprehensive introduction to the kinematics of special relativity based on Minkowski diagrams and provide a graphical alternative to each and every topic covered in a standard introductory sequence. Compared to existing…
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional…
Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors).…
In order to ask for future concepts of relativity, one has to build upon the original concepts instead of the nowadays common formalism only, and as such recall and reconsider some of its roots in geometry. So in order to discuss 3-space…
Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of…
It is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincare algebra.…
Mermin [Am. J. Phys. {\bf 51}, 1130--1131 (1983)] derived the relativistic addition of the parallel components of velocity using the constancy of the speed of light. In this note, the derivation is extended to the perpendicular components…
What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer.…
Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a…
The second Poincar\'e kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincar\'e symmetry is presented and their properties are analyzed. On the geometries, the new…