Related papers: The rules of 4-dimensional perspective: How to imp…
It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that…
Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Assume that arc length is measured with the flat spacetime metric. Then, for the most general Poincare group representation for translating 4-vectors, curves with parallel translated tangent vectors must have accelerations that are the…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
A general representation of the quaternion gradients presented in the literature is proposed, and an universal update equation for QLMS-like algorithms is obtained. The general update law is used to study the convergence of widely linear…
Explicit formulae for the $4\times 4$ Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well-known. Significantly less well-known is the explicit formula for a general Lorentz…
We develop a relativistic velocity space called \emph{rapidity space} from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-colinear Lorentz boosts.…
The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a…
A submarine moving at relativistic horizontal velocity sinks in Earth's rest frame due to length contraction while appearing to float in its own frame. Using spacetime geometry and the Lorentz transformations, we show that the resolution…
Starting from a five-dimensional (5D) vacuum theory of gravity where the extra coordinate is considered as noncompact, we investigate the possibility of inducing four-dimensional (4D) phantom scenarios by applying form-invariance symmetry…
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 starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
A five dimensional space without invariance under local Lorentz transformations is studied, and the transformations under which the theory is invariant are introduced. We show that the Lorentz force is included in the ensuing equations of…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
In this article, Generalized Principle of "limiting 4-dimensional symmetry": The laws of physics in non-inertial frames must display the 4-dimensional symmetry of the Generalized Lorentz-Poincare group in the limit of zero acceleration,is…
In this study, beginning with the 4D asymptotically flat Kerr black hole solution in the Boyer-Lindquist (BL) coordinate system, then by using the technique of frame-dragging and some coordinate transformation to incorporate the…