Related papers: Relativity for games
This contribution shows that the main topics of Relativity can be discussed at an elementary level and in a considerable extent - including the formal results of "Time Dilation" and "Lorentz Contraction" - by a minor modification of the…
Lorentz transformation on two-dimensional spacetime is obtained without assumption of linearity. To obtain this, we use the invariance of wave equations, which is recently proved to be equivalent to the causality preservation.
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
The theoretical framework of electromagnetism played a foundational role in Einstein's development of special relativity. To support conceptual understanding, we present a fully special relativistic computer simulation that visualizes…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
We have developed a relativistically-accurate computer graphics code and have used it to produce photo-realistic images and videos of scenes where special relativistic effects dominate, either in astrophysical contexts or in imaginary…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
Exploring Einstein's theories of relativity in quantum systems, for example by using atomic clocks at high speeds can deepen our knowledge in physics. However, many challenges still remain on finding novel methods for detecting effects of…
A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and…
The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
In general relativity, only relative acceleration has an observer-independend meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We derive the equations governing both…
Relativistic aberration influences apparent luminosities of objects moving with relativistic relative velocities. The superluminosity or dimming of incoming or receding jets ejected from Active Galactic Nuclei is believed to be the…
The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light remains always the same. Consequently, a wave packet of light exhibits…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…
The special theory of relativity teaches us that, although distinct inertial frames perceive the same dynamical laws, space and time intervals differ in value. We revisit the problem of time contraction using the paradigmatic model of a…