Related papers: Relativity for games
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
The effect of the linear-fractional transformations on the parallel lines in the spacetime has been studied. Fock-Lorentz transformations maps a line to a line, from which one can obtain the combinations rule for the velocities in the…
The absence of an identified consequence at solar system scale of the cosmological space expansion is usually explained considering that space expansion does not affect local anysotropies in matter distribution. This can also be explained…
The action for a $(3+1)$-dimensional particle in very special relativity is studied. It is proved that massless particles only travel in effective $(2+1)$-dimensional space-time. It is remarkable that this action can be written as an action…
Real-time depth of field in game cinematics tends to approximate the semi-transparent silhouettes of out-of-focus objects through post-processing techniques. We leverage ray tracing hardware acceleration and spatio-temporal reconstruction…
The observed flat rotation curves of galaxies require either the presence of dark matter in Newtonian gravitational potentials or a significant modification to the theory of gravity at galactic scales. Detecting relativistic Doppler shifts…
In special relativity theory the physical quantities are generally expressed as function of the velocity. In the particular case of an extended object, the factor 1/gamma of Lorentz contraction of its length in the direction of motion is…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
In the context of special relativity, we describe with detail the Doppler effect between a light source at rest and an observer in linear motion and constant proper acceleration. To have an Englis version of this article, ask the authors.…
The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…
Special Relativity is often seen as a conceptually difficult topic, which in turn is difficult to effectively teach. This work focuses on the role of visualizations as a tool in teaching Special Relativity at the secondary or university…
A special case of the relativistic Doppler effect, which occurs when light reflects from a moving mirror, is discussed. The classic formula for the Doppler shift is derived in a fully non-relativistic fashion using basic facts from…
This article explores the constraints of perception and cognition in relativistic physics. Describing reality as a cognitive representation of our sensory inputs, the article shows how the limitations in perception translate to the…
We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the…
This article presents a simple model that reproduces key concepts of modern cosmology within the framework of special relativity, at a level that is suitable for an undergraduate or high school setting. The model includes cosmic expansion…
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…
Principle of Relativity involving all, not only subluminal, inertial frames leads to the disturbance of causal laws in a way known from the fundamental postulates of Quantum Theory. We show how quantum indeterminacy based on complex…
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…
Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on…