Related papers: Visual relativistic mechanics
We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword…
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.
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for 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…
In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial…
We present hydrodynamic equations with relativistic pressure and velocity in the presence of weak gravity, in a cosmological context. Previously we consistently derived special relativistic hydrodynamic equations with weak gravity in…
We present visual calculations in special relativity using spacetime diagrams drawn on graph paper that has been rotated by 45 degrees. The rotated lines represent lightlike directions in Minkowski spacetime, and the boxes in the grid…
In this article we exploit the fact that the special relativistic formula which relates the energy and the 3-momentum of an elementary particle with its rest mass, resembles the pythagorean theorem for right triangles. Using such triangles,…
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…
Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black-hole perturbations to analyzing wave equations. Despite their significance, many of their…
Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light…
Some useful kinematical relations for the absorption of a photon by a nucleus and its recoil are derived for the relativistic incident energies. These expressions provided for the relativistic kinematics of photoabsorption reactions, though…
The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is…
This paper has pedagogical motivation. It is not uncommon that students have great difficulty in accepting the new concepts of standard special relativity, since these seem contrary to common sense. Experience shows that geometrical or…
This paper presents a pedagogical introduction to the issue of how to implement Lorentz transformations in relativistic visualization. The most efficient approach is to use the even geometric algebra in 3+1 spacetime dimensions, or…
Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.