Related papers: A one-map two-clock approach to teaching relativit…
In Newtonian space-time there exist four, and only four, causal classes of frames. Natural frames allow to extend this result to coordinate systems, so that coordinate systems may be also locally classified in four causal classes. These…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
The apparent times and positions of moving clocks as predicted by both `non-local' and `local' Lorentz Transformations are considered. Only local transformations respect translational invariance. Such transformations change temporal but not…
The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are…
Elementary particles, i.e. the basic constituents of nature, are characterized by quantum recurrences in time. The flow of time of every physical system can be therefore decomposed in elementary cycles of time. This allows us to enforce the…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
We motivate and construct a mathematical theory for the separation of space and time in general relativity. The formalism only requires a single observer and an optional choice of reference frame at each instant. As the splitting is done…
Although the quantization of relativistic systems in a proper-time framework gives new insights concerning the understanding of the so-called localization problem, classical observers cannot be treated as quantum comoving frames and real…
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…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
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…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
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…
We consider a scenario that involves a machine gun, the bullets it fires and a moving target, considered from the rest frame of the machine gun and from the rest frame of the target respectively. Involving the special relativity via its two…
Several space missions that will use atomic clocks on board of an Earth-orbiting satellite are planned for the near future, such as the Atomic Clock Ensemble in Space (ACES) or the Space Optical Clock on the ISS (I-SOC). The increasing…
A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in…
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most…
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students…