SearcharxivSearch

arXiv · 2007.07780

Special Relativity -- Applications to astronomy and the accelerator physics

Abstract

There are many books on the classical subject of special relativity. However, after having spent a number of years, both in relativistic engineering and research with relativity, I have come to the conclusion that there exist a place for a new book. I do believe that the present book is not quite the same as the others, mainly due to attempt to cast light on dark corners. I should make it clear what this little book is not. It is not a textbook on relativity theory. What the book is about is the nature of special relativistic kinematics, its relation to space and time, and the operational interpretation of coordinate transformations. Every theory contains a number of quantities that can be measured by experiment and an expressions that cannot possibly be observed. Whenever we have a theory containing an arbitrary convention, we should examine what parts of the theory depend on the choice of that convention and what parts do not. The distinction is not always made and many authors claim some data to be observable, according to arbitrary conventions, which do not correspond to any physical experiment. This leads to inconsistencies and paradoxes that should be avoided at all cost.

Explore related subjects

Keep this discovery

BibTeXRIS

Evgeny Saldin. 2020-07-14. Special Relativity -- Applications to astronomy and the accelerator physics. https://arxiv.org/abs/2007.07780

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Projection Angles of Projectiles in Sports: Qualitative Assessment of the Effects of Aerodynamic Forces or Run-Up

We examine two major factors that influence the optimum projection angle: aerodynamic forces and the effect of run-up. With respect to aerodynamics, we consider not only the drag but also the lift generated by spin during flight. By linearizing the equations of motion that include these forces, we derive perturbation solutions with respect to drag and lift coefficients and clarify their qualitative effects. The results show that both drag and lift reduce the optimum projection angle, with the latter exerting a stronger influence. To investigate the effect of run-up, we use an extended projection model in which the initial speed depends on the initial angle. Analysis of this model reveals that a stronger run-up increases the relative projection angle but decreases the launch angle observed from the ground. These findings provide a mechanical explanation for the release angle in shot put and the takeoff angle in long jump. The present study establishes a simple theoretical framework for clarifying the respective roles of aerodynamic and run-up effects in determining the optimum projection angles in sports.

physics.class-ph

Dunkl-Based Modeling of Vibrational Modes in Lightweight Elastic Beams

Optimizing slender elastic structures for renewable energy applications requires non-classical continuum formulations capable of accounting for spatial micro-interactions without sacrificing analytical tractability. Here, we extend beam vibration mechanics by replacing standard spatial derivatives with the Dunkl differential operator. This modification introduces a reflection-coupled mathematical structure that accounts for spatial parity effects across the beam domain. We formulate the governing dynamic equations into a generalized eigenvalue problem and derive exact analytical expressions for modal characteristics under standard boundary conditions. The classical limit confirms exact convergence to classical Euler-Bernoulli formulations. Parametric analyses reveal that the Dunkl parameter acts as a reflection-induced modulation parameter, significantly shifting natural frequencies and altering the modal characteristics of higher modes. These results provide an analytical baseline for dynamic optimization in lightweight structural components.

physics.class-ph

A purely mechanical system realizing a Coulomb-like interaction

We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $V\propto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.

physics.class-ph