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Using elementary knowledge of Special Relativity, we design a computational classroom experiment in excel and python. Here, we show that any inertial observer $\mathcal{B}$ with an arbitrary speed $u_\mathcal{B}$ is associated with a unique…
This tutorial, addressing physics teachers and undergraduate students, aims at clarifying some aspects of time in special relativity. In particular, time dilation is usually presented only as the well-known ratio of lab time over proper…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
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…
The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property…
Treating time as a local variable permits robust approaches to kinematics that forego questions of extended-simultaneity, which because of their abstract nature might not be addressed explicitly until a first relativity course and even then…
Relativistic Newtonian Dynamics (RND) was introduced in a series of recent papers by the author, in partial cooperation with J. M. Steiner. RND was capable of describing non-classical behavior of motion under a central attracting force. RND…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
Special Relativity (SR) kinematics is derived from very intuitive assumptions. Contrary to standard Einstein's derivation, no light signal is used in the construction nor it is assumed to exist. Instead we postulate the existence of two…
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…
The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the…
Based on the principle of relativity and the postulate on universal invariant constants (c,l), all possible kinematics can be set up with sub-symmetries of the Umov-Weyl-Fock transformations for the inertial motions. Further, in the…
Einstein's relativity theory demands that all meaningful physical objects should be defined covariantly, i.e. in a coordinate independent way. Concepts of relative velocity, acceleration, gravity acceleration and gravity potential are…
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…
To describe the ``slow'' motions of n interacting mass points, we give the most general 4-d non-instantaneous, non-particle symmetric Galilei-invariant variational principle. It involves two-body invariants constructed from particle…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
We take J. S. Bell's commendation of ``frame-dependent'' perspectives to the limit here, and consider motion on a ``map'' of landmarks and clocks fixed with respect to a single arbitrary inertial-reference frame. The metric equation…