Related papers: Dynamics of a Relativistic Particle in Discrete Me…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…
In this work a new mechanics will be studied which is based on the hypothesis that the change of linear momentum of a particle happens as a discrete pulses. By using this hypothesis and by considering Newton's relation between energy and…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
The attempt to unify the laws of physics is approached from a discrete vision of space and time, abandoning the continuous medium paradigm that presided over the derivation of certain equations of physics-Navier-Stokes., Navier-Lam{\'e},…
We show that the relativistic expressions for momentum and energy as well as the way in which they transform could be derived without involving collisions and conservation laws. Our approach involves relativistic kinematics via the addition…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for…
In relativistic dynamics, force and acceleration are no longer parallel. In this article, we revisit the relativistic motion of a particle under the action of a constant force, $\boldsymbol{f}$. \ For a two-dimensional motion, the final…
It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein…
Newton's law of motion relative to an inertial frame ("the laboratory") for a particle subject to a force acting at a certain time may be interpreted in either of two ways: (1) The force acting on the particle during an infinitesimal time…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
It is shown that the correct expressions for momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics…
Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The…
The fundamental equations of relativistic dynamics are derived from a thought experiment and from the transformation of relativistic velocity avoiding collisions and conservation laws of momentum and energy.