相关论文: A note on the computation of geometrically defined…

There is a vast literature showing the connection between a deformed relativistic kinematics and a curved momentum space, and, in particular, how the former can be obtained from the geometrical properties of the latter. However, there is…

We show that standard Relativistic Dynamics Equation F=dp/d\tau is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor…

We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…

The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…

Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…

Relying on the equivalence principle, a first approach of the general theory of relativity is presented using the spacetime metric of an observer with a constant proper acceleration. Within this non inertial frame, the equation of motion of…

In flat spacetime, as a simple 4-vector, a particle's 4-velocity cannot be changed by translation. Parallel translation then produces constant velocity, motion without force. Here we consider a richer, but less well-known, representation of…

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…

We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…

A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational…

Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background…

We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via…

Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors).…

This Letter, i.e. for the first time, proves that a general invariant velocity is originated from the principle of special relativity, namely, discovers the origin of the general invariant velocity, and when the general invariant velocity…

The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…

In this paper, we present a series of techniques to describe General Relativity using Geometric Algebra (GA). We emphasize the physical interpretation of quantities and provide a step-by-step guide for performing calculations. In doing so,…

Cosmological peculiar velocities have traditionally been studied within the framework of Newtonian theory. Around the turn of the century, a few quasi-Newtonian analyses appeared in the literature, but led to equations and results identical…

The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead,…

We investigate the possibility of accounting for the observed anomalous velocities of stars in galaxies to be a result of a dynamic prescription for having a galaxy generate and prescribe its own inertial frame. It is demonstrated that…

Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…