Related papers: Velocity addition in Special Relativity and in New…

The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…

Even though the usual form of relativistic mechanics does not allow superluminal particle velocities and nonlocal interactions, these features are not forbidden by relativity itself. To understand this on a deeper level, we study a…

Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition…

Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other…

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…

Let S_1 and S_2 be ergodic extensions of finite measure preserving transformations T_1 and T_2, where the extensions are by rotations of a compact group G. Then there is an N-valued function k, measurable with respect to the factor T_1, so…

The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…

When introducing special relativity, an elegant connection to familiar rules governing Galilean constant acceleration can be made, by describing first the discovery at high speeds that the clocks (as well as odometers) of different…

The velocity of light is invariant under transformations that alter space-time metrics, while leaving Maxwell's equations invariant. A one-parameter special conformal invariance group of the equations exposes an ambiguity in current…

A full nexus between Newtonian and relativistic mechanics is set. Contrarily to what is commonly thought, Newtonian mechanics can be amended to suit all speeds up to c. It is demonstrated that when introducing the fact that the pulse of…

We consider the presence of odd powers of the speed of light $c$ in the covariant nonrelativistic expansion of General Relativity (GR). The term of order $c$ in the relativistic metric is a vector potential that contributes at leading order…

We derive the relativistic velocity addition law, the transformations of electromagnetic fields and space-time intervals by examining the drift velocities in a crossed electromagnetic field configuration. The postulate of the light velocity…

Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…

There have been a number of papers proposing that the light speed of a homogeneous and isotropic universe is variable. This paper outlines a simple way that the vectors and tensors of special relativity can be extended to allow such a…

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…

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation…

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…

Jaynes' transformation group principle is used to derive the objective prior for the velocity of a non-zero rest-mass particle. In the case of classical mechanics, invariance under the classical law of addition of velocities, leads to an…

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 relation among instantaneous, mean and average velocities in one-dimensional motion with constant acceleration is studied. It was shown that the instant velocity evaluated in the time $t_{p}=\left(t_2+t_1\right)/2$ is similar to the…