Related papers: Covariant Uniform Acceleration
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…
We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit…
We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We…
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…
We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…
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…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
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…
This contribution adds to the points on the <indeterminacy of special relativity> made by De Abreu and Guerra. We show that the Lorentz Transformation can be composed by the physical observations made in a frame K of events in a frame…
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant…
We study the Lie symmetries of non-relativistic and relativistic higher order constant motions, in $d$ spatial dimensions, like constant acceleration, constant rate-of-change -of-acceleration (constant jerk), and so on. In the…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal…
We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit…
Based on the generalized principle of relativity and the ensuing symmetry, we have shown that there are only two possible types of transformations between uniformly accelerated systems. The first allowable type of transformation holds if…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity,…
The aim of this article is the formulation of the basic laws of Physics by frames, i.e. quadruples of exterior differential one forms. The basic operator is a modification of the Hodge-de Rham Laplacian d*d*+*d*d, where * is the hyperbolic…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…