Related papers: Deriving relativistic momentum and energy. II. Thr…
In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
This paper presents an alternative {\it relativistic nonlinear} approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature.…
A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…
We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force…
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of…
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,…
We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…
The partial derivative of the kinetic energy of a dynamical system with respect to a generalized coordinate as it appears in the Lagrangian formalism is not equal to the derivative of the kinetic energy with respect to the same coordinate…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
Three dimensional time and energy operators are introduced and an uncertainty relation between them is proved.
We establish an extended version of the kinetic theory of the relativistic axionically active multi-component plasma, which is based on the inclusion of a unit time-like vector field, associated with the velocity of dynamic aether, into the…
In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution and other observables from the solution and compare them to measurements from the Relativistic Heavy Ion Collider (RHIC).…
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested…