Related papers: The Lavrentiev phenomenon
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…
The problem studied is formulated in the title: proper mass variation under gravitational and Coulomb force action in Relativistic Mechanics of point particle. The novelty is that equations of motion are obtained in the relativistic…
Let $F(y):=\displaystyle\int_t^TL(s, y(s), y'(s))\,ds$ be a positive functional, unnecessarily autonomous, defined on the space $ W^{1,p}([t,T]; \mathbb R^n)$ ($p\ge 1$) of Sobolev functions, possibly with prescribed one or two end point…
We consider an Einstein-Maxwell action modified by the addition of three terms coupling the electromagnetic strength to the curvature tensor. The corresponding generalized Maxwell equations imply a variation of the speed of light in a…
Taking into account only luminous objects, the kinematics of clusters of galaxies, galaxies and their interior, require a much higher mass than the luminous one to explain the observations. This situation has provoked more than 30 years of…
We show that a slowly varying Newton's constant, consistent with existing bounds, can potentially explain a host of observations pertaining to gravitational effects or phenomena across distances spanning from planetary to the cosmological,…
In this paper, we revive a special, less-common, variational principle in analytical mechanics (Hertz' principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori.…
Variational inference consists in finding the best approximation of a target distribution within a certain family, where `best' means (typically) smallest Kullback-Leiber divergence. We show that, when the approximation family is…
Discussions on the Langevin Twins 'paradox' are most often based on a "triangular" diagram which outlines the twins spacetime travels. It won't be our way, avoiding what we think to be a problem at the basis of numerous controversies. Our…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
In this study, the problem of overcoming the infinite energy barrier separating the bradyonic and tachyonic realms is investigated. Making use of the Majorana equation for particles with arbitrary spin and the Heisenberg uncertainty…
Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional…
The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences, like the Casimir effect which is now measured with good accuracy and agreement…
We consider various mechanisms of modifying the effect of intrinsic curvature in gravity with respect to general relativity. Two primary approaches are studied. First, by considering a Lagrange multiplier or an auxiliary field. Second, by…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to…
Astroparticle physics has recently reached a new status of precision due to the construction of new observatories, operating innovative technologies and the detection of large numbers of events and sources. The precise measurements of…
Particle-antiparticle pairs are predicted by quantum field theory to appear as vacuum fluctuations. The model of the vacuum used here is postulated to have the following properties: To minimize the violation of conservation energy allowed…