Related papers: Conservative relativistic algebrodynamics induced …
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
The coupled Maxwell-Lorentz system describes feed-back action of electromagnetic fields in classical electrodynamics. When applied to point-charge sources (viewed as limiting cases of charged fluids) the resulting nonlinear weakly…
It is proved that the class of stable interatomic potentials admits an exact representation in the form of a finite or infinite superposition of Yukawa potentials. An auxiliary scalar field is introduced to describe the dynamics of a system…
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous…
We propose a novel interpretation of Quantum Mechanics, which can resolve the outstanding conflict between the principles of locality and realism and offers new insight on the so-called weak values of physical observables. The discussion is…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic…
I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schr\"odinger equation. The laws of physics are determined solely by the energy eigenspectrum of the…
We show that a modified Relativity Principle could explain in a "classical" way the strange correlations of entangled photons. We propose a gedanken experiment with balls and boxes that predicts the same distribution of probability of the…
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest…
A new approach to the electroweak properties of two--particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main novel feature of this approach is the new…
We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of…
The natural constraints for the weak-field approximation to composite gravity, which is obtained by expressing the gauge vector fields of the Yang-Mills theory based on the Lorentz group in terms of tetrad variables and their derivatives,…
The notion of conservative algebras appeared in a paper by Kantor in 1972. Later, he defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra $W(n)$ does…
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
Conservation of energy and momentum in the classical theory of radiating electrons has been a challenging problem since its inception. We propose a formulation of classical electrodynamics in Hamiltonian form that satisfies the Maxwell…
In 1990 Kantor defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on the $n$-dimensional vector space. If $n>1$, then the algebra $W(n)$ does not belong to any well-known class of algebras (such as associative,…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…