Related papers: Abstract Coordinate Transforms in Kinematic Change…
The treatment of the principle of general covariance based on coordinate systems, i.e., on classical tensor analysis suffers from an ambiguity. A more preferable formulation of the principle is based on modern differential geometry: the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
The most general transformation connecting inertial frames is derived from rather general and simple assumptions, without the postulate of constancy of the speed of light in vacuo.
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
It is proved by means of the dynamical effects of special relativity that velocity caused by accelerating process is not a relative concept. The influence of accelerating process should be considered in space-time theory. Besides the…
The most general coordinates transformations that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. We…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
We consider the question of computing invariant measures from an abstract point of view. We work in a general framework (computable metric spaces, computable measures and functions) where this problem can be posed precisely. We consider…
Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article,…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
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…
Emergent modified gravity has shown that the canonical formulation of general relativity gives rise to a larger class of covariant modifications than action-based approaches, so far in symmetry-reduced models. This outcome is made possible…
The derivation of the transformations between inertial frames made by Mansouri and Sexl is generalised to three dimensions for an arbitrary direction of the velocity. Assuming lenght contraction and time dilation to have their relativistic…
I here investigate what is arguably the most significant residual challenge for the proposal of phenomenologically viable "DSR deformations" of relativistic kinematics, which concerns the description of composite particles, such as atoms.…
The kinematical part of general theory of deformational structures on smooth manifolds is developed. We introduce general concept of d-objects deformation, then within the set of all such deformations we develop some special algebra and…
The analysis of the dynamics of radial movement in different reference frames used in cosmology is made. Use of different frames leads to the difference in inertial forces resulting in different observable effects. The important effect is…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity,…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…