Related papers: Minimal information in velocity space
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…
We postulate that all the presently known kinematic effects on physical quantities related to a material particle (e.g., masss increase) are due to its velocity relative to surrounding matter, and not to the observer's reference frame. The…
I discuss the physical basis of classical mechanics, such as expressed commonly using the framework of Newton's Principia. Newton's formulation of the laws of motion is seen to have quite a few ambiguities and shortcomings. Therefore I…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way speed of light in all inertial frames of reference, the special theory of relativity uses the assumption about the Euclidean structure…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum,…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…
The central concept of the theory of relativity is the relativity of velocity. The velocity of a material body is not an intrinsic property of the body; it depends on a free choice of reference system. Relative velocity is thus…
The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics…
Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it…
We attempt to describe geometry in terms of informational quantities for the universe considered as a finite ensemble of correlated quantum particles. As the main dynamical principle, we use the conservation of the sum of all kinds of…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We present a self-contained introduction to the classical theory of spacetime and fields. This exposition is based on the most general principles: the principle of general covariance (relativity) and the principle of least action. The order…
All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…