Related papers: Acceleration-induced nonlocality: kinetic memory v…
The issue of inertia as opposition to acceleration of a massive point particle in Minkowski space-time is investigated in the context of a Hamiltonian constraint system. It is shown that the inertia as a locally-originating force in…
Lifelong machine learning or continual learning models attempt to learn incrementally by accumulating knowledge across a sequence of tasks. Therefore, these models learn better and faster. They are used in various intelligent systems that…
A velocity of a point particle in the kappa-Minkowski spacetime is investigated. Characteristic points of the spacetime are that the Poincare group becomes a quantum group with kappa, which is a mass dimension parameter, and is a kind of…
In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". In Part 1, we focused on senses in which a relativistic spacetime may be said to be "locally…
We consider here kinematical quantization: a first and often overlooked step in quantization procedures. $\mathbb{R}$, $\mathbb{R}_+$ and the interval are considered, as well as direct (Cartesian) products thereof. Some simple…
Zitterbewegung, as it was originally described by Schr\"odinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with…
We discuss in Minkowski spacetime the differences between the concepts of constant proper $n$-acceleration and of vanishing $(n+1)$-acceleration. By $n$-acceleration we essentially mean the higher order time derivatives of the position…
Peculiar velocities change the expansion rate of any observer moving relative to the smooth Hubble flow. As a result, observers in a galaxy like our Milky Way can experience accelerated expansion within a globally decelerating universe,…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr-Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers…
The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
The emergence of memory is a hallmark feature of non-Markovian dynamics. However, the type of memory -- classical or quantum -- required to realize certain dynamics remains unknown. We study the quantum homogenizer as a minimal model of…
We show that while some non-uniformly accelerating observers (NUAOs) do indeed see a Bose-Einstein distribution of particles for the expectation value of the number operator in the Minkowski vacuum state, the density matrix is non-thermal…
Dynamical properties of a Vicsek-like gas of self-propelled particles are investigated by means of kinetic theory and agent based simulations. While memory effects have been observed in disordered systems, we show that they also occur in…