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We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a…
We study the limits to the localizability of events and reference frames in the $\kappa$-Minkowski quantum spacetime. Our main tool will be a representation of the $\kappa$-Minkowski commutation relations between coordinates, and the…
The aim of the paper is to develop a unified algebraical approach to representing the Minkowski difference for convex polyhedra. Namely, there is proposed an exact analytical formulas of the Minkowski difference for convex polyhedra with…
We propose a scheme to investigate whether non-uniform motion degrades entanglement of a relativistic quantum field that is localised both in space and in time. For a Dirichlet scalar field in a cavity in Minkowski space, in small but…
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…
Understanding natural relative motion trajectories is critical to enable fuel-efficient multi-satellite missions operating in complex environments. This paper studies the problem of computing and efficiently parameterizing satellite…
By using simplified 2D gravitational, non-local Lorentz invariant actions constructed upon the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a…
It is argued that the Rindler quantization is not a correct approach to study the effects of acceleration on quantum fields. First, the "particle"-detector approach based on the Minkowski quantization is not equivalent to the approach based…
We define an $S$-matrix for massive scalar fields on a fixed de Sitter spacetime, in the expanding patch co-ordinates relevant for early Universe cosmology. It enjoys many of the same properties as its Minkowski counterpart, for instance:…
An accelerating Rindler frame in Minkowski spacetime acting for a finite time interval is used to carry a box of particles or waves between two relativistic inertial frames. The finite spatial extent of the box allows treatment of the…
Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…
Some studies interpret quantum measurement as being explicitly non local. Others assume the preferred frame hypothesis. Unfortunately, these two classes of studies conflict with Minkowski space-time geometry. On the contrary, in Aristotle…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violating. The directional dependence of the Finsler metric provides a way to encode the Lorentz violating effects into the geometric structure…
The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures…
In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker…
An approach is developed which enables one to analyze gravitational effects without usage of any concrete model of geometry (or a class of models of geometry) of space-time and even without any coordinate system. Instead, the formalism of…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane,…