Related papers: Special Relativity and its Newtonian Limit from a …
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups,…
Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees…
As shown in the famous Dyson's paper "Missed Opportunities", even from purely mathematical considerations (without any physics) it follows that Poincare quantum symmetry is a special degenerate case of de Sitter quantum symmetries. Then the…
Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this paper how a Brownian motion on a short scale can originate a relativistic motion on scales that are larger than particle's Compton wavelength. This can be described…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and…
A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincar\'e group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles…
Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince…
A new formulation of Special Relativity is described. It is based on Cellular Automata theory and on a new theory of inertia called Quantum Inertia. The universe consists of a huge 3D array of cells given by C(x,y,z), whose numeric states…
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…
In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based…
We propose a general framework to describe Planckian deviations from Special Relativity (SR) compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to SR going beyond the energy…
In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to…
This work analyzes the difficulties in learning and teaching Einstein's theory of special relativity. An extensive bibliographic review has been performed, considering articles published in the most relevant journals on science education,…
When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes…
Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable…
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the…