Related papers: Simultaneity in Minkowski spacetime: from uniquene…
We show that alternative relativity theories that are essentially based on varied distant clock synchronization procedures can be recovered by using the standard Lorentz-Einstein transformations for the space-time coordinates of the same…
A new interpretation of the causality implementation in the Lienard-Wiechert solution raises new doubts against the validity of the Lorentz-Dirac equation and the limits of validity of the Minkowski structure of spacetime.
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
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…
In this paper we extend our 2007 paper, Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions, arXiv:0710.5046 to include consideration of universal expansion, various implications of extendibility and…
In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis…
The history of the particle concept is briefly reviewed, with particular emphasis on the `foliation dependence' of many particle creation models, and the possible connection between our notion of particle and our notion of simultaneity. It…
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincar\'e inequality", we provide a simple example of a metric space $X$ that admits Poincar\'e inequalities for a continuum of…
We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by sequences of subspaces whose elements belong to a finite…
In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow the approach of G. Royer (1999) and obtain uniqueness by showing…
Can global internal and spacetime symmetries be connected without supersymmetry? To answer this question, we investigate Minkowski spacetimes with d space-like extra dimensions and point out under which general conditions external…
In Einstein's Special Theory of Relativity, all observers measure the speed of light, $c$, to be the same. However, this refers to the round trip speed, where a clock at the origin times the outward and return trip of light reflecting off a…
We prove an inequality on the Kantorovich-Rubinstein distance --which can be seen as a particular case of a Wasserstein metric-- between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, but with a…
It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity…
We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We…
The process of identifying a time variable in time reparameterization invariant theories results in great ambiguities about the actual laws of physics described by a given theory. A theory set up to describe one set of physical laws can…
Based on the principle of relativity and the postulate of invariant speed and length, we propose the theory of special relativity with cosmological constant ${\cal SR}_{c,R}$ if the invariant length whose square is the inverse of the…
We submit a classical unification of the special and general relativities via the new isominkowskian geometry in which the two relativities are differentiated by the basic unit. We then show that the unification admits an operator image in…
Einstein based his special theory of relativity on two postulates: (a) physical laws appear the same in all inertial frames, and (b) the speed of light in vacuum is an observer-independent constant. However, it is already known that the…
We observe strong violation of Bell's inequality in an Einstein, Podolsky and Rosen type experiment with independent observers. Our experiment definitely implements the ideas behind the well known work by Aspect et al. We for the first time…