arXiv subjects

Jacques L. Rubin

Publications and source records attributed to Jacques L. Rubin.

11 recordsLinked to original sources

arXiv2017

Relativistic Localizing Processes Bespeak an Inevitable Projective Geometry of Spacetime

Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might then be strongly compromised. In the present paper, we give the principles of relativistic localizing systems so as to bypass this issue. Such systems will allow to locate users endowed with receivers and, in addition, to localize any spacetime event. These localizing systems are made up of relativistic auto-locating positioning sub-systems supplemented by an extra satellite. They indicate that spacetime must be supplied everywhere with an unexpected local four dimensional projective structure besides the well-known three dimensional relativistic projective one. As a result, the spacetime manifold can be seen as a generalized Cartan space modeled on a four dimensional real projective space, i.e., a spacetime with both a local four dimensional projective structure and a compatible (pseudo-)Riemannian structure. Localization protocols are presented in details, while possible applications to astrophysics are also considered.

physics.gen-ph↗

arXiv2014

Relativistic Stereometric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold

Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known emission and reception coordinates. Such a constellation of five satellites defines a so-called relativistic localizing system. The determination of such systems is motivated by the need to not only locate (within a grid) users utilizing receivers but, more generally, to localize any spacetime event. The angles measured on the celestial spheres of the five satellites enter into the definition. Therefore, there are, up to scalings, intrinsic physical coordinates related to the underlying conformal structure of spacetime. Moreover, they indicate that spacetime must be endowed everywhere with a local projective geometry characteristic of a so-called generalized Cartan space locally modeled on four-dimensional, real projective space. The particular process of localization providing the relativistic stereometric coordinates is based, in a way, on an enhanced notion of parallax in space and time generalizing the usual parallax restricted to space only.

math-ph↗

arXiv2013

Equivalent Generic Forms for Metric Fields Yielded by Relativistic Positioning Systems

Relativistic positioning systems provide tensors represented in $\{\ell\ell\ell\ell\}$-frames ($\ell$ for light) dual to systems of emission coordinates. We show that any Lorentzian metric field given in such a frame is isometrically equivalent to a generic metric field defined by only four positive functions depending on another specific system of emission coordinates.

gr-qc↗

arXiv2009

Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. As such, the differential aging differs far beyond the first and second clock effects in Weyl geometries, with the latter finally appearing to not be suitable.

gr-qc↗

arXiv2004

Navigation of Spacetime Ships in Unified Gravitational and Electromagnetic Waves

On the basis of a "local" principle of equivalence of general relativity, we consider a navigation in a kind of "4D-ocean" involving measurements of conformally invariant physical properties only. Then, applying the Pfaff theory for PDE to a particular conformally equivariant system of differential equations, we show the dependency of any kind of function describing "spacetime waves", with respect to 20 parametrizing functions. These latter, appearing in a linear differential Spencer sequence and determining gauge fields of deformations relatively to "ship-metrics" or to "flat spacetime ocean metrics", may be ascribed to unified electromagnetic and gravitational waves. The present model is based neither on a classical gauge theory of gravitation or a gravitation theory with torsion, nor on any Kaluza-Klein or Weyl type unifications, but rather on a post-Newtonian approach of gravitation in a four dimensional conformal Cosserat spacetime.

gr-qc↗

arXiv2004

Spacetime deployments parametrized by gravitational and electromagnetic fields

On the basis of a "Punctual" Equivalence Principle of the general relativity context, we consider spacetimes with measurements of conformally invariant physical properties. Then, applying the Pfaff theory for PDE to a particular conformally equivariant system of differential equations, we make explicit the dependence of any kind of function describing a "spacetime deployment", on n(n+1) parametrizing functions, denoting by n the spacetime dimension. These functions, appearing in a linear differential Spencer sequence and determining gauge fields of spacetime deformations relatively to a "substrat spacetime", can be consistently ascribed to unified electromagnetic and gravitational fields, at any spacetime dimensions n greater or equal to 4.

hep-th↗

arXiv2004

Time 'betwins'

Discussions on the Langevin Twins 'paradox' are most often based on a "triangular" diagram which outlines the twins spacetime travels. It won't be our way, avoiding what we think to be a problem at the basis of numerous controversies. Our approach relies on a fundamentally different Equivalence Principle, namely the so-called "Punctual Equivalence Principle", from which we think that a very conformal aspect proceeds. We present a resolution of this paradox in the framework of the so-called "scale gravity". This resolution hinges on a clear determinism of the Twins proper times, in some definite situations, and a fundamental under-determinism in some other particular ones, the physical discrimination of which being achieved out of a precise mathematical description of conformal geometry. Moreover, we find that the time discrepancy between the twins, could somehow be at the root expression of the second fundamental law of thermodynamics.

gr-qc↗

arXiv2002

Relativistic Crystalline Symmetry Breaking And Anyonic States In Magnetoelectric Superconductors

There exists a connection between the creation of toroidal moments (TM) and the breaking of the one-cell relativistic crystalline symmetry (RCS) associated to any given crystal into which non-trivial magnetoelectric coupling effects (ME) exist. Indeed, in this kind of crystals, any interaction between a charge carrier and an elementary magnetic cell can breaks the RCS of this previous given cell by varying, in the simplest case, the continuous defining parameters of the initial RCS. This breaking can be associated to a change of the initial Galilean proper frame of any given carrier to an "effective" one, into which the RCS of the interacting cell is kept. We can speak of a kind of "inverse" kineto-magnetoelectric effect. The magnetic groups compatible with such process have been computed. Moreover, one can notice that the TM's break the P and T symmetries but not the PT one as in anyons theories. This breaking creates so-called Nambu-Goldstone bosons generating "effective" magnetic monopoles. These consequences allow us to claim, first, that anyons are charge carriers associated with "effective" magnetic monopoles, both with TM's, and second, that ME can be highly considered in superconductors theory.

cond-mat.supr-con↗

arXiv2002

Broken Relativistic Symmetry Groups, Toroidal Moments and Superconductivity in Magnetoelectric Crystals

A connection between creation of toroidal moments and breaking of the relativistic crystalline group associated to a given crystal, is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, Goldstone bosons, also associated to toroidal moments, are created and, as a consequence, corresponding toroidal phases in crystals. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.

cond-mat.supr-con↗

arXiv2001

Pfaff systems theory and the unifications of gravitation and electromagnetism

We show in the framework of Pfaff systems theory, the functional dependences of the general analytic solutions of a suitable system of involutive differential equations describing the differences between the analytic solutions of the conformal and "Poincaré" Lie equations. Then we ascribe to the infinitesimal variations of the parametrizing functionals some physical meanings as the electromagnetic and gravitation potentials. We also deduce their corresponding fields of interactions together with the differential equations they must satisfy. Then we discuss on various possible physical interpretations.

gr-qc↗

arXiv1998

From a Relativistic Phenomenology of Anyons to a Model of Unification of Forces via the Spencer Theory of Lie Structures

Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogroups, we build up a non-linear relative complex assigned to a gauge sequence for electromagnetic and gravitational potentials and fields. Then, using a conformally equivariant Lagrangian density, we deduce, first, the two first steps of its corresponding Janet complex and second, the dual relative linear complex. We conclude by giving suggestions for higher unification with the weak and strong interactions and interpretations of the Lagrangian density as a thermodynamical function and quantum wave-function.

dg-ga↗