7,064 research outputs found
On the Dynamics of Accelerated Observers in Special Relativity Theory
This paper investigates the dynamics of the motion of accelerated observers in Special Relativity (SR)
theory. The presented discussion highlights the memristive character of the force dynamics. This
description contrasts with the standard phase-space representation used in Physics
On Logical Analysis of Relativity Theories
The aim of this paper is to give an introduction to our axiomatic logical
analysis of relativity theories.Comment: 19 pages, 1 figure
The Hypothesis of Locality and its Limitations
The hypothesis of locality, its origin and consequences are discussed. This
supposition is necessary for establishing the local spacetime frame of
accelerated observers; in this connection, the measurement of length in a
rotating system is considered in detail. Various limitations of the hypothesis
of locality are examined.Comment: LaTeX file, no figures, 14 pages, to appear in: "Relativity in
Rotating Frames", edited by G. Rizzi and M.L. Ruggiero (Kluwer Academic
Publishers, Dordrecht, 2003
The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics
A modern re-visitation of the consequences of the lack of an intrinsic notion
of instantaneous 3-space in relativistic theories leads to a reformulation of
their kinematical basis emphasizing the role of non-inertial frames centered on
an arbitrary accelerated observer. In special relativity the exigence of
predictability implies the adoption of the 3+1 point of view, which leads to a
well posed initial value problem for field equations in a framework where the
change of the convention of synchronization of distant clocks is realized by
means of a gauge transformation. This point of view is also at the heart of the
canonical approach to metric and tetrad gravity in globally hyperbolic
asymptotically flat space-times, where the use of Shanmugadhasan canonical
transformations allows the separation of the physical degrees of freedom of the
gravitational field (the tidal effects) from the arbitrary gauge variables.
Since a global vision of the equivalence principle implies that only global
non-inertial frames can exist in general relativity, the gauge variables are
naturally interpreted as generalized relativistic inertial effects, which have
to be fixed to get a deterministic evolution in a given non-inertial frame. As
a consequence, in each Einstein's space-time in this class the whole
chrono-geometrical structure, including also the clock synchronization
convention, is dynamically determined and a new approach to the Hole Argument
leads to the conclusion that "gravitational field" and "space-time" are two
faces of the same entity. This view allows to get a classical scenario for the
unification of the four interactions in a scheme suited to the description of
the solar system or our galaxy with a deperametrization to special relativity
and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of
Theoretical Physics, "Current Mathematical Topics in Gravitation and
Cosmology", Ladek, Poland, 6-11 February 200
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - I: Dynamical Synchronization and Generalized Inertial Effects
This is the first of a couple of papers in which, by exploiting the
capabilities of the Hamiltonian approach to general relativity, we get a number
of technical achievements that are instrumental both for a disclosure of
\emph{new} results concerning specific issues, and for new insights about
\emph{old} foundational problems of the theory. The first paper includes: 1) a
critical analysis of the various concepts of symmetry related to the
Einstein-Hilbert Lagrangian viewpoint on the one hand, and to the Hamiltonian
viewpoint, on the other. This analysis leads, in particular, to a
re-interpretation of {\it active} diffeomorphisms as {\it passive and
metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose the (nearly unknown) connection of
a subgroup of them to Hamiltonian gauge transformations {\it on-shell}; 2) a
re-visitation of the canonical reduction of the ADM formulation of general
relativity, with particular emphasis on the geometro-dynamical effects of the
gauge-fixing procedure, which amounts to the definition of a \emph{global
(non-inertial) space-time laboratory}. This analysis discloses the peculiar
\emph{dynamical nature} that the traditional definition of distant simultaneity
and clock-synchronization assume in general relativity, as well as the {\it
gauge relatedness} of the "conventions" which generalize the classical
Einstein's convention.Comment: 45 pages, Revtex4, some refinements adde
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