152 research outputs found
An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity
In this paper we treat the so called clock paradox in an analytical way by
assuming that a constant and uniform force F of finite magnitude acts
continuously on the moving clock along the direction of its motion assumed to
be rectilinear. No inertial motion steps are considered. The rest clock is
denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which
(1) is at rest in its origin and (2) is seen moving is I and, finally, the
accelerated frame in which (2) is at rest in its origin and (1) moves forward
and backward is A. We deal with the following questions: I) What is the effect
of the finite force acting on (2) on the proper time intervals measured by the
two clocks when they reunite? Does a differential aging between the two clocks
occur, as it happens when inertial motion and infinite values of the
accelerating force is considered? The Special Theory of Relativity is used in
order to describe the hyperbolic motion of (2) in the frame I II) Is this
effect an absolute one, i.e. does the accelerated observer A comoving with (2)
obtain the same results as that in I, both qualitatively and quantitatively, as
it is expected? We use the General Theory of Relativity in order to answer this
question.Comment: LaTex2e, 19 pages, no tables, no figures. Rewritten version, it
amends the previous one whose results about the treatment with General
Relativity were wrong. References added. Eq. (55) corrected. More refined
version. Comments and suggestions are warmly welcom
Locality hypothesis and the speed of light
The locality hypothesis is generally considered necessary for the study of
the kinematics of non-inertial systems in special relativity. In this paper we
discuss this hypothesis, showing the necessity of an improvement, in order to
get a more clear understanding of the various concepts involved, like
coordinate velocity and standard velocity of light. Concrete examples are
shown, where these concepts are discussed.Comment: 23 page
Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants
We analyze the number N of functionally independent generalized Casimir
invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{%
oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and
\frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a
representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that
for any dimension n >= 6 there exist Lie algebras
\frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition
such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page
Standard and Generalized Newtonian Gravities as ``Gauge'' Theories of the Extended Galilei Group - I: The Standard Theory
Newton's standard theory of gravitation is reformulated as a {\it gauge}
theory of the {\it extended} Galilei Group. The Action principle is obtained by
matching the {\it gauge} technique and a suitable limiting procedure from the
ADM-De Witt action of general relativity coupled to a relativistic mass-point.Comment: 51 pages , compress, uuencode LaTex fil
Newtonian Gravity and the Bargmann Algebra
We show how the Newton-Cartan formulation of Newtonian gravity can be
obtained from gauging the Bargmann algebra, i.e., the centrally extended
Galilean algebra. In this gauging procedure several curvature constraints are
imposed. These convert the spatial (time) translational symmetries of the
algebra into spatial (time) general coordinate transformations, and make the
spin connection gauge fields dependent. In addition we require two independent
Vielbein postulates for the temporal and spatial directions. In the final step
we impose an additional curvature constraint to establish the connection with
(on-shell) Newton-Cartan theory. We discuss a few extensions of our work that
are relevant in the context of the AdS-CFT correspondence.Comment: Latex, 20 pages, typos corrected, published versio
Static Observers in Curved Spaces and Non-inertial Frames in Minkowski Spacetime
Static observers in curved spacetimes may interpret their proper acceleration
as the opposite of a local gravitational field (in the Newtonian sense). Based
on this interpretation and motivated by the equivalence principle, we are led
to investigate congruences of timelike curves in Minkowski spacetime whose
acceleration field coincides with the acceleration field of static observers of
curved spaces. The congruences give rise to non-inertial frames that are
examined. Specifically we find, based on the locality principle, the embedding
of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit
form for arbitrary acceleration fields. We also determine, from the Einstein
equations, a covariant field equation that regulates the behavior of the proper
acceleration of static observers in curved spacetimes. It corresponds to an
exact relativistic version of the Newtonian gravitational field equation. In
the specific case in which the level surfaces of the norm of the acceleration
field of the static observers are maximally symmetric two-dimensional spaces,
the energy-momentum tensor of the source is analyzed.Comment: 28 pages, 4 figures
LA SIEROLOGIA TIPO-SPECIFICA PER HERPES SYMPLEX TIPO 2 NELLA GESTIONE DEI PAZIENTI HIV POSITIVI
none8noVedi allegato.Pauri, P.; Balercia, M.; Barchiesi, F.; Butini, L.; Costantini, A.; Del Gobbo, R.; Marinelli, K.; Tomassini, T.Pauri, P.; Balercia, M.; Barchiesi, Francesco; Butini, L.; Costantini, Andrea; Del Gobbo, R.; Marinelli, K.; Tomassini, T
Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge
We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.Comment: RevTeX file, 141 page
Handmade clay bricks: chemical, physical and mechanical properties
The clay brick masonry that is much used in historical structures often is in a rather poor state of conservation. In order to intervene correctly in these buildings, it is convenient to characterize the old material. For this purpose, a large sample of clay brick specimens from the 12th to 19th century were collected from six Portuguese monasteries, and were characterized chemically, physically and mechanically. A large variability of the properties was found. Additionally, a sample of handmade new bricks, which are commonly used as replacing material, was also analysed. The results were compared to the old bricks and could be possibly adequate as substitution bricks. Still, significant differences were found in chemical composition, and in water absorption and porosity, which are much lower in modern handmade bricks. With respect to mechanical properties, the range of values found in old bricks was rather high and the degree of deterioration exhibited a large scatter, meaning that a conclusion is hardly possible.The authors gratefully acknowledge the Instituto de Gestao do Patrimonio Arquitectonico e Arqueologico (IGESPAR) for providing the old clay bricks used in the present work. The first author acknowledges the partial funding of this work by the FCT through the following scholarships POCTI SFRH/BD/6409/2001 and POCTI SFRH/BPD/26706/2005
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
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