9,374 research outputs found
PROCRUSTES: A computer algebra package for post-Newtonian calculations in General Relativity
We report on a package of routines for the computer algebra system Maple
which supports the explicit determination of the geometric quantities, field
equations, equations of motion, and conserved quantities of General Relativity
in the post-Newtonian approximation. The package structure is modular and
allows for an easy modification by the user. The set of routines can be used to
verify hand calculations or to generate the input for further numerical
investigations.Comment: 20 pages, 3 figures. The latest version of the package can be
obtained from http://www.thp.uni-koeln.de/~dp/procrustes.htm
Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies
We derive explicit Lorentz-invariant solution of the Einstein and null
geodesic equations for data processing of the time delay and ranging
experiments in gravitational field of moving gravitating bodies of the solar
system - the Sun and major planets. We discuss general-relativistic
interpretation of these experiments and the limitations imposed by motion of
the massive bodies on measurement of the parameters gamma_{PPN}, beta_{PPN} and
delta_{PPN} of the parameterized post-Newtonian formalism.Comment: 17 pages, 1 figure; accepted for publication to MNRA
Why the Quantum Must Yield to Gravity
After providing an extensive overview of the conceptual elements -- such as
Einstein's `hole argument' -- that underpin Penrose's proposal for
gravitationally induced quantum state reduction, the proposal is constructively
criticised. Penrose has suggested a mechanism for objective reduction of
quantum states with postulated collapse time T = h/E, where E is an
ill-definedness in the gravitational self-energy stemming from the profound
conflict between the principles of superposition and general covariance. Here
it is argued that, even if Penrose's overall conceptual scheme for the
breakdown of quantum mechanics is unreservedly accepted, his formula for the
collapse time of superpositions reduces to T --> oo (E --> 0) in the strictly
Newtonian regime, which is the domain of his proposed experiment to corroborate
the effect. A suggestion is made to rectify this situation. In particular,
recognising the cogency of Penrose's reasoning in the domain of full `quantum
gravity', it is demonstrated that an appropriate experiment which could in
principle corroborate his argued `macroscopic' breakdown of superpositions is
not the one involving non-rotating mass distributions as he has suggested, but
a Leggett-type SQUID or BEC experiment involving superposed mass distributions
in relative rotation. The demonstration thereby brings out one of the
distinctive characteristics of Penrose's scheme, rendering it empirically
distinguishable from other state reduction theories involving gravity. As an
aside, a new geometrical measure of gravity-induced deviation from quantum
mechanics in the manner of Penrose is proposed, but now for the canonical
commutation relations [Q, P] = ih.Comment: 33 pages (TeX, uses mtexsis) plus 3 figures (epsf). To appear in
``Physics Meets Philosophy at the Planck Scale'' (Cambridge University
Press). Two footnotes adde
Gravitational Radiation from Two-Body Systems
Thanks to the new generation of gravitational wave detectors LIGO and VIRGO,
the theory of general relativity will face new and important confrontations to
observational data with unprecedented precision. Indeed the detection and
analysis of the gravitational waves from compact binary star systems requires
beforehand a very precise solution of the two-body problem within general
relativity. The approximation currently used to solve this problem is the
post-Newtonian one, and must be pushed to high order in order to describe with
sufficient accuracy (given the sensitivity of the detectors) the inspiral phase
of compact bodies, which immediately precedes their final merger. The resulting
post-Newtonian ``templates'' are currently known to 3.5PN order, and are used
for searching and deciphering the gravitational wave signals in VIRGO and LIGO.Comment: 19 pages, to appear in the Proceedings of the Spanish Relativity
Meeting ``A Century of Relativity Physics'' (ERE05), Edited by Lysiane Mornas
and Joaquin Diaz-Alons
On the Speed of Gravity and Relativistic v/c Corrections to the Shapiro Time Delay
Recent papers by Samuel declared that the linearized post-Newtonian v/c
effects are too small to have been measured in the recent experiment involving
Jupiter and quasar J0842+1845 that was used to measure the ultimate speed of
gravity defined as a fundamental constant entering in front of each time
derivative of the metric tensor in the Einstein gravity field equations. We
describe our Lorentz-invariant formulation of the Jovian deflection experiment
and confirm that v/c effects are do observed, as contrasted to the erroneous
claim by Samuel, and that they vanish if and only if the speed of gravity is
infinite.Comment: 7 pages. Final version published in Physics Letters
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