6,363 research outputs found
Quantum Mechanics of Extended Objects
We propose a quantum mechanics of extended objects that accounts for the
finite extent of a particle defined via its Compton wavelength. The Hilbert
space representation theory of such a quantum mechanics is presented and this
representation is used to demonstrate the quantization of spacetime. The
quantum mechanics of extended objects is then applied to two paradigm examples,
namely, the fuzzy (extended object) harmonic oscillator and the Yukawa
potential. In the second example, we theoretically predict the phenomenological
coupling constant of the meson, which mediates the short range and
repulsive nucleon force, as well as the repulsive core radius.Comment: RevTex, 24 pages, 1 eps and 5 ps figures, format change
Coordinate time and proper time in the GPS
The Global Positioning System (GPS) provides an excellent educational example
as to how the theory of general relativity is put into practice and becomes
part of our everyday life. This paper gives a short and instructive derivation
of an important formula used in the GPS, and is aimed at graduate students and
general physicists.
The theoretical background of the GPS (see \cite{ashby}) uses the
Schwarzschild spacetime to deduce the {\it approximate} formula, ds/dt\approx
1+V-\frac{|\vv|^2}{2}, for the relation between the proper time rate of a
satellite clock and the coordinate time rate . Here is the gravitational
potential at the position of the satellite and \vv is its velocity (with
light-speed being normalized as ). In this note we give a different
derivation of this formula, {\it without using approximations}, to arrive at
ds/dt=\sqrt{1+2V-|\vv|^2 -\frac{2V}{1+2V}(\n\cdot\vv)^2}, where \n is the
normal vector pointing outward from the center of Earth to the satellite. In
particular, if the satellite moves along a circular orbit then the formula
simplifies to ds/dt=\sqrt{1+2V-|\vv|^2}.
We emphasize that this derivation is useful mainly for educational purposes,
as the approximation above is already satisfactory in practice.Comment: 5 pages, revised, over-over-simplified... Does anyone care that the
GPS uses an approximate formula, while a precise one is available in just a
few lines??? Physicists don'
Towards gravitationally assisted negative refraction of light by vacuum
Propagation of electromagnetic plane waves in some directions in
gravitationally affected vacuum over limited ranges of spacetime can be such
that the phase velocity vector casts a negative projection on the time-averaged
Poynting vector. This conclusion suggests, inter alia, gravitationally assisted
negative refraction by vacuum.Comment: 6 page
Asymptotic Conformal Yano--Killing Tensors for Schwarzschild Metric
The asymptotic conformal Yano--Killing tensor proposed in J. Jezierski, On
the relation between metric and spin-2 formulation of linearized Einstein
theory [GRG, in print (1994)] is analyzed for Schwarzschild metric and tensor
equations defining this object are given. The result shows that the
Schwarzschild metric (and other metrics which are asymptotically
``Schwarzschildean'' up to O(1/r^2) at spatial infinity) is among the metrics
fullfilling stronger asymptotic conditions and supertranslations ambiguities
disappear. It is also clear from the result that 14 asymptotic gravitational
charges are well defined on the ``Schwarzschildean'' background.Comment: 8 pages, latex, no figure
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
Spin and Center of Mass in Axially Symmetric Einstein-Maxwell Spacetimes
We give a definition and derive the equations of motion for the center of
mass and angular momentum of an axially symmetric, isolated system that emits
gravitational and electromagnetic radiation. A central feature of this
formulation is the use of Newman-Unti cuts at null infinity that are generated
by worldlines of the spacetime. We analyze some consequences of the results and
comment on the generalization of this work to general asymptotically flat
spacetimes.Comment: 20 page
Freely falling 2-surfaces and the quasi-local energy
We derive an expression for effective gravitational mass for any closed
spacelike 2-surface. This effective gravitational energy is defined directly
through the geometrical quantity of the freely falling 2-surface and thus is
well adapted to intuitive expectation that the gravitational mass should be
determined by the motion of test body moving freely in gravitational field. We
find that this effective gravitational mass has reasonable positive value for a
small sphere in the non-vacuum space-times and can be negative for vacuum case.
Further, this effective gravitational energy is compared with the quasi-local
energy based on the formalism of the General Relativity. Although some
gauge freedoms exist, analytic expressions of the quasi-local energy for vacuum
cases are same as the effective gravitational mass. Especially, we see that the
contribution from the cosmological constant is the same in general cases.Comment: 11 pages, no figures, REVTeX. Estimation of the effective mass of
small spheres in non-vaccum spacetime and Schwarzschild spacetime are added.
The negativity of the latter is discusse
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