6,246 research outputs found
A Geometrical Characterization of the Twin Paradox and its Variants
The aim of this paper is to provide a logic-based conceptual analysis of the
twin paradox (TwP) theorem within a first-order logic framework. A geometrical
characterization of TwP and its variants is given. It is shown that TwP is not
logically equivalent to the assumption of the slowing down of moving clocks,
and the lack of TwP is not logically equivalent to the Newtonian assumption of
absolute time. The logical connection between TwP and a symmetry axiom of
special relativity is also studied.Comment: 22 pages, 3 figure
Hubble's law and faster than light expansion speeds
Naively applying Hubble's law to a sufficiently distant object gives a
receding velocity larger than the speed of light. By discussing a very similar
situation in special relativity, we argue that Hubble's law is meaningful only
for nearby objects with non-relativistic receding speeds. To support this
claim, we note that in a curved spacetime manifold it is not possible to
directly compare tangent vectors at different points, and thus there is no
natural definition of relative velocity between two spatially separated objects
in cosmology. We clarify the geometrical meaning of the Hubble's receding speed
v by showing that in a Friedmann-Robertson-Walker spacetime if the
four-velocity vector of a comoving object is parallel-transported along the
straight line in flat comoving coordinates to the position of a second comoving
object, then v/c actually becomes the rapidity of the local Lorentz
transformation, which maps the fixed four-velocity vector to the transported
one.Comment: 5 pages, 2 figures, to appear in Am. J. Phy
Coup Agency and Prospects for Democracy
This research note introduces new global data on military coups. Conventional aggregate data so far have conflated two distinct types of coups. Military interventions by leading officers are coups "from above,"characterized by political power struggles within authoritarian elite coalitions where officers move against civilian elites, executive incumbents, and their loyal security personnel. By contrast, power grabs by officers from the lower and middle ranks are coups "from below,"where military personnel outside of the political elite challenge sitting incumbents, their loyalists, and the regime itself. Disaggregating coup types offers leverage to revise important questions about the causes and consequences of military intervention in politics. This research note illustrates that coup attempts from the top of the military hierarchy are much more likely to be successful than coups from the lower and middle ranks of the military hierarchy. Moreover, coups from the top recalibrate authoritarian elite coalitions and serve to sustain autocratic rule; they rarely produce an opening for a democratic transition. Successful coups from below, by contrast, can result in the breakdown of authoritarian regimes and generate an opening for democratic transitions
Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors
We report for the first time general geometrical expressions for the angular
resolution of an arbitrary network of interferometric gravitational-wave (GW)
detectors when the arrival-time of a GW is unknown. We show explicitly elements
that decide the angular resolution of a GW detector network. In particular, we
show the dependence of the angular resolution on areas formed by projections of
pairs of detectors and how they are weighted by sensitivities of individual
detectors. Numerical simulations are used to demonstrate the capabilities of
the current GW detector network. We confirm that the angular resolution is poor
along the plane formed by current LIGO-Virgo detectors. A factor of a few to
more than ten fold improvement of the angular resolution can be achieved if the
proposed new GW detectors LCGT or AIGO are added to the network. We also
discuss the implications of our results for the design of a GW detector
network, optimal localization methods for a given network, and electromagnetic
follow-up observations.Comment: 13 pages, for Phys. Rev.
Removing non-stationary, non-harmonic external interference from gravitational wave interferometer data
We describe a procedure to identify and remove a class of non-stationary and
non-harmonic interference lines from gravitational wave interferometer data.
These lines appear to be associated with the external electricity main
supply, but their amplitudes are non-stationary and they do not appear at
harmonics of the fundamental supply frequency. We find an empirical model able
to represent coherently all the non-harmonic lines we have found in the power
spectrum, in terms of an assumed reference signal of the primary supply input
signal. If this signal is not available then it can be reconstructed from the
same data by making use of the coherent line removal algorithm that we have
described elsewhere. All these lines are broadened by frequency changes of the
supply signal, and they corrupt significant frequency ranges of the power
spectrum. The physical process that generates this interference is so far
unknown, but it is highly non-linear and non-stationary. Using our model, we
cancel the interference in the time domain by an adaptive procedure that should
work regardless of the source of the primary interference. We have applied the
method to laser interferometer data from the Glasgow prototype detector, where
all the features we describe in this paper were observed. The algorithm has
been tuned in such a way that the entire series of wide lines corresponding to
the electrical interference are removed, leaving the spectrum clean enough to
detect signals previously masked by them. Single-line signals buried in the
interference can be recovered with at least 75 % of their original signal
amplitude.Comment: 14 pages, 5 figures, Revtex, psfi
Time-Optimal Adiabatic-Like Expansion of Bose-Einstein Condensates
In this paper we study the fast adiabatic-like expansion of a one-dimensional
Bose-Einstein condensate (BEC) confined in a harmonic potential, using the
theory of time-optimal control. We find that under reasonable assumptions
suggested by the experimental setup, the minimum-time expansion occurs when the
frequency of the potential changes in a bang-bang form between the permitted
values. We calculate the necessary expansion time and show that it scales
logarithmically with large values of the expansion factor. This work is
expected to find applications in areas where the efficient manipulations of BEC
is of utmost importance. As an example we present the field of atom
interferometry with BEC, where the wavelike properties of atoms are used to
perform interference experiments that measure with unprecedented precision
small shifts induced by phenomena like rotation, acceleration, and gravity
gradients.Comment: Submitted to 51st IEEE Conference on Decision and Contro
Results of the First Coincident Observations by Two Laser-Interferometric Gravitational Wave Detectors
We report an upper bound on the strain amplitude of gravitational wave bursts
in a waveband from around 800Hz to 1.25kHz. In an effective coincident
observing period of 62 hours, the prototype laser interferometric gravitational
wave detectors of the University of Glasgow and Max Planck Institute for
Quantum Optics, have set a limit of 4.9E-16, averaging over wave polarizations
and incident directions. This is roughly a factor of 2 worse than the
theoretical best limit that the detectors could have set, the excess being due
to unmodelled non-Gaussian noise. The experiment has demonstrated the viability
of the kind of observations planned for the large-scale interferometers that
should be on-line in a few years time.Comment: 11 pages, 2 postscript figure
Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
The Planck spectrum of thermal scalar radiation is derived suggestively
within classical physics by the use of an accelerating coordinate frame. The
derivation has an analogue in Boltzmann's derivation of the Maxwell velocity
distribution for thermal particle velocities by considering the thermal
equilibrium of noninteracting particles in a uniform gravitational field. For
the case of radiation, the gravitational field is provided by the acceleration
of a Rindler frame through Minkowski spacetime. Classical zero-point radiation
and relativistic physics enter in an essential way in the derivation which is
based upon the behavior of free radiation fields and the assumption that the
field correlation functions contain but a single correlation time in thermal
equilibrium. The work has connections with the thermal effects of acceleration
found in relativistic quantum field theory.Comment: 23 page
Nonlinear Gravitational Waves: Their Form and Effects
A gravitational wave must be nonlinear to be able to transport its own
source, that is, energy and momentum. A physical gravitational wave, therefore,
cannot be represented by a solution to a linear wave equation. Relying on this
property, the second-order solution describing such physical waves is obtained.
The effects they produce on free particles are found to consist of nonlinear
oscillations along the direction of propagation.Comment: 15 pages, no figures. v2: presentation changes aiming at clarifying
the text; matches published versio
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