5,557 research outputs found
Nonisomorphic curves that become isomorphic over extensions of coprime degrees
We show that one can find two nonisomorphic curves over a field K that become
isomorphic to one another over two finite extensions of K whose degrees over K
are coprime to one another.
More specifically, let K_0 be an arbitrary prime field and let r and s be
integers greater than 1 that are coprime to one another. We show that one can
find a finite extension K of K_0, a degree-r extension L of K, a degree-s
extension M of K, and two curves C and D over K such that C and D become
isomorphic to one another over L and over M, but not over any proper
subextensions of L/K or M/K.
We show that such C and D can never have genus 0, and that if K is finite, C
and D can have genus 1 if and only if {r,s} = {2,3} and K is an odd-degree
extension of F_3. On the other hand, when {r,s}={2,3} we show that genus-2
examples occur in every characteristic other than 3.
Our detailed analysis of the case {r,s} = {2,3} shows that over every finite
field K there exist nonisomorphic curves C and D that become isomorphic to one
another over the quadratic and cubic extensions of K.
Most of our proofs rely on Galois cohomology. Without using Galois
cohomology, we show that two nonisomorphic genus-0 curves over an arbitrary
field remain nonisomorphic over every odd-degree extension of the base field.Comment: LaTeX, 32 pages. Further references added to the discussion in
Section 1
A Superluminal Subway: The Krasnikov Tube
The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
We consider two approaches to evading paradoxes in quantum mechanics with
closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure
states and using path integrals, we show that the problems of paradoxes and of
unitarity violation are related; preserving unitarity avoids paradoxes by
modifying the time evolution so that improbable events bewcome certain. Deutsch
has argued, using the density matrix, that paradoxes do not occur in the "many
worlds interpretation". We find that in this approach account must be taken of
the resolution time of the device that detects objects emerging from a wormhole
or other time machine. When this is done one finds that this approach is viable
only if macroscopic objects traversing a wormhole interact with it so strongly
that they are broken into microscopic fragments.Comment: no figure
Hyperfast Interstellar Travel in General Relativity
The problem is discussed of whether a traveller can reach a remote object and
return back sooner than a photon would when taken into account that the
traveller can partly control the geometry of his world. It is argued that under
some reasonable assumptions in globally hyperbolic spacetimes the traveller
cannot hasten reaching the destination. Nevertheless, it is perhaps possible
for him to make an arbitrarily long round-trip within an arbitrarily short
(from the point of view of a terrestrial observer) time.Comment: The final version, close to (but better than) what will be published
in Phys. Rev. D. The explanatory part is made more detaile
Superluminal travel requires negative energies
I investigate the relationship between faster-than-light travel and
weak-energy-condition violation, i.e., negative energy densities. In a general
spacetime it is difficult to define faster-than-light travel, and I give an
example of a metric which appears to allow superluminal travel, but in fact is
just flat space. To avoid such difficulties, I propose a definition of
superluminal travel which requires that the path to be traveled reach a
destination surface at an earlier time than any neighboring path. With this
definition (and assuming the generic condition) I prove that superluminal
travel requires weak-energy-condition violation.Comment: 5 pages, RevTeX, 2 figures with epsf. This paper now contains all the
material of gr-qc/6805003 and gr-qc/9806091 since these became a single
article in Phys. Rev. Let
Policy Support Within a Target Group: The Case of School Desegregation
This study empirically tests three theoretical approaches to explaining specific support for a policy output among members of its target group. The utilitarian model posits support as a function of objective costs and benefits to the individual stemming directly from the policy. The attitudinal model relates specific support to diffuse predispositions rooted in socialization. The perceptual model holds that specific support derives from beliefs about the character of the political decision process by which the policy was formulated. Tests of these three approaches are based on survey data on specific support for school district desegregation plans among a large sample of black and white parents of public school children in Florida. In both subsamples, the utilitarian approach explained very little of the variance in support, but the attitudinal and perceptual models were corroborated. Implications of these findings are drawn for desegregation policy making and for public policy theory
Policy Support Within a Target Group: The Case of School Desegregation
This study empirically tests three theoretical approaches to explaining specific support for a policy output among members of its target group. The utilitarian model posits support as a function of objective costs and benefits to the individual stemming directly from the policy. The attitudinal model relates specific support to diffuse predispositions rooted in socialization. The perceptual model holds that specific support derives from beliefs about the character of the political decision process by which the policy was formulated. Tests of these three approaches are based on survey data on specific support for school district desegregation plans among a large sample of black and white parents of public school children in Florida. In both subsamples, the utilitarian approach explained very little of the variance in support, but the attitudinal and perceptual models were corroborated. Implications of these findings are drawn for desegregation policy making and for public policy theory
A Method to Find Community Structures Based on Information Centrality
Community structures are an important feature of many social, biological and
technological networks. Here we study a variation on the method for detecting
such communities proposed by Girvan and Newman and based on the idea of using
centrality measures to define the community boundaries (M. Girvan and M. E. J.
Newman, Community structure in social and biological networks Proc. Natl. Acad.
Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical
clustering that consists in finding and removing iteratively the edge with the
highest information centrality. We test the algorithm on computer generated and
real-world networks whose community structure is already known or has been
studied by means of other methods. We show that our algorithm, although it runs
to completion in a time O(n^4), is very effective especially when the
communities are very mixed and hardly detectable by the other methods.Comment: 13 pages, 13 figures. Final version accepted for publication in
Physical Review
The unphysical nature of "Warp Drive"
We will apply the quantum inequality type restrictions to Alcubierre's warp
drive metric on a scale in which a local region of spacetime can be considered
``flat''. These are inequalities that restrict the magnitude and extent of the
negative energy which is needed to form the warp drive metric. From this we are
able to place limits on the parameters of the ``Warp Bubble''. It will be shown
that the bubble wall thickness is on the order of only a few hundred Planck
lengths. Then we will show that the total integrated energy density needed to
maintain the warp metric with such thin walls is physically unattainable.Comment: 11 pages, 3 figures, latex. This revision corrects a typographical
sign error in Eq. (3
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