5,045 research outputs found
The high energy limit of the trajectory representation of quantum mechanics
The trajectory representation in the high energy limit (Bohr correspondence
principle) manifests a residual indeterminacy. This indeterminacy is compared
to the indeterminacy found in the classical limit (Planck's constant to 0)
[Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed
region, the classically forbiden region, and near the WKB turning point. The
differences between Bohr's and Planck's principles for the trajectory
representation are compared with the differences between these correspondence
principles for the wave representation. The trajectory representation in the
high energy limit is shown to go to neither classical nor statistical
mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty.
The relationship between indeterminacy and 't Hooft's information loss and
equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of
the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August
2001, U. of Maryland. Proceedings available at
http://www.physics.umd.edu/robo
Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds
The twisted face-pairing construction of our earlier papers gives an
efficient way of generating, mechanically and with little effort, myriads of
relatively simple face-pairing descriptions of interesting closed 3-manifolds.
The corresponding description in terms of surgery, or Dehn-filling, reveals the
twist construction as a carefully organized surgery on a link.
In this paper, we work out the relationship between the twisted face-pairing
description of closed 3-manifolds and the more common descriptions by surgery
and Heegaard diagrams. We show that all Heegaard diagrams have a natural
decomposition into subdiagrams called Heegaard cylinders, each of which has a
natural shape given by the ratio of two positive integers. We characterize the
Heegaard diagrams arising naturally from a twisted face-pairing description as
those whose Heegaard cylinders all have integral shape. This characterization
allows us to use the Kirby calculus and standard tools of Heegaard theory to
attack the problem of finding which closed, orientable 3-manifolds have a
twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm
Trajectories in the Context of the Quantum Newton's Law
In this paper, we apply the one dimensional quantum law of motion, that we
recently formulated in the context of the trajectory representation of quantum
mechanics, to the constant potential, the linear potential and the harmonic
oscillator. In the classically allowed regions, we show that to each classical
trajectory there is a family of quantum trajectories which all pass through
some points constituting nodes and belonging to the classical trajectory. We
also discuss the generalization to any potential and give a new definition for
de Broglie's wavelength in such a way as to link it with the length separating
adjacent nodes. In particular, we show how quantum trajectories have as a limit
when the classical ones. In the classically forbidden regions,
the nodal structure of the trajectories is lost and the particle velocity
rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed,
to appear in Physica Script
Scientific Standards and the Regulation of Genetically Modified Insects
Experimental releases of genetically modified (GM) insects are reportedly being evaluated in various countries, including Brazil, the Cayman Islands (United Kingdom), France, Guatemala, India, Malaysia, Mexico, Panama, Philippines, Singapore, Thailand, the United States of America, and Vietnam. GM mosquitoes (Aedes aegypti) have already been released for field trials into inhabited areas in the Cayman Islands (2009–?), Malaysia (2010–2011), and Brazil (2011–2012). Here, we assess the regulatory process in the first three countries permitting releases (Malaysia, US, and the Cayman Islands) in terms of pre-release transparency and scientific quality. We find that, despite 14 US government–funded field trials over the last 9 years (on a moth pest of cotton), there has been no scientific publication of experimental data, and in only two instances have permit applications been published. The world's first environmental impact statement (EIS) on GM insects, produced by US authorities in 2008, is found to be scientifically deficient on the basis that (1) most consideration of environmental risk is too generic to be scientifically meaningful; (2) it relies on unpublished data to establish central scientific points; and (3) of the approximately 170 scientific publications cited, the endorsement of the majority of novel transgenic approaches is based on just two laboratory studies in only one of the four species covered by the document. We find that it is not possible to determine from documents publically available prior to the start of releases if obvious hazards of the particular GM mosquitoes released in Malaysia, the Cayman Islands, and Brazil received expert examination. Simple regulatory measures are proposed that would build public confidence and stimulate the independent experimental studies that environmental risk assessments require. Finally, a checklist is provided to assist the general public, journalists, and lawmakers in determining, from documents issued by regulators prior to the start of releases, whether permit approval is likely to have a scientifically high quality basi
Advanced tracking systems design and analysis
The results of an assessment of several types of high-accuracy tracking systems proposed to track the spacecraft in the National Aeronautics and Space Administration (NASA) Advanced Tracking and Data Relay Satellite System (ATDRSS) are summarized. Tracking systems based on the use of interferometry and ranging are investigated. For each system, the top-level system design and operations concept are provided. A comparative system assessment is presented in terms of orbit determination performance, ATDRSS impacts, life-cycle cost, and technological risk
- …