122,009 research outputs found
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
I show how there is an ambiguity in how one treats auxiliary variables in
gauge theories including general relativity cast as 3 + 1 geometrodynamics.
Auxiliary variables may be treated pre-variationally as multiplier coordinates
or as the velocities corresponding to cyclic coordinates. The latter treatment
works through the physical meaninglessness of auxiliary variables' values
applying also to the end points (or end spatial hypersurfaces) of the
variation, so that these are free rather than fixed. [This is also known as
variation with natural boundary conditions.] Further principles of dynamics
workings such as Routhian reduction and the Dirac procedure are shown to have
parallel counterparts for this new formalism. One advantage of the new scheme
is that the corresponding actions are more manifestly relational. While the
electric potential is usually regarded as a multiplier coordinate and Arnowitt,
Deser and Misner have regarded the lapse and shift likewise, this paper's
scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose
corresponding velocities are, respectively, the abovementioned previously used
variables. This paper's way of thinking about gauge theory furthermore admits
interesting generalizations, which shall be provided in a second paper.Comment: 11 page
Quantum Cosmological Relational Model of Shape and Scale in 1-d
Relational particle models are useful toy models for quantum cosmology and
the problem of time in quantum general relativity. This paper shows how to
extend existing work on concrete examples of relational particle models in 1-d
to include a notion of scale. This is useful as regards forming a tight analogy
with quantum cosmology and the emergent semiclassical time and hidden time
approaches to the problem of time. This paper shows furthermore that the
correspondence between relational particle models and classical and quantum
cosmology can be strengthened using judicious choices of the mechanical
potential. This gives relational particle mechanics models with analogues of
spatial curvature, cosmological constant, dust and radiation terms. A number of
these models are then tractable at the quantum level. These models can be used
to study important issues 1) in canonical quantum gravity: the problem of time,
the semiclassical approach to it and timeless approaches to it (such as the
naive Schrodinger interpretation and records theory). 2) In quantum cosmology,
such as in the investigation of uniform states, robustness, and the qualitative
understanding of the origin of structure formation.Comment: References and some more motivation adde
Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme
I approach the Problem of Time and other foundations of Quantum Cosmology
using a combined histories, timeless and semiclassical approach. This approach
is along the lines pursued by Halliwell. It involves the timeless probabilities
for dynamical trajectories entering regions of configuration space, which are
computed within the semiclassical regime. Moreover, the objects that Halliwell
uses in this approach commute with the Hamiltonian constraint, H. This approach
has not hitherto been considered for models that also possess nontrivial linear
constraints, Lin. This paper carries this out for some concrete relational
particle models (RPM's). If there is also commutation with Lin - the Kuchar
observables condition - the constructed objects are Dirac observables.
Moreover, this paper shows that the problem of Kuchar observables is explicitly
resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach
for nontrivial linear constraints that is also a construction of Dirac
observables, I consider theories for which Kuchar observables are formally
known, giving the relational triangle as an example. As a second route, I apply
an indirect method that generalizes both group-averaging and Barbour's best
matching. For conceptual clarity, my study involves the simpler case of
Halliwell 2003 sharp-edged window function. I leave the elsewise-improved
softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide
comments on Halliwell's approach and how well it fares as regards the various
facets of the Problem of Time and as an implementation of QM propositions.Comment: An improved version of the text, and with various further references.
25 pages, 4 figure
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier
We analyze the efficiency of different methods for the calculation of
reaction rates in the case of two simple analytical benchmark systems. Two
classes of methods are considered: the first are based on the free energy
calculation along a reaction coordinate and the calculation of the transmission
coefficient, the second on the sampling of dynamical pathways. We give scaling
rules for how this efficiency depends on barrier height and width, and we hand
out simple optimization rules for the method-specific parameters. We show that
the path sampling methods, using the transition interface sampling technique,
become exceedingly more efficient than the others when the reaction coordinate
is not the optimal one.Comment: 22 pages, 5 figure
Online Gaming Can Make a Better World: Jane McGonigal
With personal feelings put aside and sociological theoretical depictions brought to the forefront, it is interesting to compare some of Jane\u27s ideas with that of both Emile Durkheim and Max Weber. The theorist who stood out right away, being exemplified through Jane\u27s positive attitude claims on a much larger, macro-level scale, was Emile Durkheim. Jane\u27s ideas about transcending human\u27s as a resource through the social fabrics of gaming into something that might solve world hunger, poverty, and global warming was nothing short of functionalism at it\u27s best. Jane\u27s platform for social structure and maintaining positive social order is the online world, and online gaming is the vehicle for change
The implications of precise timekeeping of Doppler gravitational wave observations
Gravitational radiation from galactic and extragalactic astrophysical sources will induce spatial strains in the solar system, strains which can be measured directly by the Doppler radio link to distant spacecraft. Current noise sources in Pioneer and Voyager Doppler data are delineated and a comparison is made with expected signal levels from gravitational wave sources. The main conclusion is that it is possible to detect gravitational radiation with current DSN hydrogen maser systems stable in fractional frequency + or - 2 x 10 to the minus 14th power over 1000 sec. In the future, however, a serious Doppler observational program in gravitational wave astronomy will require frequency systems stable to at least 10 to the minus 16th power, but at the same time the current single frequency S-band uplink transmission will have to be replaced by a dual frequency capability
An extended classical solution of the droplet growth problem
Problems of applying the classical kinetic theory to the growth of small droplets from vapor are examined. A solution for the droplet growth equation is derived which is based on the assumption of a diffusive field extending to the drop surface. The method accounts for partial thermal and mass accommodation at the interface and the kinetic limit to the mass and heat fluxes, and it avoids introducing the artifact of a discontinuity in the thermal and vapor field near the droplet. Consideration of the environmental fields in spherical geometry utilizing directional fluxes yields boundary values in terms of known parameters and a new Laplace transform integral
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