1,582 research outputs found
Interacting classical and quantum ensembles
A consistent description of interactions between classical and quantum
systems is relevant to quantum measurement theory, and to calculations in
quantum chemistry and quantum gravity. A solution is offered here to this
longstanding problem, based on a universally-applicable formalism for ensembles
on configuration space. This approach overcomes difficulties arising in
previous attempts, and in particular allows for backreaction on the classical
ensemble, conservation of probability and energy, and the correct classical
equations of motion in the limit of no interaction. Applications include
automatic decoherence for quantum ensembles interacting with classical
measurement apparatuses; a generalisation of coherent states to hybrid harmonic
oscillators; and an equation for describing the interaction of quantum matter
fields with classical gravity, that implies the radius of a Robertson-Walker
universe with a quantum massive scalar field can be sharply defined only for
particular `quantized' values.Comment: 31 pages, minor clarifications and one Ref. added, to appear in PR
Minimal size of a barchan dune
Barchans are dunes of high mobility which have a crescent shape and propagate
under conditions of unidirectional wind. However, sand dunes only appear above
a critical size, which scales with the saturation distance of the sand flux [P.
Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. {\bf{89,}} 264301 (2002);
B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B {\bf{28,}} 321 (2002);
G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E {\bf{64,}} 31305
(2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys.
Rev. Lett. {\bf{89,}} 264301 (2002) that this flux fetch distance is itself
constant. Indeed, this could not explain the proto size of barchan dunes, which
often occur in coastal areas of high litoral drift, and the scale of dunes on
Mars. In the present work, we show from three dimensional calculations of sand
transport that the size and the shape of the minimal barchan dune depend on the
wind friction speed and the sand flux on the area between dunes in a field. Our
results explain the common appearance of barchans a few tens of centimeter high
which are observed along coasts. Furthermore, we find that the rate at which
grains enter saltation on Mars is one order of magnitude higher than on Earth,
and is relevant to correctly obtain the minimal dune size on Mars.Comment: 11 pages, 10 figure
Saltation transport on Mars
We present the first calculation of saltation transport and dune formation on
Mars and compare it to real dunes. We find that the rate at which grains are
entrained into saltation on Mars is one order of magnitude higher than on
Earth. With this fundamental novel ingredient, we reproduce the size and
different shapes of Mars dunes, and give an estimate for the wind velocity on
Mars.Comment: 4 pages, 3 figure
The emergence of Special and Doubly Special Relativity
Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this
paper how a Brownian motion on a short scale can originate a relativistic
motion on scales that are larger than particle's Compton wavelength. This can
be described in terms of polycrystalline vacuum. Viewed in this way, special
relativity is not a primitive concept, but rather it statistically emerges when
a coarse graining average over distances of order, or longer than the Compton
wavelength is taken. By analyzing the robustness of such a special relativity
under small variations in the polycrystalline grain-size distribution we
naturally arrive at the notion of doubly-special relativistic dynamics. In this
way, a previously unsuspected, common statistical origin of the two frameworks
is brought to light. Salient issues such as the role of gauge fixing in
emergent relativity, generalized commutation relations, Hausdorff dimensions of
representative path-integral trajectories and a connection with Feynman
chessboard model are also discussed.Comment: 21 pages, 1 figure, RevTeX4, substantially revised version, accepted
in Phys. Rev.
(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces
We develop a kind of pregeometry consisting of a web of overlapping fuzzy
lumps which interact with each other. The individual lumps are understood as
certain closely entangled subgraphs (cliques) in a dynamically evolving network
which, in a certain approximation, can be visualized as a time-dependent random
graph. This strand of ideas is merged with another one, deriving from ideas,
developed some time ago by Menger et al, that is, the concept of probabilistic-
or random metric spaces, representing a natural extension of the metrical
continuum into a more microscopic regime. It is our general goal to find a
better adapted geometric environment for the description of microphysics. In
this sense one may it also view as a dynamical randomisation of the causal-set
framework developed by e.g. Sorkin et al. In doing this we incorporate, as a
perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor
changes added relating to previous wor
(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks
In the following we undertake to describe how macroscopic space-time (or
rather, a microscopic protoform of it) is supposed to emerge as a
superstructure of a web of lumps in a stochastic discrete network structure. As
in preceding work (mentioned below), our analysis is based on the working
philosophy that both physics and the corresponding mathematics have to be
genuinely discrete on the primordial (Planck scale) level. This strategy is
concretely implemented in the form of \tit{cellular networks} and \tit{random
graphs}. One of our main themes is the development of the concept of
\tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes
of the network and their respective web, establishing something like
\tit{(proto)causality}. It may perhaps be said that certain parts of our
programme are realisations of some early ideas of Menger and more recent ones
sketched by Smolin a couple of years ago. We briefly indicate how this
\tit{two-story-concept} of \tit{quantum} space-time can be used to encode the
(at least in our view) existing non-local aspects of quantum theory without
violating macroscopic space-time causality.Comment: 35 pages, Latex, under consideration by CQ
Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
A major problem in the consistent-histories approach to quantum theory is
contending with the potentially large number of consistent sets of history
propositions. One possibility is to find a scheme in which a unique set is
selected in some way. However, in this paper we consider the alternative
approach in which all consistent sets are kept, leading to a type of `many
world-views' picture of the quantum theory. It is shown that a natural way of
handling this situation is to employ the theory of varying sets (presheafs) on
the space \B of all Boolean subalgebras of the orthoalgebra \UP of history
propositions. This approach automatically includes the feature whereby
probabilistic predictions are meaningful only in the context of a consistent
set of history propositions. More strikingly, it leads to a picture in which
the `truth values', or `semantic values' of such contextual predictions are not
just two-valued (\ie true and false) but instead lie in a larger logical
algebra---a Heyting algebra---whose structure is determined by the space \B
of Boolean subalgebras of \UP.Comment: 28 pages, LaTe
Gravitational Energy Loss and Binary Pulsars in the Scalar Ether-Theory of Gravitation
Motivation is given for trying a theory of gravity with a preferred reference
frame (``ether'' for short). One such theory is summarized, that is a scalar
bimetric theory. Dynamics is governed by an extension of Newton's second law.
In the static case, geodesic motion is recovered together with Newton's
attraction field. In the static spherical case, Schwarzschild's metric is got.
An asymptotic scheme of post-Minkowskian (PM) approximation is built by
associating a conceptual family of systems with the given weakly-gravitating
system. It is more general than the post-Newtonian scheme in that the velocity
may be comparable with . This allows to justify why the 0PM approximation of
the energy rate may be equated to the rate of the Newtonian energy, as is
usually done. At the 0PM approximation of this theory, an isolated system loses
energy by quadrupole radiation, without any monopole or dipole term. It seems
plausible that the observations on binary pulsars (the pulse data) could be
nicely fitted with a timing model based on this theory.Comment: Text of a talk given at the 4th Conf. on Physics Beyond the Standard
Model, Tegernsee, June 2003, submitted to the Proceedings (H. V.
Klapdor-Kleingrothaus, ed.
The structure of causal sets
More often than not, recently popular structuralist interpretations of
physical theories leave the central concept of a structure insufficiently
precisified. The incipient causal sets approach to quantum gravity offers a
paradigmatic case of a physical theory predestined to be interpreted in
structuralist terms. It is shown how employing structuralism lends itself to a
natural interpretation of the physical meaning of causal sets theory.
Conversely, the conceptually exceptionally clear case of causal sets is used as
a foil to illustrate how a mathematically informed rigorous conceptualization
of structure serves to identify structures in physical theories. Furthermore, a
number of technical issues infesting structuralist interpretations of physical
theories such as difficulties with grounding the identity of the places of
highly symmetrical physical structures in their relational profile and what may
resolve these difficulties can be vividly illustrated with causal sets.Comment: 19 pages, 4 figure
Kochen-Specker Vectors
We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly
rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192
(117) vector system translated into MMP diagram notation with a new graphical
representation, results on Tkadlec's dual diagrams added, several other new
results added, journal version: to be published in J. Phys. A, 38 (2005). Web
page: http://m3k.grad.hr/pavici
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