4,764 research outputs found
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
Quantum Gravity: Has Spacetime Quantum Properties?
The incompatibility between GR and QM is generally seen as a sufficient
motivation for the development of a theory of Quantum Gravity. If - so a
typical argumentation - QM gives a universally valid basis for the description
of all natural systems, then the gravitational field should have quantum
properties. Together with the arguments against semi-classical theories of
gravity, this leads to a strategy which takes a quantization of GR as the
natural avenue to Quantum Gravity. And a quantization of the gravitational
field would in some sense correspond to a quantization of geometry. Spacetime
would have quantum properties. But, this strategy will only be successful, if
gravity is a fundamental interaction. - What, if gravity is instead an
intrinsically classical phenomenon? Then, if QM is nevertheless fundamentally
valid, gravity can not be a fundamental interaction. An intrinsically classical
gravity in a quantum world would have to be an emergent, induced or residual,
macroscopic effect, caused by other interactions. The gravitational field (as
well as spacetime) would not have any quantum properties. A quantization of GR
would lead to artifacts without any relation to nature. The serious problems of
all approaches to Quantum Gravity that start from a direct quantization of GR
or try to capture the quantum properties of gravity in form of a 'graviton'
dynamics - together with the, meanwhile, rich spectrum of approaches to an
emergent gravity and/or spacetime - make this latter option more and more
interesting for the development of a theory of Quantum Gravity. The most
advanced emergent gravity (and spacetime) scenarios are of an
information-theoretical, quantum-computational type.Comment: 31 page
The gravitational content of lorentzian complex structures
The definition of a positive energy is investigated in a renormalizable
4-dimensional generally covariant model, which depends on the lorentzian
complex structure and not the metric of spacetime. The gravitational content of
the lorentzian complex structures is revealed by identifying the spacetime with
special 4-dimensional surfaces of the G{2,2} Grassmannian manifold. The
lorentzian complex structure is found to be a codimension-4 CR structure and
its classification is studied using the Chern-Moser and Cartan methods. The
spacetime metric is found to be a Fefferman-like metric of this codimension-4
CR structure. The open CR manifolds "hanging" from the points of the U(2)
characteristic boundary of the SU(2,2) classical domain belong into
representations of the Poincar\'e group and are related to the particle
spectrum of the model.Comment: 18 pages; Sections 4, 5 and 6 revise
Coupling Non-Gravitational Fields with Simplicial Spacetimes
The inclusion of source terms in discrete gravity is a long-standing problem.
Providing a consistent coupling of source to the lattice in Regge Calculus (RC)
yields a robust unstructured spacetime mesh applicable to both numerical
relativity and quantum gravity. RC provides a particularly insightful approach
to this problem with its purely geometric representation of spacetime. The
simplicial building blocks of RC enable us to represent all matter and fields
in a coordinate-free manner. We provide an interpretation of RC as a discrete
exterior calculus framework into which non-gravitational fields naturally
couple with the simplicial lattice. Using this approach we obtain a consistent
mapping of the continuum action for non-gravitational fields to the Regge
lattice. In this paper we apply this framework to scalar, vector and tensor
fields. In particular we reconstruct the lattice action for (1) the scalar
field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward
application of our discretization techniques to these three fields demonstrates
a universal implementation of coupling source to the lattice in Regge calculus.Comment: 10 pages, no figures, Latex, fixed typos and minor corrections
Towards general spatial intelligence
The goal of General Spatial Intelligence is to present a unified theory to support the various aspects of spatial experience, whether physical or cognitive. We acknowledge the fact that GIScience has to assume a particular worldview, resulting from specific positions regarding metaphysics, ontology, epistemology, mind, language, cognition and representation. Implicit positions regarding these domains may allow solutions to isolated problems but often hamper a more encompassing approach. We argue that explicitly defining a worldview allows the grounding and derivation of multi-modal models, establishing precise problems, allowing falsifiability. We present an example of such a theory founded on process metaphysics, where the ontological elements are called differences. We show that a worldview has implications regarding the nature of space and, in the case of the chosen metaphysical layer, favours a model of space as true spacetime, i.e. four-dimensionality. Finally we illustrate the approach using a scenario from psychology and AI based planning
Supersymmetry versus Gauge Symmetry on the Heterotic Landscape
One of the goals of the landscape program in string theory is to extract
information about the space of string vacua in the form of statistical
correlations between phenomenological features that are otherwise uncorrelated
in field theory. Such correlations would thus represent predictions of string
theory that hold independently of a vacuum-selection principle. In this paper,
we study statistical correlations between two features which are likely to be
central to any potential description of nature at high energy scales: gauge
symmetries and spacetime supersymmetry. We analyze correlations between these
two kinds of symmetry within the context of perturbative heterotic string
vacua, and find a number of striking features. We find, for example, that the
degree of spacetime supersymmetry is strongly correlated with the probabilities
of realizing certain gauge groups, with unbroken supersymmetry at the string
scale tending to favor gauge-group factors with larger rank. We also find that
nearly half of the heterotic landscape is non-supersymmetric and yet
tachyon-free at tree level; indeed, less than a quarter of the tree-level
heterotic landscape exhibits any supersymmetry at all at the string scale.Comment: 29 pages, LaTeX, 4 figures, 7 table
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