Causal evolution of spin networks

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1+1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.Comment: latex, 32 pages, 17 figure

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Stability analysis of coupled map lattices at locally unstable fixed points

Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for exploring fundamental features of CMLs, such as their stability properties. Since CMLs can be considered as graphs, we apply methods of spectral graph theory to analyze their stability at locally unstable fixed points for different updating rules, different coupling scenarios, and different types of neighborhoods. Numerical studies are found to be in excellent agreement with our theoretical results.Comment: 22 pages, 6 figures, accepted for publication in European Physical Journal

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