Are Dark Energy and Dark Matter Different Aspects of the Same Physical Process?

It is suggested that the apparently disparate cosmological phenomena attributed to so-called 'dark matter' and 'dark energy' arise from the same fundamental physical process: the emergence, from the quantum level, of spacetime itself. This creation of spacetime results in metric expansion around mass points in addition to the usual curvature due to stress-energy sources of the gravitational field. A recent modification of Einstein's theory of general relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime expansion around mass points, which accounts well for the observed galactic rotation curves, is adduced in support of the proposal. Recent observational evidence corroborates a prediction of the model that the apparent amount of 'dark matter' increases with the age of the universe. In addition, the proposal leads to the same result for the small but nonvanishing cosmological constant, related to 'dark energy, as that of the causet model of Sorkin et al.Comment: Some typos corrected. Comments welcome, pro or co

Taking Heisenberg's Potentia Seriously

It is argued that quantum theory is best understood as requiring an ontological duality of res extensa and res potentia, where the latter is understood per Heisenberg's original proposal, and the former is roughly equivalent to Descartes' 'extended substance.' However, this is not a dualism of mutually exclusive substances in the classical Cartesian sense, and therefore does not inherit the infamous 'mind-body' problem. Rather, res potentia and res extensa are proposed as mutually implicative ontological extants that serve to explain the key conceptual challenges of quantum theory; in particular, nonlocality, entanglement, null measurements, and wave function collapse. It is shown that a natural account of these quantum perplexities emerges, along with a need to reassess our usual ontological commitments involving the nature of space and time.Comment: Final version, to appear in International Journal of Quantum Foundation

Teleportation, Braid Group and Temperley--Lieb Algebra

We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley--Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version of the preprint, quant-ph/0601050, which includes details of calculation, more topics such as topological diagrammatical operations and entanglement swapping, and calls the Temperley--Lieb category for the collection of all the Temperley--Lieb algebra with physical operations like local unitary transformation

Maximum Power Efficiency and Criticality in Random Boolean Networks

Random Boolean networks are models of disordered causal systems that can occur in cells and the biosphere. These are open thermodynamic systems exhibiting a flow of energy that is dissipated at a finite rate. Life does work to acquire more energy, then uses the available energy it has gained to perform more work. It is plausible that natural selection has optimized many biological systems for power efficiency: useful power generated per unit fuel. In this letter we begin to investigate these questions for random Boolean networks using Landauer's erasure principle, which defines a minimum entropy cost for bit erasure. We show that critical Boolean networks maximize available power efficiency, which requires that the system have a finite displacement from equilibrium. Our initial results may extend to more realistic models for cells and ecosystems.Comment: 4 pages RevTeX, 1 figure in .eps format. Comments welcome, v2: minor clarifications added, conclusions unchanged. v3: paper rewritten to clarify it; conclusions unchange

Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity

We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs embedded into a 3-space to a category of representations of the quasi-triangular ribbon Hopf algebra $U_q(sl(2,\bf C))$. Coefficients in expansions of them with respect to $x$ ($q=e^x$) are known as the Vassiliev invariants of finite type. In the present paper, we construct two types of tangle operators of vertices. One of them corresponds to a Casimir operator insertion at a transverse double point of Wilson loops. This paper proposes a non-perturbative generalization of Kauffman's recent result based on a perturbative analysis of the Chern-Simons quantum field theory. As a result, a quantum group analog of Penrose's spin network is established taking into account of the orientation. We also deal with the 4-dimensional canonical quantum gravity of Ashtekar. It is verified that the graph invariants of Vassiliev type are compatible with constraints of the quantum gravity in the loop space representation of Rovelli and Smolin.Comment: 34 pages, AMS-LaTeX, no figures,The proof of thm.5.1 has been improve

Unanimity Rule on networks

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.Comment: 7 pages 4 fig

Entwined Paths, Difference Equations and the Dirac Equation

Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are `self-quantizing'. We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process in the same sense that the Diffusion and Telegraph equations are phenomenological descriptions of stochastic processes.Comment: 15 pages, 5 figures Replacement 11/02 contains minor editorial change

A 20 Ghz Depolarization Experiment Using the ATS-6 Satellite

A depolarization experiment using the 20 GHz downlink from the ATS-6 satellite was described. The following subjects were covered: (1) an operational summary of the experiment, (2) a description of the equipment used with emphasis on improvements made to the signal processing receiver used with the ATS-5 satellite, (3) data on depolarization and attenuation in one snow storm and two rain storms at 45 deg elevation, (4) data on low angle propagation, (5) conclusions about depolarization on satellite paths, and (6) recommendations for the depolarization portion of the CTS experiment

Quantifying the complexity of random Boolean networks

We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)], does not distinguish between the spatial inhomogeneity of the ordered phase and the dynamical inhomogeneity of the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical regimes and for highly disordered networks, peaking somewhere in the disordered regime. Individual nodes with high complexity are the ones that pass the most information from the past to the future, a quantity that depends in a nontrivial way on both the Boolean function of a given node and its location within the network.Comment: 8 pages, 4 figure