A Spin-Statistics Theorem for Certain Topological Geons

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with nontrivial spin and statistics. In a theory without topology change there is no obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral abelian geons do satisfy a spin-statistics correlation if they are described by a wave function which is given by a functional integral over metrics on a particular four-manifold. This manifold describes a topology changing process which creates a pair of geons from $R^3$.Comment: 21 pages, Plain TeX with harvmac, 3 figures included via eps

The Random Walk in Generalized Quantum Theory

One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a certain condition of ``strong positivity'', the most general Markovian, translationally invariant ``decoherence functional'' with nearest neighbor transitions.Comment: 25 pages, no figure

Energy extremality in the presence of a black hole

We derive the so-called first law of black hole mechanics for variations about stationary black hole solutions to the Einstein--Maxwell equations in the absence of sources. That is, we prove that $\delta M=\kappa\delta A+\omega\delta J+VdQ$ where the black hole parameters $M, \kappa, A, \omega, J, V$ and $Q$ denote mass, surface gravity, horizon area, angular velocity of the horizon, angular momentum, electric potential of the horizon and charge respectively. The unvaried fields are those of a stationary, charged, rotating black hole and the variation is to an arbitrary `nearby' black hole which is not necessarily stationary. Our approach is 4-dimensional in spirit and uses techniques involving Action variations and Noether operators. We show that the above formula holds on any asymptotically flat spatial 3-slice which extends from an arbitrary cross-section of the (future) horizon to spatial infinity.(Thus, the existence of a bifurcation surface is irrelevant to our demonstration. On the other hand, the derivation assumes without proof that the horizon possesses at least one of the following two (related)properties: ($i$) it cannot be destroyed by arbitrarily small perturbations of the metric and other fields which may be present, ($ii$) the expansion of the null geodesic generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil

Large Fluctuations in the Horizon Area and what they can tell us about Entropy and Quantum Gravity

We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the teleological character of the event horizon implies that the consequent entropy fluctuations must be taken seriously in any interpretation of the quantal formalism. We then indicate how the entropy can be well defined despite the teleological character of the horizon, and we argue that this is possible only in the context of a spacetime or ``histories'' formulation of quantum gravity, as opposed to a canonical one, concluding that only a spacetime formulation has the potential to compute --- from first principles and in the general case --- the entropy of a black hole. From the entropy fluctuations in a related example, we also derive a condition governing the form taken by the entropy, when it is expressed as a function of the quantal density-operator.Comment: 35 pages, plain Tex, needs mathmacros.tex and msmacros.te

Topology Change and Causal Continuity

The result that, for a scalar quantum field propagating on a ``trousers'' topology in 1+1 dimensions, the crotch singularity is a source for an infinite burst of energy has been used to argue against the occurrence of topology change in quantum gravity. We draw attention to a conjecture due to Sorkin that it may be the particular type of topology change involved in the trousers transition that is problematic and that other topology changes may not cause the same difficulties. The conjecture links the singular behaviour to the existence of ``causal discontinuities'' in the spacetime and relies on a classification of topology changes using Morse theory. We investigate various topology changing transitions, including the pair production of black holes and of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure removed), conclusions remain unchanged. Accepted for publication in Physical Review

A Causal Order for Spacetimes with C0C^0 Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves

We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space of closed subsets of a compact set. We are led to work with a new causal relation which we call $K^+$, and in terms of it we formulate extended definitions of concepts like causal curve and global hyperbolicity. In particular we prove that, in a spacetime \M which is free of causal cycles, one may define a causal curve simply as a compact connected subset of \M which is linearly ordered by $K^+$. Our definitions all make sense for arbitrary $C^0$ metrics (and even for certain metrics which fail to be invertible in places). Using this feature, we prove for a general $C^0$ metric, the familiar theorem that the space of causal curves between any two compact subsets of a globally hyperbolic spacetime is compact. We feel that our approach, in addition to yielding a more general theorem, simplifies and clarifies the reasoning involved. Our results have application in a recent positive energy theorem, and may also prove useful in the study of topology change. We have tried to make our treatment self-contained by including proofs of all the facts we use which are not widely available in reference works on topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by R.S. Garcia. No change to chief results. 33 page

Cosmological Constant and Noncommutative Spacetime

We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra restricts general coordinate transformations to four-volume preserving noncommutative coordinate transformations. The noncommutative gravitational action is thus an unimodular noncommutative gravity. We show that spacetime noncommutativity provides a very natural justification to an unimodular gravity solution to the cosmological problem. We obtain the right order of magnitude for the critical energy density of the universe if we assume that the scale for spacetime noncommutativity is the Planck scale.Comment: 7 page

A Classical Sequential Growth Dynamics for Causal Sets

Starting from certain causality conditions and a discrete form of general covariance, we derive a very general family of classically stochastic, sequential growth dynamics for causal sets. The resulting theories provide a relatively accessible ``half way house'' to full quantum gravity that possibly contains the latter's classical limit (general relativity). Because they can be expressed in terms of state models for an assembly of Ising spins living on the relations of the causal set, these theories also illustrate how non-gravitational matter can arise dynamically from the causal set without having to be built in at the fundamental level. Additionally, our results bring into focus some interpretive issues of importance for causal set dynamics, and for quantum gravity more generally.Comment: 28 pages, 9 figures, LaTeX, added references and a footnote, minor correction

Timesharing performance as an indicator of pilot mental workload

Attentional deficits (workloads) were evaluated in a timesharing task. The results from this and other experiments were incorporated into an expert system designed to provide workload metric selection advice to non-experts in the field interested in operator workload

WASH and Tsg101/ALIX-dependent diversion of stress-internalized EGFR from the canonical endocytic pathway

Stress exposure triggers ligand-independent EGF receptor (EGFR) endocytosis, but its post-endocytic fate and role in regulating signalling are unclear. We show that the p38 MAP kinase-dependent, EGFR tyrosine kinase (TK)-independent EGFR internalization induced by ultraviolet light C (UVC) or the cancer therapeutic cisplatin, is followed by diversion from the canonical endocytic pathway. Instead of lysosomal degradation or plasma membrane recycling, EGFR accumulates in a subset of LBPA-rich perinuclear multivesicular bodies (MVBs) distinct from those carrying EGF-stimulated EGFR. Stress-internalized EGFR co-segregates with exogenously expressed pre-melanosomal markers OA1 and fibrillar PMEL, following early endosomal sorting by the actin polymerization-promoting WASH complex. Stress-internalized EGFR is retained intracellularly by continued p38 activity in a mechanism involving ubiquitin-independent, ESCRT/ALIX-dependent incorporation onto intraluminal vesicles (ILVs) of MVBs. In contrast to the internalization-independent EGF-stimulated activation, UVC/cisplatin-triggered EGFR activation depends on EGFR internalization and intracellular retention. EGFR signalling from this MVB subpopulation delays apoptosis and might contribute to chemoresistance