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

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

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

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

Discreteness and the transmission of light from distant sources

We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to lengths and durations - or more specifically, replacing the Lorentzian manifold with an underlying discrete structure - need not disrupt the usual dynamics of propagation.Comment: 16 pages, 1 figure. Version 2: reference adde

Energy-momentum diffusion from spacetime discreteness

We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set background. At large scales, the microscopic swerves induced by the underlying atomicity manifest themselves as a Lorentz invariant diffusion in energy-momentum governed by a single phenomenological parameter, and we derive in full the corresponding diffusion equation. Inspired by the simplicity of the result, we then derive the most general Lorentz invariant diffusion equation for a massless particle, which turns out to contain two phenomenological parameters describing, respectively, diffusion and drift in the particle's energy. The particles do not leave the light cone however: their worldlines continue to be null geodesics. Finally, we deduce bounds on the drift and diffusion constants for photons from the blackbody nature of the spectrum of the cosmic microwave background radiation.Comment: 13 pages, 4 figures, corrected minor typos and updated to match published versio