Scientific Series

Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as degrees of vertices and numbers of shortcycles. It has been argued that such models can be useful in studying how an extended geometry might emerge from a background independent dynamical system. As statistical systems, graphity models can be studied analytically by estimating their partition functions or numerically by Monte Carlo simulations. In this talk I will present recent results obtained using both of these approaches. In particular, I will describe the transition between the high and low temperature regimes and arguethat matter degrees of freedom must play an important role in order for the graph states dominating in the low temperature regime to resemble interesting extended geometries.

It is well known that the derivation of the Bell Inequality rests on two major assumptions, usually called outcome independence and parameter independence. Parameter independence seems to have a straightforward motivation: it expresses a non-signalling requirement between space-like separated sites and is thus motivated by locality. The status of outcome independence is much les clear. Many authors have argued that this assumption too expresses a locality requirement, in the form of a \'screening off\' condition. I will argue that the assumption also admits of an entirely different interpretation, suggested by the concept of sufficiency in the general theory of statistical inference. In this view, the assumption of outcome independence can be explained as expressing the idea that the specification of the hidden variable is sufficient, i.e. it exhausts all the relevant statistical information about the measurement outcomes. In this view, the assumption has no roots in locality at all. Rather, I would claim, it stems from the assumption that there exists such an exhaustive state description in our putative hidden variable theories.

In this talk I will analyse the stochastic background of gravitational waves coming from a first order phase transition in the early universe. The signal is potentially detectable by the space interferometer LISA. I will present a detailed analytical model of the gravitational wave production by the collision of broken phase bubbles, together with analytical results for the gravitational wave power spectrum. Gravitational wave production by turbulence and magnetic fields will also be briefly discussed.

We discuss recent developments in the study of black holes and similar compact objects in string theory. The focus is on how these solutions are effected by higher-derivative terms in an effective action. The setting of this investigation is an off-shell formulation of five-dimensional supergravity, including terms of order four-derivatives whose precise form are determined by embedding this theory in M-theory. We find that certain singular solutions are fully regularized by the higher-derivative terms and that generic solutions receive calculable corrections to the entropy, or other relevant quantities such as the dual central charge. A particular solution studied corresponds to the geometry sourced by a fundamental string and may set the stage for a new and exciting example of holography.

This talk is concerned with the existence of spectral triples in quantum gravity. I will review the construction of a spectral triple over a functional space of connections. Here, the *-algebra is generated by holonomy loops and the Dirac type operator has the form of a global functional derivation operator. The spectral triple encodes the Poisson structure of General Relativity when formulated in terms of Ashtekars variables. Finally I will argue that the Hamiltonian of General Relativity may emerge from the construction via the requirement that inner automorphisms vanish on the vacuum sector.

The last years have seen tremendous progress in simulations of inspiral and coalescence of binary black holes. I will present recent results of the Caltech/Cornell collaboration simulating inspiral and collision of two black holes. Furthermore, while currently no talk on numerical relativity seems to be complete without a discussion of binary black hole coalescence, there are many more aspects of Einstein\'s equations that can be probed numerically. I will discuss some of these unexpected and intriguing features, among them black holes with five horizons and super-extremal black holes.

The focus of this talk is a particular feature of the statistical behavior of elementary particles, simple composite systems of them and the quantum probability theory to which this behavior gives rise. The standard interpretation of a generalized probability theory of the sort found in quantum mechanics is that its probabilities are probabilities of propositions belonging to particles, where a proposition belongs to a particle if its constituent dynamical property is a possible property of the particle. The feature of interest is the fact that there exist simple systems and finite combinations of propositions belonging to them for which no two-valued measures are possible. I will argue that quantum probabilities are not satisfactorily interpretable as probabilities of propositions belonging to particles, and that such an interpretation is possible only when the propositions to which probabilities are assigned form (an algebraic structure which is homomorphic to) a Boolean algebra. The idea I will develop is that the probabilities of quantum mechanics are probabilities of “effects,” probabilities of the traces of particleinteractions with objects and processes that are epistemically accessible to us. I hope to make it clear that such a view is not committed to any kind of anti-realism about the micro-world, that its mildly instrumentalist flavor is not a defect but a strength, and that it illuminates at least one otherwise paradoxical feature of quantum mechanics.

For quantum gravity, the requirement of metric positivity suggests the use of noncanonical, affine kinematical field operators. In view of gravity\'s set of open classical first class constraints, quantization before reduction is appropriate, leading to affine commutation relations and affine coherent states. The anomaly in the quantized constraints may be accommodated within the projection operator approach, which treats first and second class quantum constraints in an equal fashion. Functional integral representations are derived for expressions both with and without constraint imposition. As with all coherent state formulations, close contact between the classical and quantum theories is maintained throughout. Perturbative nonrenormalizability is understood as a partial hard-core behavior of the interaction, which as soluble models suggest, leads to a perturbative formulation, not about the traditional free theory, but rather about a suitable pseudofree theory that properly incorporates the essence of the hard core.