Joe Henson

Spectral geometry as a probe of quantum spacetime

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large-scale behavior to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity - the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifshitz gravity, among other approaches to quantum gravity.

Observables in causal set cosmology

For the theories known as classical sequential growth (CSG) models, it has been conjectured that, up to sets of measure zero, the “stem sets” generate the full σ-algebra of label-invariant measurable sets of causal sets. We prove this for a generic family of CSG models (the “generalized percolation models”). In consequence, we are able not only to identify the “observables” of these theories, but, more importantly, to provide them with an accessible physical interpretation. We suggest that the stem sets will play the same role of fundamental observable in the quantum analog of these theories, i.e. for quantum gravity.

Quantum histories and quantum gravity

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that the results of all measurements in suitably defined classical situations can be identified with properties of the histories. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of emergent geometry, are discussed.

Spontaneous Collapse Models on a Lattice

We present spontaneous collapse models of field theories on a 1+1 null lattice, in which the causal structure of the lattice plays a central role. Issues such as “locality,” “nonlocality,” and superluminal signaling are addressed in the context of the models which have the virtue of extreme simplicity. The formalism of the models is related to that of the consistent histories approach to quantum mechanics.

Imposing causality on a matrix model

We introduce a new matrix model that describes Causal Dynamical Triangulations (CDT) in two dimensions. In order to do so, we introduce a new, simpler definition of 2D CDT and show it to be equivalent to the old one. The model makes use of ideas from dually weighted matrix models, combined with multi-matrix models, and can be studied by the method of character expansion.

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.

Noncontextuality in Quantum Measure Theory

The Clauser‐Horne‐Shimony‐Holt‐Bell inequalities are necessary conditions for a set of no‐signalling probabilities for two measurers each with two alternative experiments each with two possible outcomes to admit a joint probability distribution. An analogue of these inequalities in the context of quantum measure theory is presented. Talk given by Fay Dowker.