Scientific Series

How sure are you that spacetime is continuous? One of the more radical approaches to quantum gravity, causal set theory, models spacetime as a discrete structure: a causal set. Allowing the possibility that spacetime is discrete then how should we do physics on it? Carrying over the usual continuum descriptions in terms of differential equations seems like a difficult option. This talk begins with a brief introduction to causal sets then describes an approach to modelling the propagation of scalar particles on a causal set. We obtain the continuum causal retarded propagator by summing quantum mechanical amplitudes assigned to paths in the causal set - a kind of \'discrete path integral\' that agrees with the continuum result. The propagator so obtained should serve as a building block towards a model for quantum field theory on a causal set.

The problem of time is studied in a toy model for quantum gravity: Barbour and Bertotti\'s timeless formulation of non-relativistic mechanics. We quantize this timeless theory using path integrals and compare it to the path integral quantization of parameterized Newtonian mechanics, which contains absolute time. In general, we find that the solutions to the timeless theory are energy eigenstates, as predicted by the usual canonical quantization. Nevertheless, the path integral formalism brings new insight as it allows us to precisely determine the difference between the theory with and without time. This difference is found to lie in the form of the constraints imposed on the gauge fixing functions by the boundary conditions. In the stationary phase approximation, the constraints of both theories are equivalent. This suggests that a notion of time can emerge in systems for which the stationary phase approximation is either good or exact. As there are many similarities between this model of classical mechanics and general relativity, these results could provide insight to how time might be emergent in a theory of quantum gravity.

Hawking\'s black hole information paradox is one of the great thought experiments in physics. It points to a breakdown of some central principle of physics, though which one breaks down is still in dispute. It has led to the discovery of ideas that seem to be key to unifying quantum mechanics and gravity, namely the holographic principle and gauge/gravity duality. I review this subject, and discuss ongoing work and future directions.

Chris Isham in pre-recorded video, with Andreas Doring fielding questions and clarifications. Like watching commentators Scott Hamilton and Katarina Witt analyze Kristi Yamaguchi\'s performance at the World Figure Skating Championships for CBS News, join us for something different in quantum foundations. Chris Isham parries the intricacies of topos theory; Andreas Doring shows us how to see the moves in slow motion. Bring your own popcorn and plenty of questions.

I will summarize current observational constraints in cosmology with emphasis on what we have learned about the properties of the primordial density perturbations. I will describe future directions including observations of high redshift neutral hydrogen through is 21 cm line.

Quantum measure theory describes quantum theory as a generalization of a classical stochastic process, which may be fruitful for quantum gravity. I will describe the approach, and show that, in the context of an EPRB setup with two distant experimenters, two alternative experiments, and two outcomes per experiment, any set of no signaling probabilities can be realized, albeit by violating a `strong positivity\' condition.

The talk concerns a generalization of the concept of a minimum uncertainty state to the finite dimensional case. Instead of considering the product of the variances of two complementary observables we consider an uncertainty relation involving the quadratic Renyi entropies summed over a full set of mutually unbiased bases (MUBs). States which achieve the lower bound set by this inequality were introduced by Wootters and Sussman, who proved existence for every prime power dimension, and by Appleby, Dang and Fuchs who showed that in prime dimension the fiducial vector for a for a symmetric informationally complete positive operator valued measure (SIC-POVM) covariant under the Weyl-Heisenberg group is a state of this kind. Subsequently Sussman proved existence for a class of odd prime power dimensions. The purpose of this talk is to complete the existence proof by showing that minimum uncertainty states exist in every prime power dimension, without exception. Along the way we establish a number of properties of the Clifford group, and Galois extension fields, which might be of some independent interest.

The Great Plague of London, which claimed the lives of one fifth of London\'s population in 1665, is one of the most famous epidemics of all time. We have recently digitized the mortality records for London during the Great Plague, yielding weekly data for each of the 130 parishes. I will describe the temporal and spatial dynamics of the plague, and discuss our efforts to estimate the transmissibility of the infectious agent. I will also briefly describe other projects in progress inspired by disease-specific mortality records for London over the past 650 years.