Michaelmas Term
Monday, 6 October, 5.15-6.45pm
Sam Fletcher (MCMP Minnesota)
On the local flatness of spacetime
Many discussions of the foundations of general relativity put a special emphasis on describing every relativistic spacetime as “locally flat,” or as “locally Minkowskian”. Such claims are prima facie puzzling: after all, curvature is itself a local property, being described by a tensor field on spacetime. In general, relativistic spacetimes have non-vanishing curvature, so there is a straightforward sense in which they are not locally flat. Still, there is a natural intuition behind claims of “local flatness” arising from analogy with a sufficiently small region of a curved surface, like that of the Earth, which can to a good approximation be described as planar. But like many “principles” of general relativity, there does not seem to be much consensus regarding how to make this intuition more precise. Without attempting a comprehensive survey, we note three common articulations of what it could mean for spacetime to be “locally flat” or “locally Minkowskian,” arguing that each of them is unsatisfactory. We then explore a different, but precise and coordinate-independent sense in which relativistic spacetimes might be described as (approximately) locally flat. (This talk is based on a joint work with Jim Weatherall)
Monday, 27 October, 5.15-6.45pm
Kasia Rejzner (York)
Causality in the modern approach to foundations of quantum field theory
According to the present state of knowledge, the Universe in small scales is described by the laws of quantum theory. On the other hand, the fundamental theory of gravity is believed to be Einstein's relativity. Its effects become relevant when we consider large masses or (equivalently) large energies. One of the main features of Einstein's theory is the fact that the information cannot travel faster than light, so observations performed in spatially disjoined regions have to be independent. On the other hand, quantum mechanics tells us about the existence of entanglement. The fundamental question how to combine the principles of special relativity with quantum mechanics has lead to the invention of quantum field theory (QFT). In this talk I will focus on the algebraic approach to QFT, which allows to study foundational problems and underlying mathematical structures. In particular, I would like to discuss the notion of Einstein causality in quantum theory and show how it can be formulated using modern mathematical tools.
Monday, 1 December, 5.15-6.45pm
Edward Anderson (Cambridge)
Spaces of Spaces
John Archibald Wheeler asked that we study superspace: the space of 3-geometry configurations for GR (3-metrics quotiented by 3-diffeomorphisms). Moreover, Chris Isham has studied a far wider range of spaces of spaces, from the point of view of quantization. I here present
a) classical preliminaries for this study. These do not only include the obvious classical dynamics precursors on these spaces but also the phrasing of stochastic theory thereupon (following e.g. several different works of David Kendall).
b) A relational and background independent analysis of the choices made in adopting such spaces of spaces; this is in the vein of my and Julian Barbour's meanings of relational notions.
These considerations greatly generalize Wheeler's questions about superspace. Two particular points of focus are
1) on the commonplace appearance of stratified manifolds as configurations.
2) On the lattice of topological spaces based on a fixed set.