Tomasz Miller (Jagiellonian University, Krakow): Lorentzian causality for probability measures

Friday 4 Oct 2019, 11:00 → 13:00 Europe/Budapest

Tanacsterem

Spacetime is usually modelled as a time-oriented Lorentzian manifold M, naturally endowed with the so-called causal precedence relation J+, containing all pairs of points which can be connected by means of a future-directed causal (i.e., timelike or null) curve. In a series of papers written jointly with M. Eckstein,
we have proposed and developed a natural extension of this relation onto the space P(M) of all Borel
probability measures on M. Using the tools from the optimal transport theory, one can utilize thus obtained notion of `causality between measures' to model a causal time-evolution of a spatially distributed physical entity in a globally hyperbolic spacetime, in sense providing a `non-local' generalization of a worldline.
In my talk, after briefly presenting the above mentioned extension of J+ and explaining what it means for a measure to evolve causally, I will discuss how this formalism can be further extended to encompass
many-particle systems. This in particular requires generalizing several definitions and facts from basic causality theory into a broader, `N-particle' setting.