# 7th International Conference on New Frontiers in Physics (ICNFP2018)

Jul 4 – 12, 2018
Europe/Athens timezone
Group photo: indico.cern.ch/event/663474/images/19808-ICNFP_2018_Group_Photo.JPG

## Causal evolution of probability measures

Jul 5, 2018, 3:20 PM
20m
Room 3

### Room 3

Oral presentation

### Speaker

Tomasz Miller (Warsaw University of Technology)

### Description

The causal structure of a spacetime $\mathcal{M}$ is usually described in terms of a binary relation $\preceq$ between events called the casual precedence relation (often referred to as $J^+$). In my talk I will present a natural extension of $\preceq$ onto the space $\mathscr{P}(\mathcal{M})$ of (Borel) probability measures on $\mathcal{M}$, designed to rigorously encapsulate the common intuition that probability can only flow along future-directed causal curves.

Using the tools of the optimal transport theory adapted to the Lorentzian setting, 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. I will define what it means that a time-dependent probability measure $\mu_t \in \mathscr{P}(\mathcal{M})$ evolves causally. I will discuss how such an evolution can be understood as a 'probability measure on the space of worldlines'. I will also briefly present some preliminary results concerning the relationship between the causal time-evolution of measures and the continuity equation.

### Primary author

Tomasz Miller (Warsaw University of Technology)