Past, future, what's the difference?

Abstract

The laws of Physics are time-reversible, making no qualitative distinction between the past and the future—yet we can only go towards the future. This apparent contradiction is known as the “arrow of time problem”. Its current resolution states that the future is the direction of increasing entropy. But entropy can only increase towards the future if it was low in the past, and past low entropy is a very strong assumption to make, because low entropy states are rather improbable, non-generic. Recent works from the Physics literature suggest, however, we may do away with this so-called “past hypothesis”, in the presence of reversible dynamical laws featuring expansion. We prove that this is the case, for a synchronous graph rewriting-based toy model. It consists in graphs upon which particles circulate and interact according to local reversible rules. Some rules locally shrink or expand the graph. Generic states always expand; entropy always increases—thereby providing a local explanation for the arrow of time. This discrete setting allows us to deploy the full rigour of theoretical Computer Science proof techniques.

Pablo Arrighi

Professor

Pablo Arrighi studied at Imperial College, London, and defended his doctoral thesis at Cambridge University in 2003. He was appointed Maître de Conférences at the Université Grenoble-Alpes in 2005, Professor at Aix-Marseille Université in 2014, and finally Professor at the Université Paris-Saclay in 2020.

During his thesis, Pablo Arrighi described the first blind quantum computation protocol. He then pioneered the study of quantum programming languages. He next became one of the founders of the field of quantum cellular automata, i.e. discrete space discrete time quantum mechanics. His research also draws bridges between quantum networks and quantum gravity eg through the QISS consortium.