The emergence of time

04/09 2019

12:15-13:15, D-IAS Conference Room (Ø18-509-1) in Odense

By Professor Roberto Longo, Dipartimento di Matematica, Università di Roma Tor Vergata, Italy

Classically, one could imagine a completely static space, thus without time. As is known, this picture is unconceivable in quantum physics due to vacuum uctuations. The fundamental difference between the two frameworks is that classical physics is commutative (simultaneous observables) while quantum physics is intrinsically noncommutative (Heisen-berg uncertainty). In this sense, we may say that time is generated by noncommutativity; if this statement is correct, we should be able to derive time out of a noncommutative space.

The interplay between Mathematics and Physics has been constant over the centuries, with a sort of discontinuity soon after the Quantum revolution. Physics always provided a direct, or indirect, source of inspiration for Mathematics. On the other hand, Physics theories were established on mathematical grounds.

I will explain how Operator Algebras provide a natural framework for a noncommutative space, a von Neumann algebra: the modular theory of Tomita-Takesaki gives us an intrinsic evolution. In particular, I shall discuss aspects of my recent work extending the modular evolution to a quantum operation, and how Jones’ index then leads to universal bounds on quantum information.