Prof. Julian Barbour, A New Theory of Time's Arrows in an Expanding Universe

Monday 8 Apr 2019, 14:30 → 15:30 Europe/Rome

2G26 (Dipartimento di Fisica, M.S. Angelo)

The laws of phenomenological thermodynamics were discovered through the study of confined systems, for example gas in a closed cylinder. Two theorems in dynamics played a key role in the statistical-mechanical explanation of these laws: Liouville's theorem and Poincaré's recurrence theorem. The proof of the latter employs the former and the further assumption that the accessible phase space of the system has a bounded measure. The recurrence theorem is the fundamental reason why hitherto all attempts have failed to reconcile the time-reversal symmetry of the laws of nature with the universal unidirectionality of processes observed in the universe. In my talk I will point out that if the law which governs the universe allows it to expand without limit the phase space of the universe does not have a bounded measure. In turn, this means that the behaviour of the universe is not subject to the recurrence theorem. This opens up the possibility of reconciling the apparent conflict between time-reversal symmetry and observed reversible phenomena. This is the case if in all of its solutions the law of the universe dictates the existence of a unique 'Janus point' of minimal size, either side of which the size of the universe grows without bound. It is then a direct consequence of Liouville's theorem that there will be attractors on the phase space of the degrees of freedom that describe the observable shape of the universe. They define arrows of time pointing in opposite directions away from the Janus point. Observers within the universe must be on one or the other side of the Janus point and, despite the time-reversal symmetry of the observed dynamical laws, will find only irreversible phenomena around them. I will provide examples of such behaviour in the Newtonian N-body problem and a non-empty set of cosmological solutions of general relativity.