The Idea of the Eternal Return: From Zawirski to the Present Day

Abstract

Zygmunt Zawirski, a member of the Lwow-Warsaw Philosophical School, in 1927-28 published an extensive paper (in three parts) devoted to the critical examination of the eternal return hypothesis - the idea that the history of the universe is fundamentally a cyclic process. After presenting the development of this idea throughout the ages Zawirski discusses arguments on its behalf coming mainly from the second law of thermodynamics and from the Poincaré recurrence theorem. Zawirski's criticism is confronted with the present state of art. in this domain. Three new theoretical inputs are taken into account: first, our present knowledge of the global structure of space-time geometries with closed timelike curves; second, some results of relativistic thermodynamics; third, Tipler's no-return theorem (relativistic counterpart of the Poincaré theorem). Our knowledge regarding the eternal return, although not less hypothetical, is more „formalized” and more sophisticated than it was in Zawirski's time.