The Alexandroff Present and Minkowski Spacetime: Why it Cannot Do What it has Been Asked to Do¹

Abstract

In recent times there have been interesting attempts to introduce a mind-independent present in Minkowski spacetime, a structure that has also been regarded as capable of explaining some aspects of our subjective experience of time, in particular the fact that we share a “now” but not a “here”. Considering that Minkowski spacetime is the arena for three out of the four interactions postulated by contemporary physics, this claim, if correct, would be remarkable. Against the prevailing opinion of last century’s major physicists and philosophers, we would have in fact discovered that it is possible to find a now (even a “transient one”) in any contemporary physical theory whose spatiotemporal arena has the structure of Minkowski spacetime. At the same time, we would have gone some way toward a rapprochement of “the manifest image” of time − characterized by a cosmically extended, transient now − with the physical image, traditionally dominated by the picture of a block universe in which “the present is absent” because regarded as purely mind-dependent.

¹ Thanks to Richard Arthur and Steven Savitt for extensive discussions and written exchanges over many of the topics discussed here. From them, I have in any case learnt a lot also in the past. Our exchange has reduced, but possibly not completely eliminated, the number of misunderstandings on my part. Carl Hoefer has read a previous version of this paper and helped with critical comments and questions.