A locus for “now”

We investigate the concepts of past, present, and future that build upon a modal distinction between the settled past and the open future. The concepts are defined in terms of a pre-causal ordering and of qualitative differences between alternative histories. Finally, we look what an event’s past, present, and future look like in the so-called Minkowskian Branching Structures, in which histories are isomorphic to Minkowski spacetime. “What is the present?” We typically understand this question as being relative to events, that is, we fix our attention on some event (frequently, an event of our utterance) and query what the present of this event is. The question has many facets, two of which we have set apart for the purposes of this paper. First, we may be concerned with when the “now” is, or what a locus for “now” is. The aim is to indicate a part of our world, or a region of spacetime, as a locus for the present of an arbitrary event. In other words, the aim is to define the set of events co-present (contemporaneous) with a given one, or the set of locations of such events. Secondly, one may wonder what differentiates the present of an event from its past and its future. This second question quickly leads us to considerable metaphysical queries: “Is becoming real?”, or “Is the distinction between tenses objective or mind-dependent?”. Clearly, the second question is much harder; moreover, a positive answer to it presupposes some answer to the first question. So we put it aside, and focus upon what a locus for “now” is. The problem is that starting with the papers of Rietdijk (1966) and Putnam (1967), there have been arguments showing that special relativity (SR) is inimical to any intuitive notion of the present, where “intuitive” here means that it is based on co-presence that is transitive and neither the identity nor the universal relation on Minkowski spacetime. Although these arguments deserve a separate analysis, to keep the length of this paper short, we will limit ourselves to this not-so–rigorous formulation of the result: