Minkowski Spacetime and the Dimensions of the Present

Richard T. W. Arthur


In Einstein-Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are (i) that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and (ii) that present existence is not an absolute notion, but is relative to inertial frame; the world-at-an-instant is a three dimensional, but relative, reality. According to a third view, advanced by Robb, Capek and Stein, (iii) what is present at a given spacetime point is, strictly speaking, constituted by that point alone. I argue here against the first of these views that the four-dimensional universe cannot be said to exist now, already, or indeed at any time at all; so that talk of its existence or reality as if that precludes the existence or reality of the present is a non sequitur. I maintain that the second is vitiated by a misconception of the status of the time co-ordinate function in relativistic physics; and that the third, although formally correct, is tarnished by its unrealistic assumption of instantaneous events. For, whether one assumes that only the present is real, or that compresent events are those such that each has become for the other, it collapses into the Buddhist Theory of Instantaneous reality; and in any case it is at variance with our normal intuitions of the present. I argue that a defensible concept of the present is nonetheless obtainable when account is taken of the non-instantaneity of events, including that of conscious awareness, as (iv) that region of spacetime comprised between the forward lightcone of the beginning of a small interval of proper time t (e.g. that during which conscious experience is laid down) and the backward lightcone of the end of that interval. This gives a serviceable notion of what is present to a given event of short duration, as well as saving our intuition of the "reality" or robustness of events that are present to conscious awareness.