THE INCOMPATIBILITY OF STR AND THE TENSED THEORY OF TIME

by Quentin Smith

Published In: The Importance of Time, editor, L. Nathan Oaklander. Kluwer: Philosophical Studies Series, 2002.

Many philosophers think that the Special Theory of Relativity is compatible with the tensed or A-theory of time (“mind-independent temporal becoming”). They have argued that the future can be indeterminate or future relative to a reference frame. However, “relative futurity” is not a tensed or A-determination, but a relation that obtains in a B-series in a universe in which the tenseless theory of time (temporal features consist only of earlier than, later than and simultaneity) is true. I shall argue this point in this paper.

2. Relational presentness

Let us suppose, as we need to in order to have mind-independent temporal becoming, that presentness is not observer dependent. This supposition leads to the following conditionals: If presentness is a relational property, then this theory is compatible with STR but inconsistent with the tensed theory of time (the theory of objective time flow). But if presentness is a monadic property, the theory of time is incompatible with STR but consistent with the A-theory of time (the theory of mind-independent temporal becoming).

If "being present" expresses relational properties, e.g., present relatively to frame F1, being present relatively to frame F2, etc., then presentness is not an A-property, constituting temporal becoming, but is a B-relation in a becomingless universe. We may say "E1 is present relative to frame F2", but this is a tenseless statement; it means only that E1 is simultaneous with frame F2.

 To explore this idea further, we need more precise terminology, since "presentness is frame relative" is at best misleading and at worst contradictory. The relational property in question is being present relative to an event on a world line; it is not the property of being present relative to a world line. A worldline is a maximal chain that is a timelike path; it consists of causally related events which are present successively, so if something is present relative to the worldline, it would be simultaneous with a sequence of events none of which are simultaneous with each other. This, of course, is a contradiction. Since a reference frame includes the successive events on this world-line, we should not talk of being present relative to a reference frame. The relational property of presentness is instead the property of being present relatively to an event E on a worldline W.

However, this relational property is not an A-property but a B-property. For each of the successive events E1, E2, E3 on any given world-line W, there is some other event B that has the property of being present relatively to E1 (or E2, etc.) on W. Each event, such as E1, exists on a plane of simultaneous events, such that each event on this plane is present relatively to E1. For example, event B that is on the plane of simultaneity P1 that runs through E1 is present relatively to E1 on worldline W. This shows that the phrase "presently relatively to the event E on worldline W" expresses a B-property--a relation of simultaneity--not an A-property. It is true at every time that D is present relatively to E1, that C is present relatively to E2, and so on. This is not a universe in which there is temporal becoming.

3. Monadic Presentness

Let us pursue the idea that presentness is a monadic property. We can then say that event E1 on worldline W is present, and that any event B that is present relatively to E1 is presently occurring. This is a theory of objective time flow. But our theory is no longer consistent with STR, for if E1 on worldline W1 is present, then there is a privileged reference frame. Presentness, if a monadic property, is not the relativistic sort of property required by STR; it is not being present relatively to something, but being present absolutely. If E1 is present, no event that is not on the plane of simultaneity of E1 on W1 is present. Consider some event E0 on a non-parallel worldline W0 that is earlier than E1. If E1 is present, E0 has the monadic property of pastness. It can be true that E0 is present relatively to some event on some other world line W0. But it cannot be true that E0 is present. If it were true that E0 is present, then we would have the implicit contradiction: “E1 is present, E0 is present, E0 is earlier than E1”; therefore that it is false that E1 and E0 are both present. What is true is that E0 is present relatively to some event on the worldline W0. But this is not an A-property, an objective time-flow property. Rather, it is a B-relation, the relation of E0 being simultaneous with some event on worldline W0.

If we are to have objective time flow, the worldline W must belong to a privileged reference frame and STR must be false.

A critic might respond that if we change reference frames and represent time flow in a different frame, it will be the case that E0 is present. However, if there is objective time flow, we cannot change reference frames in this manner, either physically or in thought. We are on the worldline W1 and E1 is present and E0 is past. Can we imagine that we are on W0 and that E0 is present? We can do this only in the sense that we can entertain what we know to be a false proposition, that we are on W0 and E0 is present, and pretend that it is true. But this remains a pretence; the proposition that E0 is present is false, and we cannot switch reference frames in an ontologically pertinent sense, which would involve knowing E0 is present is true or at least it being the case that E0 is present. Once we assume that E1 is present, we have to conclude that E0 is not present. If we want to say with truth that both E1 and E0 are present, we have to talk of their being present relatively to events on different world lines. We can "change frames" in the sense that we know that E1 is present relatively to one event on one worldline and E0 is present relatively to an event on another world line, but we are now talking about relational presentness, which is just the B-relation of simultaneity.

3. Mind-Independent Temporal Becoming in the General Theory of Relativity

If there is objective time flow, it is logically necessary that there is a privileged reference frame. Objective time flow and STR are not compatible. But it is compatible with GTR. STR is the vacuum solution to the field equations of GTR; it is the solution for a universe with no matter. It follows immediately that STR is not the solution of the field equations that describes our universe, and thus that the participants in the debate about whether or not “STR is compatible with the tensed theory of time” are working with a false solution to the field equations. The solutions of the field equations accepted by contemporary cosmologists are Friedmann's solutions, which describe an expanding universe that contains homogenous and isotropically distributed matter. (I here ignore all the qualifications required by quantum mechanics.) The Freidmann solutions admit of an objective time flow which consists in the successive becoming present of the surfaces of simultaneity that coincide with the surfaces of homogeneity. Relative to these surfaces, the universe expands (or contracts) uniformly, and matter appears uniformly distributed on a large scale.