Who’s Afraid of Special Relativity?

Peter Forrest

Who’s Afraid of Special Relativity? Too many philosophers who shouldn’t be. In particular presentists and Growing Block theorists tend to prefer alternatives. The presentist William Craig, for instance, holds a neo-Lorentzian position and the Growing Block theorist Michael Tooley endorses Winnie’s theory. My claim is that neither Presentism nor the Growing Block is threatened by Special Relativity. What is under threat is the Newtonian conception of time as necessarily flowing uniformly.

My aim in this paper, which is an improved version of two earlier ones, < footnote> is first to explicate the familiar idea of the flow of time and then to use this explication to assess the force of the two objections from Special Relativity that I know of: the Objection from the Relativistic Invariance of all laws; and the Epistemic Objection.

The explication of the flow of time is slightly different in the two cases of a discrete succession of presents and a continuous succession. In the discrete case, time flows at a rate of seconds, not, note seconds per second, where the flow is the temporal thickness between successive presents. Special relativity implies that the rate of flow is frame-relative but not the system of successive presents. Moreover there is an absolute comparative rate of flow which is measured in seconds per second and is the ratio of the rates of flow of time at two points of spacetime. In the continuous case this comparative rate of flow may still be characterised but only for two “contemporary” points (ie those at one stage co-present). Time flows uniformly if these absolute conparative rates are the same everywhere , and in the case of discrete successive presents, at all times. The Newtonian conception is that necessarily time flows uniformly.

The argument from relativistic invariance may be stated thus
1. Any given pervasive uniformity in space time almost certainly holds of (nomic or metaphysical) necessity.
2. The structure of successive presents would be a pervasive uniformity in space time
3. So if time flows there is a necessary structure of successive presents
4. If Special Relativity is correct any necessary structures in Spacetime are relativistically invariant (or maybe covariant)
5. The structure of successive presents cannot be relativistically invariant
6. So time does not flow.

The first premises holds because we rightly take uniformity as a mark of necessity. Because of the qualification “almost certainly” the inference is defeasible and those adherents of a dynamic theory who grant that Special Relativity is a problem may be interprerted as saying that the above argument is prima facie persuasive but defeated by their case for the flow of time. Hence my claim that there is nothing to be afraid of is based upon my rejection of one of the other premises, namely 2. I grant, however, that the Newtonian conception of time is one in which 2 is satisfied. This enables me to explain why special relativity has widely been taken as a serious obstacle to the thesis that time flows or passes. Prior to relativity the Newtonian conception was widely assumed and its refutation was therefore taken as a refutation of the flow of time. It is to be noted that the case against Newtonian time extends to any theory in which the successive presents are hyperplanes. My case against 2 is therefore based upon the thesis of a "lumpy bumpy" present.

But how can we reject the thesis that the structure of successive presents is a uniformity, the sort of thing we take to be necessary? The answer is that the structure of successive presents is law-governed but not itself necessary. because the laws that govern it, although relativistically invariant, are not deterministic.. I present two different hypotheses about the laws governing the flow of time. Both are speculative, although they are inspired by quantum mechanical considerations.

The Epistemic Objection is that there is something peculiar in positing an account in which Spacetime is divided by successive hypersurfaces of co-presence withoiut us having any idea of which pairs of distant past events are co-present. To the suggestion of Swinburne and others that we rely upon the expanding universe to give us a cosmic clock, the epistemic objector may well reply that just because a clock is large it does not follow that it is accurate. Fortunately, my speculative hypotheses about the flow of time imply that the cosmic clock is nearly but not quite accurate, and that the flow of time is approximately uniform.

One of my hypotheses is a "many universes" theory in which in each "universe" time flows uniformly unless and until it stops flowing. Another is one in which reality is added to the past in a series of "volcanic eruptions" in which a small light cone is added (the larger the hyper-volume of the additional reality the less probable the "eruption")


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Footnote: Presented at the Wittgenstein Symposium, Kirchberg am Wechesel, August 2005, and the AAHPSS Conference , Dunedin, December 2005.