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Time Order, Time Direction, and the Presentist's View on Spacetime

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Time Order, Time Direction, and the Presentist's View on Spacetime Cord Friebe Abstract The physical possibility of spacetimes containing closed timelike curves (CTCs) challenges the philosophy of time in the way that temporal ordering is, at best, remarkably non-standard: events on CTCs precede themselves. Apparently, such universes do not possess a consistent time order but only a consistent time direction. Thus, temporal directionality seems to be more fundamental than ordering in earlier-later or past-present-future. I will argue that this favors presentism as the adequate ontology of spacetimes: only presentism consistently copes with the idea that temporal ordering depends on empirical constraints. The presentist Now is fundamentally undivided and productively directed towards existence. Time order arises by extending the Now, which can fail and in fact fails in universes containing CTCs. Keywords: general relativity, philosophy of time, presentism 1 Introduction In 1949, Kurt G¨odelfamously presented a solution of Einstein's generally relativistic field equations that permits the occurrence of closed timelike curves (CTCs).1 According to G¨odelhimself, the possibility of CTCs confirms `the' idealist philosophy of time, namely what he takes to be the view that time is unreal, i.e., that the objective world is timeless: [I]t seems that one obtains an unequivocal proof for the view of those philosophers who, like Parmenides, Kant, and the modern idealists, deny the objectivity of change and consider change as an illusion or an appearance due to our special mode of perception. ([6], 202) Kriterion { Journal of Philosophy, 2016, 30(2): 91{106. http://www.kriterion-journal-of-philosophy.org c 2016 The author 92 KRITERION { Journal of Philosophy, 2016, 30(2): 91{106 Consequently, the inference drawn above as to the non-ob- jectivity of change doubtless applies at least in these worlds [containing CTCs] [...] strengthening further the idealistic viewpoint. ([6], 205) [N]o reason can [hence] be given why an objective lapse of time should be assumed at all. ([6], 206) Nowadays, philosophers of physics disagree. They hold that even space- times containing CTCs have a temporal dimension (see, e.g., [4]; [5]; [9]). Thus, they are realists about time, at least as long as spacetime is `time orientable'. I agree that the occurrence of CTCs does not contradict the objectivity of time. It is unclear, however, in which sense time is `objective' or `real', and, correspondingly, in which sense CTC-spacetimes have a `temporal dimension'. The analytic philosophy of time offers, roughly, two different views about what real time consists in: either it is \B-time" or \A-time", i.e., either it is essentially the ordering of earlier-later or the directionality of a moving Now. I will argue that the possibility of CTCs is in conflict with B-time-order but requires A-time-direction. Then, the question arises of whether spacetime grounds A-time or rather the other way around: that presentness grounds spacetime, containing CTCs or not. I will suggest this latter option: universes containing CTCs motivate to develop a reasonable theory of presentism. The plan is as follows: In Section 2, I will briefly recap both the essentials of general relativity and of the analytic philosophy of time. Upon these physical and metaphysical basics, Section 3 provides the argument in favor of time directionality being more fundamental than ordering. Finally, Section 4 argues that presentness is more fundamental than spacetime. 2 Physical and Philosophical Basics The paper aims to demonstrate the relevance of the A- vs. B-time dis- tinction for the ontology of relativistic spacetimes. This section presents the basic elements of general relativity and central themes from the cur- rent philosophy of time, as they are relevant for my purpose. Cord Friebe: Presentist's View on Spacetime 93 2.1 General Relativity To begin with, take a 4-dimensional (differentiable) manifold to rep- resent spacetime. Every physically possible spacetime has a lightcone structure, i.e, with every spacetime point p is associated a lightcone such that the distinction between timelike, lightlike, and spacelike vectors is `everywhere', at every p, available. In particular, a timelike vector points inside the lightcone and is conventionally called \future-directed" iff it points into the upper lobe (and \past-directed" otherwise, i.e., iff it points downwards). Then, spacetimes are time orientable iff a con- tinuous designation of \future-directed" and \past-directed" for timelike vectors can be made over the entire manifold.2 Figure 1: Time orientability: any continuous transport of a timelike vector must preserve its orientation. It should be emphasized that any simply connected spacetime is time orientable, a spacetime that is not time orientable is hence topologi- cally strange. Consider, in particular, a timelike curve: a curve is called \timelike" iff its tangent vectors are `always', at every point of the curve, timelike. Such a curve lies inside all of its lightcones. Given time ori- entability, one may say that such a curve is `always' future(or, past)- directed, and only given this, monotonically increasing parameters may consistently run along timelike curves { the (even invariant) proper times along worldlines. Therefore, time orientability is generally taken to be a necessary condition for time to be real. 94 KRITERION { Journal of Philosophy, 2016, 30(2): 91{106 Figure 2: Proper time τ consistently parametrize every timelike curve !. However, it is questionable whether time orientability is also sufficient for spacetime to have a temporal dimension. For it does not exclude the possibility that a timelike, even `always' future-directed, curve can be closed (or, almost closed). Intuitively, in such a case, the event located at a given starting point p precedes itself. G¨odel'schallenge precisely was that even Einstein's field equations allow for such a possibility so that it is not only mathematically compatible with time orientability but also physically possible. He concluded that the objective world is timeless. Still, it is undoubtedly not the case that the events on a CTC are simultaneous. Rather, the distinction between events being simultaneous and being non-simultaneous { a distinction which seems to be crucially temporal { is still available. Given this, one has good reason to sustain that universes containing CTCs are temporal. To sharpen the problem, it is instructive to confront an event/observer on a CTC with a freely falling body along a geodesic (see Figure 3): the hypothetical observer on the CTC is not simultane- ous with any event on the CTC but, e.g., with the body/event located at p0. However, (s)he is located at p `more than once', namely modulo (periodic) τ!. Does that mean { and what exactly could that mean { that the observer is `again and again' simultaneous with the body/event Cord Friebe: Presentist's View on Spacetime 95 at p0? I will argue that the B-theorists of time, focusing on the (partial- )order of earlier-simultaneous-later, are in trouble here and, so, that the possibility of CTCs favors tensed (A-) theories of time. Figure 3: Is the observer at p again and again, at periodic τCTC , simul- taneous with the event at p0? 2.2 Analytic Metaphysics of Time Before arguing in favor of tensism, let me rewrite carefully the A- vs. B-time distinction from the analytic philosophy of time. One might have the impression that, according to the B-theorists, the world is a rather static block universe, whereas, according to the A-theorists, the objective world is really dynamical { `growing', or whatever { in virtue of an ontologically distinguished present. So, seemingly, a B-theory is much closer to allegedly static CTC-universes than the A-theories. However, this impression is misleading. For, on the one side, self-declared B-theorists, such as Mellor ([8]), defend \real" time and \real" change and so apparently do not intend 96 KRITERION { Journal of Philosophy, 2016, 30(2): 91{106 to be closest to static block universes. And, on the other side, there is a very prominent A-theory { namely, the so-called moving-spotlight view { which in fact assumes an existentially static block universe: the moving Now is rather an irreducible property than an existentially distinguished event. Therefore, the distinction between A- and B-theories of time is fairly independent from the (alleged) dynamics of existence.3 It is rather about ordering and directionality. According to the B-theorists, real time consists in the relation of earlier-later. Events (et al.) are temporal in the B-theorist's sense, i.e., they are in B-time iff they are earlier and/or later than some other events, perhaps also simultaneous with some other events, respectively. B-time is hence fundamentally time order. B-time direction, by contrast, is a derivative concept: nothing more than the convention or a physical fact of whether p is earlier than p0 or vice versa. According to the A-theorists, real time is grounded in the present. The meaning of \A-time" depends on that single point rather than on an infinite set of points to be ordered.4 Its motion is (somehow) directed, and A-time is hence fundamentally time direction. Time order emerges derivatively, in virtue of the directed motion of the present. Accordingly, the moving-spotlight view (usually) presupposes the existence of a so- called C-series of events { a non-temporal ordering of events. The present is in relative motion against this C-series and turns it into a (temporal) B-series. However, there is a tendency in the philosophy of physics to downplay the provided sharp contrast between A- and B-theories of time. One prominent example is the metaphysics of time, found by Maudlin ([7], chap. 4) within physics.
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