time's error: is time's asymmetry extrinsic?

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  • FERREL Ct tR ISTENSEN

    T IME 'S ERROR: IS T IME 'S ASYMMETRY EXTRINS IC?

    1. T I lE THEORY

    The subject of this paper is the asymmetry of time, also spoken of as its anisotropy or directionality. As it is commonsensically conceived, time's two directions are not only opposite to one another but struc- turally different: the earlier-to-later direction is different from the later-to-earlier one. By contrast, space is ordinarily regarded as being isotropic, the same in all directions. Or, to state this idea in terms that don't sound committed to a "substantivalist" view of temporality, the temporal relation of precedence (or subsequence) is asymmetrical: if e is earlier than jr, then f is not earlier than e. But the nearest spatial analog of that relation is betweenness along a line, which is sym- metrical (in the sense that if x is between y and z then x is between z and y). The only asymmetry had by a one-dimensional region of space is such as might be imposed from the outside - as with "r ight" and "left," which involve relations to an asymmetrical object; or via a sheer convention - say, to arbitrarily call one direction "plus" and the other "minus."

    Now, though space itself is isotropic, the arrangement and move- ment of objects can be such as to display an asymmetry with respect to space. In other words there are asymmetries in space, ones involving the non-spatial aspects of its contents, even though there is evidently no asymmetry of space. This somewhat abstract idea is best under- stood in terms of examples like the familiar north-south asymmetry, which is tied to such features as the direction of the earth's rotation relative to the sun and stars. Another instance is the up-down asym- metry, which has to do with earth's gravity. In everyday language, things are pulled in one of two opposite directions but not the other; in the terminology of field theories, there is a gravitational gradient in the neighborhood of the earth. The interesting thing about the latter asymmetry in space is that untutored common sense takes it to be an asymmetry of space itself. It was an important scientific breakthrough when thinkers first decided that matter tends to move, not simply

    Erkenntnis 26 (1987) 231-248. 9 1987 by D. Reidel Publishing Company.

  • 232 FERREL ( 'HR ISTENSEN

    "down," but toward other matter. It is intriguing that we should so naturally take something which is extrinsic to space to be a part of its own character.

    The next question is almost automatic: might it not be the same for time? Might it be that the seeming directionality of time also represents an illusion or inferential error of some sort, resulting from a mere asymmetry in time'? That would mean time in itself is sym- metrical: there is the temporal betweenness relation (the possibility of topologically closed time will be ignored here, for simplicity) but no such thing as temporal subsequence. And as it turns out, many modern thinkers have claimed that this is the case (see, e.g., Davies, 1974).

    Indeed, a second view of this same general sort has also been held: that temporal relations are after all asymmetrical, but dependently so. In other words, temporality is in this respect not absolute; temporal relations are dependent for their nature on other sorts of properties and relations borne by things in time. To explain by way of analogy - indeed, the motivation seems to be the same - consider the widely- held philosophical view that temporal separation is dependent on the existence of change: two states of the universe can't be temporally distant from one another (hence numerically distinct) unless they, or other states temporally between them, are qualitatively different from each other, in some non-temporal respect. Similarly, the Leibnizian "identity of indiscernibles" doctrine makes the topological character of time, as open or closed, dependent on the non-temporal features of things in time. Likewise, then, the claim is sometimes made that time is anisotropic only because of the asymmetrical arrangement of its contents (e.g., van Fraassen, 1967). In what follows, both the no- asymmetry claim and the dependent-asymmetry claim will be covered under the assertion that time's asymmetry is extrinsic.

    It may help make the basic idea more clear to mention one possible consequence of it at this point: the extrinsic asymmetry might be either universal or localized. To explain, note that the up-down anisotropy is merely local: pervasive as it seems in daily life, it is limited to the region of the earth. Our "up" direction, followed into outer space, may become "down" in the vicinity of another massive body, and in between (where gravitational fields are balanced or negligible), neither direction is up or down. Conceivably, then, the earlier-later asymmetry of common experience is limited to our region of time or of space. Indeed, suppose it were so highly spatially

  • T IM[~'S ERROR 233

    localized that different persons could have opposite time-senses: then one would remember events which for another are still in the future. (Given the difficulties that this situation could pose for com- munication, however, it might not be possible for either to tell the other what to expect.) Such conjectures reveal graphically just how revolutionary is the hypothesis we are about to investigate.

    The first question to be answered is what sort of phenomenon might supply the extra ingredient to symmetrical time. One possibility that comes to mind is causation, which is intimately linked to temporality in ordinary thought. Prima facie, it is the right sort of thing to provide an asymmetry, since it is conceived as being not only asymmetrical in itself (if e caused f then f did not cause e) but also asymmetric in time: we do not commonsensically accept the possibility of causation back- ward in time, with the cause later than the effect. True, retrocausation is often considered by creative thinkers - e.g., in putative cases of precognition - but generally as the rare exception rather than the rule. Reflecting on the ways causation may be involved in our experience of time, then, might make clearer how the latter could come out seeming different than it really is in regard to symmetry. Not many scientists and philosophers seem to support this particular view, however. Among those who propose an extrinsic asymmetry for time. in fact, many hold a Humean view of causation; that means any temporal asymmetry it may have must come from thai c~f time. And certain others believe in "necessary connections," but take them to be sym- metrical: neither of two causally joined events is the cause lot the effect) of the other (Griinbaum, 1{~73). Hence wc will turn elsewhere in attempting to answer the question before us, to the sort of thing that is usually invoked to provide time's asymmetry.

    In a word, the standard answer is irreversible processes. Roughly, an irreversible or t ime-asymmetrical type of process is one such that instances of its temporal inverse either (i) never do occur (de facto if not of necessity), or, for the statistical version of the definition, l ii~ occur appreciably less frequently than do its own instances. Let me explain this in terms of the simplest case, a process-type consisting of just two different states. Because of the difference between them, the temporal direction from the one (say, state O) to the other (say H) is distinguishable from that from the H to the C). A time-asymmetrical process-type, then, is one such that the H always or most always occurs on the same temporal side of the O - or in other words, the O

  • 234 FERREL (? | tR ISTENSEN

    (almost) always falls on the same side of the H. A time-symmetrical process-type, by contrast, is one which either has no temporal inverse (e.g., it is of the form HQH) or else has one which occurs with comparable frequency: there are about as many ABCDE's as there are EDCBA's. On reflection, it should be obvious that irreversible processes surround us constantly. One has only to see just about any movie run backward to appreciate this fact. Seedlings turn into sunflowers, but the reverse does not occur.

    There is one highly general sort of irreversible process, however, that is most often proposed as supplying time's asymmetry, namely the kind that involves increase of entropy. It is beyond my purposes to discuss this highly complex subject, beyond reminding the reader of the following: the statistical version of the Second Law of Ther- modynamics states that the entropy (in very crude terms, the degree of disorder) of an isolated system of particles virtually never decreases with increasing time. And when two such systems interact, the com- posite system which has the two of them as its parts will also almost certainly not decrease in entropy; hence if the interaction should result in one of the subsystems decreasing its disorder, it will almost inevit- ably be at the expense of increased entropy in the other. Extrapolating this idea, if such is legitimate, the universe as a whole must be tending towards ever greater disorder.

    So pervasive is this phenomenon in nature - the chemical processes that go on around us and inside our own bodies depend essentially on it - that as long as there has been a statistical theory of entropy, certain scientists and philosophers have wanted to attribute the ear- lier-later asymmetry of time to it. These include Ludwig Boltzmann, the father of statistical thermodynamics, Sir Arthur Eddington, who dubbed entropy "t ime's arrow," and many others. If they are right, of course, we'll have to state the theory a little differently than has been done so far. We should then not say things like "entropy always tends to increase" or "disorder increases with increasing time," for these would normally imply that there is