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.

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    "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

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    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

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    (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 both the entropic asymmetry in time and the earlier-later asymmetry of time as well. Instead we will have to say that entropy tends to increase always in the same temporal direction - or equivalently, that it tends always to decrease in only one direction of time. In other words, in different isolated systems the entropic changes "run parallel," with their higher- (and lower-) entropy ends virtually all on the same temporal side.

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    Though entropic asymmetry is the one most commonly associated with the view that time's directionality is extrinsic, there are evidently other types of irreversible process as well. One that is sometimes mentioned by proponents of intrinsically symmetrical time is the class of "centro-symmetr ic" processes, which may be illustrated by such common occurrences as the spreading of a series of concentric waves on the surface of a pool of water when an object is dropped into it. This is a significant class of physical phenomena, for all sorts of waves - mechanical waves in solid matter, electromagnetic radiation, etc. - are propagated in centro-symmetric fashion. The temporal asymmetry of processes of this sort is revealed in the fact that we often encounter waves spreading out from a common center, but rarely see waves collapsing precisely to a single spot. For example, a piece of wood dropped in a quiet pond will send out a series of circular disturbances, but we would be surprised to see such waves rush in coherently upon a piece of wood and hurl it into the air - unless, that is, the whole thing had been carefully orchestrated in advance. To make this statement in terms that don't presuppose an earlier-later asymmetry for time itself, once again, we may say that the great majority of such processes are oriented in time with their larger concentric rings or spheres in one temporal direction, their smaller ones in the other.

    There may be yet other sorts of irreversible processes which we could discover on reflection. One possibility that has occurred to the author will now be pointed out: we might call it "similarity-after- contact" asymmetry, or more abstractly, "information copying" asymmetry. As an illustration consider the case of a barefoot person stepping on loose damp sand, leaving a footprint (cf. Griinbaum, 1973). The patch of sand and the sole of the person's foot display a very similar (though reversed) shape after the interaction, whereas before only the foot had had that configuration. In most other cases of temporary contact between two bodies, of course, the resulting similarity between them is not nearly so great, but it is very often present. The colliding of two automobiles usually results in one or both of them leaving traces of paint on the other, so that the regions of collsion share color-properties afterward that they didn't before. Even a stick dragged across the ground may impart one of its dimensions (its width) to the resulting furrow. And so on. Eschewing mention of earlier-later asymmetry and causal asymmetry, the general pattern here may be described thus: on one temporal side of a case of

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    contact between two things, they often share a similarity they don't display on the other temporal side, and instances of such processes are oriented in time in such a way that the great majority have their greater-similarity ends on the same side. This notion of a similarity- after-contact occurrence obviously needs further development, but it would seem to represent yet another general kind of irreversible process.

    Now, the idea with which this paper began isn't just about temporal asymmetry in the abstract, but specifically concerns the earlier-later asymmetry. A question that naturally presents itself, then, is what there is to tie that particular sort of anisotropy to irreversible proces- ses. This matter seems especially acute now we're aware that there is a plurality of distinct asymmetries in time. To return to the comparison with the relation of being higher in altitude than, notice that that spatial asymmetry is accompanied by all sorts of others: air pressure, average temperature, cosmic ray density, pollen count and perhaps hundreds more. Yet surely these latter are quite incidental. Gravita- tional asymmetry is the only reasonable candidate for being identified with the up-down anisotropy - indeed, it is responsible for most of the others. (Though cosmic ray density is a function of the amount of atmosphere they have to pass through in order to reach the earth's surface.) Even if there were only one known type of irreversible process, however, one would still want to know exactly what its connection is with the already-familiar concept of subsequence: what is there to identify what is prima facie a different asymmetry with that asymmetry? Unfortunately, few of those who have defended Boltz- mann's thesis have attempted explicitly to answer this question. The standard pattern in articles on the subject begins by wondering where the earlier-later asymmetry comes from, casually identifies it with the time-asymmetry of one or more irreversible...