This is part of the second chapter of Of Time and Lamentation due to be published in 2014. Copyright reserved.
Is There an Arrow of Time?
2.2.1 The Origin of the Arrow
That is the road where once I went
And cannot come again.27
[A] fundamental asymmetry in all the possible structures of the universe could provide a basis for the arrow of time. 27a
While most philosophers of time would be content to abandon the notion that time “flows”, “passes” or “moves”, the idea that time has a “direction” is more adhesive. Insofar as it is a consequence of the conception of time as a fourth dimension on a par with the three of space, it should, like flow , etc be incompatible with it. After all, the spatial dimensions do not have a direction. Collectively the spatial dimensions are the possibility of direction, just as they are the possibility of movement. Clearly, the direction of time – or the possibility of its having a direction - could not be provided by space. It would not make sense to say that time was pointing from left to right or up and down.
But there is something else, which is absolutely central; namely that the unfolding of time appears to be one way. This is in contrast to any direction in space – or any line marking a direction or trajectory in space. The line from A to B is also from B to A; any path going from a lower point to a higher point is also a path going from a higher point to a lower point. The apparent absence of this reversibility is all that there is to the direction of time. The link between earlier time t1 and later time t2 can be traversed in one direction- earlier-to-later – but not in the other direction – later-to-earlier. The path from t1 to t2 is inescapable while the path from t2 to t1 is blocked.
The hunt has therefore been on for something that will give time a direction in this very restricted sense of moving “forward” but not “backward”. This something will account for the difference between time and its spatial companions, a difference that will account for the fact that we can wander at will in space but not in time (as we shall discuss in Section 2.4). For the connect fact that there is no intrinsic spatial order in the way that there is an intrinsic temporal order. Let us examine this in a little more detail.
There is no privileged, or mandatory, order at which we pass through spatial locations or visit objects set out in space. Consider three objects:
There is no constraint on the order in which I visit them or visit the spatial locations they occupy. The journey A-->B-->C is no more legitimate than A-->C-->B or C-->B-->A. The fact that B is between A and C does not of itself oblige me to visit B before I visit C if I am setting out from A. I can take any route and if necessary deviate in order to by-pass B to get to C before visiting B. Indeed, we could argue that it is the order in which we visit A, B and C that confers an ordering on them: they are arranged along our chosen trajectory. Time, however, appears to have a built in trajectory: it is a trajectory. 28
It is tempting to explain this difference by saying that temporal points happen in a certain order while spatial do not happen at all and so are not ordered. This temptation ought to be resisted not only because of the doubtful status of “points” in space (see Chapter 3 Section..) and secondly because there is something deeply suspect about the suggestion that points in time – or “times” – occur at a certain time and in a certain temporal order. It makes them quasi-events, as occurrents, and also threatens to locate them in a higher order or meta-time. Even so, there is a clear difference between uni-directional time and intrinsically directionless space. It is this that motivates the all-too-familiar metaphor of “the arrow” of time, introduced by Arthur Eddington 29 IN
Since it is at least one function of philosophy to make the familiar unfamiliar, to say ‘Stop!’ when we rush past the taken for granted preliminaries that frame an inquiry, let us pause to look at this seemingly unobjectionable, even inescapable, metaphor. I want to take it literally – entirely literally – because it is part of the literal meaning that makes it seem an appropriate analogy. (This is a continuation of the Wittgensteinian strategy of turning disguised nonsense into patent absurdity.)
An arrow seems to have two features that commend it: it has a direction and (for those who want time to flow30) it is sometimes in motion. What is more, its direction of flight comes from its differentiation into head, shaft and tail. The direction of flight comes from the alignment of the shaft (this will determine that it goes from North to South rather than, say, East to West) and from the necessity for the head to be in advance of the tail (which will determined that it goes from North to South rather than South to North). So far, so good: it captures the “movement” and the mandatory direction of time – from earlier to later rather than the other way round. After this, the analogy falls apart. Unlike a literal arrow, time’s arrow can move in only one direction. Real arrows can be pointed in any direction and ven sent back to where they have come from.
This may seem a silly point to make. After all, it is characteristic of metaphors to capture similarities between items that are otherwise different. When I say of someone that she has roses in her cheeks, you would not object to my saying this on the grounds that you cannot see petals or smell the relevant fragrance. In present case, however, the “pick and mix” nature of the metaphor is grounds for objection. It reveals the residual spatialisation in the very idea of the “direction” of time, even though, as we have discussed, space itself is not directed in any meaningful sense. Which explains the ubiquity about the arrow metaphor that pervades much of our thinking about time.
Here are a couple of examples. When we look at the successive states of a system we tend to link them with an arrow, that points from the earlier to the later state, thus:
S1 at t1 à S2 at t2
You might say ‘This is only a convention’ but it is a remarkably adhesive one. It is present throughout chemistry:
2H2 + O2 à 2H2 O
And the relationship between cause and effect - something to which we shall return briefly in Section 2.3.5 and at greater length in Section 11.2 - is often pictured thus:
CAUSE à EFFECT
And, finally, it is not unusual to see successive moments of time presented in this way:
Earlier à Later
So when we are thinking about ‘the arrow of time’ we have to bear in mind that it is doubly faulty – it is a spatialised notion of time and it is a notion that does not work on its own terms – while at the same time it is a seemingly inescapable one.
The question that provokes the arrow metaphor may seem to be an empty one: “What is it makes one event E1 earlier than or later than another E2?” The answer would seem to be pretty straightforward: “The fact that E1 was earlier than E 2 . Next question please”. In short, the relationship “earlier than” and “later than” is irreducible to anything else. As we shall discover this may well be the right answer: that looking outside of time itself for criteria to justify saying of an event that it is “earlier” or “later” than another and to explain why it is possible (indeed inescapable) to pass from earlier events to later ones but not from later ones to earlier ones. It is, however, illuminating to examine the extra-temporal bases that have been invoked to explain this phenomenon: the thermodynamic, psychological, informational and causal arrows. They do not quite answer the same questions but they are closely connected aspects of a single inquiry.
2.3.2 The Thermodynamic Arrow
It is not a priori that the world becomes more disorganised with time. It is a matter of experience that the disorganisation comes at a later rather than an earlier time. 31
I find myself more than half-convinced by the oddly repellent hypothesis that the peculiarity of the time dimension is not..primitive but is wholly a resultant of those differences in the mere de facto run and order of the world’s filling. 32
If we are looking for a characteristic of the material world that will give time a direction, the least we should require of it is that it, too should have a direction and that it should be universal. The Second Law of Thermodynamics has been alighted upon as supplying this characteristic. According to this law, a closed system will tend towards increasing entropy or disorder. “Later” means in a state of higher entropy compared with “earlier”. This one-way trend in all closed systems will provide the basis for the uni-directionality of time. This was expressed as follows by the astronomer and physicist Sir Arthur Eddington (who coined the phrase “the arrow of time”):
Let us draw an arrow arbitrarily. If we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted the introduction of randomness is the only thing which cannot be put it, “the introduction of randomness is the only thing that cannot be undone. I shall use the phrase “time’s arrow” to express this one-way property of time which has no analogue in space. 32a
It has a multitude of manifestations, but its most common feature is de-differentiation within closed systems. Examples would include: the spread of heat from a local area of increased temperature to the cooler world outside and not vice versa; the diffusion of gases into the space made available to them, so that any unevenness of distribution is ironed out, and the absence of the reverse process; the spread of milk into coffee which cannot be reversed – the milk does not gather itself up. The spontaneous trend towards “thermodynamic equilibrium” is essentially a mixing up and evening out of the material contents in the world, one manifestation of which is the degradation of complex items. The one way passage of events towards de-differentiation is associated in physics with loss of available energy (as when heat is lost into the surroundings of the heated object) and in homely everyday life with upsets such as the breaking of a cup which can be brought about by a simple event such as its being dropped and cannot be easily reversed. There is a striking asymmetry in time: the passage from earlier, comparatively lower entropy states (whole cup) to later, higher entropy states (the broken cup) and the obstacle to the reverse ordering of states – higher entropy broken cup to lower entropy whole cup – suggests that there is a natural tendency in the material world to a state in which earlier states of the universe as a whole are tagged by higher order and later states by lower order, or increased entropy.
Such a net change in the universe over time will seem to be puzzling given that the laws of classical physics are time reversible. For example, the laws of motion do not dictate that the passage from whole cup to broken cup should be privileged over the passage from broken cup to whole cup. A film showing the broken cup reassembling itself would not show the laws of physics being broken. So there should be no overall trend towards increased entropy over time: there should be to-ing and fro-ing here and there without a net change. However, the apparent clash between the reversibility of Newtonian mechanics and the irreversibility of thermodynamics can be resolved.32b It is, as Ludwig Boltzmann pointed out, a statistical consequence of the fact that there are more (many more) possible disordered states than there are ordered ones. Statistical probability dictates therefore that random change – as is seen at the molecular level – will overwhelmingly result in a passage from lower to higher entropy rather than the other way round. The notion of “disorder” here is very generously interpreted. For example, a local area of warmth will correspond to a collection of molecules whose average speed is greater than that of the speed of the molecules in the surrounding universe. As a result, heat will be dissipated. The only way that this can be reversed is by putting in energy from the outside.
In the case of the universe as a whole there is no outside. Successive states of the universe will thus be increasingly disordered, even though there may be local decreases in disorder as when an organism (a blob of negative entropy) grows or a human being makes an artefact or in some other way manipulates the world to conform to his idea of order. This overall tendency will, it is argued, deliver time’s arrow: a state S2 of the universe as a whole is after state S1 if S2 is more disordered, closer to thermodynamic equilibrium, than S1.
There are two reasons why the universal tendency of entropy to increase does not generate the requisite arrow. Firstly, the relationship of succession, of before and after, requires that the two states – or any states – should be brought into relation, so that one counts as “before” and the other as “after”. Something (more precisely someone, as we shall discuss) has to relate them. There is nothing intrinsic in S1 that makes it “earlier than S2” particularly as S2 won’t have occurred as long as S1 is around. “Earlier than” and “later than” are inescapably relational and the successive states of the material universe are what they are in themselves: they do not relate to anything other than themselves. Indeed, the relations that would be required to turn increasing entropy to temporal ordering are even more complex. If “later” means “in a more disordered universe” and ‘earlier’ means ‘in a less disordered universe’, then the sense that Event2 took place after Event1 would have to be derived from a relationship to the universe as a whole and, what is more, to the perception that it is temporally located at the same time as a particular state of the universe. In short, we have to get “at the same time as” free – without reference to the order or disorder of the universe.
Secondly, as Henri Poincaré demonstrated, given a long enough time, even very improbable outcomes could come about, and the trend of entropy could reverse, with the universe becoming less disordered in successive moments. He demonstrated that a finite collection of particles confined to a container and moving in accordance with Newton’s laws of motion that Boltzmann had relied upon would eventually return to its initial state, so called Poincaré cycling. This would then mean that in one part of the cycle the same two states S1 and S2 would have the opposite time relationship, with S2 (less disordered) , by the thermodynamic criterion now occurring being before S1 (more disordered).
There is a third problem: if entropy tends to increase with time, the universe must have begun in a relatively ordered state. What is the explanation of the low entropy of past states of the universe? Boltzmann himself acknowledged the possibility that:
when we follow the state of the universe into the infinitely distant past, we are actually just as correct in taking it to be very probable that we would reach a state in which all temperature differences had disappeared, as we would be in following the state of the world into the distant future.33
Given that the universe had to start in some state, it might be argued, there is no reason why it should not start in a low entropy state. When there is no population of possibilities to draw upon, each state is equally possible. What is at issue are the probabilities governing the transition from one state to another. The passage from State 1 at t1 to State 2 at t 2 has to be along the flattest a probability gradient – from the less probable to the more probable, the latter being defined as “having more possible realizations”. State 2 doesn’t have in itself to be probable: it simply has to be more probable than State 1. And the latter, also, does not have to be probable, only more probable than the state that preceded it. What is more, no given state of the universe, or of a locality within it, is probable, given the zillion-trillion possible configurations it might have. What are at issue are second-order probability considerations: namely, that it is more probable that there should be a transition from a less probable state to a more probable one than vice versa. A state is more probable if it is an example of a larger population of (relatively disordered) possibilities than if it is an example of a smaller population of (relatively ordered) possibilities. This may answer the question of how earlier low entropy states were possible, given that they are less probable than later states; in short, the mystery of the initial low entropy of the universe. In the case of the first moment of the universe, there is no preceding state and all states are equally possible, so the universe could just as well have started in a low entropy state (as it did) as opposed to a high entropy one (which it didn’t). It is what follows after that which is governed by probabilities.33a.
More fundamentally, Poincaré cycling reminds us of something that we should not perhaps need reminding of: that we have to identify the temporal sequence of events prior to determining the time trend of entropy, the disorder increases with time. So the latter cannot give us the basis for the arrow of time. To put this another way: “less” or “more” disordered do not translate into “earlier” and “later”: it is merely a fact that “less” disordered states of the universe preceded “more” disordered states. The characteristics of states of the universe may lead us to see something as earlier but the temporal facts of the ordering of events are not to be found in their intrinsic properties. The egg shell is overwhelmingly likely to be in a state of wholeness before it is in a state of brokenness but this does not mean that the temporal order of the states resides in “wholeness-brokenness”.
In short, we have to determine, independently of any of their characteristics, which of two events, or even which of two states of the universe, is “earlier” and which “later”. The very idea that we progress from “less probable” (low entropy) states to “more probable” states seems to presuppose a temporal order not to create it. Time, and the direction of time, is built into the very idea of change, of an entity moving from one (a prior) state to another (posterior) state. A similar point is argued with great clarity by Huw Price:
we are inclined simply to help ourselves to the principle that the past explains the future, but what could possibly justify that inclination here, where the temporal asymmetry of the universe is what we are seeking to explain. 34
We smuggle in temporal directionality, and the idea of a progress from “earlier” to “later” when we describe the aspect of the unfolding of the universe that is supposed generate the directionality of time. This criticism goes deeper than another (more conventional) critique of the thermodynamic arrow that
No theory of the evolution of a physical system over time can produce different results for the two temporal directions, unless it treats them differently in the first place. 35
Philosophers and physicists have looked to other seemingly one-way or irreversible trends in the universe to account for the apparent unidirectionality of time. There is the cosmological arrow that gets its direction from the expansion of the universe and may turn round if, as some believe, there are alternating phases of expansion from the Big Bang and contraction towards the Big Crunch. Particle physics offers kaon decay which may be time irreversible. Quantum mechanics offers wave function collapse which is also time irreversible and which, according to modern interpretations, may be a consequence of the putative thermodynamic arrow. Intuitively easiest to grasp is the arrow of radiation. It is illustrated by dropping a stone into a pool, which results in concentric waves spreading across the surface of the water. This is clearly a process that could not happen in reverse; for in order for it to happen, it would be necessary as Karl Popper pointed outto assemble “a vast number of distant coherent generators of waves, the coordination of which, to be explicable, would have to be…originating from one centre” 36
I won’t discuss these different arrows separately. It has been argued that they are all in some direct or indirect way a manifestation of the Second Law. At any rate, they do seem to share a family resemblance in which in all cases the transition from past to future is from a relatively tidy to a relatively untidy state – something we shall touch on in Section 2.3.5. and discuss in more detail in Section 11.3. However, the reason I will not deal with them in detail is that they fail to generate the requisite temporal asymmetry, the difference between the tip and the tail of the arrow, for the same reason as The Second Law does; namely, that we have to see that certain states are temporally prior to other states in order to see that there are trends which are irreversible. In other words, “earlier” and “later” have to be established independently of the observed phenomena to that the phenomena cannot be used to define, even less be seen to constitute, the temporal difference or relation. They require us to have the concepts “earlier” and “later” already in place in order for them to deliver time’s arrow. If these concepts are not already in place, then we have no grounds for arriving at the conclusion that the more disordered states typically succeed less disordered states; or (as we shall discuss presently) that causes typically precede effects. They may enable us to identify particular pairs of states as “earlier” and “later” in the absence of other clues – as when we are presented with series of pictures – but they do not constitute earlier and later in themselves.
That is why Poincaré cycling, which envisages phases in the history of the universe when entropy is falling as well as phases in which it is increasing, is so worrying for proponents of the Thermodynamic Arrow. It opens up the possibility that the arrow of time can do a 1800 turn and “point” or even “flow” backwards. One particularly baffling consequence of this would be that a particular event could be both before and after another event. Let time t1 be defined by a specific state of the universe associated with a particular level of entropy S 1 and (later) time t2 be defined by another state of the universe S 2 with a higher level of entropy. S2 is defined as later than S 1 because it is more disordered. Any event E occurring when the universe is in S 2 will be later than any event occurring when the universe is in S 1. When the universe reverses entropic direction and it becomes increasingly ordered, S’ 2 will be reached before S’ 1, in the tidying up process. E at S’ 2 will be before E’ at S 1. This will be fine so long as we think of the Es in question as token events which, although they are identical in type are unconnected. There is no reason, for example, why a roll of thunder should not be followed by a bolt of lightning, so long as the roll in question is not supposed to be an effect of the bolt of lightning. But if the events are causally connected, or E at S 1 is part of the conditions that permit E at S 2, there is a problem. Events will have to occur before the conditions which permit them or the causes that bring them about. (We shall look at this again in Sections 2.3.5. and 11.3 when we look at the apparent connection between the causal arrow and the thermodynamic arrow of increasing untidiness.)
2.3.3 The Psychological Arrow
Universal, irreversible physical processes fail to generate time’s arrow because they depend upon pre-existing sense of “earlier” and “later” . The S 1 (less disordered) state of the universe and S 2 (more disordered) state of the universe would not between them generate the relationship “earlier” and “later” unless it were already somehow known that increasing disorder were associated with later times. Only then would the fact that it is possible to pass from S 1 to S 2 but not from S 2 to S 1 seem to underpin the uni-directionality of time, and why we pass from t 1 which is earlier to t 2 which later but not in the opposite direction. To put it in this way, of course, to conflate and confuse many issues; in particular issues of definition of “times” and the experience of time with physical time. The fact that it is not easy to tease them apart is, however, revealing so let us not try and “unmuddle” the muddle yet.
The sense of earlier and later begins locally and extends outwards. It relates to particular events experienced by a particular observer. Without an observer to experience the events, and to connect them, they are neither “early” nor “late” not “before” or “after”. For example, an unobserved event on a distant planet is not temporally related to the events that are am aware of as going on around me now or indeed other unobserved events on that planet. The arrow of time must be constituted out of events that are linked up in a succession. That is why many have felt that the only arrow is a “psychological arrow”.
And there is another deficiency they have in common: the linking of picked out events to give the required sense of succession, of flow and direction. There is an implicit observer required to note that certain happenings are “earlier” and others are “later”. Without that observer, the two happenings would not exceed their own temporal boundaries and be connected via an external relationship which is one thread in a temporally joined up universe which expresses the (uni-)directionality of time. (This is something to which we shall return.) For this reason, it is not surprising that some thinkers have considered the arrow of time to be essentially psychological. The question, so far as we are concerned, is whether the directionality of time transcends the merely psychological (so that the latter merely reflects something that pre-exists conscious beings) and exists in itself or as an intrinsic property of the physical universe. The testimony from physics on this is somewhat confused.
The overall trend of the natural sciences has been to liberate the observer from the individual perspective. By instrument-enhanced, quantitative and more broadly mathematised observation we endeavour to transcend the bodily-dependent and biographically-tinged limitations of our eyes and ears in order to see things as they are in themselves; we endeavour to ascend to Nagel’s famous “the view from nowhere” and (indeed, a Huw Price puts it) an atemporal “view from nowhen”. The result if a body of knowledge that belongs to no-one in particular, but belongs to the community of human minds, and is equally faithful to everyone’s actual experience and defines our possible experience in the broadest possible terms. The question then arise as to whether the notions of the direction of time and of “earlier” and “later” survive at this great distance from our actual conscious experience. Whether, there comes a point as we shed more and more of the living breathing, parochial observer, and aspire to the condition of a universal observer forged in the community of minds as expressed in mathematical physics, we lose the stuff that makes the arrow.
There is one very straightforward answer to that, if we believe that the arrow depends on events being located at a fixed place in an absolute time frame: no. While in the local frame of reference in which we pass our lives, the temporal relationships between events is fixed: there is no question that E 1 took place before E 2 and the relationship of succession between them, which gives the experience of succession, is secure. However, viewed from the Nowhere of Relativity Theory, the relationship between the two events – unless they are causally connected - is intrinsically neither one of succession nor of simultaneity. There is no temporal order independent of any observer. This is a consequence of Mach’s principle, which Einstein embraced, though not consistently (least of all when he was affronted by the unintelligibility of quantum theory), that there is no reality beyond that which can be observed, no reality-in-itself beyond actual or possible experiences. Reality is the sum total of possible experiences, not something separate from experience, not something to which experience gives us (limited) access. This seems simultaneously to put the arrow of time into human consciousness and at the same to discredit it – at least in the view the fundamentalist physicist who believes that what physics reveals is the metaphysical truth, and will be the whole truth, about the world. The only way to save it for physics would be to find it not in the irreversible succession of experienced events (because that succession can be reversed from another frame of reference) but in the actual nature of the laws governing those events and linking one state of the universe with another – hence the appeal to time-irreversible processes and laws. Instead of saying that time has a direction because, once it has been observed that E1 occurs before E2, this is an irrevocable fact, it can be asserted that state S 1 is prior to State S 2 because the entropy levels in the former are lower than in the latter. The temporal relationship is not generated from within perception (of succession or simultaneity) but from measurements of something that appears to be independent of time. While these measures are ultimately derived from perceptions, they are not based on observations of temporal relationships that are observer dependent. However, it is this latter virtue that disqualifies them, as we have seen from the previous section.
Locating the arrow of time in the human psyche raises as many questions as it answers. If we reduce the directionality of time to the experience of the succession of events, within our minds, our bodies, or the observed material world, we run into trouble accounting for those aspects of succession that are more objective, or less observer-dependent, than other. It does not accommodate the fact that something other than consciousness, or a conscious individual, has the last word on the succession of events. What is more, it is implicit in the notion that time’s arrow is based on our perception of the succession of events that there is a succession of events to be perceived – that temporal order and direction is intrinsic to the events we perceive. Granted that the order in which we perceive things also so some extent depends on us, just as what we perceive depends to some extent on us. What I see, for example, depends (in part, though not, of course wholly) on where I choose to look from and the direction and trajectory of my gaze. But this does not determine the order of events.
Consider a simple example. Supposing I am looking round at a group of smiling people, I will see the smile on the face of Mr A before I see the smile on the face of Mrs B if I pan round in one direction and the reverse if I pan round in another direction. This does not, however, determine the temporal order of the smiles. If Mr A smiled before Mrs B, this is not altered by the fact that I perceive Mrs B’s smile first. The psychologising of time’s arrow, in other words, does not accommodate the objective reality of temporal order or those features of it that cannot be relativized, as, for example that which is expressed in the relationship between cause and effect. We acknowledge that the sequence of events and the sequence of our experience of events are distinct – something that is more obvious when we consider the order in which we get to know or to know of something. The Big Bang (if it occurred) was the first event but it has only recently become an object of knowledge.
The reduction of the directionality of time – and of what makes “before” before and “after” after - is open to a variety of objections. The most obvious relates to what the French philosopher Quentin Meillassoux has called “ancestrals” – events that took place before human or any other kind of consciousness came on the scene – and the present evidence of them – what he calls “fossils”. It is obvious that the solar system came into being before there were living creatures, living creatures before sentient beings and sentient beings before human beings. The overwhelming majority of the history of the universe with ordered events took place before any kind of psyche emerged to register them. And if our perception of the succession of events reflects their temporal order in our locality, then the psychological arrow seems to depend on a physical arrow. At any rate, the private perception of the succession of events is transcended by dates that at the very least belong to the shared history of humanity and in fact seem to transcend it.
So we have reached an impasse. The endeavour to find the directionality of time in the asymmetry of physical processes overlooks the necessity for a conscious observer to translate the states of the universe or of local systems within them into a succession that has been picked out and connected. The conclusion that the directionality of time is entirely internal to our psyche – and to our sense of the past and the future - makes it difficult to see the connection between our successive experiences and events that appear to have a succession that is independent of our experiences. The complementary deficiencies of physical and psychological bases for the direction of time may in part explain why the notion of time’s arrow being an arrow of information has had such a good run for its money. “Information” in the present sloppy usage is something can be seen as something that has a recto of psychological contents and a verso of physical events.
2.3.4 The Arrow of Information
Many of those who look for the arrow of time in information seem to have a rather psychological starting point, focussing on tensed time. We look back at the past in knowledge of what has taken place and we look forward to the future in ignorance of what may come to pass. There is thus a psychological asymmetry between past and future – an asymmetry of information – and it is this that provides respectively the head and tail of the arrow. To put this way, the forward movement of time is an accumulation of information. This is expressed most clearly by the physicist Paul Davies who has devoted all his professional life to thinking about the asymmetry of time. “The fact that we remember the past, rather than the future” he says “is an observation not of the passage of time but of the asymmetry of time’ 38 . For him (as for many others) memory is a matter of ‘information’; so the difference between the determinate past and the indeterminate future is also matter of information. We obviously have more information about the past than we do about the future. In one sense we have no information about the future, except at a probabilistic level. So as the indeterminate future becomes a determinate past, the information level rises
Now it is of course obvious that the difference between past and future, or between “before time t” and “after time t” cannot be the difference between what I know and what I don’t know; that the difference between past and future cannot be reduced to the difference between my knowledge and my ignorance. No ‘Arrovian’ would wish to advance an hypothesis so vulnerable. It would have all sorts of undesirable consequences, such as for example that an event would pass from the future to the past only when I got to know of it and, even, that it would be returned to the future when I had forgotten it. It is not about information understood as personally held knowledge, nor about what I happened to know, but about what, for reasons that lie outside of me, about I could possibly know. So while I might remember what happened last year, and I cannot know what will happen next year, this is not because of a deficiency within me but because there is nothing yet corresponding to what will happen next year, though I may have some pretty good guesses. Nor is the Arrow of Information solely it about information as knowledge we have collectively – the factual knowledge that is potentially available to all of us and actually available to some of us. After all, to return to an earlier example, nobody knew about the Big Bang until a few decades ago and it was not even possible to know about it until the science of astrophysics reached a certain level of conceptual and instrumental sophistication. While knowledge of the Big Bang was in the future 100 years ago, this did not mean that the Big Bang has moved from the future to 13.7 billion years over the last century.
No: there are two further criteria necessary to differentiate the relatively information-poor future from the relatively information-rich past. They are closely connected. The first is that there has to have been some interaction between a conscious being and events for those events to enter the (that is to say someone’s) past39; and the second is that those events, to qualify as events, have to be determinate.40 The reasons I cannot see (recall, be aware of, know with confidence) future events is that they have not happened yet. There is nothing yet to see. The range of possibilities that we might envisage have not narrowed down to actuality. Unlike the determinate past, the future is indeterminate so its contents are not there to be seen: they are not in a position to interact with me so as to bring about an experience of them. The connection between these two differences should make us suspicious of the very notion of the information arrow. The grounds for our suspicion become clear as the idea of “information” is widened to include the passage from determinacy to indeterminacy in the case of material events in the absence of consciousness.
The huge expansion of the catchment area of the word ‘information’ is one of the mast striking features of present day philosophical and scientific discourse. I won’t go into this in any detail here as I have discussed it at great length elsewhere. 41 Suffice it to note that a word that originally designated intelligence, news, gossip, facts etc exchange between people – between an informant and one who is informed – is now being used to designate any kind of transaction in the material world. The rationale for this is set out by David Chalmers, who speaks for many:
[W]herever there is causal interaction, there is information, and wherever there is information there is experience. One can find information states in a rock – when it expands and contracts, for example – or even in the different aspects of an electron. 42
This greatly expanded notion of information has been particularly attractive to some philosophically inclined physicists. John Wheeler has famously argued that IT = BIT – that the universe is a massive information processing machine.43 This vision of the History of Everything as a progressive accumulation of information conflates the fact that the past is known, while the future isn’t with the fact that the past is determinate while the future is not; between knowledge and knowability. This confusion is sometimes confounded with another that brings the thermodynamic arrow back into the frame: the conflation of information with, on the one hand, entropy (something remote from consciousness) and, on the other, memory (which, in my case at least, is inseparable from consciousness). Paul Davies again:
As physicists have realised over the past few decades, the concept of entropy is closely related to the information content of a system. For this reason, the formation of memory is a unidirectional process – new memories add information and raise the entropy of the brain. We might perceive this unidirectionality as the flow of time.44
Memory is the accumulation of information; information is increased entropy; the increased entropy of our brains gives us a sense of the passage of time but underpins the reality of the directionality of time.45 Let us deal with each of these assumptions in turn.
The first is easily dealt with. To reduce memory to information in the sense of factual knowledge is to traduce i. It is much wider than that: it includes much that is not accessible as information (such as changes in unconscious presuppositions and the acquisition of skills); and much that, though accessible to recall, is not information in anything other than a constrained sense – such as the sad recollection of a day that has past. This would not be a problem for Davies and others. Their notion of information is much wider than this. Information is identified with entropy. It is worth tracing the argument that leads to this conclusion.
When you are sending me a signal, the quantity of information (according to the engineering definition) that you send depends on how much uncertainty you resolve. If there are only two possibilities, and the signal tells me which one, then the delivery of the signal has given me one binary digit of information. If I were sending randomly determined letters, then each letter would resolve a greater uncertainty: the probability of any given letter being sent is 1 in 26 and the arrival of a signal bearing a letter delivers 5.5 bits of information. There seems to be a correlation between the amount of uncertainty resolved and the quantity of information transmitted.
What is lost by the conflation of “information” in the engineer’s sense with “information” in the conventional sense is the uncertainty that has to be generated in order for an event to count as something that resolves it. And the uncertainty will be very context- and, indeed, interest-dependent. If I am expecting a letter then the letter that turns up will deliver 5.5 bits of information. If I am uncertain whether I will receive a letter or a number, then the receipt of the letter will count as one bit of information. If I am wondering whether the transmission system is working, then the arrival of anything would count as an additional bit of information. Other information may be carried by the transmission of the letter; for example, whether you – the sender – are cooperating with me, are competent, are still there at the other end.
The next step linking information and entropy is ingenious but faulty. It is the assumption that a disordered system, which has more unpredictability and requires more messages to describe, is richer in information than an ordered one. This step transfers the informational richness of the signal to the system or region of matter (with or without any system) it describes. Only by that means can a more disordered system be in itself be richer in information than a less disordered one and the passage towards increased disorder count as increased information.
This is, of course, nonsense, and it has arisen from separating the notion of information from any conscious being who is informed and who has a sense of uncertainty that needs resolving; it has collapsed the difference between a signal that resolves uncertainty from that which the signal is about; and it has made every event into a signal, so that the unfolding of the universe becomes a uni-directional accumulation of information. That this notion gets past even the sleepiest auditor is because we are used to talking about information being embedded in systems that information is supposed to be about. In other words, it collapses the gap of “aboutness” and finds information in the material substance of the world. Overlooking “aboutness” lies at the heart of the wrong path taken by the metaphysics in the physics of time and we shall look to this – to intentionality – to develop a true image of the nature of time in Part 3 of this book.
For the present, it is sufficient to note that the removal of consciousness from memory (or the information it is supposed to consist of) is a key step which creates the supposed connection between the thermodynamic trend towards higher entropy and the difference between a remembered past and a future of which we are ignorant. Memory is simply the altered state of the brain which is supposed to be more entropic. Increased information means more entropy means “later” compared with “earlier”. If, however, this were true, then any system that became more chaotic would be richer in information and hence have a state that was “later” than its earlier states. Its later state would count as memory-rich, though what its memories would be about is entirely unclear What is more, its present state would be a bidirectional glimpse into the past (which it would be related to its own past) and a future. In short, the lowliest item in the physical universe would have the very tensed time that “believing physicists” (according to Einstein himself) exists only as an illusion in the human brain (including the brain of physicists) that doesn’t seem to believe what their owners believe.
Many of those who seek the directionality of time in “the flow” or “accumulation” of information confuse the difference between “earlier” and “later” with the difference between a past we can remember and a future we may anticipate; a past of which we can have certain knowledge and a future about which we can only speculate. In other words, they confuse a putative intrinsic directionality of time with the asymmetry of the temporal gaze of a conscious individual located in time. The reduction of time asymmetry to information asymmetry conflates tenseless time with tensed time – losing the difference between “earlier” and “later” on the one hand an past and future on the other – and also confuses an epistemic difference with something more substantial. The difference between past and future is not just the difference between something we know and something we do not know. After all, there are parts of the past that we do not know and could not get to know – for example the unrecorded path taken by a worm under a stone in a country neither I nor anyone I am in communication has visited. The difference is between that which is or could be known and that which cannot under any circumstances be known: between a determinate past and an indeterminate future. The difference in short is not merely epistemic but also ontological. Not knowing the future is more fundamental than ignorance of the past because there is nothing to be known – though it can be guessed at with more or less shrewdness – as the future hasn’t happened, hasn’t gone one way or another yet. Regarding the future, we are all (relatively) in the same boat. Even when I have a privileged position (as when I can see two cars on a collision course, though the drivers cannot see one another or when I have insider information relevant to the stock market) I still cannot be sure that there will be a crash or the shares I am considering buying will rise. The determination of the future as it enters the present is not merely a matter of becoming potential information: it is about something out there that has changed.
2.3.5 The Causal Arrow and “The Asymmetry of Influence” 48
Attempts to meddle with the past are futile 49
The Second Law of Thermodynamics failed to deliver directionality in time – an external reason for regarding one moment as earlier than another and for creating the asymmetry between “earlier” and “later” moments or events such that it is possible, indeed inescapable, to proceed from the former to the latter but not from the latter to the former. The increasing disorder of the universe in successive moments of time failed to make this the basis of a universal clock not only because Poincaré cycling would make the clock go backwards but also because also because this illustrates that the relationship between temporal succession and increasing disorder seems contingent. There is no reason why the universe should begin in a low entropy state. We must look elsewhere for a characteristic of states of the universe and of the events that arise out of them that is sufficient to fix their temporal order. We must try to find something in the character of events that is inseparable from a necessary temporal order. For some writers the basis for the directionality of time is to be found in an “asymmetry of influence”. That which we consider past can influence the future but the future cannot influence the past. An Event E can bring about consequences in the world after it has happened but cannot anything that has happened before it. The consequences of E will always be after and never before time t at which it happened. This asymmetry has been translated into the asymmetric relationship between cause and effect. Hugh Mellor takes this further and asserts that “Time is the causal dimension of spacetime” 50. The correlation between causal and temporal order “is not because time order fixes causal order. It must be the other way round.”51
This approach is attractive for several reasons. Firstly, relativity theory does not relativize the temporal relationship between cause and effect. If I observe that A causes B, then it is not possible for there to be a frame of reference in which B causes A. This is because, in order to interact, A and B have to occupy adjacent locations in space-time and space-time relations (unlike purely temporal or purely spatial relations) are invariant, irrespective of the frame of reference from which they are viewed. Their relationship is real in the sense of being observer-independent. Given that causal chains extend indefinitely, this applies to the entire nexus of causation. That is why Hastings may have a distant effect in bringing about Agincourt but Agincourt could not return the compliment. Secondly, our common sense experience of what is happening around appears to us as a network of causes and effects in which the former precedes the latter. We cannot imagine an effect bringing about its cause and not just for purely definitional reasons. It makes physical sense that the lightning flash causes the thunderclap and not the other way round. Finally, it seems to bring temporal succession into the very structure of necessity that is built into the world.
The reasons why the causation does not deliver time’s arrow go very deep and are of the greatest interest; they would alone be sufficient reason for thinking the nature of time. I will return to them when, in Part 3, I try to get time itself into focus. I will simply make a few preliminary comments here.
Firstly, identifyingsomething discrete as a cause and something else as its effect depends on observing that causal relationship. The events in question are not self-defining, self-circumscribing. The physical world is not in itself a linear chain of causes and effects: it is a broad unfolding of densely interwoven processes from which particular chains of causes and effects are picked out, according to our interests. You could not, for example, even in principle, state how many causal pairings there are in a room, any more than you could say how many facts there are in the room. Causes are those things that we see as salient, most obviously because – as many philosophers have pointed out - they may be handles by which we manipulate the world in accordance with our wishes or may allocate responsibility, as when we say that the cause of a crash was a driver’s carelessness, although we could have identified many other causal ancestors. In other words, what counts as a cause of an event, and what event shall count as the effect of another event, is relative to observers and their interests. You might concede this and still maintain that there is a non-negotiable temporal relationship between picked-out events and picked-out causes. However, the picking out cannot be ignored and it is this that takes us to the heart of the matter: the relationship between causation, consciousness, intentionality and explicit time. This is the theme of the final chapter.
Secondly, the observations that effects succeed their causes may not provide an independent marker of the intrinsic directionality of time because we judge of two events E1 and E2 that E1 is the cause because it occurs first and that E2 is the effect because it occurs later. In other words, we allocate roles on the basis of the perceived temporal order and not the other way round. This becomes evident when we allocate a temporal order to events that do not appear to be causally connect – and indeed are not. I see you walking along the road and shortly after observe a plane pass overhead. They are obviously causally unconnected events but I have no difficulty saying of the former that it is “earlier” and of the latter that it is “later”. This puts Mellor’s assertion, just quoted, that the correlation between causal and temporal order “is not because time order fixes causal order. It must be the other way round.” Mellor tries to deal with the problem (for his theory) of the temporal order of items that are not causally connected but not, in my view, successfully. But the reasons why he fails go very deep and discussion of them will be postponed until we have quite a few more ideas in place. Suffice it to say for the present that they touch in the relationship between time and consciousness, and the vexed and puzzling relationship between “physical” and “human” time.
2.3.6 Quivering the Arrow
The Moving Finger writes; and having writ
Moves on; not all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.Note
Vulnerant omnes, ultima necat
“All of them wound, the last one kills”
(A common tag on sun-dials, referring to the hours)
One thing that will come through clearly in the preceding discussion is the prevailing confusion. It is not, first of all, entirely clear what the arrow metaphor is supposed to mean. At its very least, it is an attempt to capture the notion that time has a direction. This is a pared down version of the vision of time, derived from (though at odds with) the understanding of time as a dimension on a par with the three dimensions of space. The more florid notion of time as “flowing” (again, a spatial image and again incompatible with the notion of time as a quasi-spatial dimension) is still adhered to by some but most will settle simply for time being unidirectional. The search for a satisfactory arrow has taken the form of finding a basis for the asymmetry of time.
The latter is most fundamentally expressed in the fact that there are times called “earlier” and “later” such that it is not possible to go from the latter to the former and mandatory to go from the former to the latter. This may seem a mere truism. You can, by definition, only reach a later time after an earlier time. If you came to an earlier time later than the earlier time, it would be called the later time. Or, if it were possible to re-visit the earlier time, it would be at a later time. Specifically, if t1 occurs before t 2, then the former is earlier and the latter later. If someone travelled to t 1 after t 2, then the latter would be earlier than t 1. Revisiting t 1 would only be possible only if it “occurred” twice.Note The Arrovians, however, are after more than trying to uphold a truism. They want to understand the basis of the asymmetry between the past and the future; of the sense we have of passing from future into the past and of the former being open to manipulation and the latter not. There is, however, still a feeling that there is something intrinsically directional in pure, non-human and tenseless time-in-itself.
This muddled idea of the problem (because it is something inherited from an image of time as a dimension rather than something argued into place) explains why it has spawned such a heterogeneous range of solutions. As we have seen, most work has gone into identifying what Julian Barbour (to repeat the quote) characterised as “[A] fundamental asymmetry in all the possible structures of the universe” that could “provide a basis for the arrow of time”; hence the appeal to thermodynamic, radiative, cosmic and other purely physical arrows. They all fail because there is no way of getting from the fact that things have a tendency to go one way rather than another as we move from time to time the fact that time goes one way rather than another, expressed in the facts that a) we proceed from earlier to later and not vice versa and/or b) the present appears to move from the past to the future and not in the other direction. Time asymmetries cannot be got out of asymmetries in the successive states of an unfolding universe. The causal arrow addresses the directionality of time through a perceived “asymmetry of influence” rather than an asymmetry of time, such that event E1 at t1 could increase the probability of event E 2 at a later time t 2 but not vice versa. The psychological arrow focuses particularly on the asymmetry seen in tensed time such that the past is determinate and known (or at least knowable in principle) while future is indeterminate and unknown. And the information arrow tries to provide a basis for both tenseless and tensed asymmetries and for asymmetries of both the material world and of knowledge by extending the idea of information to encompass all that happens in the world.
The idea of the arrow first of all is a response to the notion that time is a dimension. We are used to representing dimensions by means of lines and lines have a direction and therefore time, being a dimension, must also have a direction. However, it does not follow from the fact that they are represented by lines that dimensions are intrinsically directional. When we depict the three dimensions of space, we draw lines at right angles to one another representing respectively the x, y, and z axes. Of course they don’t really have a direction: they simply have a directional relationship to one another. The x axis does not point in a certain direction: it simply has to be at right angles to the y and the z axes. The y axis likewise: it simply has to be at right angles to the x and z axes. It is the mutual separation by 90 degrees that defines the axes and these in turn will define the direction of something that does have a direction – for example a movement of an object in the space defined by the axes. The axes themselves no more have a direction than “length” has a length, “height” a height and so on. So, if we think of time as a dimension, we cannot think of it as having a length or imagine it as moving or growing. In short, if we take seriously the idea of time as a dimension on all fours with the three of space, we should not countenance the idea of it as directed in the sense of a) moving and b) moving in a certain direction.
So both the features of the arrow are not only unnecessary but are incompatible with the very idea that gave birth to them. Nevertheless, this does not stop the trend to outsourcing the directionality of time to other items when there is a failure to find directionality, or even make sense of it, in time itself. Or, when this does not deliver what is required, to changing the question to one of the asymmetry of influence (causal arrow) or the asymmetry between past and present (the psychological and informational arrows). We find, in the end that nothing else can fix the temporal sequence of events other than their de facto order of occurrence.
The quest for the basis of an arrow of time is as fruitless irrespective of whether or not we first remove the seemingly more vulnerable notion of the “flow” or “passage” of time. They can be addressed only by overcoming the spatialising tendency. This tendency is in fact inseparable from the notion of “flow”, “passage” etc because only a movement can have a direction. If a (static) arrow seems to have a direction, this is only because it is differentiated into a head and a tail and these define its potential, “proper” direction.53 Acknowledging that the idea of the unidirectionality of time cannot be separated from that of flow, helps us to see what motivates the search for an arrow: the projection the passage of events that necessarily take place into time itself. It is this that creates the “mystery” of the unidirectionality of time because events are for the greater part reversible in principle at least in practice. The simplest and most ubiquitous events are movements and a movement in one direction can typically be reversed by a movement in another direction and this does not seem to apply to a movement from “earlier” to “later”. We can dissolve this mystery not only by challenging the transfer of passage or flow from events to time but by looking more carefully at the initial application of these terms to events. Consider the Event E1 of an object O moving fromPosition P1 to Position P 2. What moves or flows is not E1 but O. The event itself does not pass through space: it is a passage through space. Nor is E 1 itself reversible. When O goes back from P2 to Position P 1, this is not a reversal of E 1 – it is not there to be reversed - but another event E 2. In this respect the irreversible passage of time is not different from the irreversible passage of events that take, or are located in, time. And the occurrence of events is not a kind of passing or flowing of E, though we may speak of its “passing” from its beginning to its end. “E” refers to the whole, completed event and this totality does not “pass” or “flow”, not even to pass or flow into or out of being. When an events takes place, it does not pass by us as, say, the movement of the object O from Position P1 to Position P 2 , which constitutes the event, counts as something passing by us. 54
It may seem unnecessary to highlight these distinctions but failing to observe them lies at the root of many wrong turns in the philosophy of time. It is evident in the notion of an event passing into and out of, passing through, time as it moves from the future to the present to the past. But this is entirely misconceived as we shall discuss in Chapter 7. (‘Call No Event Future Until It Is Past’.) And it may well be that it is the notion of the passage of events that takes us half way not only to that of the passage, or at least unidirectionality, of time, but to that of time as the kind of inner “whoosh” inside the “whoosh” of events. If, as we have noted, individual events do not pass in a particular direction as moving objects do (unless we falsely think of passing into and out of existence as a kind of passage), how little does the passage of all events amount to a kind of direction. Look at what is happening in the scene before you. Objects are moving in all sorts of directions, events are happening and coming to an end: there is nothing in this to suggest an overall direction of anything. 56
There may be another source of the attractiveness of the metaphor of the arrow of time – one that was active in the collective imagination long before Eddington introduced it into the philosophical discussion of physical time. Arrows wound, and then kill and the image captures the sense of the world being out of our control and potentially dangerous; it captures the way we are skewered on to the totality of things that also gave rise to us. In part, as we noted with the idea of “flow” it reflects our sense of the inevitability of things, of something essential about the material world that you cannot buck. It reflects a profound, existential anxiety that underpins the fundamental narrative of our life: the passage from birth to death. You can wind the clock back and set it to zero, and make a fresh start; but there is something you cannot wind back – time itself – in order to recover the lost days.The notion of the unidirectionality of flowing time is inseparable from our awareness of our mortality, of a life that has a diminishing quantity ahead and an increasing quantity behind; of birth as a one-ticket to the grave. There is a sense of that which is beyond recall – we cannot take back or amend what has happened; and a sense of our being propelled helplessly to our death. This death – its timing, its cause, its manner – is the greatest of the unknowns that confront us when we think of the future. And this sense of our ignorance in the face of the future – contrasted with our knowledge of the past – lies at root of the “arrow of information”. We may know how things turned out; never how they will turn out.
The Arrovians have one thing in common; namely, that they want to reduce time to something else. The attempts so far have failed and, according to GJ Whitrow’s persuasive judgement, always will:
[A]ny theory that seeks to derive the entire concept of time from some more primitive considerations – for example, assumptions of a causal, probabilistic or statistical nature is foredoomed to failure. For any theory which endeavours to account for time completely ought to explain why everything does not happen at once. Unless the existence of successive (non-simultaneous) states of phenomena is tacitly assumed it is impossible to deduce them…In the final count, time is a fundamental property of the relationship between the universe and the observer which cannot be reduced to anything else.58
If the present book has any purpose, it is to try to get a clear and just idea of the nature of the relationship between the universe and the observer in respect of time. But we have a long way to go yet.
Let us for the present continue our inquiries by returning to another very prominent manifestation of the irresistible spatialisation in the way we think about time: the idea of time travel.
Raymond Tallis February 2013