Chapter 4 took us on a tour of the physics of time, and how it relates to the philosophy of time. In particular, we looked at the central argument against the dynamic theory of time based on the special theory of relativity. In this chapter, we will focus on the static theory of time, and, in some sense, on its relation to physics. The goal of this chapter is to look in detail at the asymmetry of time (more on what this is, shortly). The asymmetry of time poses something of a challenge for static theories of time. Indeed, one argument for the dynamic theory of time is that since time is, obviously, asymmetric, and as static theories cannot account for this asymmetry, we ought to posit temporal passage to explain that asymmetry. If the static theorist cannot account for the asymmetry of time, or, alternatively, explain why time looks asymmetric even though it is not, then the dynamic theorist has a point: we do have some reason to posit temporal flow. Our goal here is to explore this challenge, as well as to map the space of options available for thinking about the asymmetry of time itself. We begin by getting a bit clearer on what it means to say that time is asymmetric.
One of the striking features of our universe is that it appears to display interesting asymmetries, many to do with time. The past seems different in various respects to the future. We know things about the past but not about the future. We can travel forwards in time quite easily but not backwards and so on. These asymmetries give rise to interesting explanatory questions that philosophers and physicists have each sought to answer. Why is the future different from the past? Why can we remember the past and not the future? Why is travel in one temporal direction so easy and travel in the other temporal direction so hard?
In order to better understand the philosophical and physical questions pertaining to temporal asymmetries, we need to differentiate between three concepts: temporal asymmetry, temporal anisotropy and temporal direction. Here is how we are going to understand the difference between these three notions. We will suppose that to talk of temporal asymmetries is to talk of processes, or phenomena, that are temporally asymmetric. So temporal asymmetries are asymmetries associated with things in time. More particularly, a process or phenomenon is temporally asymmetric if the behaviour of that process or phenomenon is different along one direction on the temporal axis than along the other direction on that axis.
So, for instance, suppose the process of cooking eggs is irreversible: once an egg is cooked, it stays cooked (or becomes more cooked) but cannot go back to being raw. (This is just an example; egg cooking is not irreversible in this manner, though have no fear, the chances of your cooked egg reverting to being raw are astonishingly low.) If egg cooking were irreversible in this way, then it would be a temporally asymmetric process. In one direction along the temporal axis we would always find eggs cooking, but never becoming raw, and in the opposite direction along the temporal axis we would always find eggs becoming raw, and never find eggs cooking. Even if egg cooking is reversible, it might still be that egg cooking is temporally asymmetric if we almost always see eggs cooking in one temporal direction, and almost never becoming raw in the same temporal direction. That, in fact, is how things are. In general it is sufficient for a process to be temporally asymmetric that the process is irreversible, but it is not necessary: a process can be temporally asymmetric just by its typically taking place in one, but not the other, direction along the temporal axis. As we will use the phrase, to talk of temporal asymmetries is to talk about asymmetries of process in time, not asymmetries of time itself.
By contrast, a dimension (such as time) is anisotropic if it has different properties along one direction of the dimension as compared to the opposite direction of the dimension. So time is anisotropic if it has different properties along the temporal dimension from past to future, than it does along the temporal dimension from future to past. At this point we should draw an important distinction between what we might call the intrinsic anisotropy and the extrinsic anisotropy of a dimension. Suppose you see a red wine glass. It might be that the glass itself is transparent, and it is filled with red wine. Or it might be that the glass itself is red. In the first case we might say that the glass is extrinsically red: it is red in virtue of bearing some relation to red wine (containing it). Further, we might say that the glass’s redness is accounted for, or reduces to the fact that the glass contains a red substance. In the second case the glass is intrinsically red. The glass is red not because it bears a relation to something else (wine) but because the glass is, in itself, red.
Now suppose that instead of containing red wine the transparent glass contains a liquid that changes colour from the bottom of the glass to the top of the glass: it goes from yellow at the bottom, through green, and then blue to purple at the top. Then the colour of the glass is up/down asymmetric. We can see that by noting that the experience of an insect swimming from the bottom of the glass to the top is different from the experience of an insect swimming from the top of the glass to the bottom: the way the colour changes varies between the two directions. So the up/down dimension is colour anisotropic.
In the case in which the up/down dimension is colour asymmetric in virtue of the glass containing differently coloured fluids, we can say that the up/down dimension is extrinsically anisotropic. In the case in which the up/down dimension is colour asymmetric in virtue of the glass itself being differently coloured at different locations, we can say that the up/down dimension (of the glass) is intrinsically anisotropic. In general, a dimension is extrinsically anisotropic if the anisotropy is the result of the way things are distributed along that dimension, and is intrinsically anisotropic if it is anisotropic in virtue of intrinsic features of the dimension itself.
Talk of temporal asymmetries and temporal anisotropy are intimately connected. One way for time to be extrinsically anisotropic is for there to be temporally asymmetric phenomena. If lots of things in time exhibit some sort of temporal asymmetry, then the temporal dimension will be anisotropic in virtue of the asymmetries that things in time display. That leaves it open whether or not time is also intrinsically anisotropic. Perhaps it isn’t. In which case it might be that time’s anisotropy is fully explained by the existence of temporally asymmetric phenomena in time (though it remains to be explained why these phenomena are temporally asymmetric in this way). Or perhaps it is. Perhaps time’s being intrinsically anisotropic is what explains why things in time are temporally asymmetric.
The exact nature of the connection between temporal asymmetries and temporal anisotropy is up for debate. Plausibly, the presence of the right sorts of temporal asymmetries is both necessary and sufficient for the presence of extrinsic temporal anisotropy. Equally, the presence of temporal asymmetries is clearly not sufficient for the existence of intrinsic temporal anisotropy, and it is unclear whether such asymmetries are even necessary. Perhaps the temporal dimension could be intrinsically anisotropic without there being anything in time that exhibits temporal asymmetry (though it is unclear on what basis one would attribute such anisotropy to time in that case, since one could not obviously gather evidence of any kind of asymmetry in time). At any rate, those who think that time is intrinsically anisotropic do, in fact, also tend to think it contains temporally asymmetric phenomena, so to a large extent we can avoid taking a stand on this issue.
This brings us to the third concept that we promised to differentiate: directionality. We will say that time has a direction just in case time is anisotropic (either intrinsically or extrinsically) and there is some fact of the matter (given by the world) as to which direction is which. So, for instance, think about walking up, or down, a mountain. The path up the mountain is anisotropic: the properties going up the mountain are different from those going down the mountain. Does the path have a direction? It does if there is an objective fact of the matter regarding whether the path goes from the bottom of the mountain to the top, or goes from the top to the bottom (which there isn’t, unless the path is impassable going up versus going down).
Or return to consider our coloured glass. An insect can swim from the bottom to the top, or from the top to the bottom. The up/down dimension of the glass will have a direction, as well as an anisotropy, if there is a fact of the matter whether the dimension really goes from up to down, or down to up. In a way, then, the dimension is directed just in case, metaphorically speaking, in addition to it being anisotropic there are little ‘arrows’ that point from the top to the bottom, or from the bottom to the top so that we know whether the glass ‘goes’ from yellow to purple, or from purple to yellow. In both cases it is hard to see what that fact might amount to. To return to the mountain path example, one might have reason to walk from the top to the bottom (to limit effort) but there is no sense in which the path itself really goes from the top to the bottom (or the bottom to the top). So although there is anisotropy, there is no directionality. By parity, time has a direction if it is anisotropic, and there is a fact of the matter as to whether time is directed from the past to the future, rather than from the future to the past. If that is right, then although it is necessary to time’s having a direction that it be anisotropic, it is not sufficient.
In what follows we begin by considering various temporal asymmetries: that is, various phenomena or processes that are temporally asymmetric. We will then move on to consider ways in which we might explain time’s direction (if indeed time has a direction).
Our world seems to contain many temporally asymmetric phenomena. That is, it seems to contain phenomena that behave differently along one direction on the temporal axis as compared to how they behave along the other direction on the temporal axis. Examples are everywhere, and mostly we probably don’t even think about them. But consider the following. We age along the temporal dimension in one temporal direction. All of us get older towards the direction we call future, and away from the direction we call past. What’s true for each of us is also true for just about everything else, from milk souring, to eggs going off, to corpses rotting. These are all specific instances of a more general phenomenon known to us all through high-school physics as the second law of thermodynamics, which says (roughly) that disorder (i.e. entropy) increases towards the future.
There are plenty of other examples of temporally asymmetric phenomena. Waves spread from an emitter, but not towards an absorber. When any of us throws a rock into a still pool we see waves emitted from the point of contact with the water. We would all be surprised to see waves converging on a point, and a rock being disgorged from the water.
There are also cosmological asymmetries. It seems that the universe is expanding, and that it is expanding away from the past and towards the future. So cosmological expansion seems to be temporally asymmetric.
Causation, too, seems to be temporally asymmetric. We expect causes to precede their effects in time. Even if backwards causation is possible, and, indeed, even if there is actually some backwards causation, in general causation seems to be temporally asymmetric. Related to this asymmetry of causation is the asymmetry of determination, or the fork asymmetry. This asymmetry is captured by the idea that a single cause can have myriad effects, but it is very rare indeed for a single effect to have myriad independent (full) causes.
For instance, imagine you spill a plate of spaghetti bolognaise all over the floor. One way of cleaning it up is to crawl all over the floor and pick up each bit of spaghetti and tomato sauce. Since the bits of spaghetti have spread far and wide, this will be quite a big job. It would have been much easier simply to prevent the plate from hitting the ground in the first place and spreading its contents. The lesson here is quite general: it’s much harder to mop up after some cause has left multiple effects than it is to prevent a single cause from obtaining in the first place (witness oil spills to fully appreciate this). Consider, once more, the floor covered in spaghetti and sauce. One way the floor could have ended up like this is if many individuals had each, independently (i.e. not in conspiracy with one another, or in virtue of some common cause), come into the kitchen and thrown a piece of spaghetti on the floor. Then it would actually be easier to clean up the floor by cleaning up all the spaghetti than it would be to try and prevent each and every person from throwing a single piece of spaghetti onto the floor. The point, however, is that we rarely see cases in which there are multiple independent causes and a single effect, while we frequently see cases in which there are multiple effects of a single cause. In this respect the causal structure is temporally asymmetric.
Finally, there are many temporally asymmetric psychological phenomena. For instance, we deliberate towards the future and not towards the past. That is, we deliberate about events that are future relative to our location in time, and not about events that are past relative to our location in time. We also seem to differently value past and future events. Suppose you know you have to undergo a painful dental procedure. It is common to prefer that that procedure be located in the past, rather than the future. Or consider a very tasty chocolate cake. It is common to prefer that the event of eating the cake is in the future, rather than the past, and indeed in the near future rather than the far future. It is often thought that if we had to choose between having had a very painful dental procedure in the past, and having to have a less painful dental procedure in the future, we will choose the former over the latter, even though overall we are subject to more pain that way. (We also typically value things that lie in the further future less than we value things that lie in the near future. This is known as discounting. This, however, will be of less interest to us here, since it doesn’t really reveal an asymmetry between the two temporal directions.)
To this list, dynamic theorists of time would also add the asymmetry of temporal flow. As time passes, events that were future become present and then past. We do not see the reverse happening. That is, as time passes we do not see events that were past become present and then recede into the yawning future. Of course, whether or not time really flows is, as we have seen, a very controversial matter. If it does, however, then we have one more asymmetry to deal with. In this case, though, we’d be looking at an intrinsic anisotropy of time itself, one that has a preferred direction.
In what follows we focus in more detail on four of these asymmetries: entropy and the second law of thermodynamics; the asymmetry of causation; the fork asymmetry; and the asymmetry of deliberation. We will briefly return to the asymmetry implicated in the flow of time in section 5.4.
Informally put, the second law of thermodynamics says that entropy always increases over time. (In fact, what the second law actually says is that the total entropy of an isolated system will always increase over time, unless that system is in equilibrium, in which case it will remain stable: the system will never decrease in entropy.) What does that mean? Entropy is a measure of disorder. The more entropy there is, the more disorder there is. So the second law of thermodynamics says that an isolated system will never decrease in disorder over time.
We can now see why ageing processes are a specific instance of increasing entropy. Think about the rotting corpse. Bodies start off in a fairly low entropy state (being alive), and gradually, as time passes, become more disordered as they fall apart and return to the soil.
If the second law of thermodynamics is a law, then the increase of entropy is one example of a temporally asymmetric phenomenon: entropy increases (or stays the same) towards the future, and thus decreases (or stays the same) towards the past. The direction towards the future is different from that towards the past when it comes to entropic processes. In section 5.6.1 we return to consider entropy and the second law of thermodynamics in much more detail. There, we revisit the question of whether the second law of thermodynamics is really a law and whether there is anything temporally asymmetric about the distribution of entropy.
Consider that when you get up tomorrow, you will deliberate about what to have for breakfast: toast or cornflakes. You will deliberate towards the direction you call the future. You will not, however, deliberate about whether you ought to wear a jumper to bed the night before. That’s not a special feature of you. We all deliberate about what we will do at later times, that is, at times towards the future, and none of us deliberate about what we did do at earlier times, that is, at times towards the past. So we might say that there is a deliberation asymmetry: we deliberate towards the future and away from the past. That asymmetry, in turn, seems to be related to another asymmetry: an asymmetry in our knowledge. Why do we deliberate about the future but not the past? Well, one answer that immediately springs to mind is that we already know what we did in the past, and so it would be pointless to deliberate about it.
The point of deliberation is to decide what to do. But one can’t try and decide what to do with respect to P if one already knows that one did P. That’s why you can’t deliberate about whether to wear a jumper last night: because you already know whether you wore the jumper or not. By contrast, you don’t know what you will have for breakfast tomorrow (you might have strong suspicions, based on what you have had every other morning, but if you decide to treat breakfast-eating as a matter for deliberation, you will take it that you do not know what you will eat until after you have made the decision). Another closely related asymmetry, which, one might think, helps explain the deliberation asymmetry, is the causal asymmetry. Causation itself seems to be temporally asymmetric. Causal processes go from past, to future.
Causation typically goes from past to future. As we will consider in Chapter 8, where we look at time travel, it might be that sometimes causal processes will go in the opposite direction ‒ from future to past. Nevertheless, in general, causes temporally precede their effects, rather than the other way around.
Indeed, that causation typically (or always) goes in one temporal direction might be thought to explain the deliberative asymmetry. After all, the reason why you deliberate about something is that you suppose yourself to have some causal control over whether or not to bring that thing about. You don’t deliberate about whether to cool the sun down because that’s not something you take yourself to have any control over. But if you only deliberate about things you can causally affect, and if causes typically precede their effects in time, then it makes sense that you only deliberate about future events and not past events. For if causes typically do not go backwards, then you will typically have no control over events in the past. You can’t deliberate about whether or not to wear a jumper last night, because you have no causal control over your wearing of a jumper last night.
The temporal asymmetry of causation is closely related to the fork asymmetry. Think about a fork. It has a single handle, and then a bunch of prongs at the end. (If you own a fork with more than three prongs, that fork is ideal for our present purposes.) The fork is anisotropic in that from one direction it runs from a single handle to a number of prongs, and from the other end it runs from a number of prongs to a single handle. Now imagine that the handle of the fork is pointing back towards the past, and the prongs towards the future. The thought is this: what we find in our world is that very many later events (the prongs on the fork) are all correlated with a single earlier event (the handle of the fork). So, for instance, imagine that you set off a firework at a crowded market. The letting off of the firework is a single event, but now if we watch to see what happens we will see many effects emanating from that cause. People in the market place will run in many directions, grabbing different possessions, and engaging in different behaviours.
That is the fork asymmetry: from a single cause, we see many dissipating effects. It’s an asymmetry because we don’t see reverse forks. In the case of the firework we see a number of correlated events (the actions of the people in the market place) preceded by a common cause (the letting off of the firework). But we don’t see cases in which there are correlated events, linked by a joint effect. That would be a case in which lots of independent, but correlated, events all come together to produce a single effect. We can imagine what that would be like by just imagining our market place scenario in temporal reverse: from people being scattered we see those people gradually converge on a market place, and come ever closer, until there is an implosion of fireworks into a box of undisturbed skyrockets. We would be very surprised to see events play out this way. What could bring about such an inverse fork? Imagine that philosophers had lots of money, and hired a film crew to depict an inverse fork, not by running film backwards, but by filming the market place just described by having actors running backwards towards what will be the firework going off. Notice that this still wouldn’t be an example of a reverse fork, since the correlated events would not, in fact, be independent: they would be the effect of a common cause, to wit, the philosophical director who is attempting to create a reverse fork. Notice that in the absence of such a director we would be surprised indeed to see the market place occurring ‘in reverse’. That’s because we don’t typically see reverse forks, while we do often see ordinary forks.
That there are so many temporally asymmetric phenomena seems to demand an explanation. One potential explanation, and one that seems to accord with the way the world seems to us, is that time has a direction. If time itself has a direction, then this can explain why things in time are arranged in a temporally asymmetric manner. The alternative view is that time has no direction, but some features of our local environment, or our psychologies, or the combination of both, makes it appear as though time has a direction. As we saw in Chapter 1, the view that time has a direction is shared by both A- and B-theorists. A- and B-theorists agree that time has a direction, but disagree about what accounts for time having a direction. By contrast C-theorists hold that time has no direction, but merely appears to do so. We consider this view in section 5.3.3.
There are two very different views about temporal direction. We call the first of these views primitivism about direction, and the second reductionism about direction. One version of primitivism about direction is the view that time has a direction because it has temporal flow, and its having temporal flow is a primitive matter. This version of primitivism is the view that A-theorists endorse, and we consider it in section 5.4. A second version of primitivism is a version defended by certain B-theorists. We discuss this B-theoretic primitivist view in section 5.5. Finally, probably the most popular view about temporal direction is the view that temporal direction reduces to something else. This is a static B-theoretic view according to which time has a direction, but its having that direction is accounted for by some other phenomenon or phenomena. In the following sections we will outline some primitivist and reductionist proposals. First, though, we need to get clear on the difference between primitivist and reductionist views.
Primitivism is the view that time has a direction, and that its having that direction is intrinsic to time itself. Reductionism is the view that time has a direction, but its having that direction is reducible to something else.
We have already met the difference between intrinsic and extrinsic anisotropy. The difference between primitivism and reductionism about direction is very similar. Recall that those who hold that time has a direction think not only that time is anisotropic, but, in addition, that there is a fact of the matter as to which direction time points. Primitivists think that time’s directedness is a primitive matter. So, for instance, remember the example of the coloured glass that gradually changes from one colour at the bottom to another colour at the top. The primitivist about up/down directionality will say that there is some primitive matter of fact that the up/down dimension really goes from up to down (or vice versa). There are, as it were, little arrows embedded in the up/down dimension which point from up to down (or vice versa), and these arrows cannot be reduced to or explained in terms of anything else. An obvious primitivist view is to pair the view that temporal anisotropy is extrinsic with the claim that temporal direction is primitive. So what makes the two directions along the temporal dimension different is some feature of how things are distributed along that dimension, but what makes one direction the way that time in fact goes is a primitive matter.
By contrast, reductionists about temporal direction hold that time has a direction, and its having that direction is reducible to some feature of things in time. It is easy to see why reductionism about anisotropy is appealing, and easily motivated. For the reductionist can simply say that the difference between the two directions along the temporal dimension is the result of processes being temporally asymmetric. It is less easy to see how the reductionist can make sense of directionality. Even if it’s true that processes ‘age’ towards what we call the future, and away from what we call the past, it in no way follows that time goes from what we call the past, to what we call the future, rather than the other way around. It seems conceptually possible that time might go from the past to the future, while beings Benjamin Button their way through time: ageing towards the past and growing younger towards the future. One possibility that suggests itself to the reductionist is to appeal to the laws of nature. Should it turn out that the laws of nature are themselves temporally asymmetric, the reductionist could argue that this is what grounds time’s having a direction, rather than merely being anisotropic. It is the laws that provide the needed ‘arrow’. We consider this suggestion in the following section.
The idea that the reductionist can appeal to asymmetric laws to ground the direction of time is appealing. But there’s a problem. The problem is that the laws of nature are time-reversal invariant. What that means is that if we take any physical law described as an equation or formula, which includes a temporal variable (t) in that equation or formula, and if we then replace t with –t in the formula or equation, the resulting equation still describes a law. What does this mean? It means that for any law-like physical process, such as, for instance, dropping an egg on the ground and the egg breaking, we can describe the reverse of this process ‒ a broken egg leaping up from the ground and reforming into a whole egg ‒ and that reversed process also conforms to the physical laws. To put it another way, the laws apply equally well regardless of which direction we take to be future, and which we take to be the past, in describing the evolution of some process.
To put this in context it’s worth noting that the laws are also space-reversal invariant. That means that if we reverse any of the spatial dimensions in the formulae expressing the laws, the laws remain unchanged. No doubt you will not find that surprising. Quite the reverse; presumably you would find it surprising if the physical laws were different going along one direction of a spatial dimension as opposed to the other direction along that dimension (imagine the laws are different going from up to down, as opposed to from down to up). The same is true for the temporal dimension as for all three spatial dimensions. What time-reversal invariance means, then, is that a mirror image of our universe in which all objects have their positions and momenta reversed would evolve under the same physical laws. That is why the world we described in Chapter 3, in which physical processes in one temporal half of the world occur in reverse order to those in the other temporal half, is taken to be nomologically possible. The laws of nature in such a reversed world may be the laws we have in our world.
At this point it is worth noting that it’s not quite right to say that the laws are time-reversal invariant. There is one very small exception: the laws featuring the kaon (a particular type of sub-atomic particle) violate time-reversal invariance. Some take this to be an important discovery, and hang their hat on the idea that what time’s direction consists in can be understood in terms of this time-reversal invariance. But this seems a bit of a stretch. Even if the kaon does behave in a non-time-symmetric manner, it’s hard to see how that could be what gives time a direction. Amongst other things, it’s hard to see why this fact about the humble kaon would explain why we typically see corpses rotting, rather than coming back to life, and why we typically see waves diverging from an emitter and not converging on an absorber, and so on. So for present purposes we will simply suppose that the laws are time-reversal invariant and set aside the perplexing features of the kaon.
The problem, then, is this. If the laws of nature are time-reversal invariant, then we cannot reduce temporal directionality to asymmetrical laws. Indeed, given the symmetry of the laws, the very presence of temporal anisotropy is puzzling. If the laws are symmetrical, it seems that we ought to predict that phenomena will be temporally symmetric, rather than temporally asymmetric. Yet we see temporally asymmetric phenomena all over the place. So now we are left with two questions. First, we need to answer the question of why there are temporally asymmetric phenomena if the laws are temporally symmetric, and, second, reductionists need to find some other reductive base to account for that direction. Indeed, if we are drawn to reductionism about direction, all of this might suggest that having failed to find a reductive base for directionality we ought to conclude that time does not, in fact, have a direction. It is to this view that we now turn.
One response to the discovery of time-reversal invariant laws is to bite the bullet and concede that in fact time doesn’t have a direction after all. This is precisely what C-theorists, who we might also call directional eliminativists, do. C-theorists hold that events stand in temporal relations with one another ‒ C-relations. There are genuine temporal distance relations between events, just as there are genuine spatial distance relations between places. But time is like space, in so far as it has no direction. So, for instance, just as Singapore and Sydney are separated by a certain spatial distance, so too are Caesar’s death and Hillary Clinton’s birth separated by a certain temporal distance. And just as there is no fact of the matter about which way space is directed (so that we can rightly say that space goes from Singapore to Sydney, or, conversely, from Sydney to Singapore), likewise there is no sense in which time is directed, so that it goes from Caesar’s death to Clinton’s birth (or vice versa). Of course, C-theorists think that time appears to have a direction, but that is all it is: mere appearance.
It is worth noting, at this point, that directional eliminativists need not deny that time is anisotropic. If there are temporally asymmetric phenomena, then time will be extrinsically anisotropic even though it lacks a direction. Indeed, the C-theorist can say that what we call the past is just the direction towards (for instance) decreasing entropy, and the direction we call the future is the direction towards increasing entropy. So the C-theorist can allow that we correctly say things like ‘Sara’s birth was in the past’ and ‘the big crunch is in the future’. What the C-theorist denies is that these claims are made true by time having a direction that runs from Sara’s birth to the big crunch, and in virtue of which the big crunch is objectively in the future as opposed to the past. Indeed, the directional eliminativist will likely allow that in a world in which one temporal half is a mirror image of the other temporal half, true claims about which direction is past, and which future, are reversed. That is, what Sara calls ‘past’ will be what those at the other temporal end of the universe rightly call ‘future’.
Of course, merely claiming that time has no direction does not absolve the directional eliminativist from explaining the temporal asymmetries that we see around us. Even if time has no direction, we still need to explain why it seems, to many at least, as though it does; and we need to explain why so many phenomena are, or seem to be, asymmetrically oriented in time, if time itself lacks a direction.
To do so, the directional eliminativist must offer an account of why various phenomena are, or at least seem to be, temporally asymmetric, one that does not appeal to time having a direction. We consider how this story might proceed, at least with regard to some temporally asymmetric phenomena, in section 5.6.
One possibility for explaining the direction of time that we have thus far neglected appeals to the dynamic theory of time. The thought is that time has a direction because time flows. The future just is the direction towards which time flows. The difference between the past and the future, then, is that time flows towards the future and away from the past. This proposal shares with primitivism the claim that time’s having a direction is an intrinsic property of time itself. That doesn’t mean that the dynamic theorist has to think that temporal flow is primitive. She might think this, and perhaps that is what some moving spotlight theorists do think. But she need not. For instance, some presentists think that temporal flow is the changing of a single three-dimensional slice. To be sure, what it is for a slice to change is itself a primitive matter, but we can reduce the flow of time itself to the changing of this thin wafer of reality. Equally, the growing block theorist might say that what it is for time to flow just is for the universe to accrete new slices. Again, she will likely say that it is a primitive matter that the universe grows in this manner, but she can nevertheless reduce time’s flow to the accretion of these slices. Having done so she will go on to say that time’s flow is intrinsic to time itself, and therefore that time’s direction is intrinsic.
One cost to views such as this is that if time’s direction is intrinsic to time itself, and so time’s direction owes nothing to the asymmetry of things in time, then it remains a mystery as to why time’s having a direction explains why there are temporally asymmetric phenomena. This mystery is particularly forceful if we accept that the laws are time-reversal invariant. Were that not so, we might try to explain why certain phenomena are temporally asymmetric by noting that time has a direction, and that it is a law of nature that phenomena behave differently along one temporal direction than the other. If one accepts that the laws are, however, symmetrical, then it is unclear just what explanatory work any primitivist view of direction can achieve.
We have already seen this problem arise in the context of temporal phenomenology, in Chapter 3. There, recall, we considered the mirror world, and asked whether the temporal phenomenology of individuals in one temporal half of the mirror world would be different from the temporal phenomenology of their physical duplicate doppelgangers in the other temporal half of the world. The worry, recall, was that if the phenomenology is not different, then it seems as though temporal flow makes no difference to the way things seem to us (i.e. to our temporal phenomenology).
We can now generalise this worry by considering the mirror world in a bit more detail. Call one direction along the temporal dimension D, and the other direction D*. Let’s suppose that the direction of temporal flow is towards D, and away from D*. Then it is very hard to see how the presence of temporal flow, and hence temporal direction, can explain the presence of temporally asymmetric phenomena. After all, in one temporal half of the mirror world the temporally asymmetric phenomena ‘point’ towards D, and in the other half they ‘point’ towards D*. So those asymmetric phenomena are aligned with the direction of flow in one half of the world, but not in the other half of the world. To put it another way, in one temporal half of the universe, given the direction of time, eggs really do typically go from being raw, to being cooked, to being eaten. But in the other temporal half of the universe eggs really do go from being eaten, to being cooked, to being raw with the passage of time. The direction of the flow of time seems to be irrelevant to these processes, and thus to be incapable of explaining them.
Of course, the defender of temporal flow (and hence temporal direction) might argue that we are demanding answers to the wrong questions. She might appeal to whatever account the directional eliminativist appeals to in explaining why there are temporally asymmetric phenomena, then insist that appealing to temporal flow does nothing more than give time a direction. That time flows in one direction and not the other is not what explains why certain phenomena are temporally asymmetric; all it explains is why one direction is objectively future, and the other objectively past. If the dynamic theorist takes this view, however, she admits that the flow of time does not explain why phenomena in the world are temporally asymmetric. There is one less thing that the flow of time can explain. This is particularly troubling because it is precisely this kind of asymmetry that one would expect the flow of time to be implicated in. So if one detaches the flow of time from the asymmetry of things in time, it will be much less clear that the explanatory benefits of positing temporal flow outweigh its ontological costs.
Much the same problem arises if instead of appealing to temporal flow to ground temporal direction, we instead suppose time to have a primitive direction. The difference between the view that time has a direction because time flows, and the view that time does not flow but has a primitive direction, is important.
The view that time has a primitive direction, but not in virtue of time flowing, is a version of the static B-theory of time. Remember once again our coloured glass. As we have already noted, the primitivist about up/down direction thinks not only that the up/down direction is anisotropic, but that the glass is directed, say, from up, to down. What makes this the direction of the dimension is that (metaphorically speaking) there are little arrows embedded in the coloured glass pointing from up, to down. Notice that none of this requires that the liquid in the glass, or the glass itself, flows. The arrows themselves (metaphorical though they may be) are entirely static. They point in a certain direction, but they do so without moving. So the view that time has a direction is entirely consistent with the B-theory of time, as long as time’s having a direction is not a matter of it having temporal flow.
But the very same worry arises for the view that direction is primitive as for the view that direction is accounted for by flow. That’s because if time’s direction is primitive, rather than being reducible to something else, then it seems plausible that the direction of time can entirely come apart from the various temporally asymmetric phenomena that we see. Return again to our mirror world. This time, however, rather than supposing that in such a world there is temporal flow, instead suppose that in that world time has a primitive direction. The future is towards D, and the past towards D*. So in one half of the world, the temporal asymmetries align with the direction of time. But in the other half of the world, they fail to align with the direction of time: instead, time goes in the opposite direction to the asymmetries present.
The defender of primitive directionality could, of course, insist that the direction of time cannot come apart from various temporally asymmetric phenomena in this way. She could offer a response similar to one offered by defenders of temporal flow (we met a version of this response in Chapter 3). Recall that one problem with positing temporal flow is that if we suppose the laws of nature to be time-reversal invariant, then we must countenance the nomological possibility of the mirror world, and that, in turn, raises the problem that it seems as if temporal flow is explanatorily idle. But of course, one response on behalf of the defender of temporal flow would be to argue that if there really is temporal flow in our world, then we must be wrong about the laws. If time does flow, then the laws surely cannot be time-reversal invariant. And if they are not time-reversal invariant, then we have little reason to suppose that the mirror world is nomologically possible.
Likewise, the defender of primitive directionality might argue that there are nomologically necessary connections between the primitive direction of time and various temporally asymmetric phenomena, so that these always go together (in nomologically possible worlds). They cannot come apart. So the mirror world is not nomologically possible and the direction of time does align with the various temporally asymmetric phenomena. Again, though, this requires that we reject the contention that the laws are time-reversal invariant. Methodologically speaking, we are making recommendations for science on philosophical grounds. If we aren’t willing to break the news to physicists, then as soon as we allow that the mirror world is nomologically possible, the primitivist about direction seems to lack any explanation for the temporally asymmetric phenomena we see around us. Or, at least, she cannot appeal to time’s having a direction to explain these phenomena. Bearing this in mind, in what follows we turn to consider reductionist approaches to the direction of time to see if they fare any better.
Reductionists hold that there is a direction of time, and that time’s having that direction is reducible to some temporally asymmetric phenomenon or other. Exactly what it means to say that X is reducible to Y is controversial, but, roughly speaking, if X reduces to Y, then there being X is in some sense nothing more than there being Y. For instance, some philosophers think that mental states reduce to brain states: they think that what it is to have a mental state just is to have a certain brain state. Or one might think that there being a table reduces to there being some arrangement of particles: there being that arrangement is all it takes for there to be a table. If X reduces to Y we will say that Y is X’s reductive base. Since reductionists about temporal direction think that the reductive base is some sort of asymmetric phenomenon ‒ they just disagree about which sort it is ‒ we can say that different reductionists posit different base asymmetries as the reductive base for the direction of time. We can now ask what options there are open to the reductionist for reducing the direction of time to some base asymmetry. Before we do that, though, we should get clearer on just what it is that the reductionist is proposing. She tells us that the direction of time reduces to some base asymmetry. Since we don’t know what that base asymmetry is yet, let’s just call it B. What does it mean to say that the direction of time reduces to B? There are two different options the reductionist might endorse:
(1) Identification Thesis: B is identical with the direction of time.
(2) Grounding Thesis: B grounds the direction of time.
According to (1), whatever B is, B is identical with the direction of time. So if, for instance, B is increasing entropy, then the direction of time is identical with increasing entropy. Then time has a direction in any world in which there is increasing entropy, and lacks a direction in any world that lacks increasing entropy. By contrast with (1), (2) says that B grounds the direction of time. Grounding is a relatively new philosophical posit, introduced by metaphysicians in an attempt to devise a relation that can accommodate dependence between things in the world. So, for instance, we might want to say that the table depends on the particles being arranged a certain way, but not that the table is identical with those particles arranged that way. So we could say that the table is grounded by the particles. What’s nice about this is that it allows us to say that the table could have depended on some other bunch of particles entirely (since it’s not identical to those particles). Likewise, (2) allows us to say that although time’s direction is in fact grounded in B, in other worlds time’s direction is grounded by something else. For instance, it allows us to say that in our world it is increasing entropy that grounds time’s direction, but in other worlds some other physical asymmetry grounds time’s direction (such as, for instance, some cosmological asymmetry). It’s worth bearing this difference in mind as we consider a few candidates for the base asymmetry.
We earlier mentioned the second law of thermodynamics and flagged the question of whether it really is a law. We can now examine that question in more detail. If it were a law that entropy never decreases towards the future, then it might seem that the temporal asymmetry of entropy is a good candidate to be the base asymmetry for the direction of time. The reductionist might say that the direction towards the future is the direction towards which entropy increases, and the direction towards the past is the direction towards which entropy decreases. But, a problem arises. Why think that the future is the direction towards which entropy increases, rather than the direction towards which entropy decreases? That is, why think that time goes from low entropy to high entropy, and not the other way around? Nothing about entropy itself tells us that time is directed from low to high entropy. Directional eliminativists make just this objection. They point out that even if entropy is asymmetric in this way, all this tells us is that time is anisotropic, not that it has a direction. For if time has a direction then there must be some objective fact of the matter that time goes from low entropy to high entropy (rather than the reverse). But the discovery that entropy is temporally asymmetric in no way guarantees this fact.
Even setting that problem aside, however, another one arises: namely, it’s not clear that it is a law that entropy is temporally asymmetric. According to contemporary statistical mechanics the second law of thermodynamics is not really a law at all, but merely reflects the probabilities of certain macrostates, conditional on local boundary conditions having certain properties. Let’s unpack what that means. A microstate is a specification of the position and velocity of each particle in the system. A macrostate is a specification of the observable properties of the system, such as volume and temperature. Each macrostate can be produced by many different microstates. So imagine a gas that is distributed through some container (which is the system in question). The microstate is a specification of the position and velocity of each particle of gas in that container. The macrostate is a specification of the observable properties of the gas ‒ its distribution, temperature, and so on. So, for instance, suppose the gas is spread out uniformly through the container. Then it has a uniform macrostate. But there are lots of ways we could distribute the very same particles to attain that same macrostate. Consider some particular particle, Freddie. There are lots of locations in the container at which Freddie could be located, consistent with the gas being uniformly distributed. Now let’s suppose that the probability of every microstate is the same. Conditional on that being the case, the probability of any macrostate will be proportional to the number of microstates that produce that macrostate. So, if there are more microstates that produce macrostates in which the gas is evenly distributed across the whole container than there are microstates that produce macrostates in which the gas is distributed across only half of the container, then it is more probable that the gas will be distributed across the whole of the container than just across half.
Entropy, recall, is a measure of order: the more order, the lower the entropy, the more disorder, the higher the entropy. So suppose we want to know how likely it is that a state will have high entropy, rather than low entropy. Well, notice that high entropy macrostates are ones that can be produced by more microstates than low entropy macrostates. Consider a very low entropy macrostate in which the particles in the container are lined up from left to right. There are far fewer microstates that can produce this state than there are microstates that can produce a uniform distribution of the gas. That is, a smaller proportion of the total microstates can produce this very low entropy macrostate, as compared to the proportion of the total microstates that can produce the higher entropy macrostate. Given this, we should expect the lower entropy macrostate to be less probable than the higher entropy state. In general, we should expect low entropy macrostates to be less probable than high entropy macrostates, because low entropy macrostates are produced by fewer microstates.
This explains why systems tend to move towards high entropy macrostates: they evolve towards states that are the most probable states, and higher entropy macrostates are more probable because a higher proportion of the total microstates are high entropy macrostates.
This is why the second law appears to be true. Equally, it tells us why it isn’t really a law at all (assuming, that is, that laws are supposed to be exceptionless generalisations). Statistical mechanics only tells us that it is more probable that a state will move towards a higher entropy state, not that it is impossible that it will move towards a lower entropy state. If the universe is big enough, then even though there is a very low probability of decreasing entropy, it is possible that there are parts of the universe in which entropy decreases.
Moreover, what holds for the direction into the future also holds for the direction into the past. For the very same reasoning we just used, which told us to expect future higher entropy states, should also lead us to expect that entropy will, in general, increase in both directions in time from an ordered state. So we should expect that entropy will increase into both the future and the past. Statistical mechanics is temporally symmetric. That’s puzzling, since it’s not what we observe.
So why does entropy in our world increase towards what we call the future, and decrease towards what we call the past? Why might we expect to see entropy decreasing towards the past? Well, according to statistical mechanics we would expect to see this if, in the past, there were a highly ordered state, and entropy has been increasing away from that state. So this suggests that somewhere in the past there is a very low entropy state. It only really matters that that state is somewhere in our distant (but not too distant) past; but usually advocates of this solution hold that the low entropy state is a boundary condition ‒ an initial or final condition of the universe. So typically it is held that the big bang generated a very low entropy condition very close to the ‘beginning’ of the universe, and entropy has been increasing away from this state ever since. That there is such a low entropy condition is called the Past Hypothesis (PH). According to PH, shortly after the big bang the initial state of the universe was in a very low entropy state. Given statistical mechanics, we should expect entropy to increase away from that state, that is, towards the direction we call the future, and we should expect entropy to decrease towards the direction we call the past.
The Past Hypothesis, in conjunction with statistical mechanics, explains why we typically see entropy increasing towards the future and decreasing towards the past. This appeal to statistical mechanics is, however, excellent news for the directional eliminativist, and not good news at all for the reductionist about temporal direction. That’s because we can explain the existence of temporally asymmetric entropy without supposing time, or the laws of nature, or anything else, to be asymmetric or directed. Moreover, if the second law of thermodynamics is not an exceptionless law, but a mere probabilistic generalisation, it remains unclear whether the distribution of entropy is a plausible base to which to reduce temporal direction. The PH posits the existence of a low entropy ‘initial’ condition. But nothing in the laws of nature prohibits there also being a low entropy ‘final’ condition: a big crunch. If entropy is very low at both ‘ends’ of the universe, then we get a world that looks like the mirror world we saw in Chapter 3. But then, which direction does time go in, in such a world? What makes one low entropy condition the ‘initial’ condition, and the other the ‘final’ condition, as opposed to the other way around? Nothing about the distribution of entropy itself seems to tells us that time is directed from one end of the universe to the other, rather than the other way around. If entropy decreases towards a big crunch at the other end of the universe then why isn’t the other end of the universe an ‘initial’ condition, and our end a ‘final’ condition? What makes it the case that the direction of time runs from what we call past to what we call future, rather than the other way around? It seems most natural to say that from the perspective of one temporal half of the universe, one direction is future, and from the perspective of the other temporal half of the universe, the opposite direction is future. But at best this would give us a number of local directions to time rather than a single global direction. At worst we might be inclined to say, with the directional eliminativist, that there is no temporal direction, there are just phenomena that are, at different locations, temporally asymmetric and which make us mistakenly think that time has a direction. In either case, matters look tricky for anyone attempting to reduce time’s direction to the increase of entropy.
We have already mentioned in this chapter that causation is temporally asymmetric: causes typically precede their effects in time. So another option for accounting for the direction of time would be to appeal to the direction of causation. Suppose, for a moment, that such a reduction is possible (we return to this shortly). Still, there is a problem. The reductionist urges that we take the direction of time to be aligned so that the future is the direction towards which there are effects, and the past is the direction towards which there are causes. Time goes, as it were, from cause, to effect. But why think that? Why not, instead, think that time goes from effects, to causes? Why not think that the future is the direction towards causes, and the past the direction towards effects? The directional eliminativist will, as always, urge that merely showing that cause and effect are temporally asymmetric might show that time is anisotropic, but not that it is directed: for we need some reason to think that time goes from cause to effect rather than the other way around, and nothing about the nature of causation itself seems to give us that reason.
But suppose the reductionist could solve that problem. Nevertheless, the reductionist project faces other issues, analogous to those we noted in the case of reducing temporal direction to the distribution of entropy over time. For just as statistical mechanics tells us that we should not expect entropy never to decrease towards what we call the future, so too, there are reasons to think that causal relations are not, or need not always be, aligned in the same direction. If backwards causation is nomologically possible, or indeed actual, then we should expect worlds like ours to be ones in which effects sometimes precede their causes. But suppose that there are large regions of the universe in which the direction of causation is reversed relative to how it is around here. Then what direction does time have in those regions? Again, it seems that the reductionist must either say that time has no direction if there are regions such as this, or that time has different local directions.
There are also other problems with reducing the direction of time to the direction of causation. The most pressing of these is that we often distinguish causes from effects by appealing to their temporal order. But we cannot do that if we wish to use the causal order as the base asymmetry for temporal direction. So we need a way to determine which of two causally related events is the cause, and which the effect, without appealing to the temporal order of the events. This has proven non-trivial, and represents another difficulty for this kind of reductionism about direction.
The final view we will consider is one that aims to reduce the direction of time to the asymmetry of one or other psychological phenomenon. The particular version of the view we consider here is one according to which the direction of time is reducible to certain features of our deliberative systems. We have already noted that beings like us deliberate about events towards what we call the future, but do not deliberate about events towards what we call the past. One might try to explain this deliberative temporal asymmetry by supposing that time itself has a direction. The direction of deliberation aligns with time’s direction. The proposal under consideration here, however, attempts to invert the order of explanation. Rather than explaining why we deliberate towards the future and away from the past in terms of time’s direction (or in terms of some further temporal asymmetry such as causation or knowledge), instead the aim is to reduce time’s direction to the direction of deliberation. How does such an account proceed?
The idea is that in order to be able to deliberate at all, each of us needs to divide the world up into the things that we take ourselves to be able to choose between (our options) and the things we take as fixed and immutable, and which we use as the basis for our deliberation. So, for instance, Sara takes it as fixed that tomorrow her kitchen will exist, and she will not be able to levitate, and that if she wants toast, she will need to use a toaster (since she won’t be able to toast bread by looking at it). But Sara takes it as open that she can choose toast or cornflakes for breakfast (these are both options). Each of us can only deliberate about things we take to be open. Sara cannot, for instance, deliberate about whether to levitate tomorrow, given that she knows I cannot levitate.
The reductionist will say that the direction of time reduces to the direction of deliberation. That is, the future just is the direction towards which we deliberate, and the past just is the direction away from which we deliberate.
Again, though, two problems arise for this strategy. The first, and most obvious, is that in a mirror world we would expect agents in one temporal half of the world to deliberate towards what we call the future, and agents in the other temporal half to deliberate about what we call the past. So we should expect that in such a world a reductionist account of temporal direction will yield at least two different local temporal directions. A second problem is that it’s not clear why we should think that the future is the direction towards which we deliberate, rather than the past being the direction towards which we deliberate. Even if deliberation is temporally asymmetric, and even if this shows that time is anisotropic, why does it show that time goes from what we call the past to what we call the future, rather than the other way around?
What consideration of these reductionist stories suggests is that reducing temporal direction to some particular temporally asymmetric phenomenon will prove difficult. That’s because the candidate base asymmetries are not always, everywhere, aligned in the same direction (entropy can decrease towards what we call the future; effects can precede their causes and so on), and because even if the candidate asymmetry is always aligned in the same direction, it’s not clear that the mere presence of that asymmetry gives us reason to think that time is directed from what we call past to what we call future, rather than the other way around.
The asymmetry of time is one of the most perplexing physical features of our universe. Attempting to come to terms with asymmetries in time brings philosophy and science into close conversation. Fully grasping the kinds of asymmetries that there are, and understanding the options for explaining those asymmetries, is really a joint project in philosophy and physics. Our goal in this chapter has been to provide an overview of some of the central issues concerning the asymmetry, anisotropy and directionality of time. The key points covered were:
(1) The asymmetry, anisotropy and directionality of time must all be carefully differentiated from one another.
(2) There are a number of temporally asymmetric phenomena, including: the asymmetry of causation, the asymmetry of entropy, the asymmetry of deliberation, the knowledge asymmetry and the directionality of time.
(3) The laws of physics appear to be temporally symmetrical, and so it is difficult to see how one might attempt to explain the various temporally asymmetric phenomena that there are in terms of lawful asymmetry.
(4) Dynamic theorists of time reduce temporal direction to the direction of temporal flow, and then attempt to explain the asymmetries of time by appealing to time’s having a direction.
(5) Reductionists about temporal direction attempt to reduce direction to temporally asymmetric phenomena, or to temporal anisotropies (intrinsic or extrinsic).
(6) Statistical mechanics plus the assumption that the universe began in a state of low entropy may provide an explanation for the temporal asymmetry of entropy.
(7) Causation and the asymmetry of deliberation present alternative options for reducing temporal direction.
i. Think of all of the physical asymmetries you can (whether to do with time or not). Make a list. Are any of these related to the asymmetries discussed in this chapter? If so, how?
ii. Describe a very basic physical system, such as the motion of a pendulum. Draw a sequence of diagrams that represent different temporal stages of this physical system. What changes, if any, do you need to make to these diagrams in order to represent the temporally reversed version of this physical system?
iii. Develop your own reductionist account of the direction of time. Compare it to one of the reductionist accounts that we have discussed here. Is your account better or worse than these accounts?
iv. Are all of the dynamic theories of time equally able to explain asymmetries in time by appealing to temporal flow, or is one of the dynamic theories better suited to providing such an explanation? Try to justify your answer.
v. Break into groups and invent a short play. Have one group perform the play forwards, and have the other perform the play backwards. Document the kinds of changes that you need to make in order to reverse the play in this manner.
Base Asymmetry
The asymmetry to which the direction of time might be reduced.
Entropy
The measure of disorder of a system.
Extrinsic
A feature that something has in virtue of bearing certain relations to other things.
Grounding
The dependence of one thing on another.
Intrinsic
A feature that something has in virtue of the way it, itself, is, and nothing else.
Macrostate
The state of the properties of a system, such as temperature.
Microstate
The state of the particles that make up a system.
Primitive
Not explainable, or reducible to anything else.
Reduction
The identification of one thing with another.
Reductive Base
The thing Y that some X is reduced to (i.e. identified with).
Temporal Anisotropy
The asymmetry of time itself.
Temporal Asymmetry
The asymmetry of phenomena in time.
Temporal Directionality
The direction that time has, if indeed it has one.
Time-Reversal Invariance
The laws of nature work equally well in one temporal direction as they do in the other.