Time's Arrow and Archimedes' Point is about the need to think about the puzzles of the direction of time from a new viewpoint, a viewpoint `outside' time. One of my main themes is that physicists and philosophers tend to think about time from too close up. We ourselves are creatures in time, and this is reflected in many ordinary ways of thinking and talking about the world. This makes it very difficult to think about time in an objective way, because it is always difficult to tell whether what we think we see is just a product of our vantage point. In effect, we are too close to the subject matter to see it objectively, and need to step back.
This a familiar idea in the history of science. For example, it took our ancestors a long time to figure out that the Earth and a pebble are the same kind of thing, differing only in size. To take this revolutionary idea on board, one needs to imagine a vantage point from which the Earth and the pebble can both be seen for what they are. Famously, Archimedes went one better, and offered to move the Earth, if someone would supply him with this vantage point, and a suitable lever.
The book tries to show that a temporal version of this Archimedean vantage point provides important insights into some of the old puzzles about time. One of its most useful roles is to highlight some old and persistent mistakes that physicists tend to make when they think about the direction of time. More surprisingly, this viewpoint also has important benefits elsewhere in physics. In particular, it throws some fascinating new light on the puzzles of quantum mechanics.
The introductory chapter deals with some important preliminaries. One is to set aside certain philosophical issues about time which are not dealt with in the book. Philosophers of time have often focused on two main issues, that of the objectivity of the past-present-future distinction, and that of the status of the flow of time. Philosophers have tended to divided into two camps on these issues. On the one side are those who treat flow and the present as objective features of the world; on the other, those who argue that these things are artifacts of our subjective perspective on the world. For most of the book I take the latter view for granted. My aim is to extend the insights of this philosophical tradition, and apply them to physics. I do not defend this presupposition in the sort of detail it receives elsewhere in the philosophical literature--that would take a book to itself--but I set out what I see as the main points in its favor.
The second important preliminary task is to clarify what is meant by the asymmetry (or `arrow') of time. A significant source of confusion in contemporary work is that a number of distinct notions and questions are not properly distinguished--for example, the question whether time itself is asymmetric, and the question whether physical processes are asymmetric in time.
With preliminaries out of the way, the remainder of the book is in two main parts. The first (chapters 2-4) focuses on the three main areas in which temporal asymmetry turns up in modern physics: in thermodynamics, in phenomena involving radiation, and in cosmology. In all these cases, what is puzzling is why the physical world should be asymmetric in time at all, given that the underlying physical laws seem to be very largely symmetric. These chapters look at physicists' attempts to solve this puzzle, and at some characteristic confusions that these attempt tend to involve.
Chapter 2 deals with thermodynamics. As everyone knows, the second law of thermodynamics is a time-asymmetric principle. It says that entropy increases over time. In the late nineteenth century, as thermodynamics came to be addressed in terms of the symmetric framework of statistical mechanics, the puzzle just described came into view: where does the asymmetry of the second law come from? This problem produced the first examples of a kind of fallacy which has often characterised attempts to explain temporal asymmetry in physics. The fallacy involves a kind of special pleading, or double standard. It takes an argument which could be used equally well in either temporal direction and applies it selectively, in one direction but not the other. Not surprisingly, this biased procedure leads to asymmetric conclusions. Without a justification for the bias, however, these conclusions tell us nothing about the origins of the real asymmetry we find in the world. Fallacies of this kind crop up time and time again, and one of the main themes of the book is that we need an atemporal starting point in order to avoid them.
Chapter 3 looks at the time asymmetry of radiation. Why do ripples on a water surface spread outwards rather than inwards, for example? Similar things happen with other kinds of radiation, such as light, and physicists have been puzzled by the temporal asymmetry of these phenomena since the early years of the twentieth century. Again, it turns out to be important to correct some confusions about what this asymmetry involves. However, the chapter's main focus is on the relation between this asymmetry and that of thermodynamics. I argue that several prominent attempts to reduce the former asymmetry to the latter turn out to be fallacious, once the nature of the thermodynamic asymmetry is properly appreciated. In particular, I look at a famous proposal by Wheeler and Feynman, called the Absorber Theory of Radiation. At first sight, this theory seems a model of respect for an atemporal perspective. I argue that Wheeler and Feynman's reasoning is confused, however, and that as it stands, their theory doesn't succeed in explaining the asymmetry of radiation in terms of that of thermodynamics. However, the mathematical core of the theory can be re-interpreted so that it does show--as Wheeler and Feynman believed, but in a different way--that radiation is not intrinsically asymmetric; and that its apparent asymmetry may be traced, if not to the thermodynamic asymmetry itself, then to essentially the same source.
Chapter 4 turns to cosmology. As chapter 2 makes clear, the search for an explanation of temporal asymmetry leads to the question why the universe was in a very special condition early in its history--why entropy is low near the big bang. But in trying to explain why the universe is like this, contemporary cosmologists often fall for the same kind of double standard fallacies as their colleagues elsewhere in physics. In failing to adopt a sufficiently atemporal viewpoint, then, cosmologists have failed to appreciate how difficult it is to show that the universe must be in the required condition at the big bang, without also showing that it must be in the same condition at the big crunch (so that the ordinary temporal asymmetries would be reversed as the universe recollapsed).
In the first part of the book, then, the basic project is to try to clarify what modern physics tells us about the ways in which the world turns out to be asymmetric in time. The basic strategy is to look at the problem from a sufficiently detached standpoint, so that we don't get misled by the in-built temporal asymmetries of our ways of thinking. In this way, I argue, it is possible to avoid some of the mistakes which have been common in this branch of physics for more than a century.
The second part of the book turns from the physics of time asymmetry to physics more generally. The big project is to show that the atemporal Archimedean perspective has ramifications for the interpretation of quantum theory. I argue that the most promising understanding of quantum theory has been almost entirely overlooked, because physicists and philosophers have not noticed the way in which our ordinary view of the world is a product of our asymmetric standpoint. Once we do notice it--and once we think about what kind of world we might expect, given what we have discovered about the physical origins of time asymmetry--we find that we have good reason to expect the kind of phenomena which make quantum theory so puzzling. This path to quantum theory removes the main obstacles to much more classical view of quantum mechanics than is usually thought to be possible. It seems to solve the problem of non-locality, for example, and to open the door to the kind of interpretation of quantum theory that Einstein always favored: a view in which there is still an objective world out there, and no mysterious role for observers.
If there is a solution of this kind in quantum theory, how could it have gone unnoticed for so long? The answer, I think, is the presuppositions opposing this suggestion are so deeply embedded in our ordinary ways of thinking that normally we simply don't notice them. If we do notice them, they seem so secure that the thought of giving them up seems crazy, even in comparison to the bizarre alternatives on offer in quantum theory. Only by approaching these presuppositions from an angle which has nothing to do with quantum theory--in particular, by thinking about how they square with what we have discovered about the physical origins of time asymmetry--do we find that there are independent reasons to give them up. Suddenly, this way of thinking about quantum theory looks not just sane, but a natural consequence of other considerations.
These presuppositions involve notions such as causation and physical dependence. As we ordinarily use them, these notions are strongly time-asymmetric. In particular, we take it for granted that events depend on earlier events in a way in which they do not depend on later events. Physicists often dismiss this asymmetry as subjective or terminological, but it exerts a very powerful influence on what kinds of models of the world they regard as intuitively acceptable. It is the main reason why the approach to quantum theory I want to recommend has received almost no serious attention.
Chapters 5-7 mount a two-pronged attack on this intuition. Chapter 5 shows that it sits uneasily with the kind of picture of the nature and origins of time asymmetry in physics which emerges from the earlier chapters. In this chapter I also explain why abandoning this intuition would have attractive ramifications in quantum theory. However, the notions of causation, dependency, and the like, are not straightforward. Their temporal asymmetry is especially mysterious. Is it some extra ingredient of the world, over and above the various asymmetries in physics, for example? Or can it be reduced to those asymmetries?
In chapter 6 I argue that the asymmetry of causation cannot be reduced to any of the available physical asymmetries, such as the second law of thermodynamics. The available physical asymmetries are essentially macroscopic, and therefore cannot account for causal asymmetry in microphysics. I argue instead that the asymmetry of causation is anthropocentric. Roughly, it reflects the time-asymmetric perspective we occupy as agents in the world--the fact that we deliberate for the future on the basis of information about the past, for example.
As I explain in chapter 7, this account has the satisfying consequence that despite its powerful grip on our intuitions, causal asymmetry does not reflect a further ingredient of the world, over and above what is already described by physics. It doesn't multiply the objective temporal `arrows', in other words. More surprisingly, the account does leave room for a limited violation of the usual causal order. In other words, it leaves open the possibility that the world might be such that from our standard asymmetric perspective, it would be appropriate to say that certain of our present actions could be the causes of earlier effects.
The last two chapters apply these lessons to the puzzles of quantum mechanics. Chapter 8 provides an informal overview of the long debate about how quantum mechanics should be interpreted, identifying the main positions and their advantages and disadvantages. The best focus for such an overview is the question that Einstein took to be the crucial one about quantum mechanics: Does it give us a complete description of the systems to which it applies? Famously, Einstein thought that quantum theory is incomplete, and his great clash with Bohr centered on this issue. Einstein is often said to have lost the argument, at least in hindsight. I argue that this verdict is mistaken. Einstein's view is less implausible than it is widely taken to be, at least in comparison to the opposing orthodoxy.
This conclusion is overshadowed by that of chapter 9, however, where I show how dramatically the picture is altered if we admit the kind of backward causation identified in chapter 7. In the quantum mechanical literature this possibility is usually dismissed, or simply overlooked, because it flies in the face of such powerful intuitions about causality. But the lesson of chapter 7 is that when we ask where these intuitions come from, we discover that their foundations give us no reason at all to exclude the kind of limited backward influence in question--on the contrary, if anything, because powerful symmetry principles can be made to work in favor of the proposal. The conclusion of chapter 9 is therefore that a promising and well motivated approach to the peculiar puzzles of quantum mechanics has been neglected, because the significance of our causal intuitions has not previously been properly understood. Had they been properly understood in advance, I suggest, quantum mechanics is the kind of theory we might well have expected.
The book concludes with an Overview chapter, which summarises the main conclusions, chapter by chapter.
Given the right sort of non-TRI dynamics we would know ... why entropy doesn't increase toward the past as well as towards the future, which would answer what I'm calling the traditional problem. Yet we wouldn't be able to answer Price's worry about why it was ever in nonequilibrium in the first place. We would only know that if the universe were out of equilibrium entropy would increase and not decrease; we wouldn't know why the universe began ... out of equilibrium. Thus on Callender's view, there are two temporal asymmetries in play:
(1) An asymmetric principle which ensures that entropy cannot decrease
towards the future, without also ensuring the same with respect to the
past. (The traditional problem is to find this principle.)
(2) The fact that the universe has asymmetric boundary condition--entropy
is low in the past, but not apparently in the future.
These asymmetries seem to be independent, on Callender's view, at least in the sense that an explanation for (1) does not require an explanation for (2).
Indeed, Callender suggests that (2) may not be the sort of thing for which it is appropriate to seek an explanation. I disagree, but suppose for the moment that Callender is right, and that "the whole enterprise of explaining global boundary conditions is suspect." Presumably this is true of (what we call) final boundary conditions as much as of (what we call) initial boundary conditions. (If not, then this in itself is a further time-asymmetric assumption, which calls for justification.) So if we rephrase (2) as the claim that the universe has a low entropy initial condition and a high entropy final condition (whether at a finite endpoint or `at infinity'), neither boundary condition requires explanation, on this view. However, if the universe has low entropy at one end and high entropy at the other, how much remains to be said about what happens in between? Is there really a need for (1)? What remains of the traditional project?
Tradition seems to hold that we need a dynamical explanation of how matter gets from its initial low entropy state to its final high entropy state. But tradition seems guilty of a double standard at this point, for it does not hold that we need an explanation of how we get from the high entropy state to the low entropy state, and yet it doesn't explain why this way of viewing things is any less appropriate than the more familiar orientation. If it is a sufficient explanation of the fact that entropy decreases towards the past that there is a low entropy boundary condition in that direction, why isn't it a sufficient explanation increases towards the future that there is a high entropy boundary condition in that direction?
The right principle seems to be this one: Once the boundary conditions are in place, what happens in between calls for further explanation only if it is statistically abnormal, given the boundary conditions in question. In effect, the boundary conditions amount to restrictions on the space of possible histories of the universe. The actual history calls for further explanation only if it turns out to be statistically unusual, given those restrictions. (Here `statistically unusual' means something like `improbable in the natural measure, which regards each possible microstate as equally probable'.) To my knowledge, physics gives us no reason to think that this is the case, and this is why I claim that there is no further asymmetry to be explained, over and above that of the boundary conditions. (In fact, it is only the low entropy initial condition which amounts to a restriction on the space of possible histories. The high entropy final condition simply amounts to an assertion that there is no further restriction based on the final macrostate of the universe.)
To sum up, the traditional problem arises from the fact that Boltzmann's statistical methods work only in one temporal direction. Essentially, these methods rely on counting the possible microstates compatible with a given macrostate, and basing one's predictions on the assumption that all such microstates are equally likely. Roughly speaking, then, the problem is that the following principle gives useful predictions only in one direction:
(*) Assume that the actual microstate of the universe is chosen at random
from those compatible with what we currently observe.
The traditional problem is to explain why this assumption works in one direction but not the other, and tradition has assumed that an answer requires an asymmetric principle to replace the principle (*).
I think that this is a mistake, and that instead, we should replace (*) with a weaker but still time-symmetric principle, such as:
(**) Assume that the actual microstate of the universe is chosen at random
from those compatible with what we currently observe, within the
region of phase space compatible with any boundary conditions.
We then explain the fact that (**) gives useful predictions but not useful retrodictions in terms of the fact that in our region of the universe, the relevant boundary conditions are asymmetric--there is a constraint in the past but not in the future. On this account, this asymmetry of boundary conditions is the only time asymmetry in the picture.
In contrast, the traditional view seems to involve an odd double counting of asymmetries, as Callender's analysis illustrates. Imagine a world without a low entropy initial boundary condition, but otherwise like our world. In such a world there is no thermodynamic asymmetry, and hence no need for an asymmetric explanatory principle of the kind described by (1). Without (2), in other words, there is no explanandum which requires an explanans of kind (1). Hence the traditional view is committed to the claim that the effect of adding (2)--on the face of it, a single asymmetry--is to create not one but two asymmetric explananda. (Callender himself then halves the workload by suggesting that boundary conditions don't need to be explained, but this doesn't touch the fact that there are two independent time asymmetries in such a picture.) I take it to be an advantage of my view that it avoids this implausible double counting.
In context, then, the time asymmetry of the orthodox interpretation of QM is not a decisive objection, but simply a further black mark against that view. The debate about the interpretation of QM is always a matter of adding up the pluses and minuses of various views, of course. I think that this particular minus has been insufficiently recognised, because many people haven't realised that the Projection Postulate amounts to a time-asymmetric law. (Many think it is related to the thermodynamics asymmetry, for example.) The main point of the section in question is simply to draw attention to this fact--to make it clear that the orthodox interpretation does have this cost.
Responses to this claim divide very sharply into two camps. Some people--e.g. the Rutgers physicist Joel Lebowitz, in his review of my book in Physics Today, January 1997--try to defend µInnocence, while denying that it conflicts with T-symmetry. Other people, like Callender and Hutchison, deny that any such intuition is at work in physics. In a sense, I have more sympathy with the latter response than the former. I agree with Callender and Hutchison that--whatever many physicists think--no such principle as µInnocence does any positive work in physics. I should have been clearer about this in the book.
What µInnocence does do in physics, I think, is negative work. It rules out of consideration a whole class of hidden variable models in QM, namely those which depend on a law-like correlation between hidden states and future measurement interactions. The orthodox interpretation allows such correlations after interactions, and almost nobody finds this problematic in itself. (The problems are thought to lie in the time asymmetry of the view, or in its exposure to the measurement problem, not in the mere postulation of postinteractive correlations.) But the possibility of analogous law-like correlations before measurements has been overlooked, or thought too implausible to pursue, even by the taxed standards of the discipline. How are we to explain this striking time asymmetry in the practice of generations of physicists and philosophers of physics, if not in virtue of the hypothesis that they take for granted µInnocence? And how are we to defend the practice, if--like Callender and Hutchison--we think there is no principle of µInnocence to defend?
Callender also objects that I view retraction of µInnocence "as a general panacea for all the ills of a quantum world", and points out that it doesn't solve the measurement problem. I agree. As I emphasise in the book, the promise of abandoning µInnocence lies in its ability to resuscitate the view that QM provides an incomplete description, and hence to avail itself of an old solution to the measurement problem: as long as collapse amounts to nothing more than a change in our state of information, it isn't problematic.
Finally, Callender objects to my optimistic assessment of the prospects for a hidden variable interpretation of QM, once µInnocence goes. He suggests that it is "unfair to those labouring ... in the foundations of QM to suggest that all the difficulties disappear by denying a principle I'm not sure anyone holds." My optimism needs to be taken in context, of course. What I think defensible is the claim that once µInnocence goes, this route to an interpretation of QM is unique in being clear of major obstacles. In effect, we have good reasons to doubt whether there is a satisfactory solution in any of the directions currently taken seriously--that's why the problem is so hard, after all. Giving up µInnocence removes the only significant reason for thinking that there can't be a solution in the new direction I propose. So if we accept that µInnocence is unjustified, the a priori prospects for a solution of this kind do look better than those of any current alternative. (If you doubt this, ask yourself whether you have really rejected µInnocence.) This is not the same as having a model in hand, of course, but the issue is whether it would be a good idea to devote one's time to looking for such a model. My claim is simply that a priori, it looks like a better use of one's time than any alternative. One can't dismiss this claim on the grounds that the project hasn't yet succeeded. That would be like refusing to fund an exploratory expedition until shown a map of the proposed route.
As for fairness, finally, my sense is that it is less of a sin to have ignored a promising line of investigation on the grounds that one subscribes to a widely accepted principle which rules it out--even if that principle later turns out to be unfounded--than to have ignored it for no apparent reason whatsoever. In this sense, then, I think that my reading of the role of µInnocence is considerably more charitable than Callender's own to workers in the field.
In particular, Hutchison doubts whether Boltzmann assumed any such principle. I find this puzzling. After all, it is clear that Boltzmann couldn't have derived his time-asymmetric H-Theorem without a time-asymmetric premise of some kind, and it is well known what this premise actually is--it is discussed in all the standard texts. As Sklar puts it, for example, "The crucial assumption is that the rate of collisions in which a molecule of velocity v1 meets one of velocity v2 ... is proportional to the product of the fraction of the molecules having the respective velocities." (Physics and Chance, Cambridge, 1993, p. 33) Perhaps Hutchison doubts that this is assumption is actually time-asymmetric--he wants to know why it doesn't apply after as well as before collisions. If so, then I have considerable sympathy, for I think that the issue as to why it doesn't hold after collisions is equivalent to the issue as to why entropy is low in the past, and I argue in the book that that's the real puzzle of the subject. However, I think it is uncontroversial both that tradition assumes an asymmetry at this point, and that some such asymmetry must actually obtain, given the facts of the thermodynamic asymmetry.
Commonplace manifestations of this asymmetry indicate the intuitive plausibility of PI3 in everyday life. A group of people leave a gathering, never to meet or communicate with one another again. Each carries the same complex text. Astounding? No, it happens all the time. (The text might be the handout for a lecture, for example.) But compare this with the case in which a group of people arrive at a meeting, with no prior communication between them (or to any two from a third party). In this case it would be truly miraculous if all of them (or even two of them) arrived carrying the same complex text.
There are many real-life illustrations of this kind of thing. Substitute coherent electromagnetic radiation for the texts, for example, and we have the phenomenon of the asymmetry of radiation. I think that in all these cases, the real puzzle is associated with the origins of the distinctive patterns of correlation we find after certain central events or interactions, not with the lack of such patterns before interaction. In other words, the puzzle is why PI3 does not hold postinteractively, not why it does hold preinteractively. (To solve the puzzle, we need to explain the ultimate source of the correlations, which is the highly ordered nature of our universe's distant past.) Whatever one's views of the proper nature of the explanans, however, it can hardly be denied that there is an asymmetric explanandum. (Hence my puzzlement with Hutchison's avowed scepticism about this.)
Thus there is a macroscopic temporal asymmetry associated with PI3. Where physicists often go wrong, I think, is in assuming that this macroscopic asymmetry reflects something asymmetric which holds at the level of individual interactions. In other words, they run together the asymmetry associated with the thermodynamic asymmetry with the microscopic, individualistic asymmetry I call µInnocence. Perhaps Hutchison's objection is simply to the idea that any such individualistic asymmetry exists to play a role in thermodynamics. If so, I agree completely, and didn't intend to suggest otherwise. As I explained in my response to Callender, however, I think that the assumption that there is some such individualistic asymmetry is implicit in the thinking of physicists and philosophers in other areas--even though, except in the case of the standard model of QM, this assumption doesn't seem to play any substantial role in physical theory.
However, it seems to me doubtful whether the how possible question could be what either Reichenbach or Hawking has in mind. Consider an analogous case: Suppose it had turned out that actual coins showed a stable long-term preference for heads over tails--a ratio of 60/40, for example. Suppose also that prolonged investigations into the physics of coin tossing had failed to find any explanation for this asymmetry. Again, we could ask how possible and how probable questions, but the former seems to have a trivial answer. This could simply be one of the rare possible universes in which the actual frequencies differ significantly from the objective chances. In other words, the observed bias is just a cosmic coincidence. Such a thing is possible, albeit very unlikely.
Similarly in the case of time asymmetry, it seems to me. The how possible question can always be answered by saying that it could be simply a fluke of nature that there are so many `irreversible' processes, all with the same temporal orientation. Indeed, modern cosmology gives us a good idea what form the fluke needs to take, in order to account for what we see. The fluke of a smooth early universe--a 1 in 1010^123 fluke, according to Penrose--will do the trick. However, it seems unlikely that Reichenbach or Hawking would regard this as progress towards as understanding of time asymmetry. Their goal from the start seems to be something more than this--something more like a law-like explanation for the time asymmetry we observe.
Note that the possibility I call the corkscrew model--that of a time-symmetric theory, all or most of whose possible realisations are individually time-asymmetric--would provide something more than this `it's just a fluke' explanation. Savitt suggests that this model (claimed by some to provide the loophole through which Hawking escapes the kind of objection to which I draw attention) would merely provide an answer to the how possible question. I think it would do more than this, however. It would show that an asymmetric universe of the kind in which we find ourselves is a natural universe, given the laws of physics. Hence it would answer the how probable question.
Thus although I acknowledge the importance of Savitt's distinction between how possible and how probable questions, I am doubtful whether it plays the role he sees for it in this particular dispute.