Forthcoming in Sankey, H. (ed.), Causation and Laws of Nature, Kluwer Academic Publishers, 1998.
Huw Price
School of Philosophy
University of Sydney
Historians often encounter striking correlations between events in different places at the same historical period: a new disease breaks out in several towns in the same month, for example, or a new phrase comes suddenly into widespread use. Sometimes these patterns are merely coincidental, but in general--in history as in ordinary life--we look for an explanation of the correlation in terms of a single common event, with which each of the original events may be seen to be associated. We look for the original source of infection, or the original use of the phrase. In any particular case, it may not be obvious where we should look for the linking event, and historians need a nose for these things. But one piece of advice seems infallible: Look in the past, not in the future. In other words, look for the linking event before, not after, the events it is supposed to explain.
This advice isn't simply pragmatic, of course. We're not advising historians to concentrate on the past because they don't have the techniques or training to investigate the future, for example. Rather, it seems to be a fact about the world that correlations of the relevant kind are linked in a time-asymmetric way. A common past can produce correlations in a way in which a common future cannot. It's a fact about the world that backward-looking historical explanation is the kind that works in these cases. We can imagine worlds in which work differently--worlds in which forward-looking, teleological explanation has a more important role to play--but our world doesn't seem to be like that.
What sort of fact about the world is it that it exhibits this kind of temporal asymmetry--let's call it the "No Teleology Principle"? Indeed, to what extent is it a fact about the world at all, rather than something much more subjective--a feature of our notion of explanation, perhaps? These issues are of considerable interest in their own right, but my concern here lies further down the track. I want to talk about whether it is legitimate to expect this kind of time-asymmetry to prevail in microphysics, and, if not, what the consequences might be for our understanding of quantum mechanics. It turns out that the contemporary debate about the interpretation of quantum mechanics takes for granted a version of the No Teleology Principle, in a way which is so intuitive, so deeply embedded in the way in which we find it natural to think about the world, that it is easy to overlook the fact that it is there. But there are two reasons for trying to bring it into the open. First, the best account of the nature of the physical origins of the No Teleology Principle seems to leave no place for it in microphysics--it seems to be associated with a different level in the physical world altogether. And second, the quantum world begins to look much more attractive, without the constraints of this intuitive asymmetry.
The rest of the paper goes like this. In the next section I sketch what seems to me to be the right account of the relationship between the No Teleology Principle and the well-known time-asymmetry thermodynamics. This account proposes that the thermodynamic asymmetry is the objective correlate of the No Teleology Principle--the contingent objective feature of our world, in virtue of which the No Teleology Principle is true. I'll then go on to argue that some intuitively plausible applications of this principle in microphysics are not compatible with this proposal. This suggests one of two things: either the proposal is mistaken, and there is a further objective time-asymmetry in the physical world, in addition to that of thermodynamics; or these extra applications of the No Teleology Principle in microphysics are misguided. I'll argue that the first option runs counter to the apparent T-symmetry of the laws of physics--that is, to the well-established principle that the laws governing the microscopic constituents of matter are (almost entirely) insensitive to the distinction between past and future--and that the second option seems to offer considerable benefits in quantum mechanics. We thus have two reasons for taking seriously the possibility that the No Teleology Principle is an unreliable intuition in microphysics--the possibility that future history plays the same role as past history in microphysics, in what at present we find a deeply counter-intuitive way.
The No Teleology Principle says that any two physical systems will be independent of one another, unless one system exerts a causal influence on the other, or both systems are influenced by some common factor in their past. More anthropomorphically, we might take it to say that when two systems encounter one another for the first time, they remain ignorant of each other's existence, until the moment at which they first interact.
Formalisations of this idea have been proposed in both physics and in philosophy. In the physical literature, Penrose and Percival (1962) formulate such a principle as what they call the Law of Conditional Independence. As they emphasise, it is time-asymmetric: it says that incoming systems are independent before they interact, not that outgoing systems are independent, after they interact. We don't expect outgoing processes to be independent--on the contrary, since otherwise we wouldn't expect correlations in cases in which both processes arise from some common source in their common past.
As their terminology indicates, Penrose and Percival suggest that conditional independence is a law-like principle. This view has not been popular, however. Most physicists hold that like other temporal asymmetries in the physical world, this asymmetry is "fact-like"--a nomologically contingent matter, associated with boundary conditions.
Penrose and Percival note that conditional independence is closely related to Hans Reichenbach's "Principle of the Common Cause", formulated a few years earlier in Reichenbach's posthumous book, The Direction of Time (Reichenbach, 1956). Reichenbach had observed that when correlations between events at different points in space are not due to a direct causal connection, they turn out to be associated with a joint correlation with a third event--what Reichenbach terms a common cause--in their common past. Reichenbach notes the temporal asymmetry of this principle, and explores the idea that it is connected with the direction of time. In philosophy, the temporal asymmetry these principles describe has come to be termed the fork asymmetry. Roughly, the fork is the V-shaped structure of correlations, whereby two spatially separated events are correlated in virtue of their joint correlations with a third event at the vertex (see Horwich 1987, for example). The asymmetry consists in the fact that forks of this kind are very common with one temporal orientation (V-shaped, or open to the future) but rare or non-existent with the opposite orientation (vel-shaped, or open to the past).
At the macroscopic level, the fork asymmetry appears to be connected with the asymmetry of thermodynamics. The easiest way to see this is to think about ordinary irreversible processes, viewed in reverse--in other words, viewed as we see them if we reverse a film. From this reversed perspective, many ordinary processes seem to involve highly correlated incoming influences from distant parts of space. Think of tiny droplets of champagne, forming themselves into a pressurised column and rushing into a bottle, narrowly escaping an incoming cork. Think of the molecules in a bath of water, organising themselves into fast and slow teams, before hurling themselves in two columns to the hot and cold taps. Or, to give a less domestic example, think of the countless fragments of the True Cross, making their meticulously coordinated journeys to meet Christ outside Jerusalem. Astounding as these feats would seem from this perspective, they are--perhaps with the exception of the last!--nothing but the mundane events of ordinary life, viewed from an unfamiliar angle. Seemingly teleological behaviour of this kind is ubiquitous in one temporal sense--when it occurs after some central event, from our usual temporal perspective--but unknown and apparently incredible in the other temporal sense.
Broadly speaking, then, the cases which look teleological when viewed in reverse seem to be the cases in which--viewed from the reverse perspective--entropy is decreasing. The existence of such reverse teleology seems to depend on the fact that the universe as we know it is not in thermodynamic equilibrium. If the universe were in equilibrium, reverse teleology of this kind would be as rare as forward teleology actually is--there would be no teleology in either temporal sense. This suggests that the No Teleology Principle is closely associated with the principle that entropy does not decrease towards the future. In particular, the time-asymmetry of the No Teleology Principle (the fact that it does not hold in both temporal directions) seems to be associated with the asymmetry of the Second Law--i.e., with the fact that the principle that entropy does not decrease holds towards the future but not towards the past. Indeed, a natural suggestion is that the No Teleology Principle simply is the principle that there are no entropy-reducing correlations towards the future.
There are some complexities here that I want to flag, but skirt around. The precise relationship between the No Teleology Principle and the Second Law is a controversial matter. A long tradition holds, in effect, that some version of the No Teleology Principle is explains (and is hence theoretically prior to) the Second Law. Famously, Boltzmann's so-called H-Theorem--a special case of the Second Law for the case of gases--relies on an asymmetric independence principle called "molecular chaos". Perhaps because the No Teleology Principle is so intuitive, it took a long time for the tradition to notice the work this asymmetric assumption does in the H-Theorem and its descendants. Even today, many people do not seem to appreciate the fundamental dilemma: Without some such time-asymmetric principle, the H-Theorem cannot yield a time-asymmetric conclusion. With such a principle, on the other hand, the H-Theorem cannot do more than to shift the puzzle of the time-asymmetry of the Second Law from one place to another, for the time-asymmetry of the principle in question will be equally problematic, in the light of the apparent T-symmetry of the underlying laws. (What is more, it is doubtful whether the required principle can be fact-like--a matter of boundary conditions--as the tradition also assumes. If it were, we would seem to have no reason to expect the Second Law to hold in previously unobserved regions of space and time. Only a prior observation that it does hold in a particular region of spacetime could give us reason to think that the initial boundary conditions were such that entropy does not decrease in the region in question.)
So the traditional attempt to derive the Second Law from some version of the No Teleology Principle is problematic, and produces no net reduction in the puzzles of time-asymmetry. It also has nothing to say on the issue of why entropy was low in the past. With its assumptions laid bare, the traditional approach presents us with two puzzling time-asymmetries: First, why is entropy low in the past, and second, what asymmetric principle causes it to increase towards the future? In my view (see Price, 1996, Ch. 2) this double counting is quite unnecessary. I think that what the statistical treatment of thermodynamics gives us is, not an asymmetric explanation why entropy increases in one direction, but an entirely symmetric expectation that entropy will be high at any time, ceteris paribus. In other words, it reveals that high entropy is a normal condition, which doesn't require further explanation. It is departures from this normal condition that need to be explained, and here we do find an asymmetry: entropy decreases towards the past, but not (so far as we know) towards the future. Once we recognise that there isn't a separate puzzle as to why entropy goes up towards the future, in addition to the puzzle as to why it goes down towards the past, there's no motive to regard the No Teleology Principle as something prior to the Second Law, from which the latter may be derived. On the contrary, we should say that the default expectation is for no teleology in either direction, and that the only puzzle is that we do find teleology towards the past--in other words, that entropy does decrease in that direction.
This view of the matter is controversial, and conflicts with a long tradition in thermodynamics. But for present purposes, I don't need to insist on it. All I need is the fact that whatever one's view of the relationship between the No Teleology Principle and the thermodynamic asymmetry, there is an evident attraction in the idea that they are closely related--in particular, in the economical idea that it is essentially the same contingent feature of the world which underlies both. As long as this is so, it is plausible to hold, as most physicists seem to hold, that the No Teleology Principle is no more problematic than the thermodynamic asymmetry: and (with the above reservations) that both are of a fact-like nature. This seems to be the orthodox view in physics.
However, I want now to argue that there are some intuitively plausible applications of the No Teleology Principle in physics which cannot be accommodated within this orthodox picture, and which have nothing to do with the thermodynamics asymmetry. If so, then either there is a further objective time asymmetry in the world, in addition to that associated with thermodynamics, or the relevant intuitions are unreliable. I want to argue for the latter view.
Consider a photon, passing through a polariser. According to the standard model of quantum mechanics, the state of the photon after the interaction reflects the orientation of the polariser. If you know the state of the photon after the interaction, you know the orientation of the polariser. Not so before the interaction, of course: in quantum mechanics, as elsewhere, we take it for granted that there are no pre-interactive correlations. The photon doesn't know the orientation of the polariser in advance. Here, as elsewhere, we assume that the No Teleology Principle holds sway.
Very few writers see this feature of the standard model as in any way problematic. Some writers are troubled by the time-asymmetry of the standard model, but their objection tends to be to the fact that the collapse of the wave function is an irreversible process, not to the asymmetry of correlations as such. And after all, why not? The fact that there is an asymmetry may be a little puzzling, but its individual components--that interactions may establish correlations, and that there are no pre-interactive correlations--surely seem plausible enough. If we were to try for symmetry, which should we give up? Besides, as we have seen, the No Teleology Principle is familiar elsewhere in physics, where it seems compatible with the T-symmetry of underlying physical laws. Thus there seems to be a precedent for the asymmetry we find in quantum mechanics, and no reason, on reflection, to doubt our initial intuitions.
I think the appearance of calm is quite illusory, however. The time asymmetry embodied in the standard model turns out to have nothing to do with the thermodynamic asymmetry, and hence to be quite distinct from its supposed analogue elsewhere in physics. This means that in taking for granted the No Teleology Principle in quantum mechanics, we are not simply applying the same well-grounded principle to new cases. It is not the same principle as before, and, I shall argue, cannot be reconciled with the T-symmetry of the laws of physics in the same way. Given T-symmetry, I want to argue, pre- and post-interactive correlations should be on the same footing in microphysics. Any reason for objecting to pre-interactive correlations is a reason for objecting to post-interactive correlations, and any reason for postulating post-interactive correlations is a reason for postulating pre-interactive correlations. Hence, I want to argue, the No Teleology Principle is unreliable in quantum mechanics.
I emphasise that for the present, my interest is in the intuitions underlying the No Teleology Principle, not in the quantum mechanical examples. For the moment, the standard model simply provides vivid examples of the intuitions I want to challenge. For the moment, what's important is just that we find it "natural" that photons should be correlated with polarisers before but not after they interact. Later, I'll discuss the significance of a challenge to this intuition for the puzzles of quantum mechanics, but until then it is the intuition and not the quantum mechanics that matters.
We'll need a name for the kind of application of the No Teleology Principle which is involved in the photon example. As I noted earlier, we find it natural to express these intuitions in a rather anthropomorphic way, in terms of what one system may be expected to know about another. We take it to be intuitively obvious that interacting systems will be ignorant of one another until the interaction actually occurs, at which point each system may be expected to "learn" something about the other. In Price (1996) I called the microscopic case of this intuitive principle the "microscopic innocence principle", or "µInnocence", for short. Here, less anthropomorphically, I'll call it "µIndependence". The first task is to show that unlike the instances of the No Teleology Principle we discussed initially, µIndependence does not depend on the thermodynamic asymmetry--in other words, on the principle that there are no correlations of the kind there would be if entropy decreased towards the future. (I'll call the principle that there are no entropy-reducing correlations "H-Independence".)
I don't know of any other writer who distinguishes µIndependence explicitly from H-Independence. However, it is not hard to see that they are distinct. For one thing, the correlations associated with low-entropy systems are essentially "communal", in the sense that they involve the behaviour of very large numbers of individual systems. But the kind of post-interactive correlation we take to be exemplified by the photon example is individualistic, in the sense that it involves the simplest sort of interaction between one entity and another.
Secondly, the photon case is not dependent on the thermodynamic history of the system comprising the photon and the polariser, or any larger system of which it might form a part. Imagine a sealed black box containing a rotating polariser, and suppose that the thermal radiation inside the box has always been in equilibrium with the walls. Intuitively, we still expect the photons comprising this radiation to establish the usual post-interactive correlations with the orientation of the polariser, whenever they happen to pass through it. The presence of these post-interactive correlations does not require that entropy was lower in the past. By symmetry, then, the absence of matching pre-interactive correlations cannot be deduced from the fact that entropy does not decrease toward the future: a world in which photons were correlated with polarisers before they interacted (so as to violate µIndependence) would not necessarily be a world in which the Second Law did not hold. Our intuitions about µIndependence seem to be independent of the existence of a thermodynamic asymmetry.
Even if µIndependence and H-Independence are distinct, however, a natural suggestion is that they have the same status, in the sense that both are fact-like--products of time-asymmetric boundary conditions, rather than asymmetric laws. But in the thermodynamic case, the observed thermodynamic asymmetry in our region provides evidence for the kind of asymmetric boundary conditions required to explain it. We have very good reason to accept the existence of the asymmetry, at least in our region, independently of any claim about boundary conditions. In the case of µIndependence, however, there is no observed asymmetry to be explained. We don't observe that the incoming photon is not correlated with the polariser through which it is about to pass. Rather, we rely on the asymmetric principle that interaction produces correlations only in one temporal direction--"towards the future", not "towards the past". In other words, we rely on a principle of No Teleology, but in a context in which it has nothing to do with the principle that entropy does not decrease.
As it guides our intuitions in quantum mechanics, then, µIndependence seems to be not an a posteriori principle derived from observation, but a law-like principle in its own right. It seems to be a kind of meta-law, which allows laws imposing post-interactive correlations, while excluding their pre-interactive counterparts. But why should we accept an asymmetric principle of this kind? I know of two main lines of argument, but I want to show that both are fallacious.
The first argument goes like this. We have seen that observational evidence for H-Independence need not be observational evidence for µIndependence--at any rate, not directly. There might be indirect evidence in the offing, however. Perhaps the Second Law supports some hypothesis about the initial conditions of the universe, an independent consequence of which is that photons are not correlated with polarisers before they interact. For example, it is often suggested that the Second Law derives from the fact that the initial microstate of the universe is as random as it can be, given its low-entropy macrostate. Would this not also explain why photons are not correlated with future polarisers?
More directly, it has been suggested that µIndependence simply depends on to the plausible principle that all initial conditions be treated as equally like, other things being equal. After all, wouldn't pre-interactive correlations require that the initial condition of the system concerned be chosen from a very special subset of its phase space. In other words, doesn't µIndependence simply embodies a contingent but highly plausible hypothesis about the initial states of physical systems, namely that they be as random as possible? (This argument is offered in defence of µIndependence by Lebowitz 1997, for example.)
In my view, however, this argument simply fails to recognise the law-like character of what is prohibited by µIndependence. Suppose, contrary to µIndependence, that there were laws imposing pre-interactive correlations. The phase space of a physical system is defined by the operative physical laws: in effect, the phase space just is the set of states allowed by the laws. Hence if a law imposed pre-interactive correlations then µIndependence would fail for any nomologically possible choice of initial conditions, and wouldn't require any special choice. After all, if the standard model of quantum mechanics is correct, then no special choice of phase space trajectories is required to ensure that a photon is correlated with a polariser after they interact, for all trajectories exhibit this correlation. This objection gets things the wrong way around, then. It begs the question in favour of µIndependence, by assuming that the phase space is such that only a special subset of trajectories would display pre-interactive correlations.
The second argument turns on the claim that by postulating µIndependence, we are able to explain certain otherwise puzzling observable phenomena (and hence, again, on the idea that these phenomena provide indirect observational evidence for µIndependence). For example, Penrose and Percival themselves argue that their Law of Conditional Independence explains a variety of otherwise inexplicable irreversible processes. Although few physicists agree with Penrose and Percival that Conditional Independence is a law-like principle, it does seem a common view that their examples provide indirect observational evidence for pre-interactive independence.
A typical example involves the scattering produced when two tightly organised beams of particles are allowed to intersect. It is argued that this scattering is explicable if we assume that there are no prior correlations between colliding pairs of particles (one from each beam), and hence that the scattering reveals the underlying independence of the motions of the incoming particles.
But µIndependence is neither necessary nor sufficient here. The explanation rests entirely on the absence of entropy-reducing correlations between the incoming beams--i.e., on H-Independence--not on µIndependence at the level of individual particle pairs. In other words, these cases involve nothing more than the familiar thermodynamic asymmetry, from which µIndependence is supposed to be distinct.
I will offer short and long arguments for this conclusion. The short argument simply appeals to cases in which it seems clear that there is no microscopic asymmetry--Newtonian particles, for example. Here there is nothing to sustain any asymmetry at the level of individual interactions, and yet we still expect colliding beams to scatter. This suggests that the scattering is associated with the lack of some global correlation, not with anything true of individual particle pairs.
The longer argument goes like this. We suppose that there is a microscopic asymmetry of µIndependence, distinct from the correlations associated with the thermodynamic asymmetry, and yet somehow compatible with the T-symmetry of the relevant dynamical laws. We then construct a temporal inverse of the scattering beam experiment, and show that it displays (reverse) scattering, despite the assumed absence of the post-interactive analog of µIndependence. By symmetry, this shows that µIndependence is not necessary to explain the scattering observed in the usual case. Finally, a variant of this argument shows that µIndependence is also insufficient for the scattering observed in the usual case.
If µIndependence were necessary for scattering, in other words, then scattering would not occur if the experiment were run in reverse. It is difficult to replicate the experiment in reverse, for we do not have direct control of final conditions. But we can do it by selecting the small number of cases which satisfy the desired final conditions from a larger sample. We consider a large system of interacting particles of the kind concerned, and consider only those pairs of particles which emerge on two tightly constrained trajectories (one particle on each), having perhaps interacted in a specified region at the intersection of these two trajectories (though not with any particle which does not itself emerge on one of these trajectories). We then consider the distribution of initial trajectories, before interaction, for these particles. If the dynamical laws are T-symmetric, the predicted distribution must mirror that in the usual case.
This can be made more explicit by describing a symmetric arrangement, subsets of which duplicate both versions of the experiment. Consider a spherical shell, divided by a vertical plane. On the inner face of the left hemisphere are particle emitters, which produce particles of random speed and timing, aimed at the centre of the sphere. In the right hemisphere is a matching array of particle detectors. Dynamical T-symmetry implies that if the choice of initial conditions is random, the global history of the device is also T-symmetric: any particular pair of particle trajectories is equally likely to occur in its mirror-image form, with the position of emission and absorption reversed.
We can replicate the original experiment by choosing the subset of the global history of the device containing particles emitted from two chosen small regions on the left side. Similarly, we can replicate the reverse experiment by choosing the subset of the history of the entire device containing particles absorbed at two chosen small regions on the right side. In the latter case, the particles concerned will in general have been emitted from many different places on the left side. This follows from the fact that the initial conditions are a random as possible, compatible with the chosen final conditions. Thus we have scattering in the initial conditions, despite the assumed lack of post-interactive µIndependence between interacting particles.
Thus if there were post-interactive correlations of the kind denied to the pre-interactive case by µIndependence, they would not prevent scattering in the reverse experiment, which is guaranteed by the assumption that the initial conditions are as random as possible, given the final constraints. By symmetry, this implies that µIndependence is not necessary to produce scattering in the normal case. We get scattering without any extra assumption in the role that µIndependence is supposed to play, provided that the choice of trajectories is as random as possible, given the initial constraints. (This cannot be the same thing as µIndependence, for otherwise µIndependence would not fail in the post-interactive case, and there would not be the assumed microscopic asymmetry.)
A third version of the experiment shows that µIndependence is also not sufficient to explain what happens in the normal case: Assume µIndependence again, and consider the subset of the first experiment in which we have collimation on the right, as well as the left--i.e., in which we impose both final and initial conditions. Here we have no scattering, despite µIndependence. (Again, the imposition of the final condition cannot amount to a denial of µIndependence: if so, the asymmetry of µIndependence in the normal case would amount to nothing more than the presence of a low-entropy initial condition, in conflict with the supposition that µIndependence differs from H-Independence.)
Thus µIndependence is both insufficient and unnecessary to explain the scattering phenomena. The differences between the various versions of the experiment are fully explained by the different choices of initial and final boundary conditions. The asymmetry of the original case stems from the fact that we have a low-entropy initial condition (the fact that the beams are initially collimated) but no corresponding final condition. The issue as to why this is the case that occurs in nature is a sub-issue of that of the origins of the thermodynamic asymmetry in general. It has nothing to do with any further asymmetry of kind described by µIndependence. In other words, contrary to popular opinion, these cases provide no indirect observational support for µIndependence.
Thus in its role as the intuition that underpins the asymmetry of the photon's behaviour in the standard model of quantum mechanics, µIndependence is not an a posteriori principle derived from observation, but a kind of tacit meta-law in its own right. We do not observe that the incoming photon is not correlated with polariser through which it is about to pass. Rather, we rely on the prior principle that laws enforcing pre-interactive correlations would be unacceptably teleological. We allow dynamical principles producing post-interactive correlations, but not their pre-interactive twins.
Conceding that µIndependence is law-like does not improve its prospects, of course. It simply owns up to the principle's current role in guiding our intuitions in microphysics. Indeed, it makes its prospects very much worse, for as a law-like principle, µIndependence conflicts with T-symmetry. We might be justified in countenancing such a conflict if there were strong empirical evidence for a time-asymmetric law, but the supposed evidence for µIndependence turns out to rely on a different asymmetry altogether.
What are the options? First, we might look for other ways of defending µIndependence. Unless this support takes the form of a posteriori evidence, however, its effect will be simply to deepen the puzzle about the T-asymmetry of microphysics. Moreover, although there is undoubtedly more to be said about the intuitive plausibility of µIndependence, I suspect that the effect of further investigation is to explain but not to justify our intuitions. For example, the intuitive appeal of µIndependence may rest in part on a feature of human experience, the fact that in practice our knowledge of things in the physical world is always post-interactive, not pre-interactive. The explanation of this asymmetry is tricky. It seems to depend in part on our own time-asymmetry as structures in spacetime, and in part on broader environmental aspects of the general thermodynamic asymmetry. Whatever its exact provenance, however, it seems to provide no valid grounds for extending the intuitions concerned to microphysics.
Similarly, as I have argued elsewhere (see Price 1996, 181-4), some apparent post-interactive dependencies turn out to be associated with a temporal asymmetry in counterfactual reasoning--roughly, the fact that we "hold fixed" the past, when considering the consequences of counterfactual conditions. Given a conventional account of this aspect of counterfactual reasoning, the asymmetries concerned are demystified, in the sense that they are shown to require no independent asymmetry in the physical systems concerned. Again, some of the intuitive appeal of µIndependence is thereby accounted for, but in a way which does nothing to solve the puzzle of the photon case.
Another response would be to try to ensure T-symmetry in microphysics by disallowing post-interactive correlations, rather than by admitting pre-interactive correlations. The standard model of quantum mechanics would thus be ruled unacceptable, for example. But the move seems misguided. It does nothing to justify µIndependence, and restores symmetry by creating two puzzles where previously we had one.
In my view, the only option which really faces up to the problem is that of admitting that our intuitions might be wrong, and that µIndependence might indeed fail in microphysics--in other words, admitting that we have no good reason to exclude teleology in microphysics, so long as it is not of the entropy-reducing kind. I want to finish with a few remarks on the possible relevance of this option in quantum mechanics. In order to clarify the force of these remarks, I emphasise again that thus far, my references to quantum mechanics have been inessential. The standard model provides vivid examples of an asymmetry we take for granted, but the case against this asymmetry is essentially classical. The main point is that despite common opinion to the contrary, it is not associated with the classical asymmetry of thermodynamics. In effect, then, the case against µIndependence is a prior constraint on the interpretation of quantum mechanics. We have reason to doubt the intuition concerned on symmetry grounds, independently of any consequences this might turn out to have in quantum mechanics.
When we do turn to quantum theory, we find that µIndependence is a fundamental assumption of most, if not all, of the range of arguments which have been taken to show that the quantum world is non-classical in puzzling ways. The most striking such argument is Bell's Theorem (1964). Bell's result has been taken to establish that quantum reality involves non-locality. Although the nature of this non-locality and the extent of its conflict with Special Relativity have been a matter for much debate, the consensus has been that quantum mechanics is committed to it in some form. As Bell and others have pointed out, however, his argument depends on the assumption that quantum systems are not correlated with the settings of measurement devices, prior to their interaction. Thanks to µIndependence, this assumption has normally seemed uncontentious. Bell himself considered relaxing it, but even he tended to think about this possibility in a way which doesn't conflict with µIndependence. (His suggestion, which he called "superdeterminism", was that the required correlation might established by an additional common cause in the past, not simply in virtue of the existing interaction in the future; see Bell, 1987, Bell et al, 1985)
The upshot is that without µIndependence, there seems to be no firm reason to think that quantum mechanics commits us to non-locality. This conclusion applies not simply to Bell's Theorem, but to other more recent arguments for non-locality, such as the Greenberger-Horne-Zeilinger (GHZ) cases (see, e.g., Mermin, 1990, Clifton, Pagonis and Pitowsky, 1992); these too depend on µIndependence, in the form of the assumption that the states of incoming particles are not correlated with the settings of instruments they are yet to encounter.
Non-locality is not the only non-classical consequence thought to flow from quantum mechanics, of course. Since the early years of quantum theory, many physicists have been convinced that quantum measurements do not simply reveal a pre-existing classical reality. In Bohr's Copenhagen Interpretation, which remains very influential in physics, the view was that reality is somehow "indeterminate" until a measurement is made--measurement was said to force reality to take on a definite condition, where none existed before. Later, and rather more precisely, a range of mathematical results (the so-called No Hidden Variable theorems) seemed to establish that no system of pre-existing properties could reproduce the predictions of quantum mechanics, at least in certain cases; see Kochen and Specker (1967), for example.
These interpretations and results also take for granted µIndependence, however. Otherwise, they would not have been entitled to assume that the pre-existing reality could not depend on the nature of a later measurement. In place of Bohr's indeterminate reality, one might have postulated a reality which, while fully determinate before a measurement is made, is partly constrained by the nature of that measurement. In the case of the No Hidden Variable theorems, similarly, µIndependence serves to justify the assumption that a single hidden state should be required to reproduce the quantum predictions for any possible next measurement. If the hidden state is allowed to vary with the nature of the measurement, the problem is relatively trivial, at least in principle. (In David Bohm's 1952 hidden variable theory, the trick is to allow measurement to have an instantaneous effect on the hidden variables; again, however, it is µIndependence which underpins the assumption that the effect must be instantaneous, rather than advanced.)
µIndependence thus plays a crucial role in the arguments which are taken to show that quantum mechanics has puzzling non-classical consequences. We might symbolise the logical relationships like this:
On the right hand side we have a list of the problematic non-classical consequences of quantum mechanics. The contents of the list vary a little with one's favoured interpretation of quantum theory, but virtually everyone agrees that there are some such consequences.
To understand the significance of these connections, try to imagine how things would have looked if we had considered abandoning µIndependence on symmetry grounds, before the development of quantum mechanics. Quantum mechanics would then have seemed to provide a dramatic confirmation of the hypothesis that µIndependence fails. Given quantum mechanics, the assumption that µIndependence does not fail turns out implies such absurdities such as non-locality and indeterminacy. Against this imagined background, then, experimental confirmation of the Bell correlations would have seemed to provide empirical data for which the only reasonable explanation is that µIndependence does fail, as already predicted on symmetry grounds.
From a contemporary standpoint it is difficult to see the issue in these terms, of course. We are so used to talk of non-locality and indeterminacy in quantum mechanics that they no longer seem entirely absurd. And of course we are still so strongly committed to µIndependence that it is hard to see that rejecting it could provide a more plausible way to understand the lessons of quantum mechanics. But I think it is worth making the effort to challenge our preconceptions. I have argued that we have reason to doubt µIndependence on purely classical grounds--simply for symmetry reasons, in effect, once we appreciate that we have no empirical reason to question T-symmetry. With this new conception of the proper form of a classical microphysics, it seems unwise to continue to insist that quantum mechanics is a radically non-classical theory, in what have become the orthodox ways.
Thus the hypothesis that µIndependence fails seems to throw open the conventional debate about quantum mechanics in a rather appealing way--it suggests that quantum mechanics might be a very much less non-classical theory than almost everybody has assumed. But is the hypothesis really one to be taken seriously? The appeal to symmetry notwithstanding, many will feel that there is something fundamentally absurd about the suggestion that µIndependence might fail.
This is not the place to attempt a comprehensive response to all such doubts--I discuss these issues at greater length in Price (1996)--but I want to finish by mentioning one surprising consequence of abandoning µIndependence, which turns out to be very much less objectionable than it seems at first sight. In the process, I think, it provides further ammunition for the claim that quantum theory provides precisely the kind of picture of the microworld we should have expected, if we had accepted in advance that T-symmetry requires us to abandon µIndependence.
The consequence concerned would manifest itself in a case in which we ourselves had influence over one member of a pair of interacting systems--over the setting of a polariser before its encounter with an incoming photon, for example. If the state of the incoming photon were correlated with that of the polariser, then if we could control the polariser without preventing the interaction, we would be able to control the photon. This would not be action at a distance--the correlation would be conducted continuously, via the interacting worldlines of the two systems involved--but it would seem to amount to a kind of backward causation. This consequence might well seem absurd, and potentially paradoxical.
The usual objection to advanced causation involves the bilking argument. The essential idea is that in order to disprove a claim of advanced causation, we need only arrange things so that the claimed later cause occurs when the claimed earlier effect has been observed not to occur, and vice versa. It might be thought that an argument of this kind will be sufficient to defend µIndependence. Any claimed pre-interactive correlation looks liable to be defeasible in this fashion--we need only ensure that the properties of one system affect those of the other, in such a way as to conflict with the claimed correlation.
But is the bilking argument effective in the kind of case we are considering? Consider the photon example. In order to set up the kind of experiment just outlined, we would need to observe the relevant state of the photon before it reaches the polariser, so as to orient the polariser in such a way as to defeat the claim that the incoming photon is correlated with polariser setting. But how would we set about making such an observation? Presumably we would have to place a second polariser, or some other measuring device, in the path of the photon, before it reaches the original polariser. But if we are entertaining the hypothesis that µIndependence fails, we have two reasons to dispute the relevance of the information yielded by this measurement procedure. Firstly, if µIndependence is in doubt then we are not entitled to assume that the state revealed by this measurement is the state the photon would have had, had the measurement not been made. After all, if measurements can affect the earlier states of the systems measured, then what measurement reveals is not in general what would have been there, in the absence of the measurement in question. Even if we found that the correlation required for backward causation failed in the presence of the measuring device, in other words, we would not be entitled to conclude that it would have failed in its absence.
Secondly, and more importantly, what the failure of µIndependence requires is that there be a correlation between the polariser setting and the state of the incoming photon from the time of that photon's last interaction with something else. For think of the usual case: How long do we expect a correlation established by interaction to survive? Not beyond the time at which the system in question interacts with something else, a process which may destroy the initial correlation. In the case we are considering, then, the effect of interposing a second measuring device in the photon's track will be to ensure that the correlation is confined to the interval between this measurement and the main interaction. The presence of the measurement ensures that the advanced effect is more limited in extent than it would be otherwise, and again the required contradiction slips out of reach.
These objections could be evaded if it were possible to observe the state of the incoming photon without disturbing it in any way--if the presence of the measuring device made no difference to the object system, in effect. Classical physics is often said to have taken for granted that perfectly non-intrusive measurements of this kind are possible, in principle, or at least approachable without limit. If this view was ever assumed by classical physics, however, it was decisively overturned by quantum mechanics. One of the few things that all sides agree on about quantum mechanics is that it shows that we cannot separate the processes of measurement from the behaviour of the systems observed. This provides a further respect in quantum mechanics is the kind of microphysical theory we might have expected, if we had questioned µIndependence on symmetry grounds, within the classical framework. The bilking argument suggests that classical non-intrusive measurement is incompatible with the kind of symmetry required if we abandon µIndependence. Transposing, then, it seems that symmetry considerations alone might have led us to predict the demise of classical measurement.
Summing up, we began with the No Teleology Principle. We saw that on the small scale, as on the large, we take for granted that interacting systems do not behave in a teleological way--they do not become acquainted before they actually meet, so to speak. I argued that on the large scale, this time-asymmetric principle seems closely associated with the time-asymmetry of thermodynamics. Not so on the small scale, however. As it guides our intuitions in microphysics, the No Teleology Principle is not only independent of the thermodynamic asymmetry, but conflicts with the widely-accepted doctrine that the laws of microphysics are insensitive to the distinction between past and future. As such, I suggested, any applications of the No Teleology Principle in microphysics should be suspect. We have good reason to think that the intuitions concerned are simply unreliable. Microscopic teleology should be no more unacceptable in one temporal direction than in the other. In looking for explanations of present correlations, microphysicists should be encouraged to consider the future of the systems concerned, as much as their past. History should play a time-symmetric role in microphysics.
Finally, I have suggested that there is already some empirical evidence in favour of this symmetric alternative, albeit of a very indirect and incomplete kind. From a classical standpoint quantum mechanics itself is naturally taken to provide such evidence, on the grounds that if combined with the principle of µIndependence, it leads to such conceptual horrors as non-locality and indeterminacy. From a contemporary standpoint, however, these ideas have lost their capacity to shock. Familiarity has bred a measure of contentment in physics, and the reductio has lost its absurdum. Regaining a classical perspective would not be an easy step, nor one to be attempted lightly, but it does seem worth entertaining. In abandoning a habit of thought which already conflicts with well-established principles of symmetry, we might free quantum mechanics of metaphysical commitments which once seemed intolerable in physics, and might yet seem so again.
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