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Abstract

Introduction

Two kinds of preinteractive independence

Initial randomness?

Colliding beams?

Facing up to the lawlike nature of *µ*Independence
*µ*Independence and quantum mechanics

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Writers who notice this time asymmetry--postinteractive correlations, but no preinteractive correlations--sometimes see it as an objection to the standard model of quantum mechanics. To most, however, it seems hardly worthy of notice. True, the asymmetry may be a little puzzling, but its individual components--that interactions may establish correlations, and that there are no preinteractive correlations--seem plausible enough. If we were to try for symmetry, which should we give up? Besides, the principle that there are no preinteractive correlations plays an important role elsewhere in the physics of time-asymmetry, where there is a well-established view to the effect that it is not in conflict 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 calm is illusory, however, and my aim here is to reveal the troubled waters beneath these rather slippery intuitions. I shall argue that the time asymmetry embodied by the standard model is quite distinct from its supposed analog elsewhere in physics, and cannot be reconciled with the T-symmetry of the laws of physics in the same way. Given T-symmetry, I contend, pre- and postinteractive correlations should be on the same footing in microphysics. Any reason for objecting to preinteractive correlations is a reason for objecting to postinteractive correlations, and any reason for postulating postinteractive correlations is a reason for postulating preinteractive correlations.

I emphasise that for the bulk of the paper, the link with quantum mechanics is indirect. The standard model provides vivid examples of the intuitions I want to examine, but my interest is in the intuitions themselves, not in the quantum mechanical examples. However, I close with a comment on the significance of my argument for the puzzles of quantum mechanics. Briefly, its effect seems to be to undermine a crucial presupposition of the standard arguments that quantum mechanics cannot be interpreted in more-or-less classical terms.

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At a more intuitive level, familiar low-entropy systems are associated with
striking postinteractive correlations. To make this point vivid, think of the
astounding preinteractive correlations we observe if we view ordinary processes
in reverse. Think of the tiny droplets of champagne, forming a pressurised
column and rushing into a bottle, narrowly escaping the incoming cork. Or think
of the countless (genuine!) fragments of the True Cross, making their precisely
choreographed journeys to Jerusalem. Astounding as these feats seem, they are
nothing but the mundane events of ordinary life, viewed from an unfamiliar
angle. Correlations of this kind are ubiquitous in one temporal sense--when
they occur *after* some central event, from our usual perspective--but
unknown and incredible in the other temporal sense.

In the macroscopic world of ordinary experience, then, the presence of
postinteractive correlations and the absence of preinteractive correlations is
closely associated with the thermodynamic asymmetry. It is an old puzzle as to
where this asymmetry comes from, and especially as to how it is to be
reconciled with the apparent T-symmetry of the underlying laws of physics. The
orthodox view is that the asymmetry of thermodynamics is a matter of boundary
conditions: factlike rather than lawlike, as physicists often say. The
contemporary version of this view traces the low-entropy history of familiar
physical systems to the condition of the early universe. True, many hope that
this early condition will itself be explicable as a natural consequence of
cosmological laws, in which case the resulting asymmetry is not strictly
factlike. Nevertheless, the success of this program would preserve the
intuitive distinction between the symmetry of *local* dynamical laws, and
the asymmetry of the boundary conditions supplied to these symmetric laws in
typical real systems.

It seems to be assumed that the kind of asymmetry exemplified by photons and polarisers can be accommodated within this general picture, but I want to show that this is not so. If there is an asymmetry in microphysics of this kind, it cannot be accorded the status of a (locally) factlike product of boundary conditions. This is because, unlike in the thermodynamic case, there is no observational evidence for the required asymmetry in boundary conditions. On the contrary, our sole grounds for thinking that the boundary conditions are asymmetric in the relevant sense is that we already take for granted the principle that there are post- but not preinteractive correlations of the relevant kind. In effect, then, this principle operates in a lawlike manner, in conflict with the assumed T-symmetry of (local) dynamical laws.

The first step is to show that the kind of postinteractive correlation displayed by the photon is quite distinct from that associated with low-entropy systems, such as the champagne bottle. With a little thought, this distinction is easy to draw. For one thing, the correlations associated with low-entropy systems are essentially "communal", in the sense that they involve correlations among the behaviour of very large numbers of individual systems. But the photon correlations are individualistic, in the sense that they involve the simplest kinds of interactions between one entity and another.

Second, 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. We still expect the photons comprising this radiation to establish the usual postinteractive correlations with the orientation of the polariser, whenever they happen to pass through it. The presence of these postinteractive correlations does not require that entropy was lower in the past. By symmetry, then, the absence of matching preinteractive correlations cannot be deduced--at any rate, not directly--from the fact that entropy does not decrease toward the future: a world in which photons were correlated with polarisers before they interacted would not necessarily be a world in which the second law of thermodynamics did not hold.

It will be helpful to have labels for the two kinds of preinteractive
independence just distinguished. I'll call the principle that there are no
entropy-reducing correlations "*H*-Independence", in light of its role in
the *H*-Theorem, and the principle that there are no preinteractive
correlations between individual micro-systems "micro-independence"
("*µ*Independence", for short).

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In my view this hypothesis is independently unsatisfactory. In particular, it is doubtful whether the required boundary condition can be specified in a nonvacuous way--i.e., other than as the condition that the initial state of the universe is such that the second law holds. (See Price 1996, 42.) General defects to one side, however, the hypothesis turns out to be irrelevant to the issue at hand. In effect, the suggestion is that if systems comprising photons and polarisers are allowed a free choice of the available initial microstates, there can be no general correlation between the states of incoming photon-polariser pairs. If this were true, what would it mean for the ordinary postinteractive correlations? Do these require that the final conditions be less than completely random? Not if we understand the choice to be made from those situations permitted by the relevant physical laws--in other words, from the phase space of the system in question. Of course, if we think of nature making its choice from some larger set of possibilities, then the laws themselves constitute restrictions on the available options. Only choices in accordance with the laws are allowed. But a random choice from phase space (or, equivalently, from the set of trajectories of a deterministic system) is by definition a choice from among (all and only) the options allowed by the laws.

Thus lawlike postinteractive correlations are not incompatible with randomness
of final conditions. By symmetry, matching preinteractive correlations would
not require non-random initial conditions. Hence *µ*Independence receives no
support from the hypothesis that initial randomness explains the thermodynamic
asymmetry.

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The claim that Conditional Independence is lawlike has not been widely accepted, but it does seem a common view in physics that Penrose and Percival's examples provide indirect observational evidence for preinteractive independence. A typical example concerns the scattering which occurs when two tightly organised beams of particles are allowed to intersect. The argument is 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 pattern reveals the underlying independence of the motions of the incoming particles.

In fact, however, *µ*Independence 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 *µ*Independence
at the level of individual particle pairs. In other words, the asymmetry
involved in these cases is nothing more than the familiar thermodynamic
asymmetry, from which--as we have seen--*µ*Independence is supposed to be
distinct.

I'll offer short and long arguments for this conclusion. The short argument simply appeals to cases in which it seems intuitively clear that there is no microscopic asymmetry--Newtonian particles, for example. In these cases there seems to be 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 *µ*Independence, distinct from the correlations associated with the
thermodynamic asymmetry, and yet 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 postinteractive analog of *µ*Independence. By symmetry, this shows
that *µ*Independence is not necessary to explain the scattering observed in the
usual case. Finally, a variant of this argument shows that *µ*Independence is
also insufficient for the scattering observed in the usual case.

If *µ*Independence 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 don't have direct control of final
conditions. But we can do it by selecting the small number of cases which do
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.
What is the most likely distribution? If the dynamical laws are T-symmetric,
then it must be simply the distribution which mirrors the predicted scattering
in the usual case.

The argument 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 is an arrangement of particle emitters, each of which produces particles of random speed and timing, directed towards 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 time-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 collimated beam 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
collimated beam 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 postinteractive *µ*Independence between interacting
particles.

Thus if there were postinteractive correlations of the kind denied to the
preinteractive case by *µ*Independence, they would not stand in the way of
scattering in the reverse experiment--scattering in that case is guaranteed by
the assumption that the initial conditions are as random as possible, given
the final constraints. By symmetry, however, this implies that *µ*Independence is
not necessary to produce scattering in the normal case. We would have
scattering without *µ*Independence, provided that the choice of trajectories is
as random as possible, given the initial constraints. (Don't suggest that this
is the same thing as *µ*Independence. If that were true, *µ*Independence would not
fail in the postinteractive case, and there not be the assumed microscopic
asymmetry.)

A third version of the experiment can be used to show that *µ*Independence is not
sufficient to explain what happens in the normal case. Assume *µ*Independence
again, and consider the subset of the first experiment in which we have
collimation on the right, as well as the left--in other words, in which we
impose a final condition, as well as an initial condition. In this case, we
have no scattering, despite *µ*Independence. Again, it is no use saying that the
imposition of the final condition amounts to a denial of *µ*Independence: if that
were true, the asymmetry of *µ*Independence in the normal case would amount to
nothing more than the presence of a low-entropy initial condition, in conflict
with the supposition that *µ*Independence differs from *H*-Independence.

In other words, *µ*Independence is both insufficient and unnecessary to explain
the phenomena observed in these scattering experiments. 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
(consisting in the fact that the beam 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 *µ*Independence.

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Conceding that *µ*Independence is lawlike does not improve its prospects, of
course; it simply 'fesses-up to the principle's current role in microphysics.
In one important sense it makes its prospects very much worse, for as a lawlike
principle, *µ*Independence 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 *µ*Independence turns out to
rely on a different asymmetry altogether.

What are the options at this point? First, we might look for other ways of
defending *µ*Independence. Unless this evidence is a posteriori, 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 *µ*Independence, I suspect that the effect of further
investigation is to explain but not to *justify* our intuitions. For
example, the intuitive appeal of *µ*Independence 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 postinteractive, not preinteractive. The exact
explanation of this asymmetry is rather 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've argued elsewhere (1996, 181-4), some apparent
postinteractive 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 thus 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 *µ*Independence is thereby accounted for, but in a way
which does nothing to clarify the puzzle of the photon case.

Another response to the puzzle would be to try to restore T-symmetry in
microphysics by excising postinteractive correlations, rather than by admitting
preinteractive correlations. The standard model of quantum mechanics might be
first in line, for example. The surgery required is likely to be rather
radical, however. Without postinteractive correlation of some sort, how is it
possible for a measuring device to record information about an object system?
That aside, the move seems misguided. It does nothing to justify *µ*Independence,
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 *µ*Independence might
indeed fail in microphysics. 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 up to this point, my references
to quantum mechanics have been somewhat inessential. The standard model of
quantum mechanics provides the most vivid examples of an asymmetry we find it
easy to take for granted in microphysics, but the case against this asymmetry
has been 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 *µ*Independence constitutes a
prior constraint on the interpretation of quantum mechanics.

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More recent arguments for nonlocality (the GHZ cases; see e.g., Clifton,
Pagonis and Pitowsky 1992) also depend on this independence assumption. Without
*µ*Independence, then, there seems to be no firm reason to think that quantum
mechanics commits us to nonlocality. Many commentators have noted that in
principle, the Bell correlations are easily explicable if hidden common causes
may lie in the future, as well as in the past. My point is that if
*µ*Independence is rejected on classical grounds, this is precisely what we
should expect.

There is a similar impact on the no hidden variable theorems (e.g. Kochen and
Specker 1967), which argue that no system of pre-existing properties could
reproduce the predictions of quantum mechanics, at least in certain cases.
*µ*Independence serves to justify the assumption that a single hidden state must
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. (In Bohm's 1952 hidden variable theory, the
trick is to allow measurement to have an instantaneous effect on the hidden
variables; again, however, *µ*Independence underpins the assumption that the
effect must be instantaneous, rather than advanced.) Abandoning *µ*Independence
might thus resuscitate the hidden variable approach, and with it an old
solution to the measurement problem: If collapse corresponds merely to a change
in information, it is unproblematic.

Thus *µ*Independence plays a crucial role in the main arguments taken to show
that quantum mechanics has puzzling nonclassical consequences. Imagine how
things would have looked if physics had considered abandoning *µ*Independence on
symmetry grounds, before the development of quantum mechanics. Quantum
mechanics would then have seemed to provide an additional argument against
*µ*Independence, by reductio: given quantum mechanics, *µ*Independence implies such
absurdities such as nonlocality and the measurement problem. Against this
background, then, experimental confirmation of the Bell correlations would have
seemed to provide empirical data for which the best explanation is that
*µ*Independence does fail, as already predicted on symmetry grounds.

Of course, from a contemporary standpoint it is difficult to see things in
these terms. Leaving aside our intuitive commitment to *µ*Independence, the
quantum puzzles have lost much of their capacity to shock--familiarity has bred
a measure of contentment in physics, and the imagined reductio has lost its
absurdum. Regaining a classical perspective would not be an easy step, or one
to be attempted lightly, but it does seem worth entertaining. By abandoning a
habit of thought which already seems to conflict with well-established
principles of symmetry, we might free quantum mechanics of consequences which
once seemed intolerable in physics, and might do so again.

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Bell, J., Clauser, J., Horne, M. and Shimony, A. (1985), "An Exchange on Local
Beables", *Dialectica* 39:86-110.

Bohm, D. (1952), "A Suggested Interpretation of Quantum Theory in Terms of
Hidden Variables", *Physical Review* 85:166-193.

Clifton, R., Pagonis, C. and Pitowsky, I. (1992), "Relativity, Quantum
Mechanics and EPR", in D. Hull, M. Forbes and K. Okruhlik, (eds.), *PSA 1992,
Volume 1*, Chicago: Philosophy of Science Association, pp. 114-28.

Kochen, S. and Specker, E. P. (1967), "The Problem of Hidden Variables in
Quantum Mechanics", *Journal of Mathematics and Mechanics* 17:59-87 .

Penrose, O. and Percival, I. C. (1962), "The Direction of Time", *Proceedings
of the Physical Society* 79:605-616.

Price, H. (1996), *Time's Arrow and Archimedes' Point*, New York: Oxford
University Press.

©Huw Price, 1996.

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