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Part of the problem, I think, stems from a possible confusion about the foundational problems of QM. Price groups the problems of nonlocality and measurement together in a peculiar way. For instance, he understands mInnocence to give rise to all of the puzzles commonly associated with QM, such as nonlocality, indeterminacy, etc. (126). Retraction of that principle is viewed as a general panacea for all the ills of a quantum world. This is mistaken. The problem of nonlocality concerns the implications of Bell’s Theorem and the problem of indeterminacy the implications of the measurement problem. Rejecting mInnocence doesn’t help us see that we can solve the measurement problem.
The measurement problem consists of the following three inconsistent propositions:
1) The wavefunction formalism of QM is representationally complete, i.e., something is an element of reality iff it is represented by the wavefunction.
2) The wavefunction always evolves according to a linear equation of motion.
3) Measurements have determinate outcomes.
If we grant all three of these propositions then systems in microscopic superpositions will (when measured) balloon into macroscopic superpositions of the sort made famous by Schrodinger’s cat.
Contrary to what Price suggests, rejecting mInnocence doesn’t solve this problem. Nor does rejecting mInnocence open the door to the rejection of any of these propositions, since the denial of each of them has been well explored. Price obviously wants to deny proposition 1). The rejection of mInnocence, or my alternative characterization of the temporal bias, shows those denying 1) that the hidden variables might lie in the future light cone of the particles. If the rejection of the temporal bias opens the door to anything, it is to spatially local hidden variable theories, not to hidden variable theories in general.
As I said, BCQM is a promising schema, but it is not a full-blown interpretation of QM. To reach that status, those denying 1) must supplement the QM formalism with an ontology and with some plausible physical laws describing how this ontology behaves. This is a highly non-trivial task, requiring that one devise a ‘natural-looking’ theory that reproduces the phenomena described and predicted by QM. No one has yet done it for BCQM, and many questions about such a theory arise. Three that immediately strike me are the following. First, it appears to be impossible to use the nonlocal correlations of QM to send superluminal signals, i.e., there is no Bell telephone. Why is this so according to BCQM? Second, the nonlocal connections enforce the conservation of spin and other quantities between the two wings of a Bell-type experiment. Without this nonlocal connection, why is spin conserved according to BCQM? Are these conservation rules derivable from BCQM, are they imposed by the adoption of extremely special initial conditions, or must we take them as basic? If the last, should we still consider the theory local? Third (and this is related to the first), what are the probabilities in QM probabilities of in BCQM?
8. Are the Asymmetries of Dependence in Us or in the World?
Widespread dissatisfaction with the Tories caused the Labour landslide of 1997; the landslide didn’t cause the dissatisfaction. In this case and in an indefinite number of similar ones we meet our strong intuition about the asymmetry of causation. Effects never, or hardly ever, precede their causes. Note that this asymmetry presupposes a further asymmetry, that the cause-effect relation is itself asymmetric. If we couldn’t already distinguish causes from effects it wouldn’t make sense to ask about the direction of causal transmission. What explains these two asymmetries? Hume famously tied the two asymmetries together by linguistic convention. What distinguishes causes and effects is that the term ‘cause’ (‘effect’) refers to the earlier (later) member of a pair of causally related events. So of course causes precede their effects! The difficulties with this view are that it seems both too weak and too strong. It is too weak because it makes it merely a linguistic matter that we can affect the future but not the past. It seems too strong because it makes backwards causation logically impossible. In Chapters 6 and 7 Price advances a sophisticated version of Hume’s conventionalism and tries to answer these two objections.
Price answers the first problem by “beefing up” the conventionalist strategy. He presents a theory of causal asymmetry that grounds the asymmetry in our perspective as agents. The key to explaining the above two asymmetries lay in the fact that deliberation seems to be essential to being an agent in the world. Arguably, deliberation is an intrinsically asymmetric process; moreover, we deliberate about what to do in the future and not the past. This asymmetry seeps into our view of the world and causes us to see the world through a temporally asymmetric ‘lens.’ The asymmetry of causation is a projection of this internal asymmetry upon dependencies that we find in the world. Here Price does an admirable job of persuading people (like myself) who are, perhaps by temperament, reluctant to place the asymmetry of causation “in us” rather than “in the world.”
The discussion then turns to counterfactual dependence, rather than simply causal dependence. Price explains the asymmetry of counterfactual dependence, the fact that the future seems to depend on the past but not vice versa, in terms of the asymmetry of agency. We think that counterfactuals like
(1) If a huge asteroid had not struck the Yucatan region 65 million years ago, then the dinosaurs would not have disappeared so quickly
are true, but that counterfactuals like
(2) If the dinosaurs did not disappear so quickly, then a huge asteroid would not have struck the Yucatan region 65 million years ago.
seem false. In judging the truth of counterfactuals we seem to use an asymmetric principle. We hold fixed the course of events prior to the time mentioned in the antecedent and consider the subsequent course of events. This is why (1) but not (2) seems correct. Price then argues that this “hold the past fixed” convention follows from our role as deliberating agents.
How do we answer the second problem for conventionalism? As Price agrees, many philosophers have argued convincingly that backwards causation is at least logically, perhaps physically, possible. It seems wrong to rule this out by fiat. In response Price develops a loophole available to him thanks to M. Dummett’s 1964 classic discussion of backwards causation. Dummett notes that the “bilking arguments” against backwards causation can be circumvented when knowledge of the earlier effect is not accessible to the agent when the cause is to be ‘bilked’. Dummett asks us to assess counterfactuals not with the “hold the past fixed” convention, but instead with “hold fixed what we have epistemic access to at the time of the antecedent condition”. Because we know much more about the past than the future, usually the two conventions will agree in their judgments. That is, the past and what we have epistemic access to will largely coincide. But in cases where we are ignorant about the past Dummett’s convention will allow the past to depend upon the future. The state of a photon from the sun impinging on my sunglasses may depend on the “setting” of my sunglasses. This is how Price escapes the second problem for conventionalism. By using Dummett’s convention instead of the “hold the past fixed criterion”, we free dependence from a definitional tie to the past. No longer need the conventionalist rule out backwards dependence as a logical impossibility.
While I sympathize with the conventionalist strategy, I would like to express a reservation I have about this loophole. I agree that the knowledge asymmetry certainly plays a role in the explanation of the asymmetry of counterfactual dependence (and perhaps vice versa). However, I’m skeptical that it is as crucial as Price needs in order to exploit this loophole. Adopting Dummett’s convention makes the asymmetry of dependence wholly a matter of the information available to an agent at a time. This doesn’t seem right. My ignorance about regions of the past doesn’t incline me to think that region is “open” like the future is “open.” The fact that I don’t know the state of an incoming photon only implies that I can’t run a bilking argument against the supposition that my subsequent measurement of the photon affects its earlier state. But the fact that I can’t prove there is no backwards causation happening doesn’t mean that I think there is backwards causation occurring. I’m completely ignorant about vast periods of history, but I don’t think anything I do now can affect any of it. I don’t know anything about these periods, nor do I deliberate about them in the same way I deliberate about how to “change” the future. Dependence just doesn’t seem to track knowledge in the right way to exploit this loophole. If this is right, and closes the loophole, then the conventionalist still has some work to do.
Price makes a strong case for thinking that agents in a world like ours will project their “internal” asymmetry onto the world. On this view the asymmetry of dependence has subjective origins (although Price accounts for these, as above, with some objective facts). Isn’t that only half the story? I admit that I still hanker after a more objective account of the asymmetry of dependence. I don’t have the full story, but it seems to me that we do not explain the asymmetry of counterfactual dependence merely by the fact that our asymmetric world produces agents who color the world in asymmetric ways. Thermodynamic behavior not only shapes asymmetric agents but it also provides an objective asymmetry in the world. Perhaps it provides the resources for claiming there is a sense in which the future objectively depends on the past in a way the past doesn’t depend upon the future. The thermodynamic asymmetry implies, for example, that the future behavior of macroscopic systems is extraordinarily stable against perturbations whereas their past behavior is unstable against perturbations. Obviously I cannot develop this idea here, but the thought is that this kind of objective asymmetry is part of the explanation of why we believe the future is mutable and the past is not -- the future is mutable in a sense the past is not thanks to the low entropy initial condition. Given the close connection between the arrow of mutability and the asymmetry of counterfactual dependence, it is natural to suspect that the latter asymmetry has objective as well as subjective roots.


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Callender, C. 1995. “The Metaphysics of Time Reversal: Hutchison on Classical Mechanics”, British Journal for the Philosophy of Science, 46: 331-340.

_______. 1997a. “What Is ‘The Problem of the Direction of Time’?”, Philosophy of Science 64 (Proceedings):

______. 1997b. “Review Symposia: The View From No-when”, Metascience, 11, 68-71.

______. 1997c. Explaining Time’s Arrow. Ph.D. thesis, Rutgers University.

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Price, H. 1996. Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time. New York: Oxford University Press.

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Vaidman, L. 1996. “Defending Time -Symmetrized Quantum Theory”, LANL preprint quant- ph/9609007.

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1 Review of Huw Price [1996]: Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time, Oxford, Oxford University Press.

2 I am very grateful to Colin Howson, Douglas Kutach, Paul Lodge, Barry Loewer, and John Worrall for helpful suggestions and to Huw Price for many useful conversations over the past few years.

3 For excellent presentations of Boltzmann’s views, see J. Lebowitz 1993 and J. Bricmont 1997. Evidence of the confusion still surrounding Boltzmann’s theory can be found in the replies to Lebowitz 1993 in the Nov. 1994 Physics Today.

4 Quantum field theory and the so-called CPT theorem suggest that neutral kaon decay is non-TRI. Because this departure from TRI is so slight and so puzzling, Price proposes to leave it to one side throughout the book. One might object that laws of nature do not have their symmetries in degree: a little bit of non-TRI makes the laws non-TRI. Though this is certainly true, I would not recommend an uncritical acceptance of the non-TRI of neutral kaons. One wants some assurance that the concept of TRI used in the CPT theorem is the same as that used in the present context, for instance. Since this topic and others have not been investigated, Price’s strategy is perhaps not unreasonable.

5Contrast with Maxwell’s equations, which are TRI but have asymmetric solutions, the retarded and advanced ones. Because they describe processes evolving in time, these two solutions really are different, unlike ‘retarded’ and ‘advanced’ universes.

6 This is the origin of the so-called ‘problem of time’ in quantum gravity; see Callender and Weingard 1996 and references therein.

7 A. Kent 1997 has recently shown that we could use this statistical pre-effect to send superluminal signals. Indeed, if we can detect any regularities in the final state of the universe then in principle we may be able to send superluminal signals. Indeed, many wild possibilities open up in a Gold universe (or at least one with a time-reversed galaxy in it); for a great science fiction story involving one such possibility, see G. Egan 1995.

8 One related issue I haven’t space to discuss is the question of whether the Past Hypothesis should be treated as a law of nature. If we ought to consider it lawlike, then this would seem to shelve the demand for its explanation. As I have pointed out earlier, certainly it seems like it would emerge as lawlike according to D. Lewis’ 1986 ‘best-system’ theory of lawhood (Callender 1997c). According to this theory (which is a development of J.S. Mill’s and F.P. Ramsey’s theories), the laws of nature are the axioms of those true deductive systems with the greatest balance of simplicity and strength. Since the Past Hypothesis conveys an awful lot of information about the world with minimum specification, it seems likely that it would emerge from the ‘best-system competition’ as a law of nature.

9 The new dynamics posited by the GRW interpretation of QM has the consequence of eliminating special initial conditions (Albert 1997). It does not eliminate the need for the Past Hypothesis, but it does imply that microstates underlying macrostates need not be ‘typical’(in the sense described in section 2). In this case the new dynamics enters as an interpretation of QM rather than a replacement of it.

10 Price agrees that the way the world is plays a role in the creation of the temporal bias. That we wear temporally asymmetric ‘blinders’ has an objective basis in the various physical asymmetries. What I am pointing out is that the bias is not solely the result of us wearing these blinders; someone not wearing these blinders might be biased in favor of initial conditions (rather than final or initial and final conditions) due to the success we have had theorizing with them.


11 Price seems to waver on whether he thinks he is offering a genuine interpretation of QM or not. In fn. 8, Ch. 9, he sounds like he is not; in fn. 22 he sounds like he is. That his ‘interpretation’ doesn’t yield answers to the questions I ask later suggests that fn. 8 is closer to the truth.



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