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5HYLHZ>XQWLWOHG@ $XWKRUV$OOHQ6WDLUV 6RXUFH6\QWKHVH9RO1R-DQSS 3XEOLVKHGE\Springer 6WDEOH85/http://www.jstor.org/stable/20116866 . $FFHVVHG Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=springer. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Springer is collaborating with JSTOR to digitize, preserve and extend access to Synthese. http://www.jstor.org REVIEW The Structure and ESSAY* R. I. G. Mechanics, and 1989 Hughes, Cambridge: Philosophical on BelVs Theorem, Consequences Theory: Reflections of Quantum James T. Cushing and Ernan McMullin. Notre Dame: University of Notre Dame Press, 1989. Interpretation of Quantum Harvard University Press, on the philosophy else had been published of quantum in 1989, these two books would have made it a good year. to the foun has written the best self-contained introduction Hughes to dations of quantum mechanics and the volume appear, yet by Cush an and is McMullin accessible but ing sophisticated snapshot of philo on a classic. Bell's that to theorem is become sophical thinking likely For the reviewer, the two books make an appealing pair. Hughes has an essay in the Cushing and McMullin volume (henceforth C&M) that If nothing mechanics sketches his own position, but also amounts in some ways to a reply to a various of the papers in the collection. I will begin by discussing selection of the essays from C&M, all of which seem to me to raise issues that bear interestingly on Hughes's position. At that point, I will take up Hughes's view, weaving together his essay in C&M with the more developed in his book. position Philosophical Consequences of Quantum Theory consists of thirteen a with papers on Bell's theorem, essay by James together background a a at historical discussion of action distance Cushing, by Ernan McMul lin and an extensive Some of the have appeared papers bibliography. elsewhere are new and part of Mermin's) but most contribution, (van Fraassen's to this collection. I will single out three papers for special attention: Bas van Fraassen's, Arthur Fine's, and Paul Teller's. In the I will refer to several of the other essays. I will not mention process, I will not be discussing the contribu every essay in C&M. In particular, tions by Abner Michael Linda Don Ho Redhead, Wessels, Shimony, ward and Henry Folse, nor the introductory and concluding essays by Cushing Synthese and McMullin 86: 99-122, 1991. respectively. However, I don't think there are 100 REVIEW ESSAY a I have made is mostly any bad essays in the book, and the selection reflection of my idiosyncrasies. Van Fraassen's contribution is a somewhat version of his expanded of Realism: Epistemological of Bell's 1982 'The Charybdis Implications an on with based 'EPR: his 1985 When together appendix Inequality',1 Not a Mystery?'. is a Correlation The thesis of "Charybdis" is that a violations of Bell's confirmed strong inequality provide experimentally calls epistemic realism. This is the argument against what van Fraassen view that we can have reasonable about future regularities, expectations in particular, of correlations, about the persistence only if we have some is that under reasonable that there causal mechanism certainty In the case of the Bell-type the writes the regularities. experiments, are of correlations between separated regularities pairs space-like causal account would events, and van Fraassen urges that a reasonable sense - an event have to appeal to a common cause in Reichenbach's in the past that renders the correlated He gives an elegant demonstration events that stochastically there are no independent. such common causes. Let us concede that there can be no (as virtually everyone does) common cause explanation for failures of Bell's Van inequality. so long as our moral: Fraassen thinks this carries an epistemological are based on well-supported theories, we are justified in expectations or not a causal account to is whether regularities expecting persist or even possible. In the end, this might be right, but not available in a way that conflicts with the deep intuitions of epistemic necessarily van Fraassen In "Charybdis", realism. realists as depicts epistemic but surely that is too strong. insisting on causal accounts of correlations, The strongest reasonable position would be that in order to have reason we need reason about the persistence of correlations, able expectations that there is some account of the correlations, able certainty whether turn out to be a it be causal or of some other form. And it might constraint on the confirmation of theories that they either embody or are consistent with some account of the correlations they predict.2 I think there is an interesting the point issue here, but let us waive a amounts to for now. Van Fraassen's in C&M concession appendix that not all accounts of correlations need be causal. He lists five ways than common cause in which correlations have traditionally been us are two most to and logical The of interest coordination explained. link - to Van takes coordination direct causal Fraassen i.e., identity. other REVIEW 101 ESSAY and require matter or energy to travel from one location to another, are space-like if the two locations he thinks that this is incoherent events he adds, "Correlations between distant Further, separated. same are to not of the extended less facto parts entity happening ipso are What that remains, then, mysterious" explanations appeal (p. 112). to "logical of this matter is in the 1985 identity". The full discussion is based. I would like to turn to that paper on which the "Appendix" account, which I find quite curious. identity explanations proceed by showing that the correlated are aspects of a single variable. Here's how van Fraassen seem to work for quantum suggests that this might systems. Suppose that A and B commute, have a set {</>,-}of common such eigenstates Logical variables that A(f)i = a?(t>i, B(?>? = />/</>,, and the that 4> = 2/c? suppose measured jointly, we can be certain for some k, the joint outcome will be is that there is a maximal quantity C distinct. Now a's, as well as the 6's, are all </>,-.In that case, if A and B are that the results will be correlated: (ak, bk). The apparent explanation such that A = /(C) and B = g(C), and the measurements of A and B are just partial measurements of C. us on sort not Van Fraassen to this that of "is tell goes explanation This is because embarrassed (1985, p. 118). by spatial separation" AI and IB for systems X and Y (I have deleted observables the tensor are are and both of AB. An functions product sign) always compatible, choice of state will produce correlations of the sort dis appropriate cussed above, and once again, it will apparently be no mystery that the are correlated: results of AI and IB measurement in measuring AI and of C = AB. IB, we are really just making partial measurements Van Fraassen to the thinks that this account breaks down. Return value z, then we could claim general case. If C had a pre-existing that the correlated and y = g(z) simply reveal partial values x = f(z) information about z. But suppose C has no such pre-existing value. Then we can't account for the x-result of the A-measurement by saying that if we had measured z, and x is just C, we would have observed nor can we can we assume that B. such about Worse, say any /(z), thing have ready-made values if we adopt a contextual quantum observables hidden variable theory, but to accept such a theory is ... to admit a radical and unverifiable difference between observables and the of Hermi among algebra . . . tian operators (1985, p 121) the relations 102 REVIEW ESSAY I find much about this discussion the initial, gen puzzling. Consider eral case of A, B, and C. At one point, van Fraassen suggests that there is something to that mechanics quantum gives the putative peculiar we its Whereas might expect in general that co explanation purchase. a not would among observables, measurablilty logical connection imply the world ismuch more "sub specie the quantum mechanical formalism, intuition and internally connected than our general tightly organized is there Nonetheless, might suggest" (1985, p. 118). nothing peculiarly to make the present about the intuitions needed quantum mechanical no reason and is also values should there run, why pre-existing example a thoroughly be required. Consider classical device: a tetrahedral die, with faces with one, two, three or four spots on them. Now consider two experiments. The first, A, consists of tossing the die and recording the number of spots mod 3 on the base of the die. The second, B, consists of tossing the die and recording the number of spots mod 2 on can be performed in these experiments jointly. Now nor us not A will B the result tell the result of of general, knowing as the reader can easily check. But suppose we have so vice-versa, of the roll contrived the state of things that even though the outcome is not completely the side that ends up as the base will determined, have either one or two spots on it. In that case, the results of A and B will be correlated: A will have result 1 iff B has result 1; A will have result 2 iff B has result 0. This is no mystery. When we perform A, we the base. Clearly, about the result of the experiment information C, i.e., get partial the number of spots on the base. tossing the die and simply noting about the result of Similarly, performing B gives us partial information C. If the state of things restricts the possible outcomes appropriately, no A and B will be strictly correlated. But notice: there is absolutely need to assume that there is a pre-existing fact about what the result of C was to be before the die was actually tossed, or that in tossing the die, we are discovering facts about the pre-existing value of some variable. to has said points My point thus far is that nothing van Fraassen at at and least the mechanical, further, anything peculiarly quantum of pre-existing values is a red herring. We general level, the question can describe a classical case that is like the quantum one in relevant but for which a and includes the feature of indeterminism, respects, is of correlations identity" explanation "logical perfectly acceptable. REVIEW ESSAY 103 in the same way in the quantum case? Why isn't Why can't we proceed this a perfectly good way to account for the correlations? An objection that won't work is that in the quantum case, we are and this measurements, presupposes pre-existing supposedly performing that quantum measurements values. We needn't presuppose merely For all we have said - for all we know reveal pre-existing information. - a information is like a roll of a die, with quantum measurement like a roll of created in the process. Suppose a quantum measurement, a die, is a process in which a system comes to be in a certain condition, events and hence in which an event from a certain range of possible will occur, though precisely which event is not, in general, fixed. The state places restrictions on the range of possibilities open to quantum the system, but quantum like other rich any theory, provides theory, resources for individuating events. In the case van Fraassen describes, the theory tells us that the event of the system coming to display A = = a? is the same event as the event of the system coming to display B to the third observable C is not b?. In fact, we see that the reference crucial; what is crucial is the identity of certain possible events. It seems that we really can explain some correlations among chance to the hidden variables, without outcomes, by appealing identity of events. Without there is no reason further argument, certain possible case. However, I want to look why we can't do this in the quantum more closely at van Fraassen's discussion of contextual hidden variables. We will find that he is straining at a gnat while standing ready to swallow a camel. Let us grant that the "radical and unverifiable difference" between and the algebra of hidden variables is a serious the algebra of operators But suppose we could somehow know that objection. epistemological structure really is correct. That leaves the real problem: the contextual in a very peculiar way. There the hidden variables will be non-local a will be pairs AB, AD such that AB has value associated with the pair to and a+a'. of numbers Now (a,b), AD is associated with (a',d), measure "here" and you use a B-apparatus AB, I use an A-apparatus and you use your D "there". To measure AD, I use my A-apparatus, I am partially measuring observable apparatus. Thus, which maximal depends on which apparatus you set up. And for the hidden state under this translates into a constraint on results: what result consideration, my apparatus will display depends on what apparatus you set up. But 104 REVIEW how does my apparatus "know" ESSAY what quantity is undergoing partial measurement? already underlying point here is actually one that van Fraassen AB and AD are non-local This suggests that the quantities. sort of extended system is a particular entity, (and peculiar) underlying and the displays of results in the two wings of the experiment are, in to parts of the same extended effect, "distant events happening entity" as van in such But Fraassen (C&M p. 112). pointed out, correlations The made. a case are not automatically unmysterious. The local entities. They are connected presumably, contact" with some aspect of a single entity, to tell the apparatus which local information should be looking at. So the real problem it is that variables is not their unverifiability; measuring devices are, by virtue of being "in but there is no obvious feature of the entity it with contextual hidden seem they incapable of their explanatory task.3 performing hidden variables We will return to contextual later. I would like to move on to a discussion of Arthur Fine's paper, 'Do Correlations Need to Be Explained?'. Fine's target is explanatory which holds essentialism, that correlations require explanation regardless of the scientific context essentialists talk of "new and quasi they arise. Explanatory or odd 'pas 'influences' processes (maybe funny mysterious physical to in of Bell Fine the failure the response inequalities. sions')" (p. 180) believes there is no need to invoke such oddities. violates The kernel of the argument is simple: quantum mechanics even no term when is in the there interaction the Bell inequalities of the two particles. Fine thinks that philosophers should Hamiltonian take their lead from the theory and stop positing influences, but he also - a offers a scheme for thinking about the experiments scheme accord in which there are no cross-wing influences of any sort, and thus, ing to which one that satisfies what Fine calls strong locality (SLOC). out The model is simple enough. Think of individual measurement comes as coming about "m a perfectly random way" (p. 184). Suppose in the A-wing, with Ai is measured the B-wing. Fine assumes, sensibly, ences the other. The have and B{ is measured in choice of setting influ the Bx measurement itself and the left over would be between dependency . . randomness that the outcome the Ax measurement. However,. implies . . .Thus . . .we . . . on which measurement not depend is performed in the B wing a framework in which is satisfied, 184-5) [SLOC] (pp. possible outcome of does result plus, that neither REVIEW 105 ESSAY it is easy to describe random sequences of outcomes that link we a to Bell's So have violate together inequality. apparently purely local model for the correlation experiments. there is the key here. In an indeterministic world, Indeterminacy can events undetermined that exhibit be of sequences individually surely an overall statistical pattern. But, Fine adds, Further, . . . are just probabilistic two sequences of events between patterns Why, from an indeterminist random should the fact that there is a pattern between perspective, to than the fact that there is a pattern internal sequences any more require explaining Correlations the sequences themselves? (pp. 191-2) forms part of the "ideal of natural order" (a phrase that in terms of which quantum from Toulmin) borrows theory is the correlations of quantum framed. Thus conceived, Fine maintains, than do uniform motions in New theory no more call for explanation tonian and post-Newtonian physics. In 'Antinomies This may puzzle readers of Fine's earlier work. of and and 'Correlations Physical Locality' Entanglement' (1981), (1982) Fine claimed that responsible indeterminism (see especially Fine 1981, of Bell's violations pp. 544-8) does not encompass inequality. What's different now? Fine, call two runs of a Bell-type Following adjacent if experiment one in in be differ the Let the Ai, A2 wing. they setting settings on the an A^ run the of and for Bi, Thus, B2. A-wing similarly experiment, is adjacent to an AXB2 run. And call two adjacent runs entangled if the Indeterminism Fine for the shared observable differ. Even ifA{, A2, sequence of outcomes to satisfy Bell's it would be very Bi and B2 were chosen inequality, that the four runs of the experiment would be untangled, but unlikely so long as Bell's in inequality stands, the statistics could be exhibited runs. However, if the inequality is violated, is untangled entanglement In 'Antinomies of Entanglement', Fine found this genuinely required. seem to have p. 743). Two considerations (see especially puzzling change his mind. first is the fact, noted above, that, Bell's inequality aside, the are minute. Violations odds for finding untangled of the experiments at in these tiny odds vanish (p. 189). Looked inequality simply make this way, failures of Bell's inequality seem less impressive. The second consideration has to do with hypothetical about a single run. questions helped The Suppose I performed a sequence of A^ measurements. Would the 106 REVIEW ESSAY instead? It Ai sequence have been the same if I had measured AiB2 is tempting to think that locality says yes. One might think that if the this would amount to an influ Ai sequence could have been different, ence of the distant setting on the local outcomes. Fine disagrees. If the are undetermined, outcomes there is no fact about what would have in any respect, local or remote. To had things been different happened seems to Fine to require determinism, or something insist otherwise like it; indeterminism blocks the derivation of a Bell inequality. This suggests weakening the premise: say simply that the same A! result might have occurred if the B-setting had been different. Fine that this won't do. True, the "might" statement doesn't presup and is a plausible of locality. But it is consequence pose determinism argues too weak. might not probability "wrong". In any actual run of an experiment, quantum mechanics for any finite experiment there is a indeed, come out that the the will numbers given by theory to So counterfactual derive Bell's strong enough reasoning be verified; counterfactual strong premises; requires overly inequality reasoning from appropriately weak premises doesn't imply the inequality. I'm puzzled. Call the principle that the result here would have been was in the setting there the "would" the same if the only difference Call the similar principle with "would" replaced by "might" principle. to a statistical the "would" principle the "might" principle. Appending not does entail that the statistics of any theory particular experiment will come out right. The interesting question is whether the "would" is compatible with the statistics coming out right. For quantum principle see David Mermin's it isn't. (For a very nice demonstration, mechanics, 'Can You Help Your Team Tonight essay, TV?') Now by Watching the "might" principle if we allow a doesn't imply a Bell inequality violation of the quantum statistics. But neither does the "would" prin to its ciple. If we offer the "might" principle the same courtesy extended brasher brother, perhaps we will get the same result. In fact, Mermin's section that this is so. (See pp. 47-9, suggests concluding strongly ('Quantum Non 47.) Further, Henry Stapp argues explicitly we and the of that if Nature') locality require the quantum Description statistics to be verified, we can extract a contradiction from locality and especially the "might" principle. I am not sure whether he would compare have every is correct. To convince me, Stapp's argument an explicit and semantics for counterfactuals move even to it But argumentative explicitly. though invoke REVIEW 107 ESSAY I'm not certain that Stapp is right, I'm not certain that he's wrong. The counterfactual here are profoundly questions tricky, and I don't think treatment of them is sufficiently Fine's to settle the matter. detailed But rather than agonize over counterfactuals, I would like to approach the question of "influences" in another way. Jon Jarrett has pointed out that the usual locality condition is the of a condition he calls locality, and another that he calls conjunction A Guide to the Implications' completeness. (See his 'Bell's Theorem: for a nice summary.) I will use Shimony's (1986) terms, parameter independence independence (PI) and outcome (OI). PI requires that the local outcome be stochastically of the distant setting. In independent the elegant notation that Mermin the for volume, proposed (PI) = p(x/i, j, A) p(x/i, A)p(ylu j, A) p(ylj, A) and B-wing outcomes, / and ; are (x and y are, respectively, A-wing on A is the and and Fine focuses whether B-wing settings, state). A-wing in the distant influence local results. However, changes setting quantum mechanics satisfies PI, and that may explain why Fine doesn't detect violations of locality. On the other hand, quantum states violate OI: (OI) = p(x, y/i,j, A) p(x/i,j, X)p(y/i,j, A).4 Thus a more fruitful question is whether violations of OI embody some sort of influence of events in one wing on events in the other. I think reasons for answering yes. An important one goes there are plausible cause. In 'A Space back to Reichenbach's principle of the common to the Bell Inequalities', Time Approach Jeremy Butterfield gives the following, slightly weaker statement of Reichenbach's principle: ... if x and y are correlated without direct causation, there is in their common past an event z that screens off. (p. 115) then them Butterfield is not willing simply to embrace this principle, he Although that it can be made plausible the argues convincingly by associating screeners-off with large regions of space-time.5 But from Reichenbach's principle, we have a corollary: If x and y are correlated, common past that screens by a direct causal link. and there them off, is no event z in their then they are connected 108 REVIEW ESSAY In one sense, to avert to this principle is to beg the question against the burden of proof lies. Fine. But there is a serious issue of where The principle of the common cause is a highly general one that serves us well we apply it to Fine's in a wide variety of contexts. When we that violated. conclude SLOC is True, quantum model, proposed term in the Hamiltonian, but mechanics does not posit an interaction are causal connections that may just be to say that certain fundamental a structure in of of the itself. the Further, theory forthcoming part deep shows that on David Lewis's analysis of causation, article, Butterfield a causal link between events in the two failures of OI do constitute is not prepared Butterfield Again, simply to embrace Lewis's is and highly general. that but analysis analysis, plausible, sophisticated that Fine has not made his case. Even So I maintain though the jury influences. may still be out, a prima facie case can be made for non-local There are, of course, reasons to doubt that the quantum correlations are causal connections. A bad one is that faster-than-light causation is a bad reason because This violates (I claim) no such relativity. conclusion follows from relativity. What relativity requires is that real Lorentz be invariant under transformations. For causes, facts physical to reverse or transform away a that it must be impossible this means If it were part of the causal connection transformation. by a Lorentz that the cause must unambiguously of a causal connection concept wings. the effect in time, then relativity would rule out superluminal precede connec causes. But I am deeply suspicious of this supposed conceptual to be causal, there tion. What ismore plausible is that for a connection cause and must be an unambiguous of some sort between distinction on than other effect. If the distinction could be made temporal grounds, causation. The more plausible this would leave room for superluminal is that failures of OI are symmetric and causation relativistic difficulty as usually understood this is open to challenge, however. isn't. Even as For example, Richard Healey conceives of the quantum correlations to causal processes" 1989) and is attempting (Healey "non-separable work out the issues in detail. are So what's the point? The point is that the quantum correlations - so much so that on some accounts very much like causal connections talk of "passion at a they are causal. This suggests that when people distance" or the like, they are not being obscurantist; they are trying to on the one hand, acknowledging the important walk the line between, and more familiar causal between similarities correlations quantum REVIEW 109 ESSAY to the differences and on the other, giving due weight connections, and the ones on which traditional analyses these phenomena between of causation were based. Fine admits in a footnote (p. 190) that the matter of "influences" needs investigation, but he doesn't give the point in his discussion. nearly enough weight A related point about causation and indeterminism. Surely there is as an ideal of on stress about Fine's indeterminism something right to terms with quantum mechanics will require natural order. Coming an to terms But there is unresolved with indeterminism. ques coming a to chalk tion of how to tell when it is appropriate up surprising simply to the manifestations of the natural order. Suppose class of phenomena we discovered states that grounded "sub-quantum" superficial viola tions of OI in deep probabilistic violations of PI. This would strongly suggest that there is an influence exerted by settings in one wing on in the other. But someone might try to insist that we need not talk of influences; that there ismerely a complicated pattern among measurement not unlike the pattern and outcomes, "setting-events" outcome in the two wings of a Bell that Fine sees between sequences I don't think we would be content with this. Whether type experiment. we are Humeans about causation or whether we adopt a thicker view, our overall notions of influence and causation would not cohere with of PI. My this story. My point is not to propose looking for violations even we not of Bell's is that the violations by inequality point explain of OI as causal. It is that in trying to decide coming to see violations events are connected whether by a relation of influence, we need to look to our more general concepts of causation and influence. We may end up modifying these in the light of the theory. Or we may simply outcomes be able to use them to make clear what the theory has been saying all along. Teller as an ideal of of indeterminism Part of Fine's aim in his presentation was was intended to put us natural order it undoubtedly therapeutic; at ease conceptually correlations with the quantum by helping us to overcome aims are also habits of thought. Teller's old deterministic a different in part, but his diagnosis suggests conceptual therapeutic ailment. Teller's Inequalities', and the Bell Holism, paper is called 'Relativity, Relational aim is to explain the nagging feeling and his immediate 110 that somehow, tum mechanics. REVIEW ESSAY of Bell's violations inequality are in conflict with quan He notes that there is an extremely simple argument the assumption such a conflict. If we combine of determi that suggests nate values for quantum observables with the requirement that local not depend on distant settings, we get a Bell inequality. But outcomes on the face of it, relativity requires both the determinateness of values and the locality condition. Here's why. for determinate values is essentially the EPR argu The argument ment. By the correlations of the singlet state, we know that a measure ment here allows us to predict an outcome at a space-like there. But to is taken forbid the transmission of relativity normally superluminal information. here could not have created the value So my measurement the value must already have existed. Further, and again measure must of this value be of choice my by relativity, independent ment and locality, and hence, setting. So we have determinateness Bell's inequality, from the correlations and relativity. Teller does not think this is a valid argument. However, it is at least as plausible as the (surely very plausible) EPR-style argument on which there. Hence, it rests. Teller's project is to figure out is what has gone wrong. To do about relativity. Teller accepts Einstein's that, he has to say something is a principle view that relativity theory; "a set of general constraints must which detailed any more theory satisfy" (p. 212). For special one most constraint the is the mentioned earlier: general relativity, invariant. But our working "real" physical processes must be Lorentz theories as describing picture is more detailed. We think of relativistic at space-time the world in terms of the values of physical quantities theory. Further, points. That is, we think of relativity as a space-time "classic" relativistic theories describe processes in terms of That is, there is no "action at a distance" in space or time; are always between connections close" "infinitesimally or light-like. causal chains are always time-like finally, local action. direct points. Teller causal And calls theories Causal Theories. satisfying all of these constraints Relativistic are so we to wed relativistic As causal theories? Teller sees it, Why it is because we accept an even more basic metaphysical doctrine, which is the view that Particularism he calls particularism. . . . the world is composed ties, and that all relations of the relata, (p. 213) of individuals, that the individuals on individuals between supervene have nonrelational the nonrelational proper properties REVIEW 111 ESSAY that physical Teller doesn't think that particularism literally entails theories must satisfy contact action and no superluminal propagation, but he does believe that both of these theses are natural adjuncts to particularism. next question is a particularistic is whether quantum mechanics no. as answer is Teller's States such the singlet state theory. superposi to pairs states tions of tensor product ascribe relational properties on non and larger collections, but the relations do not supervene relational facts about the individuals. Now relational holism is compat ible with Lorentz invariance, as relativistic quantum theory makes clear. But relational holism clashes with the idea that all respectable theories must be relativistic local action causal theories, i.e., must incorporate and no superluminal This is not because relational holism propagation. or action-at-a-distance it is because superluminal propagation; posits for that doesn't allow the there be non may possibility particularism The relations between systems. supervening How does this help us shake off the grip of the EPR-style argument are to that for Bell's be told there Merely inequality? nonsupervening relations is not to be told enough. Teller doesn't address this question directly, but the answer seems to be a corollary of his treatment of the stochastic case. The standard locality condition for stochastic theories has been Factorizability. A metaphysically naive like this: go something a direct causal link or and A are sufficiently p(x,y/i,j, A) = p(x/i, A)/?(y//, A). argument from relativity to factorizability a correlation between x and y presupposes a common cause.6 But (recall Butterfield) would either if /, /, common any possible x causal link between inclusive, they encompass a direct cause. And for Bell-type experiments, and y is ruled out by the relativistic No Superluminal Propagation naivit? here resides in thinking that relativ principle. The metaphysical to be accounted for by positing either a com ity requires correlations mon cause or a direct causal link. As Teller sees it, these are presupposi not of relativity. tions of particularism; In fact, we can be more precise. We know from Jarrett that factoriz of PI and OI. We also know that quantum ability is the conjunction mechanics argues that the respects PI and violates OI. And Teller failure of OI can be seen as a failure of particularism. To see this, we need two premises: 112 REVIEW ESSAY First Assumption: When holds, nonaccidental particularism correlations arise only through (a) The action of a common cause, or (b) The action of a direct causal chain. Second Assumption: When holds, relativistic particularism causal theories exclude superluminal causal propagation, (p. 220) This yields a simple argument: of a common cause has been eliminated by mak on conditional the list of all A, ing everything possible known common causes. The action of a direct causal and unknown 2. Thus, there are no nonacci link is ruled out by assumption on A. That is, outcome dental correlations conditional inde The action pendence holds, (p. 221) are failures failures of outcome Hence, by contraposition, independence of particularism. But the perfect correlations of the EPR thought ex are special cases of the failure of outcome periment independence. out in one wing are perfectly correlated with appropriate Outcomes comes in the other not because of a direct causal link, not through a common cause, and not by the obtaining of locally definite, correlated values, but because mechanics embody the conditional probabilities a nonsupervenient relation provided by quantum the two part between icles. on his thinking that when the grip of particularism Teller writes became clear to him, his resistance to the "random devices in harmony" of Fine's 1981 and 1982 melted away.7 - as an correlation of the pair of property objective is simply a fact about the pair. This objects taken together The fact. . . need not be . . . supervenient upon some facts. There need be no mechanism can be analysed, the correlations (p. 222) nonrelational more basic, into which I find that the gestalt of Teller's view switches uncomfortably back and forth between a species of realism about relations and a deflationary view. Is the claim that there are real relations that ground and, in a or account for is it simply that the the sense, correlations, quantum REVIEW 113 ESSAY patterns among events have formal features that our classical leads us not to expect? Teller spends much time talking the experience he talks of ontological of locality of values vs. language metaphysics: or He that "relational holism holism. relational says nonsupervenience relations" takes there to be things in the world (p. nonsupervening no room. the claim think about But makes which for 223) particularism that failures of outcome just are failures of particularism. independence statistical One would expect Fine to reply that failures of outcome independence are just particular statistical patterns among events and nothing more. then we If failures of OI are ipso facto instances of relational holism, and both Hume have a grand name for a humble fact. A comparison: use the term "necessity" in talking about causation. But his opponents for is simple talk of regularities, whereas for Hume, talk of necessity it is a way of saying that something grounds the regulari his opponent, I honestly can't tell is whether relations are ties. What nonsupervening meant to be part of the glue of the universe or mere oil on troubled waters. about raises other questions The analogy with accounts of causation the nature of relational holism. The salient contrast throughout Teller's relativistic causal theories (RCTs) and nonsuperven paper is between is that (a) RCTs are particularist ient relations. The suggestion theories, causal accounts of the correlations and (b) relational holism eschews be But I find the connection (though it does not forsake relativity.) tween the principles and particularism obscure. The of RCTs quite standard relativistic construal of events as the instancing of properties But at place-times has a reasonably clear connection with particularism. are that that actually figure in Teller's the aspects of RCTs arguments I don't see that causal action is (i) "local" and (ii) subluminal. And these have any connection with the reducibility of relations. a correlation Begin with a simple question. Suppose we discovered that was not mediated i.e., that acted "at by any intervening process, a distance", but was in all other respects just like a causal connection. to a failure of particularism? Why events are "at a distance" make one? should the interpolation Why nonsupervenient events be a step in the direction series of "connecting" relations - of particularism? The possibility of such rests on the continuity But what does of space-time. Would that this amount the correlated the fact the relation a of a continuous should of supervenient an interpolation that have to do 114 REVIEW ESSAY fail if space-time with particularism? Would automatically particularism were discrete? Or would particularism events were hold if neighboring a or two? but fail when the connection connected, space-atom skips I am similarly confused about the connection between subluminal and particularism. Teller concedes propagation (p. 212) that tachyonic accounts of the Bell correlations can't be ruled out. I therefore assume that he does not want to say that tachyonic connections would amount to nonsupervenient relations. But if not, I am still puzzled about the connection between the slower-than-light signals and particularism, which after all is a view about the reducibility of relations. are causal relations not To all of this I add a related worry. Why cases of nonsupervenient Since Teller believes that failures relations? seems especially acute of OI are failures of, particularism, the question a correlation two for stochastic causal connections. Consider between cause of y. (My events x and y in which x is the complete probabilistic in part to Andrew discussion here is indebted Elby's forthcoming Then x and y the EPR Correlations 'Should We Explain Causally?') will be stochastically and there will be no event z that dependent, screens y off from x. In other words, we will have a situation that is a case outcome of So like the of failure why formally independence. in one? What between x and y a nonsupervenient isn't the relationship terms of from the supposedly causal relations distinguishes enter that failures of OI? True, failures relations into nonsupervenient are not. But of OI are symmetric, whereas, causal relations perhaps, a relation is reducible? what does symmetry have to do with whether is but my diagnosis there are answers to all these questions, Perhaps at too high a level of gen that relational holism has been formulated erality. What we need to do is look more closely at the crannies and crotchets of quantum theory itself. And with that, we turn to Hughes. is a clear, The Structure and Interpretation of Quantum Mechanics relations to the foundations of quantum me sound introduction pedagogically chanics. Part one (the first six chapters) treats the basic facts of quantum for use with under in Hubert mechanics space and is well-suited are and there are and finite The manageable, graduates. examples two six text. the Part exercises (the remaining throughout sprinkled more more covers is material and advanced self-consciously chapters) students. It will probably work best with graduate interpretive. a a at the book may look and casual is teacher, clearly gifted Hughes a a In definite it is textbook. that fact, suggest interpretive primarily REVIEW ESSAY 115 the book. Hughes's is developed essay in C&M, throughout perspective a and 'Bell's Theorem, Structural Ideology, provides Explanation', summary of many of the most important themes, as well as a perspective on Bell's theorem. I will structure the discussion by weaving back and as the forth between the book and the essay, with Bell's theorem will be to Hughes's book unless otherwise guiding focus. References indicated. Pace Fine, van Fraassen,- and Teller, Hughes thinks that quantum the What for the account is mechanics correlations. is crucial explains an explanation. his conception in providing of what is involved Two influences his view: the "Western Ontario" general quantum shape of theories. These come logical tradition and the semantic conception in the way that Hughes the idea that quantum me together develops sense. As Bub puts it, principle chanics is &principle in Einstein's theory theories "introduce abstract structural constraints that events are held to satisfy" at p. 258). Much in Hughes too 1974, p. 143. Quoted believes that mechanics structural quantum briefly, Hughes provides A principle these ground-level explanations. theory provides explana tions by "making the structural features of the models the explicit so In doing theory employs" (p. 258). (Bub ... it disassembles the black box, shows the working and puts it back together again. (C&M, p. 198) parts, is used here in the sense of abstract mathematical "Model" structures such as those studied in model theory. But these same structures are also the focus of the semantic conception of theories. So the semantic the natural setting for expounding the notion of a conception provides In the case structural explanations. theory, and for providing principle are of quantum mechanics, features of the models many important in the same structures that have been the focus of quantum embodied space, generalized logic: the lattice of subspaces of Hilbert probability measures on these subspaces and the like. of a structural explanation of the What, then, are the components There are four, dubbed Representability, Non quantum correlations? terms appear only and Entanglement. These Orthodoxy, Projectability in the essay, but the ideas are worked out in detail in the book. is just the fact that the observables and probabilities Representability on a single Hilbert of a quantum system can be represented space. This or even trivial, but chapters three and four may sound unenlightening 116 REVIEW ESSAY book make clear that this is not so. The treatment of observables in chapter three is especially nice. Here incompatible an makes but Consider very important point. any Hughes elementary and a single statis family {A,-} of, e.g., two-valued physical observables of Hughes's to represent tical state pi. It will always be possible the state and the on a single vector space. However, observables if we consider even a A and B and a pair of states pi and p2, observables pair of two-valued then unless px and p2 are related in a highly constrained it will way, not be possible to represent these observables and states on a single vector space; representability is a highly non-trivial feature of quantum systems. This theme is further developed in chapter four, 'Spin and its Repre a sentations'. Here Hughes account of how very clear gives elementary and determine the Hilbert symmetry general continuity assumptions on of electron The is, space representation symmetry spin. emphasis of course, old hat to physicists, but it has been neglected by philoso to goes on, both there and in C&M, phers for too long.8 Hughes make the point that a system can possess many of these very general in Hilbert space. Mielnik being representable an a of system that exhibits provided example possible most of the that behaviour symmetry conditions probabilistic satisfying lists for the of electron measurements, Hughes (essen probabilities spin tially continuity, invariance) but the isotropy of space, and rotational are not quantum mechanical. transition probabilities On the one hand, this emphasizes the point that Representability is a non-trivial matter. symmetries (1968) has without to force On the other hand, the additional constraint that is needed It the quantum mechanical is "natural". is that very representation a vector like be momentum, spin, angular quantity. and their representations in terms of By looking at the observables can see we as the considerations, symmetry representation intelligible I think this is part of the answer to a and, we might say, "natural". that we raised in connection with Fine, namely, when it is a some to declare that is manifestation just appropriate phenomenon of "nature". Begin by recalling an example that Fine mentions, but that Teller also appeals to (pp. 222-3). This is the switch from requiring to seeing it as "natural". Galileo be explained th^t uniform motion question didn't to be natural; in effect he offered just declare uniform motion to Now of the course, symmetry arguments symmetry support posit. can nature fail. could be consistent Indeed, any way at all; principles REVIEW ESSAY 117 to. But the guiding could have made the world any way He wanted nature is is of that or, as Einstein theorizing intelligible; assumption not to be that but malicious. the Old One subtle, it, may put Appeals are one nature also into of call way symmetry making intelligible. They To explain is sometimes the dichotomy question "explainable/natural". or unpuzzling. We may explain something to render intelligible pre cisely by showing how it can be regarded as "natural". we come to Entan order of presentation, from Hughes's Departing means to is This related what Fine glement. ultimately by the same God sense is different. has to do term, but the immediate Entanglement each with the fact that if we have two quantum systems, represented natural way of combining the space, then the algebraically by a Hilbert - also a tensor Hilbert the spaces representa product taking provides tion of the observables for the two systems. Among the vectors in this of which is ones, the existence space, we have the "non-factorizable" some states All facts: the for of deter pure striking (i) responsible pair states for the subsystems, mine "reduced" but (ii) there are pure states states for the of a pair of systems that determine mixed "reduced" to the subsys On the other mixtures hand, subsystems. (iii) assigning tems does not suffice to fix the state of the joint system. Finally, (iv) the peculiar pure states of (ii) do not render the two subsystems are the features that (C&M, p. 201). These statistically independent are Features and (iv) (ii) strikingly non-classi comprise Entanglement. cal. That is, pure states on a classical probability space never exhibit features (ii) and (iv). In one sense, this is a mere rehearsal of a formal it isn't. The fact that single systems are Representable fact, in another, is not just a brute fact; as noted above, considerations of symmetry can - into us what makes the tick into how the give insight representation of the black box fit together. But these same considerations components can be extended to pairs and larger collections to make some sense of Entanglement. is a species of holism. But the way in which Hughes, Entanglement or I in my (1984), appeal to it seems to me to have advantages over the general doctrine of relational holism. The emphasis here is on a very specific structure, and what does the work is not just the fact that on the states of the subsystems; the singlet state doesn't it supervene is the way in which this state is related to the eigenstates of the observ ables to be measured, and the way in which, via Gleason's theorem, the overall structure fixes the probabilities. We don't need to decide 118 REVIEW ESSAY whether of OI per se, or, for that matter, causal relations violations are cases of relational holism. Rather, we get a very fine-grained picture structures lead to Bell's inequality, of how it is that classical probability structures allow it to be violated. but quantum are an indication of a more general feature of quan states Entangled tum mechanics: is the fact, exhibited Non-Orthodoxy Non-Orthodoxy. as in results such Bell's theorem and Kochen and especially clearly are not functions classical. that theorem, quantum probability Specker's - in The underlying probability effect, the lattice of subspaces of space a structure. assessment of Hilbert has different very space Hughes's more in is his view from stand distinguishing Non-Orthodoxy important ard quantum-logical views. Putnam and, especially, the Western Onta as saw us rio quantum the lattice of how the telling logicians subspaces a are talk structured. But of quantum system rejects Hughes properties of properties for quantum Instead he sees the real systems altogether. in its emphasis logical program as lying precisely insight of the quantum - on Non-Ortho on the non-standard character of quantum probability is a generalization of classical doxy. But associated with Non-Orthodoxy to what has come to be known as the "L?ders Rule". conditionalization In the book, Hughes spells this out in some detail. For any probability measure ?xon the subspaces of Hilbert space, and any subspace S, there ? R is a subspace is exactly one measure such that whenever ?jls ppUS) new measure This of S, /ms(R) = p(R/S) is given by jjl(R)/p(S) (p. 224). on the non-standard comes as close to conditionalization probability sees the application to come. Hughes of L?ders's space as it is possible he uses rule as telling us how the state changes on measurement. Hence, to refer to the applicability of L?ders's rule. the term Projectability I will both follow and Let us now tie these strands together. Here account. Representability, (marginally) expand upon Hughes's supple mented insight by the account of spin in terms of symmetry, provides for a single spin-1/2 system are related. into how the spin observables the tensor product representation The story is continued by introducing for the pair, and noting that the singlet state exhibits Entanglement. is tied to a particular manifestation of Non-Orthodoxy; Entanglement leads naturally, the way in which the individual systems are represented to states that exhibit the peculiar statistics character if not inevitably, in istic of the singlet state. Finally, given the result of a measurement one wing, Projectability, rule for the non-ortho the conditionalization dox probability space, provides a revised state that predicts the perfect REVIEW ESSAY 119 and the more general statistical correlations correlations that are the subject of Bell's inequality. to van Note that this account (if it is successful) provides a response Fraassen's attack on epistemic realism. It is not a causal account. But it is a realist account. Further, it bears on the matter of contextual EPR variables. Van Fraassen's that "sub specie throwaway comment the quantum the world is much more tightly organized and formalism, our connected than intuition well internally suggests" might general serve as a motto for Hughes and for the more general quantum logical tradition into which his view fits. On the quantum logical view, what is wrong with contextual hidden variables is precisely that they ignore the tightly organized structure of the quantum observables. Further, in no way presupposes that observables have values prior to Hughes hidden measurement. Measurement elicits certain events; it localizes the values so to speak, is guided, But the pattern of localization are the in which the observables knit in the Hilbert way by together to - excludes - cases in which space. The singlet state is orthogonal have the same value. And given the way parallel spin measurements in which the singlet state is related to the eigenstates of the other the Gleason's theorem determines observables, product completely measurement outcomes. for the probabilities It should be clear that I am broadly sympathetic to Hughes's account of the correlations. This is not surprising, since (as Hughes points out) it is similar to views that I have offered in print already. I also think there is genuine and important novelty here. To mention just one thing, I think that Hughes has done more than anyone else to provide content to the important but elusive notion of a principle theory. Nonetheless, I have some complaints and some worries. account of the correlations, and the account I would favor, Hughes's is in the spirit of the discussion of the tosses of the die several pages as creating as realizing back. It portrays measurements information; a But this presupposes possibilities. particular view of the measurement of observables. I it presupposes is not a linear process. that measurement problem: think that something like this must be right, but saying more is notori is well aware of all the problems, and says some ously difficult. Hughes as a theory formulated interesting things about quantum mechanics against a "classical horizon" pp. 312 ff.) but the dis (see especially cussion peculiar leaves one thirsty for more. To be sure, this is not a problem or the quantum to Hughes logician, but it takes on a particular 120 REVIEW needs aspect there. More "event", and I find Hughes to be much this ESSAY said about the underlying notion of less informative than I would like on score. I want to raise is not crucial in the context of Bell's objection a full-scale evaluation but in of Hughes's it would inequality, position be important. we I am quite unconvinced his claim that should by eschew talk of properties in dealing with quantum The argu systems. ment for the view seems to be that any attempt to ascribe properties to quantum little ac systems will result in a change of logic with and in the will be case, any companying gain, resulting properties variants of these creatures" "pallid, scarcely recognizable (p. 217). But it is hard to see how Hughes himself can avoid talk of properties. His is an event interpretation, and the most natural way to think of events is in terms of the instancing of properties. Further, part of the pallidity of quantum-logical is that "properties" they are frequently disjunctive. are But disjunctive worse not than disjunctive properties obviously The cannot avoid disjunctive and Hughes events. This comes out in his of discussion the two-slit In order to very clearly experiment. are must L?ders's he that both when slits the rule, say apply open, event A v B occurs, which is "the event that the electron passes through either [slit] A or [slit] B" (p. 232). But Hughes also tells us that "we ... as will no longer be able to describe the electron passing either or A B" In other words, through aperture through aperture (p. 237). a disjunctive a fact characterizable event has occurred, by means of a events, statement. But neither of the disjoined events has occurred, disjunctive and so neither of the disjoined statements is true. I have no intrinsic objection to this story. But, to repeat, I don't see events are less objectionable than disjunctive why disjunctive proper ties. Indeed, if it turns out that the best analysis of events analyzes them in terms of properties, then we are likely to be stuck with disjunctive anyway. So why not just leave them in from the start? properties a substitute offers for properties, in the form of what he Hughes are probabilistic calls latencies (pp. 301-6). Latencies of generalizations sees as Whereas deterministic properties. Hughes properties grounding the disposition of a green thing to appear green dispositions (e.g., "under normal conditions") latencies ground the probabilistic disposi tions of systems. Hughes writes ... we can never find a probability function p such that, for REVIEW 121 ESSAY = = every event [E], either [p(E) 1] or [p(E) 0]. That can never to be reduced these latencies say, properties, is to (p. 304) this begs the question However, logician, who against the quantum denies that properties must have any such feature. Indeed, as near as I can tell, quantum logicians get everything that Hughes from properties we can say that from with the added bonus latencies, gets interpretive - when true like is it it what is what of about the system something is not being measured. at best a selective In spite of the length of this essay, it has presented contain. A virtue that I haven't these two volumes sample of what to stressed enough is the service that these two books will provide of quantum mechanics. instructors teaching courses in the foundations course, Either, or both, could serve as the basis for an undergraduate suitable for use with graduate but both contain plenty of material students. Pedagogical virtue aside, I hope to have conveyed my own sense of just how stimulating and McMullin's in Cushing the papers to become book are. Both volumes deserve collection and Hughes's standard works in the foundations of quantum mechanics. NOTES * SES #8720600. Research for this essay was partially by NSF Grant supported 1 on this paper before I have commented (see my 1984), but I hope the reader will find remarks to justify returning what I have to say here sufficiently different from my previous to this paper. 2 This that confirmable theories must be is not completely far-fetched. It is plausible framed in terms of "natural ness kinds of figure 3 This or genuineness in explanations. to me occurred Arthur the APA. 4 Jarrett Fine as a result in a lecture offered states kinds", "genuine properties" of properties might well these conditions the differences won't However, as Butterfield In particular, of about thinking holism in a somewhat matter about or some have such. And to do with a related delivered at the different (and the natural their ability of holism critique 1990 Pacific Division technically superior) to that of way. here. to it offered out, apparent by van exceptions points to fail because take the potential screeners-off they don't a common chunk of the encompass past (pp. 121-31). large enough 6 This is, in effect, Reichenbach's again. Teller notes (p. 220) that the statistician principle to it. also subscribes Lincoln Moses 7 were "Random in Harmony" conceived of as ways of thinking about conser Devices Fraassen, Salmon and Bell 122 REVIEW ESSAY world. laws in an indeterministic whose They were pairs of particles were but somehow at the source determined random, responses completely one another (Fine 1981, p. 547). 8 to this rule. is an exception Van Fraassen vation individual to mirror REFERENCES Dordrecht. Reidel, Mechanics, 1974, The Interpretation of Quantum 'David Lewis Meets in Philosophy J.: (forthcoming), John Bell', forthcoming of Science. J. and Ernan McMullin: Philosophical Consequences of Quantum Theory: Re Cushing, on Bell's Theorem, of Notre Dame Press, Notre Dame. flections University Bub, J.: Butterfield, 'Should We Explain the EPR Correlations forthcoming, Causally?', in Philosophy of Science. The Puzzling Case of the Tangled of Entanglement: 1982, 'Antinomies 79, 733-47. tics', Journal of Philosophy and Physical in P. Asquith and R. Giere 1981, 'Correlations Fine, A.: Locality', Elby, Andrew: coming Fine, A.: PSA Healey, New East Lansing, 1980 2, Philosophy of Science Association, pp. Michigan, R.: Mechanics 1989, The Philosophy of Quantum University Cambridge York. Hughes, R. University B.: Mielnik, I. G.: Press, 1989, The Structure and Interpretation of Quantum Mechanics, forth Statis (eds.) 535-62. Press, Harvard Cambridge. of Quantum in Mathematical Communications States', 1968, 'Geometry 9, 55-80. A.: in the Quantum in R. Penrose and World', 1986, 'Events and Processes Shimony, in Space and Time, Clarendon C. J. Isham (eds.), Quantum Press, Oxford. Concepts van Fraassen on Bell's Theorem', 1984, 'Sailing into the Charybdis: Stairs, A.: Synthese Physics 61, 351-59. B.: Van Fraassen, Bell's Inequality', of Realism: 'The Charybdis 52, 25-38. Synthese is a Correlation 1985, 'EPR: When 1982, B.: Fraassen, and Peter Mittelstaedt Van World Scientific, (eds.), Symposium on Epistemological of not a Mystery?', in Peter Lahti the Foundations Physics, of Modern Singapore. CHPS of Philosophy of Maryland University Dept. College U.S.A. Implications Park, Maryland 20742 ALLEN STAIRS