Are Probabilism and Special Relativity Incompatible? Author(s): Nicholas Maxwell Source: Philosophy of Science, Vol. 52, No. 1 (Mar., 1985), pp. 23-43 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/187596 . Accessed: 15/03/2011 09:44 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=ucpress. . 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The University of Chicago Press and Philosophy of Science Association are collaborating with JSTOR to digitize, preserve and extend access to Philosophy of Science. http://www.jstor.org http://www.jstor.org/action/showPublisher?publisherCode=ucpress http://www.jstor.org/action/showPublisher?publisherCode=psa http://www.jstor.org/stable/187596?origin=JSTOR-pdf http://www.jstor.org/page/info/about/policies/terms.jsp http://www.jstor.org/action/showPublisher?publisherCode=ucpress ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE?* NICHOLAS MAXWELL Department of the History and Philosophy of Science University College London In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole. 1. The Argument. I begin with a simple and, I hope, intuitively clear exposition of my basic argument, designed to establish that probabilism and special relativity are incompatible. I then go on to add some refine- ments to the argument, in an attempt to ensure its validity, before con- sidering its implications for interpretative problems of quantum theory, and for theoretical physics as a whole. Probabilism, as understood here, is the thesis that the universe is such that, at any instant, there is only one past but many alternative possible futures-the fundamental laws of the universe being probabilistic and not deterministic. According to probabilism, then, there is a physically real difference between past and future events-the future alone containing physically, ontologically real alternative possibilities. Because of this physically real difference between past and future, probabilism requires that, at any instant, there be a universal, absolute, unambiguous distinc- tion between past and future-to divide off the one past from the many alternative possible futures. Probabilism, in short, is only true if there does exist such an absolute distinction between one past and many pos- sible futures. Special relativity, on the other hand, is only true if there is no uni- versal, absolute, unambiguous distinction between past and future. Ac- cording to special relativity, given any two physical events, El and E2, having space-like separation from each other (so that they lie outside each other's past and future light cones), then there is no absolute, frame- independent way in which El is unambiguously either earlier than, si- multaneous with, or later than E2. Which relationship holds depends on the choice of inertial reference frame, all such choices being physically *Received November 1983; revised April 1984. Philosophy of Science, 52 (1985) pp. 23-43. Copyright ? 1985 by the Philosophy of Science Association. 23 24 NICHOLAS MAXWELL equivalent. Thus special relativity denies that there exists the kind of ab- solute, universal, frame-independent distinction between past and future, which must exist if probabilism is to be true. Hence probabilism and special relativity cannot both be true. It deserves to be noted that this objection to combining probabilism and special relativity does not arise if we seek to combine probabilism and Newtonian conceptions of space and time. This is because the 'uni- versal, absolute present' of Newtonian space-time does unambiguously separate off the one past from the many alternative possible futures of probabilism. Granted that the physical event E1 is here and now, any other physical event E2 is either (1) in the past or present, or (2) it is in the future. If (1) holds, then E2 is ontologically fixed and definite, devoid of physically real alternatives. If (2) holds, then E2 may well be ontologi- cally indefinite, there being many physically real alternative possibilities associated with the space-time location of E2. The Newtonian universal 'now' ensures that there can be no ambiguity as to which of these two cases holds. It is the relativistic denial of the Newtonian absolute, universal 'now' which renders relativistic space-time incompatible with probabilism. 2. Two Restrictions of the Argument Accepted. Two restrictions need to be placed on the scope of the argument just expounded. In the first place, one might suppose that the argument establishes that probabilism is incompatible with special relativity however the latter the- ory is interpreted. But this is not correct. Special relativity may be in- terpreted to assert only that all causally connected chains of events, that actually occur, and that are capable in principle of being used to transmit signals, occur in such a way that they can be construed to take place in a Lorentz invariant fashion. The fact that future possibilities and poten- tialities are eliminated, as time passes, in a non-Lorentz invariant fashion, does not contradict special relativity, interpreted in this somewhat phe- nomenalistic way, as long as all actual causal evolutions of physical states can be construed to take place in a Lorentz invariant manner. What we must conclude, then, is this. Probabilism is incompatible with special relativity interpreted realistically, to assert that all inertial refer- ence frames are physically, ontologically equivalent, there existing noth- ing physical (such as an ether, or instantaneous annihilation of spatially separated physically real possibilities) to distinguish one such frame from the others. Probabilism is not, however, incompatible with a more mod- est, phenomenalistic version of special relativity which asserts merely the Lorentz invariant character of all actual causal chains of events (such as particles or light). In the second place, one might suppose that the argument of section 1 ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 25 establishes that special relativity (realistically interpreted) must be false if the basic laws of nature are probabilistic in character, and not deter- ministic. Once again, this is not correct. Special relativity might be true even though the basic laws are probabilistic. The truth is that two distinct versions of probabilism need to be distinguished. On the one hand there is probabilism as this has been defined above, a view which asserts that the basic laws are probabilistic and that the future is now in reality open with many ontologically real alternative possibilities whereas the past is not. This view may be renamed ontological probabilism. On the other hand there is predictive probabilism (as it may be called), a view which asserts that the future, like the past, is now in reality entirely fixed and determined even though the basic laws are probabilistic and not deter- ministic. According to predictive probabilism, alternative possible futures represent no more than alternative possibilities relative to what can in principle be predicted on the basis of a complete specification of the pres- ent, and the basic laws: they are not alternatives in reality. Whereas on- tological probabilism asserts that the future is open and undecided in real- ity, predictive probabilism asserts that the future is now in reality fixed and decided, the present state of affairs plus the basic laws of nature being insufficient however to determine this unique future. This difference between ontological and predictive probabilism, fine though it is, crucially affects the question of the compatibility of special relativity and probabilism. The argument of section 1 presupposes on- tological probabilism. It fails if predictive probabilism is presupposed. We may thus conclude that special relativity is incompatible with onto- logical probabilism, but compatible with predictive probabilism. In brief, the argument of section 1 establishes only that ontological probabilism and realistically interpreted special relativity cannot both be true. 3. Four Objections to the Argument Rejected. In order to discuss ob- jections to this reformulated version of the argument, let us examine in a little more detail ways in which one might attempt to combine (realistic) special relativity and (ontological) probabilism. Granted, as before, that E1 is here and now, if E2 lies in the past light cone of El, then E2 can be held to be ontologically fixed and definite. If E2 lies in the future light cone of El, then E2 may well be ontologically indefinite, there being many physically real alternative possibilities as- sociated with (or corresponding to) the space-time location of E2. So far there appears to be no problem. The problem arises if E2 lies outside both the past and future light cones of El, so that El and E2 have space-like separation. Let us now stipulate that E2 is at least a candidate for ontological in- 26 NICHOLAS MAXWELL definiteness in the following sense. Consider any inertial reference frame which defines an 'instantaneous now' (a space-like hyperplane in Min- kowskian space-time), which passes through E1, and through the past light cone of E2. Consider that part of the 'instantaneous now' which lies in the past light cone of E2 . Suppose that, relative to any consistent choice of what exists here (from possible probabilistic alternatives), a specifi- cation of this, together with the basic probabilistic laws, makes only prob- abilistic predictions about what exists at the space-time point at E2. If such a reference frame and associated 'instantaneous now' exists, with these properties, then E2 can be declared to be at least a candidate for ontological indefiniteness. Is E2 ontologically definite, indefinite, or what? This is the question that must be answered if (ontological) probabilism and (realistic) special relativity are to be reconciled, in opposition to the argument of section 1. There are just four suggestions to consider. In the first place, it miay be suggested that the question of whether E2 is ontologically definite (like events in the past light cone of E1) or on- tologically indefinite (like events in the future light cone of El) depends on what reference frame is chosen. The existence or non-existence of alternatives to E2 is a frame-dependent matter, like values of mass, length and time. If E2 is in the past or present with respect to reference frame R1, then E2 is ontologically fixed; if it is sufficiently in the future with respect to R2, then it is ontologically unfixed. This suggestion succeeds as long as predictive probabilism is presup- posed. For then the definiteness or indefiniteness of E2 is solely a rela- tional matter. It depends solely on what reference frame and 'instanta- neous now' is chosen. There is, according to predictive probabilism, no absolute, nonrelational sense in which E2 is either definite or indefinite. But in sharp contrast to this, ontological probabilism asserts that the def- initeness or indefiniteness of any event such as E2-the non-existence or existence of alternative possibilities-is an absolute matter, and not merely a matter of when or where one is in relation to E2. If ontological prob- abilism is true, there must be a wholly unambiguous, absolute answer to the question 'Do alternative possibilities to E2 exist or not?' It cannot be merely a relative, relational, or frame-dependent matter (like values of mass or length). Thus the ontological definiteness or indefiniteness of E2 cannot depend merely on choice of reference frame. This argument can be reformulated as follows. Special relativity re- quires that all inertial reference frames are physically equivalent-so that anything which is true in one reference frame has its equivalent truth in any other reference frame. Predictive probabilism permits reference frames to be physically equivalent in this way-since the view permits us to conceive of the world as spread out in Minkowskian space-time, succes- ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 27 sive instantaneous states of affairs (in any reference frame) being prob- abilistically interconnected. Ontological probabilism, in sharp contrast, asserts that future events have physically, ontologically real alternative possibilities associated with them which are progressively annihilated as the future becomes the present and the past. Whether or not E2 has al- ternative possibilities associated with it does depend on whether E2 lies in one's (absolute) future or past; but it is not equivalent to, or reducible to, E2 being in one's (absolute) future or past. Future alternative possi- bilities really do exist, absolutely; and they really are annihilated as time passes. Thus a reference frame which puts E2 into the future, with as- sociated physically real alternative possibilities, cannot be equivalent to a reference frame which puts E2 into the past, devoid of real alternative possibilities. Given ontological probabilism, the world cannot be con- ceived of as spread out in Minkowskian space-time, as it can given pre- dictive probabilism, just because this ignores the physical reality of future alternative possibilities. Thus this first suggestion that the existence or nonexistence of alternative possibilities associated with E2 is a frame- dependent matter collapses. In the second place, it may be suggested that the question of whether E2 is ontologically definite or indefinite is, from the standpoint of the here and now, El, meaningless, since neither answer can even in prin- ciple be verified or falsified empirically, here and now at El. This sug- gestion is acceptable if, and only if, the logical empiricist verificationist criterion of meaningfulness, to which it appeals, is acceptable. There are, however, well known and decisive objections to this logical positivist criterion of meaningfulness. In t he third place, it may be suggested that E2 is ontologically fixed and definite absolutely, like events in the past light cone of El. This suggestion faces the fatal objection that it annihilates ontological proba- bilism. For if E2 is fixed and definite from the standpoint of El, then from the standpoint of E2 (and thus also from the standpoint of El), all events in the future light cone of El that lie outside the future light cone of E2 are also ontologically fixed and definite. As much as we please of the absolute future of El can be rendered ontologically definite merely by considering an E2 far enough away from El. Thus ontological prob- abilism collapses. In the fourth place, and finally, it may be suggested that E2 is onto- logically indefinite absolutely, like events in the future light cone of El. But this suggestion faces the fatal objection that it postulates not just future alternative possibilities, but present alternative actualities-a full- fledged multi-universe view. If E2 consists of many alternative possibil- ities from the standpoint of El, then similarly E1 itself consists of many alternative possibilities from the standpoint of E2, and thus from the 28 NICHOLAS MAXWELL standpoint of El itself. This fourth suggestion thus commits us to the view that whenever anything probabilistic occurs, there being N equally prob- able outcomes, three-dimensional space splits up into N distinct three- dimensional spaces, each space containing one of the N outcomes. Any such branching-universe or multi-universe view is, however, far too gro- tesquely ad hoc to be taken seriously. Ontological probabilism combined with Newtonian space-time does not, it should be noted, face this objec- tion since in this case alternative possibilities are all in the future; and they can thus be regarded as alternative possibilities only, and not alter- native actualities. In the relativistic case, this option is not open to us; granted that El and E2 are outside each other's light cones, and each is ontologically indefinite from the other's standpoint. However, this fourth suggestion does indicate, it must be admitted, how ontological probabilism and realistic special relativity can be com- bined in at least a logically consistent way. As we have just seen, on- tological probabilism can be represented as a multi-universe view, all possibilities being realized, probabilism being converted into a kind of determinism. In the Newtonian case, this involves postulating that when- ever a probabilistic event occurs with N equally probable outcomes, then instantaneously the entire universe branches into N distinct universes, be- tween which there is no subsequent communication, each universe con- taining one of the N outcomes. In the relativistic case, this involves pos- tulating that whenever such a probabilistic event occurs, three-dimensional space in the immediate vicinity splits into N distinct three-dimensional spaces, each space containing one outcome. The splitting of space into N distinct spaces then travels outwards in all directions at the velocity of light-the N distinct spaces joining at a closed surface which expands at the velocity of light. If another such splitting of space into M spaces is encountered, N'M spaces result. Once space has branched in this way, all communication between the distinct spaces is impossible. Probabilism results from the illusion of being invariably confined to just one branch. This is consistent but, to repeat, far too grotesquely ad hoc to be taken seriously. And yet only by adopting this space-splitting view can onto- logical probabilism be combined consistently with realistic special rela- tivity. I conclude that all suggestions as to how ontological probabilism and realistic special relativity are to be combined fail. 4. Choosing between Ontological and Predictive Probabilism. What arguments can be given to help us choose between predictive and onto- logical probabilism? On the one hand, it may be argued that predictive probabilism is to be preferred on straightforward physical grounds. Special relativity is an ex- ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 29 traordinarily successful physical theory, firmly built into the framework of theoretical knowledge in physics today. Ontological probabilism de- serves to be rejected just because it is incompatible with this especially secure part of current scientific knowledge. On the other hand, it may be argued that as our theoretical knowledge and understanding of the physical universe develops, it is to be expected that new theories will revise and correct their predecessors. Just as New- ton corrects Kepler and Galileo, and Einstein corrects Newton, so future theories will no doubt correct Einstein. Ontological probabilism should not be condemned out of hand merely because it subtly contradicts special relativity. In seeking to improve our knowledge and understanding of the structure of the physical universe, we ought indeed to seek to transform untestable metaphysical theories (such as ontological probabilism), in- compatible with existing theoretical scientific knowledge, into testable theories, since it is along some such path as this that progress is to be made. If positive reasons can be given for preferring ontological to pre- dictive probabilism, the incompatibility of ontological probabilism and special relativity may be deemed not to tell too much against the ac- ceptability of the view. 5. Objectism versus Eventism. In choosing between ontological and predictive probabilism, we are almost bound to be influenced by the way we choose between two other, more general, rival metaphysical positions, which may be called objectism and eventism (referred to as C2 and C1 respectively in Maxwell 1968, pp. 5-9). According to objectism, the world is three dimensional and not four dimensional. The basic entities-objects-are spread out in space, but not in time. Objects change; they have a past and a future: but it is facts about objects, rather than objects themselves, that are (or can be con- strued to be) spread out in time. Spatial relations are between objects, but temporal relations are between facts-about-objects. This constitutes a fundamental difference between space and time. It is not objects, but rather the history of objects, that can be conceived as being spread out in time: and histories exist only insofar as objects persist and change. Space-time diagrams do not depict objects or the world at all: they depict facts about objects, much as any graph relating, for example, temperature and pressure, depicts not objects but facts about objects. Eventism rejects almost everything that objectism affirms. According to eventism, the world is spread out in both space and time. The basic entities are four-dimensional events, not three-dimensional objects. What would ordinarily be conceived of as persisting objects-tables, atoms, electrons-are in reality large collections of similar events spread out continuously in space-time. Objects are thus made up of events, as op- 30 NICHOLAS MAXWELL posed to events being made up of objects. Events are spatially and tem- porally related: in this respect there is no difference between space and time, and time may be conceived in quasispatial terms. Space-time dia- grams depict the four-dimensional world as it really is, compounded of events imbedded in space-time. It deserves to be noted in passing that common sense tends to amount to an inconsistent combination of objectism and eventism. We ordinarily tend to think of the present, the immediate past, and the immediate future in terms of objectism: the immediate past is what has just happened to objects that now exist, and is not a place where other entities (events), resembling present entities, exist. The distant past (and to a lesser extent the distant future) does tend, however, to be conceived of in terms of eventism: a distant place, existing elsewhere in the dimension of time, stocked with different things. This common sense inconsistent jumble of objectism and eventism accounts for much of our ordinary confusion about time. We conceive of time in eventist, space-time terms and then, dis- cerning that something has been left out, we seek to make good the omis- sion by adding the instantaneous 'now', flowing along time, creating 'be- coming', the world as we ordinarily experience and conceive of it. Versions of this view have been propounded by such diverse authors as Weyl, Reichenbach, Eddington, Bondi, Whitrow, Bergmann, James, Bergson, Capek, and Grunbaum (see Grunbaum 1963, chap. 10). All such views, which seek to add the 'now', the 'flow of time', and 'becoming' to the world conceived of in space-time terms, amount, I suggest, to nothing more than a hopelessly confused attempt to do justice to the inconsistent combination of eventism and objectism of common sense. From the per- spective of objectism, eventism and space-time diagrams are not inade- quate or incomplete because they leave out the instantaneous 'now', the specious present, becoming, etc.; they are inadequate or incomplete be- cause they leave everything out, depicting facts about objects but not per- sisting, changing objects themselves. The common sense combination of eventism and objectism needs to be recognized for what it is, an incon- sistent picture that must be rejected. Nothing but confusion is created by transforming this inconsistent common sense combination of eventism- plus-objectism into eventism-plus-the-instantaneous-'now'-and-becom- ing. It also deserves to be noted that special relativity may be formulated in terms of either objectism or eventism. Einstein originally formulated special relativity in such a way that objectism is presupposed; it was Min- kowski who was responsible subsequently for the space-time, eventism formulation. After some initial dismay, this interpretation was taken up by Einstein in developing general relativity, which, as a result, has sub- sequently usually been interpreted in terms of eventism. Presumably, ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 31 however, general relativity is open to being interpreted in terms of ob- jectism, just as special relativity is. It might be thought that the fact that all ordinary physical objects- human bodies, rocks, tables, and even molecules and atoms-are pro- cesses rather than unchanging objects, in itself tells against objectism. But this is wrong. Objectism might well be true-fundamental physical entities being objects in the sense of objectism, these entities interacting in persisting ways to form enduring processes we ordinarily conceive of as macroscopic objects. Choosing between objectism and eventism is relevant to choosing be- tween ontological and predictive probabilism in the following way. If eventism is true, then ontological probabilism cannot be true. Eventism plus probabilism implies predictive probabilism. For eventism asserts that the future exists, like the past, and like states of affairs at other places. Eventism denies that the future is really, ontologically open and unde- cided; it is at most open only with respect to what can be in principle predicted on the basis of a full specification of the present, and basic (probabilistic) laws of nature. If objectism is true, on the other hand, then it is possible for ontological probabilism to be true. Objectism, in rejecting the eventist picture of a four-dimensional universe spread out in space and time, makes it possible for the future to be genuinely, ontologically open and undecided. We might even conclude that objectism plus probabilism implies ontological probabilism-given that objectism and probabilism together are taken to assert that nothing exists to determine the shape of the future over and above the basic probabilistic laws of nature, and the state of affairs that obtains in the present. The conclusion of the above argument can be put like this. Let prob- abilism be the thesis that the basic laws of nature are probabilistic in character. it being left entirely open whether ontological or predictive probabilism holds. We then have: (i) probabilism plus objectism implies ontological probabilism; (ii) probabilism plus eventism implies predictive probabilism. Thus, granted probabilism, if strong arguments can be given for preferring objectism to eventism, then these are also strong arguments for preferring ontological to predictive probabilism. 6. Arguments for Objectism and against Eventism. I have two very different arguments for preferring objectism to eventism. The first amounts to this. If objectism is true, then it is possible for there to be necessary connections (deterministic or probabilistic) between successive states of affairs. If eventism is true, such necessary connec- tions are impossible. This provides decisive grounds for accepting ob- jectism and rejecting eventism. 32 NICHOLAS MAXWELL Hume, notoriously, denied that it is possible for there to exist logically (or analytically) necessary connections between successive states of af- fairs. He held that ". . . there is nothing in any object considered in itself, which can afford us a reason for drawing a conclusion beyond it" (Hume 1959, p. 139), and that "We can at least conceive a change in the course of nature, which sufficiently proves that such a change is not absolutely impossible" (Hume 1959, p. 91). Given eventism, Hume is right. Basic entities-events-are spread out both in space and time. Just as statements exclusively about what exists at one place cannot have implications for what exists at other places, so too statements exclusively about what exists at one time cannot have im- plications for what exists at other times. Given objectism, however, Hume is no longer correct. For, according to objectism, basic entities are spread out in space, but not in time. The analogy between space and time breaks down. It is facts about objects, as it were, not objects themselves, that are spread out in time. It is thus possible for logical relationships to exist between facts 'spread out in time' about one and the same set of objects. Statements exclusively about objects existing at one place cannot have implications for different objects (or different parts of the same spatially extended objects) existing at other places. Statements exclusively about objects, and their instantaneous states, at one instant, may well have implications for the subsequent states of the very same objects at subsequent times. For objects may possess un- changing powers, necessitating properties, dispositional properties or pro- pensities (deterministic or probabilistic)-analogous to such physical properties as inflammability, solidity, elasticity, gravitational and electric charge-which determine necessarily (deterministically or probabilisti- cally) how the objects change in certain respects in certain circumstances. Thus two particles, possessing Newtonian gravitational charge, of ne- cessity accelerate towards each other at a rate inversely proportional to the square of their distance apart; if they do not, then, ipso facto, they do not possess Newtonian gravitational charge. On this view, Newtonian gravitational charge is such that it can only be fully described (or attrib- uted to objects) by a term 'gravitational charge' whose meaning is such that 'particles 1 and 2 are gravitationally charged and distance d apart' analytically implies '1 and 2 accelerate towards each other at a rate in- versely proportional to d2 (assuming the absence of other forces)'. When Newtonian theory is interpreted in this way-in accordance with what may be called conjectural essentialism-so that the theory attributes pow- ers or necessitating properties to objects, then all the laws of Newtonian theory, such as F = G * ml *M2/d2 and F = m * a, are interpreted as an- alytic statements, all the factual and empirical content of the theory being ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 33 contained in the assertion that all objects everywhere possess unchanging Newtonian mass and gravitational charge.' Unchanging powers or necessitating properties of this type are possible given objectism, impossible given eventism. We cannot of course know for certain that any such invariant necessitating properties do actually ex- ist; equally, we cannot know for certain that such properties do not exist. If they exist universally, then what exists at one instant determines nec- essarily (probabilistically or deterministically) what occurs subsequently, in the sense that a full specification of what exists at one instant analyt- ically implies2 what occurs subsequently. In this case the world is such that if the full specification of what exists at one instant is weakened, so that it no longer analytically implies what occurs subsequently, then inev- itably it ceases to be a full specification of what exists exclusively at the first instant. Real physical properties possessed by objects at the instant in question are no longer fully described. If there are universal necessary connections between successive states of affairs in this world, then it is not possible to conceive consistently that this world, with all its objects and necessitating properties, suffers an abrupt change in the laws of na- ture in the future-even though of course it is possible to conceive con- sistently that a world that has so far behaved like this world, but lacks this world's necessitating properties, does suffer a change in its laws in the future. (A more detailed argument along these lines for the possibility of necessary connections between successive states of affairs is given in Maxwell [1968], reprinted in Swinbume [1974], and briefly discussed in Harre [1970]; somewhat similar arguments are to be found in Harre and Madden [1975].) In brief, it is possible for there to exist powers, necessitating properties, and (analytically) necessary connections between successive states of af- fairs if objectism is true; all this is impossible if eventism is true. There is a further point. In a universe in which (as far as it is known) 'It may be objected that this constitutes a reductio ad absurdum of conjectural essen- tialism in that, if physical laws are true analytically, they cannot be refuted empirically and revised. The reply to this of course is that from the standpoint of conjectural essen- tialism it is factual and falsifiable assertions attributing necessitating properties to physical entities that can be empirically refuted and revised as physics progresses. A refutation of essentialistic Newtonian theory may be held to disclose that nothing has gravitational charge, as explicated by the analytically true statement F = G * gi * 92/d 2 (with gravitational charge equal to inertial mass). If this is correct, then the analytic statement is discovered not to be (precisely) applicable to anything in the world, and new analytic statements need to be formulated to specify precisely the meaning of theoretical terms to be employed to attribute new necessitating properties to entities (such as the capacity of matter to curve space-time). 2p 'analytically' implies q (as I am using the term) if and only if p plus relevant analytic statements, true in virtue of the meaning of terms in P, logically imply q. In other words p analytically implies q iff 'p D q' is analytic. 34 NICHOLAS MAXWELL all events unfold in accordance with some fixed pattern of natural law, if it is meaningful and possible for necessitating properties and connec- tions to exist, then it is absurd not to postulate the actual existence of such necessitating properties and connections. The only rationale that there can be for not postulating such necessitating properties and connections is that the very idea of such necessitating properties and connections does not make sense. Hume's rejection of the existence of necessitating properties and causal connections (as these have been understood here) may well, when one first encounters it, seem too absurd to be taken seriously. For if Hume were right, all lawfulness in the world could, it seems, amount to nothing more than an utterly incredible stream of coincidences at every place and time. For if Hume were right, nothing could exist that is, in any sense, responsible for the persistence of natural regularities. Anything could fol- low anything in time; and if only those events occur which obey fixed regularities, this must be due to nothing more than a sustained, infinitely improbable stream of coincidences. This argument is valid just as long as necessitating properties and con- nections are meaningful and possible. For in this case it is meaningful and possible to make the required distinction between (i) a universe in which lawfulness is due to the existence of necessitating properties and connections; and (ii) a universe in which precisely the same lawfulness is due to nothing more than infinitely improbable coincidence, there being no necessitating properties and connections in existence. But if Hume is correct in holding that no meaning whatsoever can be given to 'neces- sitating properties and connections' (as interpreted here), then the dis- tinction between (i) and (ii) above collapses. The intuitive idea or feeling that mere natural regularity (postulated by [ii]) is utterly inexplicable and infinitely improbable because nothing exists that is responsible for the persistence of regularity, is unfounded because the very notion of some- thing in existence in the natural world being 'responsible' for regularity is meaningless. (Within the Humean position one can, it may be noted in passing, even distinguish between 'true natural laws' and 'true acci- dental generalizations': the former, by definition, cohere into a deductive structure, whereas the latter, by definition, do not.) The decisive point to recognize is that it is only reasonable to postulate natural laws or regularities devoid of necessitating properties and con- nections responsible for them just as long as Hume is correct in holding these 'necessitating' notions to be meaningless. If Hume is wrong here- necessitating properties and connections being both meaningful and pos- sible-then it at once becomes utterly absurd to postulate natural regu- larities in such a way that the existence of any necessitating properties ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 35 responsible for the regularities is simultaneously denied. To do this is to postulate infinitely many, infinitely improbable coincidences. But Hume is wrong. The notions of necessitating properties and con- nections (as explicated here) are meaningful. Such properties and con- nections may exist. It thus is absurd to postulate natural law and at the same time exclude the possibility that there exist necessitating properties and connections responsible for such lawfulness.3 But eventism does exclude the possibility that such necessitating prop- erties and connections exist. Only objectism permits them to exist. Therefore, it is absurd to presuppose anything other than objectism in pursuing physics-and natural science more generally. Eventism must be rejected. This concludes my first argument in support of objectism and against eventism. My second argument is that objectism allows, and eventism prohibits, free will. If objectism is true, then it is at least possible that the future is open and undecided (if ontological probabilism is true). It is thus possible that free will exists in the strong sense that in order to have free will (in this sense) it is necessary (i) that all our actions were not ontologically fixed and determined in the past (e.g., before we were born); and (ii) that some of the future depends crucially on whether we do, or do not, perform certain actions (ontologically undetermined in the past). Whereas free will, in this strong sense, is possible given objectism, it is not possible given eventism, even if probabilism obtains, just because eventism excludes the possibility that the future is genuinely, ontologically open and undecided. The assumption that we do have some genuine free will-some genuine power to decide the future-is not one that can be readily laid aside in any sphere of human life and action, including the sphere of scientific inquiry. Our assumption that we have the capacity to assess scientific theories rationally, and to make progress towards a greater scientific knowledge and understanding of the world, presupposes, it may be held, that we have some genuine control of, and responsibility for, our sci- entific thoughts, judgments, and deeds. Thus eventism, which makes all this impossible, is to be rejected; and objectism, which makes free will possible, is to be accepted instead. 3This argument, incidentally, provides decisive grounds for rejecting anti-realist views of science such as those of van Fraassen (1980) and Laudan (1981), insofar as these views are opposed to the thesis that theoretical physics needs to be committed to an overall essentialistic, and thus realist, research program if genuine explanations and understanding of phenomena are to be achieved. The argument also provides grounds for rejecting realist but anti-essentialist views of science such as those of Popper (1963). 36 NICHOLAS MAXWELL It might be thought that any argument in support of necessary connec- tions between successive events must be diametrically opposed to any argument in support of free will. Strikingly enough, the above two ar- guments, apparently diametrically opposed in this way, work together to support objectism. I conclude that objectism is to be accepted and eventism is to be re- jected. Thus, given probabilism, predictive probabilism is to be rejected and ontological probabilism is to be accepted. This gives strong grounds for holding that probabilism as such, and not just ontological probabil- ism, is incompatible with special relativity. I turn now to a discussion of the implications and significance of this conclusion. 7. Implications of the Argument for Quantum Theory. The above ar- gument dramatically affects the way we assess those versions of quantum theory that postulate the instantaneous, nonrelativistic wave packet col- lapse of spatially smeared out wave packets as an objectively real physical phenomenon. For some years now, I have sought to develop and advocate a 'micro- realistic, propensity' version of quantum theory (1972, 1973, 1975, 1976a, 1982). My aim has been to solve the quantum wave/particle problem in such a way that a version of quantum theory (QT) can be formulated which can be interpreted as being, in the first instance, exclusively about microsystems such as electrons-about how they evolve and interact in physical space and time wholly independent of preparation and measure- ment. Given the main argument of section 6 above in support of objectism and conjectural essentialism, it becomes an urgent matter to try to develop a microrealistic, essentialistic version of QT. Orthodox QT cannot be interpreted essentialistically, as attributing powers or necessitating prop- erties to electrons, protons, etc., just because it does not provide a con- sistent theory of the nature of these entities in the absence of measure- ment, there being within orthodox QT no microrealistic solution to the quantum wave/particle problem. Orthodox QT specifies regularities, but cannot explain why these regularities obtain in terms of (conjectured) powers or necessitating properties possessed by fundamental physical entities. Orthodox QT can only offer miraculous coincidence, not explanation and understanding. In seeking to develop a microrealistic, essentialistic version of QT, my approach has been-modifying an idea of Popper (1957, 1959)-to in- terpret QT as attributing propensities to microsystems. A propensity, as understood here, is a physical property-a probabilistic power or neces- sitating property (of the kind discussed in section 6 above). In other words, the notion of 'propensity' is a probabilistic generalization of the deter- ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 37 ministic notion of physical power or necessitating property of the kind that deterministic theories of classical physics, essentialistically inter- preted, can be regarded as attributing to classical physical entities such as particles and fields. (See Maxwell 1976a, pp. 283-89 for a more de- tailed development of this point.) This approach requires that precise, microrealistic, quantum conditions be specified for propensities to be 'ac- tualized'-for probabilistic events to occur in quantum systems even in the absence of measurement. My proposed solution to this key problem is that probabilistic 'actualizations' occur whenever, as a result of poten- tial particle creation or annihilation, a composite quantum system evolves into a superposition of two states with rest masses that differ by 5m. Reinterpreting the time/energy uncertainty relations, I suggest that such a superposition persists only for a time &t = h/8m * c2, and then jumps to one or other rest mass state. All quantum measurements can, I argue, be interpreted as special cases of this kind of probabilistic occurrence (see Maxwell 1976a, 1982). According to this approach, then, the strange wave/particle features of quantum entities such as electrons are due to the fact that these entities have propensities as fundamental physical properties, thus being unlike anything we seem to encounter in the -macroscopic world. The propensity of an electron to interact in a particle-like way evolves in a wave-like fashion in accordance with Schrodinger's time-dependent equation (to a first approximation)-just as long as this propensity is not (probabilist- ically) actualized. An electron is quite unlike a classical wave or particle; it may be called a 'wavicle', 'smearon' or 'propensiton'. This 'propensiton' version of QT can in principle reproduce all the empirical success of orthodox QT. It is much less ad hoc, much more explanatory, than orthodox QT in that it can (in principle) explain macro- phenomena arising solely as a result of interactions between microsystems (whereas orthodox QT cannot in that it presupposes the existence of ma- cromeasuring instruments in its basic formulation). It is much more pre- cise than orthodox QT, in that the physical conditions for probabilistic events to occur are much more precisely specified (orthodox QT asserting only that probabilistic events occur if and only if a measurement is made, 'measurement' here being an extremely imprecise notion). Finally, pro- pensiton QT differs empirically from orthodox QT, in principle and per- haps in practice. This is because of the fact that propensiton QT asserts that probabilistic events occur even in the absence of measurement, whereas orthodox QT denies this. In particular, the two versions of QT ought to be empirically distinguishable by means of experiments performed on de- caying systems, such as radioactive nuclei, of the kind discussed by Fonda et al. (1978). Orthodox QT predicts that such systems decay continuously in the absence of measurement, the systems persisting in a superposition 38 NICHOLAS MAXWELL of the decayed and undecayed state. Propensiton QT predicts that such systems persist as superpositions of the decayed and undecayed states only for limited times, after which each system jumps abruptly and prob- abilistically into either the decayed or undecayed state, even in the ab- sence of measurement. The two versions of QT predict the same rate of decay, in the absence of measurement, if and only if the decay rate is exponential. For short and long times, QT predicts departure from ex- ponential rates of decay (in the absence of measurement). Thus there is here a basis-certainly in principle, and perhaps in practice-for crucial experiments designed to decide between orthodox and propensiton ver- sions of QT. (For further details concerning the points of this paragraph, see Maxwell 1976a, 1982, 1984, chap. 10; and Fonda et al. 1978.) Despite these impressive credentials, propensiton QT may well be judged to be wholly unacceptable for one reason alone. The theory is irreparably incompatible with special relativity. For propensiton QT postulates that, in appropriate physical conditions, propensitons-which may be smeared out in space over large volumes-collapse instantaneously into very small volumes; and this contradicts special relativity. This contradiction is not merely because of the fact that propensiton QT postulates a faster-than- light collapse of wave packets, or propensitons. Many have argued that faster-than-light particles-tachyons-are permitted by special relativity, as long as it is conceded that such particles move in one direction in some reference frames, and in the opposite direction in others. Much more se- riously, it is the demand that propensiton collapse be instantaneous which irreparably contradicts special relativity. For special relativity asserts that all inertial reference frames are physically equivalent. In only one ref- erence frame, however, will any given probabilistic collapse of propen- siton state be instantaneous; in other, relatively moving inertial reference frames the collapse will not, according to special relativity, be instanta- neous (though always faster-than-light). There are, it may be argued, three reasons why propensiton QT needs to be interpreted as being irrevocably committed to instantaneous pro- pensiton collapse. First, it may be argued that instantaneous collapse is implicit in the basic idea of propensities becoming probabilistically 'actualized', of the potential becoming actual. Either propensities evolve smoothly and de- terministically (in accordance with Schrodinger's time-dependent equa- tion); or there is the abrupt, instantaneous probabilistic actualization of propensities. Any theory which described propensities as being actualized smoothly and gradually in time (in accordance with some sort of time reversal of Schrodinger's equation) abandons altogether the basic pro- pensity idea. Second, the very requirement for a probabilistic event to occur, pos- ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 39 tulated by propensiton QT, appeals to the notion of rest mass, and hence appeals to the existence of a privileged reference frame at rest, in terms of which the probabilistic event is to be described. This is compatible with the postulate of instantaneous wave packet collapse, and incompat- ible with the thesis that wave packet collapse occurs in a faster-than-light, Lorentz invariant manner. Third, and much the most serious, propensiton collapse must be in- stantaneous if causal anomalies are to be avoided. Suppose a wave packet or propensiton, spread throughout a large region of space R, collapses instantaneously, relative to reference frame Fo into a small region iRo because of a physical interaction that occurs in 8Ro. If this collapse is Lorentz invariant then in some other reference frame, F1, the propensiton begins to collapse in 8R1 in R a long way away from 8RO, the collapse travelling faster than light for some time towards 8Ro. In this case phys- ical events in 8R1, far from 8RO, anticipate an interaction that will occur in the future in 6Ro. The future influences the past. In order to avoid this absurdity, it is necessary to stipulate that such probabilistic collapses of propensities occur instantaneously, in a non-Lorentz invariant way. Recent experimental results, such as those of Aspect, Grangier, and Roger (1982), appear to confirm that wave packet collapsing events, as- sociated with measurement, occur in a faster-than-light way. This is a great experimental success for propensiton QT. The experimental results do not, however, in themselves decisively refute special relativity and establish the instantaneous character of wave packet collapse. As Red- head (1983) has argued, there are at least two alternatives to this view. In the first place, upholders of orthodox QT may argue that 'wave packet collapse', associated with measurement, is not a physical phenomenon at all; it cannot, therefore, conflict with special relativity. Secondly, there is the possibility that a Lorentz invariant, tachyon-like theory of wave packet collapse may be developed. The experimental results in them- selves do not exclude these possibilities, and thus do not establish that special relativity (realistically interpreted) is false. Those who uphold the orthodox interpretation of QT (still the majority of physicists today), and those who seek to develop a Lorentz invariant theory of wave packet collapse, such as Fox (1972), will continue to regard propensiton QT as highly implausible, despite the results of Aspect et al. The standing of propensiton QT changes dramatically however if the main argument of this paper is correct, and probabilism in general con- tradicts special relativity. For in this case any fundamentally probabilistic physical theory must contradict special relativity. In particular, all inter- pretations and versions of QT which hold QT to be fundamentally prob- abilistic must contradict special relativity. Thus the fact that propensiton QT contradicts special relativity in the way indicated-as a result of its 40 NICHOLAS MAXWELL fundamentally probabilistic character-cannot tell in any way at all against the theory.4 Propensiton QT deserves, I conclude, serious attention from the phys- ics community. Only the accidents of intellectual history have, I suggest, prevented propensiton QT from being adopted decades ago as the official, dominant version and interpretation of quantum mechanics, the orthodox, Copenhagen interpretation generally being regarded as a highly unsatis- factory, implausible, minority viewpoint. In particular, it is important that propensiton QT be tested experimentally against orthodox QT, for ex- ample, in the way indicated above. I conclude also that all those who, like Fox, seek a Lorentz invariant theory of wave packet collapse are- if the argument of this paper is correct-engaging in a misguided en- deavor. 8. Implications of the Argument for Theoretical Physics as a Whole. The deepest problem confronting theoretical physics today, in seeking to discover the underlying unity inherent in the laws of nature- a unity we conjecture to exist-is the problem of how to unify general relativity and quantum theory. In seeking to solve this problem, it is im- portant to try to extract the most basic, general aspects of the problem from those aspects that are secondary and peripheral. We need to do this if we are to find guidelines towards the development of a new unifying theory, guidelines of the kind found by Einstein in developing special and general relativity in the first place. If the main argument of this paper is correct, then it provides grounds for holding that the most basic aspect of the conflict between general relativity and quantum theory is that the former theory is incompatible with probabilism. The first, and most elementary, change that needs to be made to general relativity, as a step towards transforming it into uni- fied, general relativistic quantum theory, is to render it compatible with probabilism. This requires at least that a version of general relativity be formulated in which there exists in space-time a unique set of temporally successive, spacelike hypersurfaces, to constitute successive cosmic or universal 'nows'. These hypersurfaces then need to be related to the pres- ence of matter, in a way to be specified by some generalization of the propensiton QT requirement for probabilistic actualization of propensities to occur. In this way one can perhaps discern a possible route to the unification of general relativity and quantum theory-a route almost cer- tainly not being considered by any theoretical physicist today, because 4Deterministic evolutions of propensities can be Lorentz invariant; it is only probabilistic actualizations of piopensities that must violate special relativity. ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 41 of a general failure to take into account the import of the main argument of this paper. One final point. The argument of this paper is put forward in part with the intention of putting into practice and illustrating the aim-oriented, empiricist methodology of discovery, involving an interplay of physical and metaphysical considerations, which needs to be put into practice if natural philosophy is to be pursued rationally-as I have argued at length elsewhere (see Maxwell 1974, 1976b, 1979, 1984). APPENDIX The idea that interpretative problems of QT can be solved, and realism be upheld, by means of a propensity interpretation of the theory we owe primarily to Popper (1957, 1967, 1982), even though as Popper himself has pointed out Born, Heisenberg, Dirac, Edding- ton, Jeans, and Lande have on occasions made remarks in this direction (Popper 1982, pp. 130-35); and Margenau's latency view may be held to amount to a propensity inter- pretation of QT; see Margenau (1950). In the circumstances, I ought perhaps to explain how, and why, my propensity interpretation of QT differs from Popper's. Some basic differences are the following. According to Popper: "Propensities are properties of neither particles nor photons nor electrons nor pennies. They are properties of the repeatable experimental arrangement . . . (Popper 1967, p. 38). Subsequently, partly in response to criticism, Popper (1982, p. 71) has emphasized that: "Propensities are . . . not properties of the particle but of the objective physical situation" which may, but usually will not, be a repeatable experimental arrangement created by man. Popper also asserts that propensities are relational properties of objects and whole physical situations that serve to actualize propensities. Quite clearly, Popper rejects my view that propensities are to be understood as essentialistic powers or necessitating properties of objects per se, e.g., electrons, which determine (probabilisti- cally) how these objects interact with one another, analogously to the way in which de- terministic necessitating properties like solidity or charge do this. There is, closely related to this basic difference in the way propensities are conceived, a dramatic difference in the way in which the entities of the quantum domain are con- ceived. For Popper, electrons, protons, etc., are particles with definite trajectories. For me, electrons are neither particles nor waves but 'smearons' or 'propensitons'-roughly speaking, spatially smeared out wave packets interpreted as determining propensities to interact. The strange features of smearons or propensitons are owing to the fact that these entities have propensities as basic physical properties. In contrast, pennies and dice have nonbasic propensities that can be explained away in terms of nonpropensity-like deter- ministic physical properties, and initial conditions that vary, in a statistically determinate way, from toss to toss. Again, for Popper the reduction of the wave packet is not a physical phenomenon at all; it "is not an effect characteristic of quantum theory but of probability theory in general" (Popper 1967, p. 34), which arises just as much when a tossed penny comes to rest as when a quantum measurement is made. For me, the reduction of the wave packet is a real physical phenomenon, peculiar to the quantum domain, and unlike what occurs when a penny comes to rest. Wave packet reductions are probabilistic actualizations of propensities of smearons, as opposed to deterministic evolutions of propensities of smearons (in ac- cordance with Schr6dinger's time-dependent equation). For Popper, there is no general, fundamental problem of specifying the precise physical conditions for wave packet reduc- tions to occur-just because this is not, for Popper, a distinctive kind of physical phe- nomenon. For me, the basic problem confronting any attempt to develop a microrealistic propensity interpretation of QT is just to specify, in exclusively microrealistic terms, pre- cise, necessary, and sufficient physical conditions for propensities to be actualized, for wave packets to 'collapse'-no surreptitious reference being made to observables, mea- 42 NICHOLAS MAXWELL surement, or vague 'irreversibility'. In putting forward a possible solution to this problem (indicated above), I have succeeded in providing a fully microrealistic interpretation of QT-one which interprets QT as being, in the first instance, exclusively about microsys- tems and their mutual interactions. This interpretation of QT is, as a result, (i) experi- mentally distinguishable from orthodox QT; (ii) free from the grotesque ad hocness of orthodox QT arising from the fact that orthodox QT must presuppose in its basic postulates the existence of macroscopic measuring instruments, and some part of classical physics to describe such instruments, it thus being impossible for orthodox QT to explain macro- phenomena and classical physics from quantum postulates alone. As a result of failing to solve the problem of specifying microphysical conditions for wave packets to collapse- as a result, indeed, of failing even to recognize the existence of the problem-Popper's propensity version of QT fails to be microrealistic in the above sense; it is thus just as grotesquely ad hoc as orthodox QT, and it is not experimentally distinguishable from or- thodox QT. The differences just indicated all stem, I suggest, from two general philosophical dif- ferences. First, whereas I uphold conjectural essentialism, Popper vehemently opposes essentialism; see Popper 1963. Second, whereas I seek a microrealistic version of QT- a version capable in principle of explaining macrophenomena solely in terms of micro- phenomena which alone, for me, can be non-ad hoc and genuinely explanatory-Popper appears to seek only a realistic interpretation of QT, the need to explain macrophenomena and properties solely in terms of microphenomena and properties being nowhere asserted. It is Popper's anti-essentialism, I suggest, which leads him to adopt his nonessentialistic interpretation, (i) of propensities in general, and (ii) of QT in particular. Popper's anti- essentialistic, relational way of understanding quantum propensities allows him to conceive of quantum entities as particles, and to dismiss wave packet reductions as nonphysical. (Conjectural) essentialism holds, by contrast, that the physical properties and character of physical entities are given by the physical laws these entities obey; it thus becomes highly implausible to suppose that electrons, obeying fundamentally probabilistic laws, and hav- ing propensities as basic physical properties, might be particles-entities of classical, de- terministic physics. In addition, Popper's failure to give priority to the task of developing a fully microrealistic version of QT has led him to overlook the serious inadequacies of his interpretation of QT. For further criticisms of Popper's viewpoint see Feyerabend (1968), Gardner (1972), and Maxwell (1975). REFERENCES Aspect, A.; Grangier, P.; and Roger, G. (1982), "Experimental Realization of Einstein- Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequali- ties", Physical Review Letters 49: 91-94. Feyerabend, P. K. (1968-69), "On a Recent Critique of Complementarity", Philosophy of Science 35: 309-31; 36: 82-105. Fonda, L.; Ghirardi, G. C.; and Rimini, A. (1978), "Decay theory of unstable quantum systems", Reports on Progress in Physics 41: 587-631. Fox, R. (1972), "Tachyons and Quantum Statistics". Physical Review D5: 329-31. Gardner, M. R. (1972), "Quantum-Theoretic Realism: Kochen and Specker versus Popper and Einstein", British Journal for the Philosophy of Science 23: 13-23. Griinbaum, A. (1963), Philosophical Problems of Space and Time. London: Routledge and Kegan Paul. Harre, R. (1970), The Principles of Scientific Thinking. London: Macmillan. Harre, R., and Madden, E. H. (1975), Causal Powers. Oxford: Basil Blackwell. Hume, D. (1959), A Treatise of Human Nature. Vol. 1. London: Everyman. Laudan, L. (1981), "A Confutation of Convergent Realism", Philosophy of Science 48: 19-49. Margenau, H. (1950), The Nature of Physical Reality. New York: McGraw-Hill. Maxwell, N. (1968), "Can there be Necessary Connections between Successive Events?" British Journal for the Philosophy of Science 19: 1-25. . (1972), "A New Look at the Quantum Mechanical Problem of Measurement", American Journal of Physics 40: 1431-35. ARE PROBABILISM AND SPECIAL RELATIVITY INCOMPATIBLE 43 . (1973), "The Problem of Measurement-Real or Imaginary?" American Journal of Physics 41: 1022-25. . (1974), "The Rationality of Scientific Discovery", Philosophy of Science 41: 123- 53, 247-95. . (1975), "Does the Minimal Statistical Interpretation of Quantum Mechanics Re- solve the Measurement Problem?" Methodology and Science 8: 84-101. . (1976a), "Towards a Micro Realistic Version of Quantum Mechanics", Foun- dations of Physics 6: 275-92, 661-76. . (1976b), What's Wrong With Science? London: Bran's Head Books. . (1979), "Induction, Simplicity and Scientific Progress", Scientia 114: 629-53. . (1980), "Science, Reason, Knowledge and Wisdom: A Critique of Specialism", Inquiry 23: 19-81. . (1982), "Instead of Particles and Fields: A Micro Realistic Quantum 'Smearon' Theory", Foundations of Physics 12: 607-31. . (1984), From Knowledge to Wisdom. Oxford: Basil Blackwell. Popper, K. R. (1957), "The Propensity Interpretation of the Calculus of Probability and the Quantum Theory", in Observation and Interpretation in the Philosophy of Phys- ics, S. Korner (ed.). London: Butterworths Scientific Publications, pp. 65-70. . (1959), "The Propensity Interpretation of Probability", British Journal for the Philosophy of Science 10: 25-42. . (1963), "Three Views Concerning Human Knowledge", in Conjectures and Re- futations. London: Routledge and Kegan Paul, pp. 97-119. (1967), "Quantum Mechanics without 'The Observer"', in Quantum Mechanics and Reality, M. Bunge (ed.). Berlin: Springer. . (1982), Quantum Theory and the Schism in Physics. London: Hutchinson. Redhead, M. L. G. (1983), "Nonlocality and Peaceful Coexistence", in Space, Time and Causality, R. Swinburne (ed.). Dordrecht: D. Reidel, pp. 151-89. Swinburne, R. (ed.) (1974), The Justification of Induction. London: Oxford University Press. van Fraassen, B. C. (1980), The Scientific Image. Oxford: Clarendon Press. Article Contents p. 23 p. 24 p. 25 p. 26 p. 27 p. 28 p. 29 p. 30 p. 31 p. 32 p. 33 p. 34 p. 35 p. 36 p. 37 p. 38 p. 39 p. 40 p. 41 p. 42 p. 43 Issue Table of Contents Classical Antiquity, Vol. 13, No. 1 (Apr., 1994), pp. 1-144 Front Matter The Confirmation of Quantitative Laws [pp. 1-22] Are Probabilism and Special Relativity Incompatible? [pp. 23-43] The History of Quantum Mechanics as a Decisive Argument Favoring Einstein over Lorentz [pp. 44-63] A Note on Quantum Theory, Complementarity, and Uncertainty [pp. 64-77] Narrow Taxonomy and Wide Functionalism [pp. 78-97] Are Punctuationists Wrong about the Modern Synthesis? [pp. 98-109] Probabilistic Causality and Simpson's Paradox [pp. 110-125] Approximative Explanation Is Deductive-Nomological [pp. 126-140] Discussion What Would Happen If Everyone Did It? A Reply to Collier and Giere on Frequency Dependent Causation [pp. 141-150] Note on Tense and Subjunctive Conditionals [pp. 151-153] Quantum Mechanics and Value Definiteness [pp. 154-156] Book Reviews Review: untitled [pp. 157-159] Review: untitled [pp. 159-160] Review: untitled [pp. 161-163] Review: untitled [pp. 163-165] Review: untitled [pp. 165-166] Review: untitled [pp. 166-167] Review: untitled [pp. 168-169] Review: untitled [pp. 169-170] Review: untitled [pp. 170-171] Back Matter [pp. 172-176]