References

1 The metaphysics of special relativity:

three views

William Lane Craig

Introduction

A physical theory is comprised of two components: a mathematical formalism and a physical interpretation of that formalism. Competing theories which differ only in virtue of their divergent physical interpretations can be extremely difficult to assess if they are empirically equivalent in their testable predictions. Considerations which are metaphysical in nature may then become paramount.

The Special Theory of Relativity (hereafter SR) provides a case in point. Herman Bondi has remarked that ‘‘there is perhaps no other part of physics that has been checked and tested and cross-checked quite as much as the Theory of Relativity’’ (Bondi 1964: 168). Indeed, muses J. G. Taylor, ‘‘as far as special relativity is concerned all has been worked out and tested;’’ the theory has enjoyed ‘‘remarkable successes, and absolutely no failures’’ (Taylor 1975, preface). The empirical success of SR’s testable predictions can, however, be misleading, dulling us to the truly controversial nature of the correct physical interpretation of the theory’s formalism. The fact is that the only version of SR which is experimentally verifiable, as Geoffrey Builder points out, ‘‘is the theory that the spatial and temporal coordinates of events, measured in any one inertial reference system, are related to the spatial and temporal coordinates of the same events, as measured in any other inertial reference system, by the Lorentz transformations’’ (Builder 1971: 422). But this verifiable statement is underdeterminative with regard to the radically different physical interpretations of the Lorentz transformations given, respectively, by Einstein, Minkowski, and Lorentz.

During the decades in which positivism dominated the philosophy of science these differences tended to be glossed over, since empirically equivalent physical interpretations of the same mathematical formalism were regarded as but different linguistic expressions of the same theory. But with the collapse of positivism – arguably the most important event in philosophy in the second half of the twentieth century (Burge 1992: 49) – such indifference toward the fundamentally different ontological structures of space, time, and space-time which appear in these three interpretations can no longer be ignored. Unfortunately the articulation of a post-positivist philosophy of space and time has only scarcely begun. Minkowskians have issued critiques of Einsteinians in the effort to justify the former’s space-time realism, and the largely marginalized neo-Lorentzians have criticized what we might call the received interpretation of SR (an Einsteinian-Minkowskian amalgam which fails to differentiate these viewpoints) for its denial of relations of absolute simultaneity; but I know of no critical appraisal in the literature which lays these three interpretations side by side and attempts to come to some adjudication of them. In this paper I propose to do just that.

Three relativistic interpretations

The Einsteinian interpretation

SR, as Einstein originally formulated it, postulates a 3+1-dimensional ontology, not a 4-dimensional ontology (Einstein 1981). That is to say, it is a theory of familiar physical objects enduring through time. Space and time are relativised to reference frames, which serve to define distant simultaneity and along with it notions like rest, motion, speed, and velocity. Light is postulated to have the constant velocity c in every reference frame. Because physics is relativised to reference frames, clocks run at different rates and measuring rods have different lengths relative to different frames. Such an interpretation of SR implies an anti-realist or instrumentalist understanding of Minkowski space-time. There is no tenselessly subsisting manifold of events; space-time is a theoretical construct only, a geometrical representation of a theory which is really about physical objects enduring through time. A Minkowski diagram will prove to be a helpful tool, but it neither depicts reality nor implies an ontology. A good representative of this original Einsteinian perspective is the French physicist Henri Arzeliés. In his Relativistic Kinematics, Arzeliés asserts, ‘‘The Minkowski continuum is an abstract space of four dimensions, the sole role of which is to interpret in geometrical language statements made in algebraic or tensor form. . . . The four-dimensional continuum should therefore be regarded as a useful tool, and not as a physical ‘reality’’’ (Arzeliés 1966: 258). While it is true that relativity theory banishes the notions of absolute spatial and temporal intervals from physics, nonetheless ‘‘It is perfectly clear that in relativity, the ordinary three-dimensional space (which is Euclidian in special relativity) and the time of pre-relativistic physics is employed’’ (Ibid).

The Minkowskian interpretation

There is no gainsaying Arzeliés insofar as Einstein’s original formulation of SR is concerned. But it is also indisputable that once having encountered Minkowski’s geometrical formulation of the theory, Einstein became an outspoken realist concerning space-time (Einstein and Infeld 1938: 219; Einstein 1961: 150; Einstein and Besso 1979: 276–77). Minkowski took his space-time ontologically: it was not merely a geometrical representation of the world of space and time as described by Einstein’s SR; rather it was the world. When he said, ‘‘A point of space at a point of time, that is, a system of values x, y, z, t, I will call a world-point. The Multiplicity of all thinkable x, y, z, t systems of values we will christen the world,’’ (Minkowski 1952: 76) he was making self-consciously a metaphysical statement, proposing a new ontology. Heralding ‘‘a metamorphosis of our concept of nature,’’ Minkowski declared, ‘‘Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality’’ (Ibid., 75, 76). On this second interpretation of SR, the notions of reference frames, invariant velocity of light, distant simultaneity, relative motion or rest, and so forth, so central to the Einsteinian interpretation, play no role. Rather the central feature of this interpretation is the light cone structure at any space-time point, which determines the geometrical properties of space-time. In 1911 A. A. Robb was able to recover all the geometric structure of Minkowski space-time on the basis of the single relation after among its points, conjoined with several conditions of that relation (Robb 1913). Taking Robb’s relation to be extensionally equivalent to some sort of causal relation, recent theorists have defined causally the Lorentz group of transformation equations (Zeeman 1964: 490–93), orthogonality to a time-line in Minkowski space-time (Malament 1977: 293–300), and the metrical congruence of intervals in that space-time (Winnie 1977: 134–205). Space-time realists debate intramurally whether causality is truly constitutive of, rather than merely (at best) coextensive with, Robb’s fundamental relation, but the point remains that the familiar physical entities of the Einsteinian interpretation make no appearance in the space-time interpretation. These two interpretations of relativity theory thus present strikingly different metaphysical visions of reality; they are as radically divergent in their ontologies as is relativity theory itself in comparison with the Newtonian physics of absolute time and space. Minkowski’s space-time approach to relativity theory, especially with the development of the General Theory of Relativity (GR), has come to be the dominant mode of presentation and discussion of relativity.

The Lorentzian interpretation

It is an interesting historical fact that neither of the giants of late nineteenth century physics to whom Einstein looked for inspiration in his work on SR, H. A. Lorentz and Henri Poincaré, was ever convinced, despite being fully apprised of the empirical facts, of the truth of the Einsteinian or Minkowskian interpretations of the Lorentz transformations. Well after Einstein had formulated his SR and as he struggled to craft a GR, Lorentz in particular continued to study and lecture on problems of relativity, often in connection with Einstein. By 1908 Lorentz had already realized the incompatibility of his electron theory with Planck’s quantum hypothesis, and by the 1911 Solvay Congress there was a general sense that the electron theory would have to be radically reformed in light of the advent of quantum physics (McCormach 1970: 486–88). Nonetheless, since Lorentz’s attempted explanation of the phenomenon of length contraction in terms of the deformable electron was not essential to his basic physical interpretation of SR, Lorentz continued to adhere to an approach to relativity theory which preserved the classical notions of space and time. A theory may be classified as Lorentzian just in case it affirms that (i) physical objects are n-dimensional spatial entities which endure through time; (ii) the round trip vacuum propagation of light is isotropic in a preferred (absolute) reference frame R_o (with speed c = 1) and independent of the velocity of the source; and (iii) lengths contract and time rates dilate in the customary special relativistic way only for systems in motion with respect to R_o (Maciel and Tiomno 1989: 507–8).

Lorentz always spoke appreciatively of Einstein’s alternate approach and lectured sympathetically on both SR and GR, while remaining finally unconvinced that Einstein had abolished the classical conceptions of time and space. Writing in 1910, he contrasted his view with Einstein’s:

Assume there were an aether; then there would be among all systems x, y, z, t one singled out in that the coordinate axes as well as the clock is at rest in the aether. If one conjoins with this the idea . . . that space and time are something wholly different and that there is a ‘true time’ (simultaneity would then exist independently of location, in accord with the circumstance that it is possible for us to conceive of infinitely great velocities), then one easily sees that this true time would have to be indicated just by clocks which are at rest in the aether. If, then, the principle of relativity were generally valid in nature, then one would not be in a position to determine whether the coordinate system employed is that distinguished one. One thus comes to the same results as when one in agreement with Einstein and Minkowski denies the existence of the aether and the true time and treats all coordinate systems as equivalent. Which of the two modes of thought one may agree with is best left to the individual.

(Lorentz 1934: 211)

Lorentz, realizing that his aether compensatory interpretation is empirically equivalent to the Einstein-Minkowski interpretations, leaves it up to the individual to choose which he shall adopt. But Lorentz preferred the classical conceptions of time and space on metaphysically intuitive grounds, as he made clear in his 1922 lectures at Cal Tech:

All our theories help us form pictures, or images, of the world around us, and we try to do this in such a way that the phenomena may be coordinated as well as possible, and that we may see clearly the way in which they are connected. Now in forming these images we can use the notions of space and time that have always been familiar to us, and which I, for my part, consider as perfectly clear and, moreover, as distinct from one another. My notion of time is so definite that I clearly distinguish in my picture what is simultaneous and what is not.

(Lorentz 1927: 221)

Here Lorentz refuses to jettison what he took to be the intuitively obvious reality of absolute simultaneity among events in the world just because one cannot determine which spatially separated events are simultaneous or because Einstein’s operationally re-defined notion of simultaneity is relative to reference frames. Moreover, he sees no good reason to scrap the intuitive distinctness of space and time in favor of Minkowski’s unified reality, space– time.

A major reason that Lorentz remained unconvinced was that he was not a positivist. In 1913 he wrote,

According to Einstein it has no meaning to speak of motion relative to the aether. He likewise denies the existence of absolute simultaneity.

It is certainly remarkable that these relativity concepts, also those concerning time, have found such a rapid acceptance.

The acceptance of these concepts belongs mainly to epistemology . . . It is certain, however, that it depends to a large extent on the way one is accustomed to think whether one is attracted to one or another interpretation. As far as this lecturer is concerned, he finds a certain satisfaction in the older interpretations, according to which the aether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of. In regard to this last point, one may perhaps appeal to our ability of imagining arbitrarily large velocities. In that way, one comes very close to the concept of absolute simultaneity.

Finally, it should be noted that the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, [a restriction] which cannot be accepted without some reservation.

(Lorentz 1920a: 23)

Here Lorentz clearly discerns the foundational role played by Einstein’s verificationist theory of meaning in his formulation of SR and rejects it. In defense of absolute simultaneity, Lorentz appeals to the use of arbitrarily fast signals, even though they are not presently observable. He disregards the assumption that it is meaningless to speak of such unobservables. Elsewhere Lorentz affirms that it makes sense, if there is an aether, to speak of motion relative to it even if observers could not detect such motion (Lorentz 1914: 26). He writes,

But it needs to be clearly recognized that A could never assure himself of the immobility in the ether which we have attributed to him by supposition and that physicist B could with the same right, or rather with the same absence of right, claim that it is he who finds himself in these privileged circumstances. This incertitude, this impossibility of even disclosing a movement in relation to the aether, led Einstein and numerous other modern physicists to abandon completely the notion of an aether.

There, it seems to me, is a question toward which each physicist must take a position which best accords with the manner of thinking to which he is accustomed.

(Lorentz 1934: 7: 165)

Lorentz’s conception of the aether was virtually equivalent to space itself. His aether was so dematerialized that Einstein, lecturing at the University of Leiden in 1920, could tease the Dutch physicist by declaring, ‘‘As regards the mechanical nature of Lorentz’s aether one might say of it, with a touch of humor, that immobility was the only mechanical property which H. A. Lorentz left it’’ (Einstein 1920: 7). For Lorentz the aether is just the privileged spatial frame.

Lorentz thus accepts a 3+1 ontology of spatial objects enduring through a privileged time, a metaphysic which he felt no obligation to abandon out of deference to a verificationist epistemology.

Assessment of the interpretations

Metaphysical underpinnings of the classical concept of time

In another place I have argued that the collapse of positivism during the second half of the twentieth century has re-opened the discussion of the metaphysical foundations of the classical concept of time and that only Lorentz’s approach to problems of space and time, in contrast to Einstein and Minkowski’s, has remained unshaken by this epistemological revolution (see Craig 2002: 129–52). Specifically, I sought to expose the theological foundations of the classical concept of time as enunciated by Isaac Newton in his epochal Philosophiae naturalis principia mathematica.

By way of review, the locus classicus of Newton’s exposition of his concepts of time and space is the Scholium to his Definitions in the Principia. In order to overcome ‘‘common prejudices’’ concerning such quantities as time, space, place, and motion, Newton draws a dichotomy with respect to these quantities between ‘‘absolute and relative, true and apparent, mathematical and common.’’ With regard to time he asserts:

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

(Newton 1966 1:6)

Newton’s much misunderstood and greatly maligned distinction between absolute and relative time deserves our thoughtful consideration.

The most evident feature of this distinction is the independence of absolute time from the relative measures thereof. Absolute time, or simple duration, exists regardless of the sensible and external measurements which we try, more or less successfully, to make of it. Newtonian time is thus first of all absolute in the sense that time itself is distinct from our measures of time.

But, of course, Newton also conceived time as absolute in a more profound sense, namely, he held that time is absolute in the sense that it exists independently of any physical objects whatsoever. Usually, this is interpreted to mean that time would exist even if nothing else existed, that there exists a possible world which is completely empty except for the container of absolute space and the flow of absolute time. But here we must be very careful. Modern scholars tend frequently to forget how ardent a theist Newton was and how central a role this theism played in his metaphysical outlook. Noting that Newton considered God to be temporal and therefore time to be everlasting, David Griffin observes that ‘‘Most commentators have ignored Newton’s heterodox theology, and his talk of ‘absolute time’ has been generally misunderstood to mean that time is not in any sense a relation and hence can exist apart from actual events’’ (Griffin 1986: 6–7).

In fact, Newton makes quite clear in the General Scholium to the Principia, which he added in 1713, that absolute time and space are constituted by the divine attributes of eternity and omnipresence:

He is eternal and infinite . . .; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity . . . . He is not eternity and infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures forever, and is everywhere present; and, by existing always and everywhere, he constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is everywhere, certainly the Maker and Lord of all things cannot be never and nowhere.

(Newton 1966: 2: 545)

Because God is eternal, there exists an everlasting duration, and because He is omnipresent, there exists an infinite space. Absolute time and space are therefore relational in that they are contingent upon the existence of God.

In his treatise De gravitatione (Newton 1962: 89–156), Newton declares explicitly that space is not in itself absolute (non absoluta per se) and therefore not a substance. Rather it is an eminent – or emanative – effect of God (Dei effectus emanativus). It is uncreated and co-existent with God and yet ontologically dependent upon him for its being. God’s infinite being has as its consequence infinite time and space, which represent the quantity of his duration and presence. In the Neo-Platonic tradition the doctrine of emanation is associated with pantheism or panentheism. But, as Newton makes clear, he does not conceive of space or time as in any way aspects of God himself, but rather, as he says, concomitant effects of God.

It is evident that when Newton speaks of divine eternity, he does not, like scholastic theologians in the Augustinian tradition, mean a state of timelessness, but rather infinite and everlasting temporal duration. In a preliminary draft of the General Scholium, Newton had explicitly rejected the conception of God’s eternity as an eternal now: ‘‘His duration is not a nunc stans without duration, nor is his presence nowhere’’ (cited in McGuire 1990: 93). Far from being atemporal, God’s now or present is the present of absolute time. Since God is not ‘‘a dwarf-god’’ located at a place in space (Newton 1978: 114–29) but is omnipresent, every indivisible moment of duration is everywhere, as Newton states in the General Scholium. There is thus a worldwide moment which is absolutely present. Newton’s temporal theism thus provides the foundation for both absolute simultaneity and absolute becoming. These are features first and foremost of God’s time or metaphysical time and derivatively of measured or physical time.

Now Newton provides virtually no argument to think that God is temporal; he simply asserts it. But I have argued elsewhere that on a tensed or (to borrow McTaggart’s convenient terminology) an A-Theory of time, according to which tense and temporal becoming are objective features of reality, God must be temporal in virtue of His knowledge of tensed facts and His causal relation to the world (Craig 1998b: 221–50). Hence, if God exists and an A-theory of time is correct, Newton is justified so far forth in holding that there is absolute time in the sense of a metaphysical time which is independent of physical time.

Newton freely grants that although absolute time exists it may well be the case that due to the inaccuracies of our measures the true time is not disclosed to us (Newton 1966: 1:7–8). What Newton did not realize, nor could he have suspected, is that physical time is not only relative, but also relativistic, that the approximation of physical time to absolute time depends not merely upon the regularity of one’s clock, but also upon its motion. Unless a clock were at absolute rest, it would not accurately register the passage of absolute time. A clock moving relatively to oneself runs slowly. This truth, unknown to Newton, only intimated by Larmor and Lorentz in the concept of ‘‘local time,’’ was finally grasped by Einstein.

Where Newton fell short, then, was not in his analysis of absolute or metaphysical time – he had theological grounds for positing such a time – but in his incomplete understanding of physical time. He assumed too readily that an ideal clock would give an accurate measure of time independently of its motion. If confronted with relativistic evidence, Newton would no doubt have welcomed this correction and seen therein no threat at all to his doctrine of absolute time. In short, relativity corrects Newton’s concept of physical time, not his concept of absolute time.

Of course, it hardly needs to be said that there is a great deal of antipathy in modern physics and philosophy of science toward such metaphysical realities as Newtonian space and time, primarily because they are not physically detectable. But Newton would have been singularly unimpressed with this positivistic equation between physical undetectability and non-existence. The grounds for metaphysical space and time were not physical, but philosophical, or more precisely, theological. Epistemological objections fail to worry Newton because, as Lucas nicely puts it, ‘‘He is thinking of an omniscient, omnipresent Deity whose characteristic relation with things and with space is expressed in the imperative mood’’ (Lucas 1973: 143). Modern physical theories say nothing against the existence of such a God or the metaphysical time constituted, in Newton’s thinking, by His eternity. What Einstein’s relativity theory did, in effect, was simply to remove God from the picture and to substitute in His place a finite observer. ‘‘Thus,’’ according to Holton, ‘‘the RT [Relativity Theory] merely shifted the focus of space-time from the sensorium of Newton’s God to the sensorium of Einstein’s abstract Gedanken experimenter – as it were, the final secularization of physics’’ (Holton 1973: 171). But for a man like Newton such a secular outlook impedes rather than advances our understanding of the nature of reality.

Unfortunately in our secular age physicists and philosophers of space and time rarely, if ever, give careful consideration to the difference God’s existence would make for our conceptions of time and space. But in a fascinating passage in his essay ‘‘La mesure de temps,’’ Poincaré does briefly entertain the hypothesis of ‘‘une intelligence infinie’’ and considers the implications of such a hypothesis. Poincaré is reflecting on the problem of temporal succession. In consciousness, the temporal order of mental events is clear. But going outside consciousness, we confront various difficulties. One of these concerns is how we can apply one and the same measure of time to events which transpire in ‘‘different worlds,’’ that is, to spatially distant events. What does it mean to say that two psychological phenomena in two consciousnesses happen simultaneously? Or what does it mean to say a supernova occurred before Columbus saw the isle of Espanola? ‘‘All these affirmations,’’ says Poincaré, ‘‘have by themselves no meaning’’ (Poincaré 1982: 228). Then he remarks,

We should first ask ourselves how one could have had the idea of putting into the same frame so many worlds impenetrable to one another. We should like to represent to ourselves the external universe, and only by so doing could we feel that we understood it. We know we can never attain this representation: our weakness is too great. But at least we desire the ability to conceive an infinite intelligence for which this representation could be possible, a sort of great consciousness which should see all, and which should classify all in its time, as we classify, in our time, the little we see.

This hypothesis is indeed crude and incomplete, because this supreme intelligence would be only a demigod; infinite in one sense, it would be limited in another, since it would have only an imperfect recollection of the past; it could have no other, since otherwise all recollections would be equally present to it and for it there would be no time. And yet when we speak of time, for all which happens outside of us, do we not unconsciously adopt this hypothesis; do we not put ourselves in the place of this imperfect god; and do not even the atheists put themselves in the place where God would be if he existed?

What I have just said shows us, perhaps, why we have tried to put all physical phenomena into the same frame. But that cannot pass for a definition of simultaneity, since this hypothetical intelligence, even if it existed, would be for us impenetrable. It is therefore necessary to seek something else.

(Ibid. 228–29)

Poincaré here suggests that, in considering the notion of simultaneity, we instinctively put ourselves in the place of God and classify events as past, present, or future according to His time. Poincaré does not deny that such a perspective would disclose to us true relations of simultaneity. But he rejects the hypothesis as yielding a definition of simultaneity because we could not know such relations; such knowledge would remain the exclusive possession of God Himself.

But clearly, Poincaré’s misgivings are relevant to a definition of simultaneity only if one is presupposing some sort of verificationist theory of meaning, as he undoubtedly was. The fact remains that God would know the absolute simultaneity of events even if we grope in total darkness. Nor need we be concerned with Poincaré’s argument that such an infinite intelligence would be a mere demigod, since it is a non sequitur that a being with perfect recollection of the past cannot be temporal. There is no conceptual difficulty in the idea of a being which knows all true past-tense propositions. That such a being would be temporal is evident from the fact that as events transpire, more and more past tense propositions become true, so that the content of his knowledge is constantly changing. Hence, it does not follow that if God is temporal, He cannot have perfect recollection of the past.

Pioncaré’s hypothesis suggests, therefore, that God’s present is constitutive of relations of absolute simultaneity. Lorentz agreed. In a passage redolent of the General Scholium and Opticks of Newton, Lorentz in a letter to Einstein in January of 1915 broached considerations whereby ‘‘I cross the borderland of physics’’:

A ‘World Spirit’ who, not being bound to a specific place, permeated the entire system under consideration or ‘in whom’ this system existed and who could ‘feel’ immediately all events would naturally distinguish at once one of the systems U, U´, etc. above the others.

(Lorentz 1989: 274)

Such a being, says Lorentz, could ‘‘directly verify simultaneity’’. On this view, J. M. Findlay was wrong when he said, ‘‘. . . the influence which harmonizes and connects all the world-lines is not God, not any featureless, inert, medium, but that living, active interchange called . . . Light, offspring of Heaven firstborn’’ (Findlay 1978–79: 6–7). On the contrary, the use of light signals to establish clock synchrony is a convention which finite and ignorant creatures have been obliged to adopt, but the living and active God, who knows all, would not be so dependent.

In God’s temporal experience, there would be a moment which is present in metaphysical time, wholly independently of physical clock times. He would know, without any dependence on clock synchronization procedures or any physical operations at all, which events were simultaneously present in metaphysical time. He would know this simply in virtue of His knowing at every such moment the unique set of present-tense propositions true at that moment, without any need of a sensorium or physical observation of the universe.

How, then, would God’s metaphysical time relate to our physical time? From what has been said thus far, it seems that God’s existence in metaphysical time and His real relation to the world would imply that a Lorentzian interpretation of relativity is correct. Such a theory is required in view of divine temporality, for God in the ‘‘now’’ of metaphysical time would know which events in the universe are now being created by Him and are therefore absolutely simultaneous with each other and with His ‘‘now.’’ This startling conclusion shows clearly that Newton’s theistic hypothesis is not some idle speculation, but has important implications for our understanding of how the world is and for assessment of rival scientific theories.

Accordingly, we may argue

It seems to me that this argument is cogent. As a theist, therefore, I accept (13). However, I recognize that non-theistic thinkers will be little moved by the argument. Therefore, it would be interesting to ask whether for the sake of dialectical effectiveness the argument might not be freed of its theistic underpinnings. Reflection on the argument convinces me that this is, indeed, possible. For the yeoman’s work in this argument is done, not the assumption of theism, but rather by the assumption of an A-theory of time. One may plausibly argue directly, I think, that if an A-Theory of time is correct, then a Lorentzian interpretation of SR is correct. In the sequel, therefore, I shall abandon the assumption that God exists and seek to assess the three competing, physical interpretations of SR given merely the fact that we have good grounds for affirming the reality of tense and temporal becoming.

The Einsteinian interpretation

The characteristic feature of the Einsteinian interpretation of the SR formalism is its attempt to wed relativity with a classical 3+1 ontology of space and time. While this original interpretation is today largely disfavored in the foundations of physics community, it nevertheless continues to enjoy widespread acceptance among philosophers, particularly those embracing a tensed, as opposed to tenseless, theory of time and those advocating an endurantist, as opposed to a perdurantist, account of temporal persistence. It therefore merits our consideration. I shall argue that the Einsteinian interpretation is implausible and explanatorily deficient.

First, the pluralistic fragmentation of reality into distinct spaces and times associated with reference frames is an ontology which is, to put it bluntly, fantastic. This is a complaint voiced by many space-time realists. At the root of the complaint lies the conviction that there is a single world, an objective reality independent of observers, the conviction that if we both exist then what co-exists with me co-exists with you. It is fantastic to think that you and I, occupying the same location in space and time, but in relative motion, should in virtue of that motion literally dwell in two different worlds, which intersect only at a point. Yet SR requires that even if we are merely passing each other in automobiles, our hyperplanes of simultaneity do not coincide, and at sufficient distances empirically distinguishable events and things are occurring and exist for me which are future and therefore unreal for you. Other events which are in my future and therefore unreal are already actual for you. But if I decelerate and we come to relative rest, then we share the same reality; events which were once present and real in relation to me are now non-existent and future. One can change frames and, hence, realities just by changing one’s relative motion.

By contrast, on the Minkowskian interpretation, which makes no link between simultaneity and reality, events do not pop in and out of existence as I switch reference frames. All that changes is which class of events is orthogonal to my world-line in space-time at a designated point and, hence, which events I reckon to be simultaneous with my present. All the events subsist tenselessly, and different hyperplanes in space-time serve merely to mark out which events count as simultaneous relative to my inertial frame. There is a shared, objective reality which exists independently of observers or reference frames, and we all inhabit the same space-time world; we just reckon different events in that one world to stand in the relation of simultaneity with one another. On a space-time ontology, there is thus a unified, independent reality which is merely measured differently by observers using different coordinate systems. But on the Einsteinian interpretation, reality literally falls apart, and there is no one way the world is.

Second, the Einsteinian interpretation is explanatorily deficient. On the Einsteinian interpretation physical objects have properties of shape, mass, and duration only extrinsically, relative to inertial frames, yet why this is so is not explained (Christensen 1993: 260; Nerlich 1994: 5). Moreover, it is unclear why 3-dimensional objects enduring through time suffer relativistic effects such as length contraction and time dilation in virtue of their being in relative motion. It is important to realize that under the 3+1-dimensional ontology of the Einsteinian interpretation these relativistic effects are just as much real, physical effects as under aether compensatory theories such as Lorentz’s. On the Einsteinian interpretation length contraction and clock retardation cannot be dismissed as merely apparent phenomena on the analogy of the mutual observation of diminishing size when two observers retreat from each other. Admittedly, since length contraction and time dilation are reciprocal and the result of merely relative motion, it does seem incredible that they could be anything more than mere appearances, just as the so-called ‘‘pure relativists’’ like Bergson and Dingle insisted (see Dingle 1940; Bergson 1965). But Einstein realized right from the start that these effects described in his theory were real, not apparent, and could be shown to be real by various Gedankenexperimente. Examples could be multiplied (see Shaw 1962: 72; and further, Jánossy 1971: 128–31; Lorenz 1982: 308–12) to prove that, perhaps contrary to expectation, the Einsteinian interpretation of relativity theory involves real, physical length contraction and clock retardation, just as much as does the Lorentzian theory. Podlaha concludes,

In the relativity theory, the length contraction and time dilatation in all frames is often viewed as a consequence of a ‘perspective of observation,’ similarly as a rod seems to change its length as observed under different angles. . . . however, it is seen that the results of relativistic experiments have their origin in the length contraction and time dilatation effects which are so real as a change of the length of a rod caused by the change of temperature.

(Podlaha 1975: 74–75)

Podlaha’s comments are quite correct, at least as far as the Einsteinian interpretation of SR is concerned.

The Einsteinian interpretation is explanatorily deficient in that it provides, indeed, permits, no causal account of these real, physical distortions of 3-dimensional continuants. In contrast to the Lorentzian theory, which sought for a causal explanation for these relativistic effects, in the Einsteinian interpretation they are just deduced from the theory’s postulates. Lorentz himself remarked on this difference between the theories:

His [Einstein’s] results concerning electromagnetic and optical phenomena . . . agree in the main with those which we have obtained in the preceding pages. The chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electro-dynamic field. By doing so, he may certainly take credit for making us see in the negative results of experiments like those of Michelson, . . . not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle. Yet, I think something may also be claimed in favor of the form in which I have presented the theory. I cannot but regard the ether which can be the seat of an electromagnetic field with energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from ordinary matter.

(Lorentz 1952: 229–30)

According to Arthur Miller,

The principle of relativity of Bucherer, Lorentz, and Poincaré resulted from careful study of a large number of experiments, and it was on the basis of a theory in which empirical data could be explained to have been caused by electrons interacting with an ether. Einstein’s principle of relativity excluded the ether of electromagnetic theory and did not explain anything.

(Miller 1981)

On the Einsteinian interpretation, then, such relativistic phenomena involve real deformations of 3-dimensional objects enduring through time which have no causal explanation, but are merely correlated with different reference frames. They come simply as deductions from the two postulates of the theory. By contrast, on the Minkowskian interpretation, 3-dimensional objects do not suffer length contraction or time dilation for the simple reason that 3-dimensional objects do not exist. Reality is 4-dimensional, and the account of relativistic phenomena is, on this interpretation, much more akin to the change of perspective imagined by the pure relativists. Given a space-time ontology, the different length and time measurements given for specific objects and events by various observers is, as Taylor and Wheeler put it, just a matter of looking at them ‘‘from several angles’’ (Taylor and Wheeler 1966: 4). A 4-dimensional object viewed from a certain angle will appear fore-shortened in comparison with the object as viewed from a different angle. Less metaphorically, because coordinate time and length intervals, as opposed to proper time and length intervals, are not invariant under the Lorentz transformation equations, they vary from coordinate system to coordinate system. A Lorentz transformation may be regarded merely as a rotation of the coordinate axes in 4-dimensional space-time, with the result that different coordinate lengths and temporal intervals will be assigned to the same 4-dimensional object. Although this rotation of the axes is obscured in a 2-dimensional Minkowski diagram, it may be more perspicuously exhibited by means of a Loedel diagram. Thus length contraction is not the mysterious (reciprocal!) shrinking of enduring, 3-dimensional objects in relative, uniform motion, but merely the result of our applying different coordinate systems to the unchanging, 4-dimensional, spatio-temporal object and subtracting the values of the spatial coordinates of its endpoints. Similarly, time dilation does not involve a literal slowing down of relatively moving clocks as they endure through time, but rather results from the application of different coordinate systems to the changeless 4-dimensional object and calculating the difference between the temporal coordinates of two events. Moreover, in the pseudo-Euclidian Minkowski space-time a curved world-line between two points is the shortest distance, and hence, the clock of an observer tracing out such a path through space-time will record less time than a clock following a straight path. Thus in the Twin Paradox, although the path of the traveling twin appears in a Minkowski diagram to be longer than that of his stationary counterpart, that impression is due to the 2-dimensionality of the diagram. In 4-dimensional space-time, the path of the traveling sibling is actually shorter than that of the earth-bound twin (see Bondi 1964: 67; Taylor and Wheeler 1966: 34). Therefore, it is not surprising that his clock records less time and that he is younger than his brother at their reunion. Since length measurements are inherently dependent upon time measurements (lengths being a matter not simply of computing x₂ – x₁, but x₂(t₂) – x₁(t₁) on the assumption that t₂ = t₁), it is not surprising that a relatively moving rod, as viewed by a particular observer, should be calculated to suffer contraction. But, in a sense, the contraction of rods and the retardation of clocks is on the space-time interpretation ultimately a chimera, since 3-dimensional, enduring objects like rods and clocks do not exist.

Einsteinians and Lorentzians are apt to regard the space-time account as a pseudo-explanation masquerading as a genuinely explanatory account. But that is to fail to take seriously the 4-dimensional ontology of the Minkowskian. Given that such an ontology of physical objects is correct, as opposed to the ontology of continuants presupposed by proponents of the Einsteinian and Lorentzian interpretations, one can appreciate why Nerlich, an enthusiastic Minkowskian, finds ‘‘the elegant spacetime interpretation of the Fitzgerald contraction and the ‘slowing of moving clocks’ extraordinarily insightful and intuitive’’. By contrast the Einsteinian interpretation is markedly explanatorily deficient.

In summary, the Einsteinian interpretation of the SR mathematical formalism, with its pluralistic ontology and contracting and retarded 3-dimensional continuants, is fantastic and explanatorily impoverished.

The Minkowskian interpretation

The great advantage of the Einsteinian interpretation is that by retaining a classical 3+1-dimensional ontology of space and time, it makes room for the objective reality of tense and temporal becoming. By contrast, the Minkowskian interpretation through its commitment to space-time realism precludes temporal becoming and seems to permit no room for tensed properties or modes of existence like presentness. The Minkowskian interpretation thus flies in the face of our experience of time. Psychologist William Friedman, who has made a career of the study of time consciousness, reports, ‘‘Like [temporal] order and the causal priority principle, the division between past, present, and future so deeply permeates our experience that it is hard to imagine its absence’’ (Friedman 1990: 92). We have, he writes,

an irresistible tendency to believe in a present. Most of us find quite startling the claim of some physicists and philosophers that the present has no special status in the physical world, that there is only a sequence of times, that the past, present, and future are only distinguishable in human consciousness.

(Ibid. 2)

As a result, virtually all philosophers of space and time, including proponents of theories of tenseless time, admit that the view of the common man is that time involves a past, present, and future which are objectively real and that things or events really do come to be and pass away in time. For example, Oaklander grants that ‘‘non-philosophers have never doubted that there is such a phenomenon as temporal flow or passage. . . . ’’ (Oaklander 1984: 1). Horwich muses that ‘‘The quintessential property of time, it may seem, is the difference between past and future’’ (Horwich 1987: 15). Coburn confesses, ‘‘If the existence of A-facts [i.e., tensed facts] is an illusion, it is one of our most stubborn ones’’ (Coburn 1990: 118). Nerlich is forced to conclude, ‘‘Something in experience deludes us about time, something obvious and pervasive – there obtrusively in every thought and perception, yet elusive to analysis’’ (Nerlich 1998: 130). Mellor acknowledges, ‘‘the experienced presence of experience, is the crux of the tensed view of time. . . . and the tenseless camp must somehow explain it away’’ (Mellor 1981: 6).

Powerful considerations in favor of the objectivity of tensed facts and temporal becoming include (i) the indispensability and irreducibility of linguistic tense, which mirrors the tensed facts which are characteristic of reality; and (ii) our experience of presentness and temporal becoming, which, like our experience of the external world, may be plausibly taken to ground properly basic beliefs in the reality of tensed time. Powerful objections can, in turn, be lodged against theories of tenseless time, including (i) in the absence of objective distinctions between past, present, and future, the relations ordering events are only gratuitously regarded as genuinely temporal relations of earlier/later than; (ii) even the subjective illusion of temporal becoming involves itself an objective temporal becoming of contents of consciousness; and (iii) space-time realism implies perdurantism, the view that objects have spatio-temporal parts, a doctrine which is metaphysically counter-intuitive, incompatible with moral accountability, and entails the bizarre counterpart theory of transworld identity. Discussion of these several points lies far beyond the scope of this paper, but I think it is evident that any interpretation of reality which finds itself obliged to deny the reality of tensed facts and temporal becoming faces prima facie a disadvantage.

Certain Minkowskians have therefore argued that their interpretation of SR can be combined with a theory of tensed time. Thus, Howard Stein (Stein 1968: 14; 1991: 147–67; see also Capek 1976: 501–24; Denbigh 1978: 309) in response to Putnam’s claim that SR has eliminated the notion of becoming, proposes to relativise becoming to space-time points:

For an event at spacetime point a, those events, and only those, have already become (real or determinate), which occur at points in the topological closure of the past of a.

According to this explication, reality is relative to space-time points and consists in all those events lying inside or on the past-directed light cone of a, including a itself. According to Stein, in the context of SR we can only think of the temporal evolution of the world from the chronological perspective of each space-time point. There exists no knife-edge of becoming on this view, even for individual reference frames, but mere pinpoints of becoming constituted by the vertex of any hypothetical observer’s past light cone, none of which is privileged (see Clifton and Hogarth 1995: 355–87). Putnam’s error lay in thinking that the relation R ‘‘is real to’’ is transitive, such that an event at space-time point c, which is real for an observer at space-time point b, is also real to an observer at space-time point a, if events at b are real for a. Just as ‘‘is simultaneous with’’ is not a transitive relation, neither is R.

One of the major difficulties with such an attempt to combine space-time realism with temporal becoming is that it runs smack into McTaggart’s famous paradox (see Craig 1998a: 122–27). Space-time events would have somehow to remain identical over time even though they possess at different times different tense determinations like pastness and presentness, an apparently impossible feat. Moreover, this proposal relapses into the same fragmentation of reality characteristic of the Einsteinian interpretation. Worse, on this view present reality collapses to what is here at this point-instant. If this is not self-evidently absurd, Mellor also points out that if I-now am never located in London, then the bizarre conclusion follows that the tensed sentence ‘‘It is raining in London’’ is never true (Mellor 1973–74: 75–76; cf. Le Poidevin 1997: 541–46). Sklar notes the further strange consequence of this alternative that we must say that there will be events which are now such that they will be in my real past at some future time, but which will never have a present reality to me at all! (Sklar 1981: 140; cf. Dorato 1995: Chap. 12). That is because they are now in my future light cone and will be in my past light cone, but have no reality until they are past. Since neither future nor distant present events exist, how is it that such events become past without ever having been actualized in the present? Indeed, is it not self-contradictory to assert that the sentence ‘‘The Battle of Waterloo occurred’’ is true and yet that it was never true that ‘‘The Battle of Waterloo is occurring’’? Thus, the attempt to combine a theory of tensed time with a Minkowskian interpretation of relativity seems abortive.

The Minkowskian interpretation of SR thus faces the terrible dilemma of either denying the objective reality of tensed facts and temporal becoming or else succumbing to the same fragmentation of reality that plagues the Einsteinian interpretation and, if McTaggart is right, to incoherence. What is needed is a physical interpretation of the SR formalism predicated upon a coherent metaphysic which permits us to affirm both a theory of tensed time and a unified view of reality.

The Lorentzian interpretation

The Lorentzian interpretation seems to meet these desiderata. Lorentz’s 3+1dimensional ontology preserves the classical notions of space and time and so affords room for tensed facts and temporal becoming, and his aether compensatory approach to SR ensures the existence of absolute simultaneity and length without compromising empirical adequacy. Although in semi-popular expositions of SR scorn is usually poured upon the Lorentzian interpretation, the fact is that a small minority of physicists, including such notable figures as H. E. Ives, Geoffrey Builder, and S. J. Prokhovnik, have continued the Lorentzian research program down to the present day, so that the correct interpretation of relativity theory remains a matter of debate. In fact, that debate has intensified in recent years, so that an aether compensatory approach to SR ‘‘no longer has,’’ in Balashov’s words, the ‘‘distinctively pseudo-scientific flavor it has had until very recently’’ (Balashov 2000). There are a number of modern equivalents of an aether which serve to mark off a privileged frame with respect to which relations of absolute simultaneity can be defined:

The demonstration that reality is non-local seems to present us with a dilemma, either horn of which has, in turn, important implications for the existence of a privileged frame. Our first alternative is to hold that adjustments in the measuring device at point A are somehow causally linked to the state of the photon at point B. Since the collapse of the wave function occurs instantaneously over arbitrarily large distances, quantum theory on this interpretation requires that a measurement at A causes an instantaneous change at B. But such an instantaneous influence establishes absolute simultaneity and thus requires a re-interpretation of quantum theory along neo-Lorentzian lines. In his 1964 paper, Bell concluded, ‘‘ . . . there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant’’ (Bell 1983: 107). Such instantaneous causal connections serve to establish an absolute reference frame in which the events at A and B are simultaneous. Hence, Bell, later pondering the implications of Aspect’s experiments, comments,

I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincaré thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. . . . that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. . . . what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincaré, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view. . . . The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backward in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.

(‘‘John Bell,’’ (1986) interview in Davies and Brown;

cf. Bell 1987: 279; see also Bell 1984: 66–76)

If, then, we allow for causal connections between the events situated at points A and B, the EPR experiment implies the existence of absolute simultaneity and an ether frame.

And, in fact, such a theory exists in the form of the de Broglie-Bohm pilot wave model (Cushing et al. 1996). According to one recent discussant there has been ‘‘a sea change’’ in the foundations of physics community with respect to the possibility of relations of absolute simultaneity due to a new appreciation of the de Broglie-Bohm approach (Kennedy 1997). Bohmian quantum mechanics is mathematically consistent and consonant with all experimental results but is a deterministic theory featuring super-luminal causal influences. Callender and Weingard have applied Bohmian quantum mechanics cosmologically and report that ‘‘when cosmological factors are considered, the de Broglie-Bohm interpretation remains the only satisfactory interpretation of quantum theory’’ (Callender and Weingard 1994: 218). This model enables one to resolve the problem of time without having to split worlds, multiply minds, or even worry about observers’ collapsing wave functions. Time in the Bohmian model remains essentially the immutable, external, unobservable, unique time of Newtonian mechanics, in which the dynamic variables of cosmology, like the radius of the universe and the scalar field, evolve. Adoption of such an interpretation would require a Lorentzian approach to relativity theory, but an increasing number of theorists today are willing to give a serious look at Bohm’s interpretation. Even if the details of his theory undergo revision and development, the commitment to a preferred time will remain one of the defining features of such an approach.

Suppose, on the other hand, that we reject the existence of causal connections between events occurring at A and B in favor of some interpretation according to which the photons at A and B are somehow correlated, but not causally connected. On this interpretation, the composite state consisting of the two photons with their respective measuring devices constitutes a single system, which is in a definite state (see Bohr 1964: 145–51). To affect the behavior of one photon via measurement is to disturb the whole system. When the wave function of a photon at A collapses, there is an immediate and correlated collapse of the wave function of its counterpart at B. But clearly, even though this interpretation denies the super-luminal causal influence from A to B posited by the de Broglie-Bohm theory, it still just as effectively abrogates the relativity of simultaneity, since the collapse of the paired wave functions is simultaneous. Therefore, asseverations that such an interpretation would not run contrary to the received interpretation of SR because that theory prohibits only signals of super-luminal velocities, not instantaneous correlations, are quite beside the point. The point is that such correlations furnish the means of establishing relations of absolute simultaneity and a fundamental frame. As Maudlin points out

In Minkowski spacetime this theory of wave collapse no longer makes sense. The collapse can be instantaneous in at most one reference frame, leading to two possibilities: either some feature of the situation picks out a preferred reference frame, with respect to which the collapse is instantaneous, or the collapse is not instantaneous at all.

(Maudlin 1994: 196; cf. pp. 137–38, 144).

The problem posed by instantaneous collapse of the wave function for relativity theory can be clarified by realizing that since, according to SR, simultaneity is relative to reference frames, the collapse of the wave function for spatially separated photons will itself become relative to a reference frame. The problem is that properties like polarization and spin are not relational, but intrinsic properties of photons (Ryff 1992: 249). If the universe contained a single photon, it would have a definite polarization. Therefore the possession of such properties should not be made hyper-plane dependent. After surveying various attempts to integrate Bell’s Inequalities with relativity theory, Maudlin concludes that these attempts ‘‘entail such severe dislocations of our physical view that one must seriously consider whether our grounds for adhering to Relativity are really strong enough to justify such extreme measures’’ (Maudlin 1994: 239; cf. Eberhard 1978: 392–419). ‘‘Indeed, the cost exacted by those theories which retain Lorentz invariance is so high that one might rationally prefer to reject Relativity as the ultimate account of space-time structure’’ (Maudlin 1994: 220). The postulation of preferred hyper-planes of simultaneity in the structure of space-time is, in fact, the only position which does not face severe difficulties. The only objection to such an approach to quantum theory and EPR, which is essentially Lorentzian, is that it requires one to reject SR – or more strictly speaking, to reject those theories which are composed of the customary SR mathematical formalism conjoined with the physical interpretation of Einstein or Minkowski, respectively.

The above three physical realities – the cosmological fluid, the microwave background radiation, and the quantum mechanical vacuum – all serve to revitalize in a new guise the concept of the aether. Bohm himself, maintaining that there is ‘‘a unique spacetime frame, in terms of which ‘simultaneous contact’ would be specified,’’ comments, ‘‘Empirically, this should be close to the frame in which the mean velocity of the 3°K radiation background in space is zero.’’ Since the microwave background radiation is isotropic only with respect to the frame in which the fundamental particles of the expanding universe are at rest, the fundamental frame of the cosmic expansion fills the role of the preferred frame required by quantum theory. According to Prokhovnik

The notion of non-local causality, discussed by Bell, requires a criterion of simultaneity which has some absolute significance; it is seen that a cosmological basis for a universal measure of (cosmic) time resolves this problem. . . . the existence of an observationally-based fundamental frame is invaluable not only for the understanding of our universe and of Special Relativity, but also to make sense of quantum theory along the lines proposed, for example, by Dirac. . . . and John Bell.

(Prokhovnik preprint)

While differing markedly from the classical aether, the new ethers play the same essential role in marking off a unique, fundamental reference frame, the frame of expanding physical space, in which privileged relations of simultaneity may be established.

Empirical considerations may thus actually favor a Lorentzian interpretation of the mathematical formalism of SR. Lorentz’s prediction seems to have been vindicated when he mused, ‘‘In my opinion it is not impossible that in the future this road, indeed abandoned at present, will once more be followed with good results, if only because it can lead to the thinking out of new experimental tests’’ (Lorentz 1920b: 61–62). Certainly empirical considerations do not disqualify a Lorentzian approach. Are there, then, overriding non-empirical considerations for preferring the received interpretation of SR?

It is often asserted that the received interpretation is simpler and therefore to be preferred to a Lorentzian interpretation. However, as is well known, one must be very cautious about the connection between the simplicity of a theory and its truth, as opposed to its utility. In any case, the claim that the received interpretation is simpler is mistaken. Although Lorentz’s own theory was more complicated than Einstein’s, H. E. Ives was able to derive the Lorentz transformation equations from (i) the laws of conservation of energy and momentum; and (ii) the laws of transmission of radiant energy. ‘‘The space and time concepts of Newton and Maxwell are retained without alteration,’’ he wrote, ‘‘It is the dimensions of the material instruments for measuring space and time that change, not space and time that are distorted’’ (Ives 1979: 247, 255). On Ives’s achievement, Martin Ruderfer comments that he succeeded in elevating Lorentz’s ad hoc theory to an equal status with SR and did so with the same number of basic assumptions as Einstein, so that his theory has the same ‘‘beauty’’. ‘‘The Ives and Einstein interpretations represent two different, but equally valid, views of the same set of observations’’ (Ruderfer 1979: 243). Hence, assertions that the received interpretation is simpler than a Lorentzian interpretation are simply incorrect.

Probably at the root of many physicists’ rejection of a Lorentzian interpretation of relativity theory is the deep-seated conviction that comes to expression in Einstein’s aphorism: ‘‘Subtle is the Lord, but malicious He is not.’’ That is to say, if there exists a fundamental asymmetry in nature, then nature will not conspire to conceal it from us by precisely countervailing effects. D’Abro expresses this sentiment clearly:

If Nature was blind, by what marvelous coincidence had all things been so adjusted as to conceal a velocity through the ether? And if Nature was wise, she had surely other subjects to attend to, more worthy of her consideration, and would scarcely be interested in hampering our feeble attempts to philosophize. In Lorentz’s theory, Nature, when we read into her system all these extraordinary adjustments ad hoc, is made to appear mischievous; it was exceedingly difficult to reconcile one’s self to finding such human traits in the universal plan.

(d’Abro 1950: 138)

One difficulty with this objection is that it seems to be guilty of greatly over-exaggerating the extent of the alleged conspiracy. After all, SR is a restricted theory of relativity: it is only uniform motion relative to a privileged frame that fails to manifest itself. But in all other cases of motion, the absolute character of that motion is disclosed. This is not to say that acceleration or rotation proves the reality of privileged space, but it is to say that, given the classical concepts of time and space, nature does not at all conspire to conceal either absolute motion or the privileged space from us. Moreover, as we have seen, there are modern equivalents of the classical aether which serve plausibly to disclose a privileged frame. Indeed, when non-Lorentzians complain that no evidence of a privileged space and time exist, one wonders what it would take to convince them of the contrary. If no empirical evidence of a fundamental frame is incapable of being explained away, then the supposed failure of nature to disclose such a frame to us becomes trivial. The more difficult it is for nature to provide evidence of the existence of a privileged frame, the less compelling the charge that she is conspiring against us to conceal it.

But even considered in abstraction from these considerations, why accept the assumption that fundamental asymmetries in nature must disclose themselves to us? This assumption is by no means obvious, as Martin Carrier explains:

Science would be an easy matter if the fundamental states of nature expressed themselves candidly and frankly in experience. In that case we could simply collect the truths lying ready before our eyes. In fact, however, nature is more reserved and shy, and its fundamental states often appear in masquerade. Put less metaphorically, there is no straightforward one-to-one correspondence between a theoretical and an empirical state. One of the reasons for the lack of such a tight connection is that distortions may enter into the relation between theory and evidence, and these distortions may alter the empirical manifestation of a theoretical state. As a result, it is in general a nontrivial task to excavate the underlying state from distorted evidence. (Carrier 1993: 3)

On a Lorentzian theory, Carrier’s general remarks on distortions of a theoretical state in its empirical manifestation are quite literally true, for the result of uniform motion relative to privileged space is length contraction and clock retardation, phenomena which, it will be recalled, are every bit as real under the Einsteinian interpretation. If it is in general difficult to excavate the underlying state of nature from distorted evidence, if nature’s fundamental states often appear in masquerade, then why are the relativistic phenomena which mask the privileged frame improbable on a classical ontology?

As for d’Abro’s concern with finding ‘‘human traits in the universal plan,’’ the Lorentzian might plausibly appeal to the Anthropic Principle in response. According to that principle, features of the universe can only be judged in their correct perspective when due allowance has been made for the fact that certain features of the universe are necessary if it is to contain observers like ourselves (Barrow and Tipler 1986: 15). Since our existence depends on the maintenance of equilibrium states within us, the Lorentz-Fitzgerald contraction and clock retardation are necessary pre-requisites of our existence as observers. Thus, nature’s alleged conspiracy, when seen in anthropic perspective, seems much less mischievous. Therefore, this objection also falls to the ground.

Some Minkowskians might argue that a Lorentzian interpretation of SR is disfavored because of the excessive space-time structure which it posits with respect to the laws of motion. Recognizing the failure of verificationist critiques of absolute space on the basis of its unobservability, Earman, for example, suggests that ‘‘this objection of unobservability is more accurately stated as an objection based on Occam’s razor’’ (Earman 1989: 48). What Earman has in mind are criteria which would serve to establish what sort of structure space-time is endowed with. He proposes two ‘‘symmetry principles’’ which he presents as conditions of adequacy on theories of motion:

SP1: Any dynamical symmetry of a theory T is a space-time symmetry of T.

SP2: Any space-time symmetry of a theory T is a dynamical symmetry of T.

What justification is there for these criteria? Earman explains, ‘‘Behind both principles lies the realization that laws of motion cannot be written on thin air alone, but require the support of various space-time structures. The symmetry principles then provide standards for judging when the laws and the space-time structure are appropriate to one another’’ (Earman 1989: 486). With respect to (SP1), which will be crucial in the case at hand, Earman writes,

The motivation for (SP1) derives from combining a particular conception of the main function of laws of motion with an argument that makes use of Occam’s razor. Laws of motion, at least in so far as they relate to particles, serve to pick out a class of allowable or dynamically possible trajectories. If (SP1) fails, the same set of trajectories can be picked out by the laws working in the setting of a weaker space-time structure. The theory that fails (SP1) is thus using more space-time structure than is needed to support the laws, and slicing away this superfluous structure serves to restore (SP1).

(Earman 1989: 46–47)

A prime example of (SP1) at work is the demonstration that Newtonian mechanics does not, in fact, require Newtonian space-time, but only Galilean space-time. While the space-time symmetries of the theory are Newtonian, the dynamic symmetries are Galilean, a ‘‘clear violation’’ of (SP1) (Earman 1989: 48). By excising absolute space, one produces a theory whose space-time symmetries and dynamic symmetries are both Galilean, in compliance with (SP1). Now it might similarly be argued – though Earman does not do so – that a Lorentzian theory also violates (SP1) in that it posits more structure to space-time, such as hyperplanes of absolute simultaneity, than is necessary to explain the symmetries required by relativistic laws of motion, that is, the symmetries of the Lorentz-Poincaré group. Therefore, such structures should be excised by Ockham’s razor.

Now Earman is undoubtedly on to something important here. One should like to have some sort of constraint upon the postulation of gratuitous space-time structures. But the difficulty with (SP1) and (SP2) is that they are too restrictive, or to put the point another way, they can be overridden by considerations broader than the laws of motion. Indeed, one of the central lessons of our present investigation is that in questions of time and space metaphysical considerations cannot be ignored. We have seen, for example, that the 4-dimensional Minkowskian world is incompatible with the reality of tense and temporal becoming and also faces a variety of significant objections. Such metaphysical considerations qualify any force which Earman’s symmetry principles might possess.

More fundamentally, Earman’s principles presuppose a space-time ontology and therefore cannot be employed to justify a space-time interpretation of the formalism of SR over a Lorentzian space and time interpretation. Earman employs a space-time approach to all the theories he considers, speaking not only of Newtonian space-time but even of Machian space-time. This involves him in frequent anachronisms: he speaks of Newton’s ‘‘insistence that the structure of space-time is immutable;’’ he says that ‘‘If we take Newton at his word in the Scholium, the space-time setting for the theory of motion and gravitation of the Principia is supposed to be a full Newtonian space-time . . . ;’’ he explains that for Newton ‘‘the space-time is given once and for all as an emanative effect of God. . . . ’’ (Earman 1989: 35–36, 45, 48). Of course, Newton himself insisted on and believed none of this, since his was a 3+1 ontology involving physical objects enduring through time. His laws of motion are not supported by various space-time structures, as Earman assumes, for there are on Newton’s view no such structures. Time and space have intrinsic structure, and motion is to be explained, not in terms of the geometrical structure of space-time, but in terms of forces acting on bodies in space enduring through time. Earman’s principles, then, already take for granted a space-time realism. At best, therefore, with respect to SR, Earman’s symmetry principles could only serve to justify a Minkowskian space-time realism over a Lorentzian space-time realism. But if, so to speak, only a single slice of space-time actually exists, as Einsteinians and Lorentzians hold, then the question becomes whether the Einsteinian interpretation is preferable to the Lorentzian interpretation. Lorentzians and Minkowskians concur that the Einsteinian interpretation is untenable. In short, one’s ontology may warrant postulating more structure to space and time than symmetry principles alone would allow.

Occasionally arguments are offered on behalf of a Minkowskian interpretation of relativity theory which are relevant to a Lorentzian approach, and these merit our attention. For example, oft-times space and time theorists have accused space-time realists of a gratuitous hypostatization of what is only a geometrical representation of space and time. There is no reason to think that because a thing’s spatio-temporal location can be plotted on a Minkowski diagram, therefore an entity space-time exists anymore than because temperature and pressure can be similarly related in a diagrammatic way, therefore an entity temperature-pressure exists. In response to this charge D’Abro points to the 4-dimensional metric of Minkowski space-time as its distinguishing feature, in virtue of which it is not like the artificial temperature-pressure continuum (D’Abro 1950: 347). The temperature-pressure continuum can be separated into two distinct elements, but Minkowski space-time cannot. D’Abro concludes,

In short, the reality of space-time arises from Minkowski’s discovery that it was possible to discover an invariant distance between two points in space-time, holding for all observers; and that it was impossible to define any such invariant distance in space alone or in time alone, showing that space and time by themselves were phantoms. These last two concepts must henceforth be considered jointly, and no longer as separate entities.

(D’Abro 1950: 447)

One can, of course, adopt a space-time approach even to Newtonian theory. But D’Abro’s point is that there is no special 4-dimensional metric for such a continuum; it reduces to a mere geometric representation of the Galilean transformations (D’Abro 1950: 472–73). Like the temperature-pressure continuum, no real unification takes place.

This is an odd argument on behalf of space-time realism, since the wouldbe Newtonian space-time realist must be dismissed along with the temperature-pressure realist, even though he holds to a space-time realism, too. His space-time is a mathematical fiction, we are told, whereas Minkowski space-time is not, since the latter alone has a 4-dimensional metric. But the reason it has such a 4-dimensional metric is precisely because of its preclusion of relations of absolute simultaneity. In the limit case where c → ∞, the ‘‘absolute elsewhere’’ region in space-time is squeezed out, and the Newtonian dichotomy between a universal, absolute past and future is recovered (Costa de Beauregard 1987: 59–60; cf. Lucas and Hodgson 1990: 228–38). Thus the very existence of a space-time metric and a light cone structure in space-time depends upon there not existing such a global, absolute separation of past and future. The Minkowskian space-time realist can hardly justify relativistic space-time over the Newtonian realist’s classical space-time on the grounds that only the former’s has a space-time metric, since it is a necessary condition of relations of absolute simultaneity, which are the distinguishing mark of classical space-time, that no such metric exists in Newtonian space-time. But if the presence of such a metric serves merely to differentiate Minkowskian from Newtonian space-time, rather than to justify realism about the former over realism about the latter, then neither can it justify Minkowskian space-time realism over Newtonian space and time realism, since the latter does not differ metrically from Newtonian space-time realism.

What other reasons might be offered for preferring space-time realism? Earman and Friedman, in defense of space-time realism over the classical ontology, have asserted that ‘‘neglect of space-time structure in the classical context has led to a number of philosophical errors and oversights’’ (Earman and Friedman 1973: 329; cf. Earman 1970: 259–77). Presumably, they have reference, for example, to classical theorists’ overlooking Galilean space-time, which preserves absolute time without absolute space. But such examples serve to show only the admitted heuristic utility of a space-time methodological approach to questions of space and time. In the same way that possible worlds semantics is an illuminating and perhaps indispensable tool for exploring questions of modality but does not commit one ipso facto to modal realism, so also space-time methodology can enlighten without implying a space-time ontology. The same point may be made concerning the avoidance of philosophical errors – though here one must add that a space-time approach might also lead one to commit philosophical errors which a space and time approach would have avoided. For example, attempts to relativise acceleration and rotation by appeal to 4-dimensional structures come to mind, representations which may be of heuristic value but have also led some thinkers to conclude erroneously that absolute motions such as Newton pointed to have been eliminated. Or again, due to the isomorphism of the space and time dimensions in space-time, which differ only in sign, erroneous philosophical conclusions about the interchangeability of time and space, such as obtains in the Schwarzschild metric or the Hartle-Hawking cosmology, might be drawn, which a space and time approach would perhaps prevent. To return to oversights, the Lorentzian will charge that a perspectival, 4-dimensional approach to relativistic phenomena has resulted in the neglect of the search for the dynamic causes of time dilation and length contraction, a major oversight. The obvious difficulty here is that one man’s insights are another man’s oversights, and it is difficult to tell which one is correct without independent justification of one point of view.

Earman elsewhere argues that even if space-time can be ignored in the context of classical physics, one cannot neglect it in the context of relativistic physics, since space-time is not uniquely separable into space and time (Earman 1970: 259–60; cf. Earman and Friedman 1973: 352). In fact, he points out, there are relativistic space-times which resist every effort to separate them into a 3-dimensional space enduring through a 1-dimensional time. But Earman is speaking here of GR space-times, not SR space-time. So far as SR is concerned, Einstein’s original formulation of the theory shows that a space and time approach is necessarily equivalent to a space-time approach. Moreover, one cannot automatically assume that just because a particular space-time can be modeled that such a space-time represents a realistic possibility (think, for example, of imaginary space-times). One might well question whether models such as Gödel’s, alluded to by Earman, which permit pathological results like closed time-like loops, are anything more than mathematical curiosities.

In sum, even if, as we have seen, a Minkowskian interpretation of the SR formalism is in some respects, at least, superior to an Einsteinian interpretation, there do not seem to be comparably good reasons, empirical or philosophical, to prefer a Minkowskian interpretation of SR over a Lorentzian conception of space and time. If anything, the Lorentzian approach seems to have the empirical edge.

On the other hand, in addition to the considerations pertinent to tensed time mentioned earlier, I think we do have good reasons for rejecting space-time realism and, therefore, a Minkowskian interpretation of the formalism of SR. Inherent to the concept of space-time is the indissoluble unification of space and time into a 4-dimensional continuum. Hence, Minkowski’s pronouncement that ‘‘Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality’’ (Minkowski 1952: 75). It seems to me, however, that we have powerful metaphysical grounds for believing that time can exist independently of space. In making his pronouncement, Minkowski forgot Kant’s insight that time is a form applicable not only to the external world, but to consciousness as well (Kant 1970, A34/B51,

From the standpoint of the physicist, this is a thoroughly consistent solution. But the physicist will (doubtless) understand the objection, raised by philosophy, that time is by no means a merely physical matter. Time is, as Kant put it, the form not merely of our outer sense but also of our inner sense. . . . Should our experiences of successiveness and of memory be mere illusion . . . ?

(Wenzl 1949: 587–88)

A series of mental events alone is sufficient to set up a temporal sequence. Thus, for example, we can imagine God’s counting down to the moment of creation: ‘‘ . . ., 3, 2, 1, Fiat lux!’’ The beginning of space-time would then be preceded by a metaphysical time associated with the mental events of counting which would be wholly independent of space.

In addition, space-time realism confronts a host of objections due to its implication of a tenseless view of time, as previously mentioned. Thus, with little to commend space-time realism over a Lorentzian conception of space and time, good philosophical and empirical grounds for preferring a Lorentzian approach over a Minkowskian approach, and powerful objections lodged against space-time realism, we may conclude that there is good reason to prefer a Lorentzian approach to SR over a Minkowskian interpretation of the SR formalism.

Conclusion

It seems to me, therefore, that despite the widespread aversion to a Lorentzian physical interpretation of the mathematical formalism of SR, such antipathy is really quite unjustified. Admitted on all sides to be at least empirically equivalent to the Einsteinian and Minkowskian interpretations, the Lorentzian interpretation is the only one of the trio which can give us both the objective reality of tense and temporal becoming and a unified picture of the world. It is neither more complicated than its rivals nor unacceptably contrived. It is the one approach to relativity theory which promises to mesh with recent advances in cosmology and quantum mechanics and electrodynamics. At the same time it averts all the problems of space-time realism inherent in the Minkowskian interpretation. Therefore, we have good grounds – wholly apart from the theological considerations which motivated the classical concept of time – for accepting a Lorentzian physical interpretation of the mathematical formalism of the Special Theory of Relativity.

Notes

Nerlich calls such an interpretation of SR the relativity interpretation (Nerlich 1994: 63).

Tenseless time theorist D. H. Mellor does attempt to combine a 3+1 ontology with space-time realism (Mellor 1981: 105), but the combination of endurantism and space-time realism is as incoherent as the wedding of space-time realism with the objectivity of tense and temporal becoming, and for the same reason, since endurantism and a tensed theory of time are logically equivalent; see note 54 and relevant discussion in the text. See further Carter and Hestevold 1994: 269–83.

The seriousness with which Einstein took this conception may be seen in the fact that when his life-long friend Michael Besso died, Einstein sought to comfort his bereaved family by reminding them that for physicists Besso had not ceased to exist, but exists tenselessly as a permanent feature of space-time reality (Hoffman and Dukas 1972: 258).

Nerlich calls this the space-time interpretation (Nerlich 1998: 128–29).

On this score Nerlich finds himself at odds with theorists such as Reichenbach, Grūnbaum, van Fraassen, Salmon, and Winnie. On Nerlich’s view the heart of SR is the second-order constraint of Lorentz invariance on all physical laws, which springs from the inherent symmetries of Minkowski space-time. Temporal relations in that space-time cannot be reduced to causal relations because the latter presuppose the former.

Notice that Lorentz eschews operational definitions of time and does not equate time with clock readings. This is particularly evident in his failure to ascribe at first physical reality to his local times (Lorentz 1934: 262). Eventually Lorentz came to see the reality of clock retardation. But even the readings of a clock at rest in the aether are but a sensible measure of true time, not definitive of true time.

See also the outstanding historical study by Illy (1989: 272), who comments, ‘‘Lorentz distinguishes the existence of a state of motion from its observability – a distinction void of meaning according to Einstein.’’

Indeed, I should venture to surmise that it is the majority view among A-Theorists and endurantists. Process philosophers also often appear to favor this view.

See the seminal article by Putnam (1967: 240–47), which is, however, a very incoherent presentation. For more cogent, recent versions of the complaint, see Savitt (1998); Callender (1998); and especially Balashov (2000: 129–66).

See the Auseinandersetzung between V. Varicak (1911: 169, 509–10). For helpful discussion see Winnie (1972: 1091–94).

It is important to note that accepting the superiority of the space-time interpretation does not without further ado commit one to space-time sub-stantivalism. Space-time realists disagree among themselves whether space-time should be construed substantivally or relationally, substantivalists maintaining that space-time is a substance existing independently of objects and events located in it, relationalists holding that space-time is not a substance, but depends for its existence on the existence of objects and events. Both are united in opposition to the Einsteinian interpretation in contending that all space-time points are equally real. For discussion, see Horwich (1978: 397–419).

For an illustration see Angel (1980: 89).

Marder (1971: 78) paradoxically endorses Rindler’s interpretation that the traveler’s path is Lorentz-contracted.

Nerlich, personal communication, June 20, 1991.

For an outstanding defense of this point, see Smith (1993); see also Craig (1996a: 5–26; 1996b: 249–69; 2000a: 165–85).

One of the most eloquent spokesmen for this point of view has been Schlesinger (1980: 34–39, 138–39). See also Craig (1999a: 515–37; 1999b: 107–20; 2001: 159–66).

There is no good treatment of this yet, but see Gale (1968: 90–97) and Mellor (1981: 140). See also Craig (2000b: Chap. 7).

Again, this point needs to be better developed, but see Geach (1972: 306) and McGilvray (1979: 275–99). See also Craig (2000b: Chap. 8).

See the excellent study by Merricks (1994: 165–84); see also Lewis (1986: 305–9) and the incisive piece by Van Inwagen (1990: Chap. 9).

It is noteworthy that in Zahar’s analysis, SR did not by itself supersede Lorentz’s program. Zahar can claim that Einstein’s research program superseded Lorentz’s only by taking GR to be continuous with SR and by then appealing to the empirical confirmation of GR (Zahar 1973: 95–123; 223–62). But as is well known, GR is not an extension of SR; it is a theory of gravitation, not a theory of relativity. It therefore follows that Einstein’s program never in fact did supersede Lorentz’s, in the sense of demonstrating its superiority over Lorentz’s.

Cf. Kanitscheider’s remark: ‘‘The cosmic background radiation . . . furnishes a reference frame, relative to which it is meaningful to speak of absolute motion’’ (Kanitscheider 1984: 256).

One can only speculate whether, had this microwave background radiation and the measure of our motion relative to it been known to Einstein prior to 1905, he would have claimed that no fundamental frame exists relative to which all local inertial frames are in motion. See Miller’s paper (1980: 66–91) in connection with the remarks of Dirac (1980: 110–11). Cf. the remark of Munsouri and Sexl: ‘‘The discovery of the cosmic background radiation has shown that cosmologically a preferred system of reference does exist. This system is defined and singled out much more unambiguously to be a candidate for a possible ‘ether frame’ than was the solar rest frame in Einstein’s day’’ (Munsouri and Sexl 1997: 497–98).

Such asseverations may not even be true. It is very difficult to see why the entanglement-based quantum cryptography suggested by the experiments of the Geneva Group (Clifton and Hogarth 1995: 355–97) would not involve the instantaneous transmission of information even in the absence of super-luminal propagation of causal influences.

See Stapp (1988: 71–72). See further Popper (1982: xviii, 20). Even Popper’s use of the expression ‘‘infinite velocity’’ is misleading, since the salient point is the simultaneous collapse of the correlated two wave functions, as if they were joined by an influence of infinite velocity. See Shimony (1978: 13).

Although Maudlin interprets the counterfactual dependence relation which exists between the separated polarization events in EPR as a causal connection, his emphasis lies on the fact that relativity cannot make physical sense of instantaneous collapse of the wave function.

On their coincidence see Cushing (1996: 175); Popper (1982: 30).

David Bohm to D. R. Griffin, May 17, 1992, cited in Griffin, ‘‘God and Relativity Physics,’’ p. 110. When Callender and Weingard contrast the cosmic time of Bohmian cosmology with ‘‘the arbitrary parameter found in general relativity,’’ the contrast concerns the arbitrariness permitted by GR taken in abstracto (Callender and Weingard 1994: 227), not taken with the existing boundary conditions of isotropy and homogeneity. GR cosmic time and Bohmian cosmic time may well be extensionally equivalent, even though intentionally diverse.

‘‘Raffiniert ist der Herr Gott, aber boshaft ist er nicht,’’ remark of Albert Einstein during a visit to Princeton, upon being informed that D. C. Miller, a former colleague of Michelson, had claimed to have detected the ether wind (cited in Pais 1982: 113–14).

Tim Maudlin has emphasized and illustrated Carrier’s point. He surveys what he characterizes as the ‘‘teratological collection’’ of theories attempting to explain the Bell Inequalities and integrate the EPR results with relativity theory and concludes, ‘‘One way or another God has played us a nasty trick’’ (Maudlin 1994: 241). One cannot dismiss neo-Lorentzian relativity on the grounds that it would be deceptive, since partisans of each theory could say the same of rival positions. ‘‘ . . . the real challenge falls to the theologians of physics, who must justify the ways of a Deity who is, if not evil, at least extremely mischievous’’ (Ibid. p. 242).

It is perhaps noteworthy that D’Abro mistakenly holds that ‘‘The Fitzgerald contraction is no longer a real physical contraction, as it was assumed to be in Lorentz’s theory’’ (D’Abro 1950: 151).

I owe this point to Robin Collins.

Notice that the foundations of Newtonian time and space, for example, were laid in Newton’s theism (as Earman acknowledges Earman 1989: 10), but Earman simply ignores such metaphysical considerations, choosing instead to put a ‘‘modern gloss’’ on Newton’s views.

A point emphasized by Reichenbach:

An act of thought is an event and therefore defines a position in time. If my experiences are always produced within the framework of a ‘now,’ that means that each act of thought defines a point of reference. We cannot escape the ‘now’ because the attempt to escape signifies an act of thought and therefore defines a ‘now’.

(Reichenbach 1952: 157)

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