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Whitehead, Special Relativity and Simultaneity

by Villard Alan White

Villard Alan White is a graduate student in the philosophy department at the University of Tennessee, The following article appeared in Process Studies, pp. 275-285, Vol. 13, Number 4, Winter, 1983. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.


Since the appearance of The Principle of Relativity in 1922, Whiteheadís departures from the traditional Einsteinian interpretation of the special and general theories of relativity have been discussed and criticized. Throughout most of this discussion, however, the central issue has been perceived to be whether Whiteheadís 1922 interpretation is superior to or inferior to Einsteinís interpretation. An issue that has been grossly neglected, however, is whether Whitehead ever modified his view of relativity from the one presented them. Since Whiteheadís later work comprises for the most part his metaphysical views, with questions of physics treated only peripherally, they have figured just slightly or not at all into discussions of Whiteheadís interpretation of relativity. This impression that Whitehead forsook purely scientific considerations for metaphysical ones in work subsequent to The Principle of Relativity thus has issued into a tacit assumption that Whiteheadís views on relativity never significantly changed after 1922. In the following I wish to challenge this assumption with regard to only one but a very central relativistic concept -- simultaneity -- and thus I will show that Whitehead indeed not only modified that concept, but in Process and Reality he actually repudiated his earlier concept in favor of one what is more compatible with Einsteinís. In support of this argument I will also forward an explanation of why such a shift occurred, and what such a shift might imply in terms of Whiteheadian metaphysics.

In the early works on the philosophy of science, Whitehead established that he takes exception to the Einsteinian concept of simultaneity. Oddly enough, in The Principle of Relativity, where one expects a rigorous treatment of such topics, one does not find Whiteheadís own definition of simultaneity or even an argument against Einsteinís. The reason for this seemingly egregious oversight is twofold. First, Whitehead lays out in The Principle of Relativity assumptions carried over from his philosophy of nature which are different from Einsteinís and which imply a concept of simultaneity different from Einsteinís.1 ĎSecond, Whiteheadís concept of simultaneity can be found to be implicit in his discussions of his theory of spacetime, though he never draws specific attention to it or directly asserts the nature of his divergence from the Einsteinian concept.

Whiteheadian and Einsteinian relativity both embody views of time which stipulate that time measurement is to some degree observer-dependent. This enables both views to claim equally that what is a simultaneous set of occurrences for one observer may not be for another. But what is very distinct in these views is the manner in which simultaneity is defined and the assumptions which underlie these definitions.

For Einstein, simultaneity is an operationist concept that is defined by actual measurement under certain specified conditions (RSGT 22f.).2 The simultaneity of two or more spatially distant events is determinable for an observer by correlating their spatial distance from the observer with their observed occurrence by the means of light signals. If the events are equidistant from the observer and are observed to occur at the same time, then the events are said to be simultaneous.3 On the basis of this operationist definition of simultaneity, Einstein then proceeds to establish how the clock-time of distant events may be simultaneous. Assuming that clocks of identical construction and running-rate are placed at the events, then when "a particular position of the pointers of the one clock is simultaneous (in the above sense) with the same position of the pointers of the other clock, then identical Ďsettingsí are always simultaneous (in the sense of the above definition)" (RSGT 24, italics his). Note that this establishes the clock simultaneity of events distant from the observer, though the same determination of clock simultaneity of distant events with events of the observerís world-line may be deduced from the description as outlined by Whitehead (PNK 51f.). What is important about this measurement of simultaneity is that it depends upon the operationist definition of simultaneity.

There are two important assumptions that underlie Einsteinís definition. One is that the determination of spatial distance between events is possible, which Einstein provides by stipulating that the events occur within a fixed coordinate reference frame (the so-called Galilean space or inertial frame) (RSGT 11). Another is that light signals connecting events have a uniform and finite velocity for all possible observers (RSGT 17).

Evidently Whitehead could not countenance the latter assumption, not because he could not accept the constancy of the speed of light as a physical law, but rather because Einstein used this assumption in order to define simultaneity (PNK 51f.). But as I shall show below, Whitehead believed that Einsteinís definition of simultaneity actually only provides a possible means of establishing the clock simultaneity of events, and that there is a further and more fundamental sense of simultaneity which is secreted in the former of Einsteinís assumptions cited above.

As evidence for my contention, I direct attention to Whiteheadís explication of the Einsteinian concept of simultaneity (PNK 51f.). In those passages Whitehead notes that Einstein provides a means for establishing the clock simultaneity of an event distant from some event of an observerís world-line. Whitehead then states that this account is defective not as a measurement, but only as a definition of simultaneity.

But there are certain objections to the acceptance of Einsteinís definition of simultaneity, the Ďsignal-theoryí as we will call it. In the first place light signals are very important elements in our lives, but still we cannot but feel that the signal-theory somewhat exaggerates their importance. The very meaning of simultaneity is made to depend upon them. (PNK 53)

Two important points issue from Whiteheadís criticism. First, it is evident that Whitehead is taking exception to Einsteinís definition of simultaneity, not to the specific means of employing light signals to synchronize distant events chronologically. At no point does Whitehead state or insinuate that the Einsteinian method is theoretically inadequate for the determination of clock simultaneity. Rather, Whitehead believes that simultaneity is something above such operations. Second, as Whitehead explains elsewhere in his criticism, the meaning of simultaneity is actually contained in the preconditions by which such operations are made possible.

Certainly, once granting the idea of time-order being a local affair connected with a specific body P1, the acceptance of the electromagnetic formula connecting ta [the time coordinate of P1 as determined for one inertial frame] and tb [the time coordinate of P1 as determined for another inertial frame] is a slight affair. There is no presumption against it, once granting the conception of diverse time-orders which had not hitherto been thought of. (PNK 53)

Standard interpretations of Whiteheadian relativity have slighted this and other similar statements by Whitehead in regard to his displeasure with Einsteinís view. Whitehead is not dismissing the Einsteinian method of determining clock simultaneity theoretically (although in PNK 53f. he certainly downplays its practicality); rather he is rejecting it as a definition of simultaneity. Whitehead believes that the true definition of simultaneity is found within the first assumption of the Einsteinian account given above, namely, the assumption that events must occur within a single reference frame in order for their occurrence as simultaneous to be meaningful at all. Apparently, Whitehead feels that such an assumption clearly carries with it a concept of simultaneity that is logically prior to an operationist one:

Furthermore local time does not concern one material particle only. The same definition of simultaneity holds throughout the whole space of a consentient set in the Newtonian group. The message theory does not account for the consentience in time-reckoning which characterizes a consentient set, nor does it account for the fundamental position of the Newtonian group. (PNK 54)

It is imperative to note here that Whitehead does not maintain that all members of a consentient set share the same intuitive or phenomenological definition of simultaneity, but only the same potential chronometry of clock simultaneity.4 Hence, Whiteheadís consentient sets are nothing more than classes of events which are at absolute rest relative to one another. In other words, members of a consentient set share the same inertial frame (cf. PNK 31). It is this fact that Whitehead believes conceals the true meaning of simultaneity, for Whitehead clearly believes that the existence of such frames is indeed factual: "This spatio-temporal framework is not an arbitrary convention . . . Thus, the space of a consentient set is a fact of nature; the traveler with the set only discovers it" (PNK 32). Involved in this factuality besides the spatial element is a corresponding temporal one, and thus granting the existence of these frames entails granting the existence of a Newtonian-like simultaneity that holds within the frame.

Whiteheadís own definition of simultaneity is unfortunately not very clear in these early works. In The Principles of Natural Knowledge simultaneity is introduced as a relation characteristic of durations.

Perception is an awareness of events, or happenings, forming a partially discerned complex within the background of a simultaneous whole of nature . . . The simultaneity of the whole of nature comprising the discerned events is the special relation of that background of nature to the percipient event, which is itself part of the whole. Such a complete whole of nature is called a Ďdurationí. (PNK 68)

Two features of simultaneity can be inferred from this passage. The first is that although the presence of a duration to a percipient is epistemically possible through sense-awareness, simultaneity itself is the relation that constitutes the qualifying characteristic binding all events perceived and unperceived into the duration. Thus, another feature of simultaneity is that it is some sort of objective relation extending to all events fulfilling that relation beyond the events present to a particular observerís sense-awareness (cf. CN 53).4

What then is the nature of this relation? Since durations have no specific temporal thickness, but vary with the particular duration of the perceiverís specious present (CN 59, 69), simultaneity cannot have to do with the relations between events as they are extended temporally, but spatially. Such a spatial relation is indeed objective for Whitehead (PNK 32); thus, the homogeneity of spatial relations is claimed in The Principle of Relativity as the basis for the uniformity of physical relations generally (R 8). However, nowhere in The Principles of Natural Knowledge does one find a precise definition of simultaneity in terms of spatial relations.

In The Concept of Nature Whitehead introduced the concept of co-presence, which is a relation that expresses the spatial separation of events distinct from their involvement in particular durations (CN 177). Whitehead defines co-presence initially as a two-termed relation between events that share the same instantaneous space (in a duration whose temporal extension is ideally reduced to zero) according to some observer (CN 177).5 Co-presence as a two-termed relation is symmetrical, but when extended to many terms may or may not be transitive (CN 177). However, when any given number of events are transitively co-present, then they are simultaneous. The simultaneity of a duration may therefore be defined as the relation of mutual co-presence of its constituent events.

As an informative definition, however, this expression of simultaneity in terms of co-presence leaves much to be desired. Recurring to Whiteheadís own explanation of co-presence, events are co-present only if "on some or other system of measurement" they "are in the same instantaneous space (CN 177). But since instantaneous spaces are determinable only by what appears to actual observers (albeit perhaps in different families of durations -- CN 177), these spaces taken together constitute all nature as it may be divided into alternate classes of durational experiences. This implies that all co-present events are actually simultaneous in some duration. Since in this sense co-present and simultaneous events are coextensive, neither relation can claim either empirical or logical precedence over the other.

Such an inability to analyze simultaneity in terms of simpler relations is really unsurprising, however, given that Whiteheadís conception of space and time assumes the homogeneity of spatio-temporal relations: "In this respect we have to dissent from Einstein who assumes for this [spatio-temporal] structure casual heterogeneity arising from contingent relations" (R 25, cf. the Preface v). In short, Whitehead believes that the preconditions that underlie the special theory of relativity reveal fundamental truths about nature, and therefore the structure of space and time should embody properties required by these preconditions. As seen above, the primary assumption about space and time required by this theory is that inertial frames must pre-exist actual measurements, and thus Whitehead asserted in his own inimitable terminology that they do in fact exist. Further, such an assumption, Whitehead urges, dispenses with the necesslty to believe that the constancy of the velocity of light is pertinent to spatio-temporal structure, for that structure is predetermined only by the existence in nature of interrelated spacetime frames (CN 193).6

Hence simultaneity for Whitehead is the spatial spread of events in a given inertial frame as defined by a given duration, and is Newtonian in the sense that each instantaneous space in a frame provides a single present class of all events in nature relative to that frame. However, it is non-Newtonian insofar as there is no single, unique definition of simultaneity, for there are many alternate families of durations in nature (CN 59, 178).

In effect, Whitehead realized that Einsteinís assumptions of inertial frames for given events introduced a tacit Newtonian-like simultaneity which makes any operationist concept of simultaneity logically dependent on it. This, I submit, is the reason Whitehead rejected a definition of simultaneity based upon light signals, not because light signals do not really have an invariant velocity or are somehow irrelevant to our operational determination of clock simultaneity:

The reason why the velocity of light has been adopted as the standard velocity in the definition of simultaneity is because the negative results of the experiments to determine the earthís motion required that this velocity, which is the Ďcí of Maxwellís equations, should have this property. Also light signals are after all our only way of detecting distant events. (PNK 53)

The following question arises quite naturally at this juncture: given the previous account, why then did most philosophers and theoreticians reject Whiteheadís concept of simultaneity for Einsteinís? After all, Whitehead apparently does not radically diverge from the Einsteinian point of view, but rather emphasizes one assumption of Einsteinís and claims that it logically supersedes his other, resulting in a shift away from Einsteinís operationist definition of simultaneity to Whiteheadís "empirical-realist" definition. Why then is the operationist approach felt to be conceptually superior?

The concept of simultaneity, whether Whiteheadís or Einsteinís, is expounded as part of the special theory of relativity.7 That theory demonstrates how inertial principles and the constancy of the speed of light may be preserved for all observers utilizing the Lorentz-Fitzgerald transformations. Moreover, Einstein realized full well that special relativity required the assumption of the existence of inertial frames, much as Whitehead insisted:

In accordance with classical mechanics and according to the special theory of relativity, space (space-time) has an existence independent of matter or field. In order to be able to describe at all that which fills up space as dependent on the co-ordinates, space-time or the inertial system with its metrical properties must be thought of at once as existing, for otherwise the description of Ďthat which fills up space would have no meaning. (RSGT 154f.)

However, it is clear that Einstein regarded the existence of such frames heuristically, and not as a factual existence, for he resumes the above quotation with the statement, "On the basis of the general theory of relativity, on the other hand, space as opposed to Ďwhat fills space,í which is dependent on the co-ordinates, has no separate existence" (RSGT 155). It is this link of spatial relations with the theory of gravitation in the general theory which Whitehead criticizes as evidencing the "casual heterogeneity" of spacetime "arising from contingent relations" (R 25). Whitehead cites in defense of his own view the a priori necessity of uniform spacetime in order for empirical measurements to be possible and to have universal application (R v, 9, 25).

The difference between Whitehead and Einstein on this head amounts to a disagreement over the status of special relativity. It is no minor difference as to their respective views on the status of spacetime, however. For Whitehead, the Lorentz-Fitzgerald transformations reflect absolute relations between real frames which exist in nature. For Einstein, however, they merely represent particular exemplifications of more generalized transformations which in the case of the proved existence of non-Euclidean spacetime more precisely describe actual spatio-temporal structure than do the former (RSGT 152f).8

But again, why did the majority of thinkers prefer Einstein to Whitehead on the subject of relativity? For the most part, I believe the reasons boil down to two. The major reason is that Einsteinís principle of equivalence, which correlates and consolidates the concepts of inertial and gravitational mass and which in turn introduces the curvature of spacetime in the general theory, has no analogue in Whiteheadís theory.9 But perhaps more importantly for the purposes of this essay, Einsteinís entire approach in special relativity presumes that the nature of causality in the universe has a direct bearing upon spatio -- temporal structure. This approach is reflected in Einsteinian special relativity in the use of the constancy of the speed of light as an assumption which determines in part the spatio-temporal metrical relation for any observer. Whitehead, conversely, assumes the existence of given spatio-temporal metrical relations which relegates the finitude of causal propagation to the status of a factor within those relations, not constitutive of them.

Simultaneity for Einstein is thus a concept intrinsically related to causality. Given any particular world-line event, events not causally related to that event (lying in the "space-like" direction of a Minkowski diagram) are simultaneous with the event in some time-frame.10 However, for Whitehead simultaneity merely is the factual occurrence of events in durations which are spatially separated according to the instantaneous spaces of moments in those durations.

Later in the Lowell Lectures of February, 1925, Whitehead again reiterates these same themes (SMW 179,181f.), making it apparent that at this time he still subscribed to this departures from Einstein on simultaneity and relativity. However, Science and the Modern World also marks the introduction of the novel idea of epochal time (SMW 182-86, 196-98), and in so doing, marks the beginning of a subtle but considerable change in Whiteheadís view about spacetime and causality.11

These changes are not fully evident until the appearance of Process and Reality in 1929. Of course, in the typical manner of Whiteheadian conceptual transition, these changes are quietly interwoven into old and new ideas. The clearest and possibly most concise indication of Whiteheadís change of mind may be found where he remarks that the "misapprehension [concerning potentiality and actuality] is promoted by the neglect of the principle that, so far as physical relations are concerned, contemporary events happen in causal independence of each other" (PR 61/ 95, emphasis his). This abruptly contrasts with Whiteheadís earlier position, for, following Einstein, Whitehead here proclaims explicitly that causality is a limitation placed upon physical relations. Consequently, simultaneity as a physically relevant relation is at least restricted by a causal parameter. No such limitation of simultaneity as a physically relevant relation exists in his earlier philosophy of nature.12 In addition, Whitehead appends a note to this statement which has an oddly apologetic tone, especially when one reads the note (as I think one must) as explaining how the statement above is compatible with Einsteinian assumptions: "This principle lies on the surface of the fundamental Einsteinian formula for the physical continuum (PR 61/ 96). This appears to be no less than an admission that causality indeed is an assumption needed for spatio-temporal relationships, and is not a concept merely derivative from them.

I use this passage to characterize Whiteheadís shift away from his own earlier views to those of Einsteinís, but more solid evidence can be found elsewhere. The absence of any remarks about or definitions of simultaneity by Whitehead, or of any criticisms forwarded against Einsteinian simultaneity is very significant.13 One might object that since this is a metaphysical work, such a divergence from Einstein might have been felt to be non sequitur or redundant of earlier work. But this is an essay about cosmology as well as metaphysics (note the title page), and Part IV is meant to be an exposition of matters pertinent to spacetime. Therefore I submit that no divergence is noted between Whitehead and Einstein on the topic of simultaneity because one no longer exists. If indeed I have correctly interpreted the connotation of the above passage, this is the case.

As a more persuasive argument for my contention, note the definition of this loci relative to an occasion M (PR 123f./ 188f.), as well as the later definition of durations also provided (PR 320f./ 487f.). In both passages Whitehead utilizes as his principle of differentiation the physical property of causal relatedness. There is no suggestion that alternate spacetime systems exist in nature which determine the loci or durations relative to M, but rather the issue is whether in fact M is causally related or relatable to other occasions or not. Further, Whitehead no longer distinguishes between "co-present" and "simultaneous" events, but only establishes whether events are contemporary or not. This single relation -- "contemporaneity" -- has come to supplant the older relations simply because the older assumptions behind these relations have been dropped in favor of the more orthodox Einsteinian assumption that causality is intrinsically bound to spatio-temporal concepts in this cosmic epoch.14 Thus, Whitehead defines all occasions that are contemporary with M as lying in a single locus (PR 123/ 188), and all that are mutually contemporary as lying in a single duration (PR 125f./ 192, 320/ 487). Hence simultaneity (contemporaneity) as a physically relevant relation has become a function of causal independence only, and thus to this degree Whitehead has moved away from his own earlier stance closer to that of Einsteinís.

It is important to note that I have referred to this simultaneity as a physically relevant relation, and not as a physical relation. This is so because simultaneity thus understood is a logical relation which establishes classes of events satisfying it, although no two events satisfying it actually have any sort of physical relationship of simultaneity. In fact, simultaneity in this analysis precisely is the denial of physical or causal relationships. Nevertheless, this appraisal of simultaneity stands in great contrast to earlier claims, for example, where Whitehead proclaims that "simultaneity is a definite natural relation" (CN 53). It is this Einsteinian character of Whiteheadís later account which distinguishes it so markedly from the Newtonian character it had earlier. Moreover, this definition of simultaneity implies that clock simultaneity must be established empirically by the means of causally connected events. Thus simultaneity for Whitehead is now an extensional concept the actual membership of which is established indirectly through measurement and its associated theoretical structure. But to say this is merely to say that simultaneity has thus become for Whitehead an operationist concept.

Granting that there is this conceptual evolution of simultaneity from the earlier to the later Whitehead, when and why did such a shift occur? As to when, there is no indication that Whitehead significantly altered his opinions on relativity from 1919 to the Lowell Lectures of 1925. However, Science and the Modern World also introduces the epochal theory of time, which stands as a great modification of Whiteheadís event ontology. It is the advent of this theory which best accounts for the conceptual transformation I have attempted to show. According to Whiteheadís earlier theory of events, events in a duration were assumed to overlap in such a manner so as to produce the spatial relation of co-presence. It is this spatial extensiveness which was shown earlier to serve as the basis for the relation of simultaneity. However, the epochal theory of time disposes of this foundation of spatial extensiveness, and hence this distinguishing characteristic of durations is likewise lost.15

These latter conclusions must have occurred to Whitehead as well, for only after Science and the Modern World Whitehead introduced the concept of causal efficacy as the primitive relation which binds events together. Thus it was quite appropriate for Whitehead to redefine the distinguishing characteristic of durations in terms of causality, or to be more precise, the lack of it. Consequently, Whiteheadís concept of simultaneity likewise underwent a transformation from a geometrical concept with direct physical relevance to an extensional concept with much more indirect physical import. It is this transformation that I have attempted to underscore by my previous exposition.

Finally, it remains to be seen what impact such a conceptual change in Whiteheadís scientific thought had upon his metaphysics. In Whiteheadís early view of simultaneity, this property expressed a certain real togetherness or objective becoming between events which occur in the same duration. The objective nature of this property was expressed by Whitehead in his claim that the space of consentient sets was a fact of nature (PNK 31, CN 53). Thus events which share the same instantaneous spaces of a particular family of durations all become within durations which share the same meaning of chronometry for their constituent events (at least potentially, by Einsteinís method of clock synchronization). However, there is not just a single family of durations, and each family constitutes a different spatiotemporal system (CN 59). Hence, any given event partakes of an indefinite number of relations of simultaneity, since any given event occurs in an indefinite number of spacetime systems. In terms of this property of objective simultaneity, events d)f different spacetime systems become as their associated spacetime systems dictate, and thus becoming is a complex matter of the interlaced becoming of diverse spacetime systems (CN 178).

The theory of epochal time dispenses with this difficult concept of simultaneity qua objective becoming. One should expect therefore that thereafter becoming would be something other than an objective property holding between occasions. In Process and Reality it is quite evident that this is the case. Becoming is associated with the subjective processes of concrescence (PR 25/ 38, 35/ 53, 283/ 434, and others), while the relationship which obtains between occasions in durations is an extensional concept of simultaneity. This results in the events of such durations sustaining a "unison of becoming" (PR 125f./ 192), which expresses (a) that these events are disconnected causally and transitively so, and (b) that they may share the same chronometry. It is easy to see that (a) and (b) reflect a conceptualism which only differs from that of Einsteinian special relativity with regard to the Whiteheadian theory of atomic events. While this difference is certainly more than trivial, it is certainly a smaller difference than had existed only a few years earlier.16

 

References

RSGT -- Albert Einstein. Relativity: The Special and the General Theory, translated by Robert W. Lawson, fifteenth edition. New York: Crown Publishers, Inc., 1961.

 

Notes

1I have not found a reason to believe that Whitehead significantly changed his scientific views from 1919 to 1925. His own testimony in CN vii shows a close tie between PNK and that work, and the notes appended to the second edition of PNK in 1924 indicate more of a honing of earlier thoughts than a rejection of them. The discomfiture that Whitehead shows in those notes does portend of conceptual changes to come, however.

2 I use the term "operationist" here only to stress the empirical content of Einsteinís concept of the temporal measurement of spatially separated events. It is not my intent to associate Einstein with the philosophical school of operationalism.

3 It is important to note that this definition is not merely an intuitive one, though it does rely upon an intuitive notion of "at the same time."

4 See F. S.C. Northrop, "Whiteheadís Philosophy of Science," in The Philosophy of Alfred North Whitehead, ed. by Paul Schilpp (La Salle, Illinois: The Open Court Publishing Company, 1951), pp. 193f., for an exposition of the view that Whiteheadian relativity in the early works requires merely an intuitive definition of simultaneity. Such an interpretation, though consistent with Whiteheadís overall empiricist approach, does violence to the passages cited above as well as others. Thus, I argue that Whitehead does not insist that all observers in a consentient set share the same intuitive perception of events in their durations, but only that the spatially separated events in those durations may share the same clock synchronization.

5 To be precise, this relation should be shared not by events, but by event-particles.

6 The importance of this claim should he emphasized. My view opposes that of many traditional interpreters who criticize Whiteheadís use of "c" in his transformations as unjustifiably ad hoc. If one should take the sort of position that I have argued for above, this awkward ad hoc nature of c disappears. Of course, the vengeance of such an assumption as I have ascribed to Whitehead is that it makes impossible the development of a general theory of relativity along the lines of Einsteinís.

7 Whitehead never terms his theory "special" because, as I argue below, he develops no general theory analogous to Einsteinís.

8 Whitehead admits that a non-Euclidean geometry would be consistent with his theory so long as its axioms produce a uniform geometry (R v). A defect of Whiteheadís theory, however, is that it shows no way an empirical determination of this question can he made.

9 Whiteheadís own account of gravitation is ensconced in his idea of "impetus," which appears to treat gravitation as an old-fashioned Newtonian force (CN 181f.). However, it is possible that later (in PR) Whitehead began to see defects in his view (see note 14).

10 Whitehead also resorts to Minkowski diagrams (R 31), but of course his view of duration alters his interpretation of them from the normal one.

11 I follow Ford in his argument that the epochal theory of time was a discovery Whitehead made subsequent to his delivery of the Lowell Lectures. See Lewis S. Ford, "Whiteheadís First Metaphysical Synthesis," International Philosophical Quarterly 17/3 (September, 1977), 251-64,

12 Of course, this mention of a physically relevant concept of simultaneity is meant to distinguish it from the intuitive sense that often pops up in the early work (e.g., PNK 184, which refers to ". . . the apparent character of an event simultaneous with our percipient event Ö")

13 In fact, I find in none of Whitehead works after 1925 any criticism suggestive of the type in PNK.

14 In R 97f./ 149 Whitehead sets out what may possibly be the most explicit embrace of the Einsteinian assimilation of causality with the gross structure of spacetime in the present cosmic epoch. In this passage Whitehead states that the geometrical properties of the present cosmic epoch (as opposed to other possible "geometric societies" -- PR 97/ 148) are effected by the predominance of the "electromagnetic society" of occasions, which I take it includes the predominance of the important property of the finitude of causal propagation. This is tantamount to the admission that it is this factor of causality that determines the metrical properties of spacetime in this epoch, which is Einsteinís very assumption in special relativity. However, I relegate this capitulation on the part of Whitehead to Einsteinian special relativity because of Whiteheadís assumption, carried over from R, that the geometry of spacetime must be systematic (PR 330/ 503). Hence Whiteheadís divergence from Einstein on general relativity is in PR much for the same conceptual reasons as it was in the earlier work. However, note the conciliatory air of PR 332f./ 506-08, and especially paragraph three of Section VI as contrasted with CN 181f.

15 Here see Whiteheadís note pointing out that no distinction between durations and strain-loci existed in CN (PR 128/ 190).

16 I am indebted to Rem B. Edwards for his encouragement, as well as Roger Jones for his many spontaneous and lengthy expositions on relativity. I owe special thanks to Lewis S. Ford for a seminar he presented in June, 1981, during which some of the arguments in this article first came to mind. I also much appreciate the incisive comments on this paper from James W. Felt, S.J.


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