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Whiteheadís Theory of Relativity

by Dean R. Fowler

Dean B. Fowler is completing his Ph.D. at the Claremont Graduate School with a dissertation on the impact of Einsteinís relativity theory on Whiteheadís doctrine of God. The following article appeared in Process Studies, pp. 159-174, Vol. 5, Number 3, Fall, 1975. 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.


I

During a time of conflict, crisis, and revolution in the scientific community, when the world witnesses the emergence of a new scientific theory, the philosophical community is placed in a period of uneasy ambiguity, which is heightened when the "truth" or "falsity" of the new theory has not been established. In such a period the response of the philosophical community usually follows three patterns. (1) The philosophical community can ignore the impact of the new theory by arguing that the world of science and the world of philosophy are distinct. Such a response was manifested in Kantís distinction of the phenomenal realm and the noumenal realm, science being confined to the former realm. The Kantian attitude toward the relation of science and philosophy characterizes the response of most contemporary philosophers. (2) Philosophy can respond by showing that the new theory is false for philosophical reasons. In this spirit the Catholic church, dominated by Aristotelian philosophy, condemned Galileo in his defense of Copernicus.1 (3) Philosophy can accept the theory as true and rework its own principles to conform to the demands of the new scientific theory. This response has characterized the attitude of much current cosmological philosophy in the wake of the advances of science in the modern era.

The differences among the three responses can best be understood by distinguishing two aspects of any scientific theory, which I term the predictive content and the explanatory content.2 The predictive content of a scientific theory dominates the concern of science in most periods and in most aspects of the scientific life, guiding the normal activity of scientists as they use the theories and equations of the scientific system for research or practical application. The explanatory content of a scientific theory represents the philosophical foundation upon which the predictive content is constructed. It describes the vision of the world, especially the natural world, which the scientific theory propounds. Although always present, the explanatory content goes virtually unnoticed except in periods of crisis and conflict. It is the explanatory content of a theory which revolutionizes an epoch, for it functions to lead science to the establishment of new principles and procedures. The explanatory content, representing the philosophical basis of the theory, opens our vision to a new world.

Each of the three responses represents a different attitude toward the mutual relation between the predictive content and explanatory content of a scientific theory. The first response, in claiming that science and philosophy are incommensurate, fails to recognize the philosophical foundation of a new scientific theory. The second response recognizes the philosophical aspects of a new theory, but views the explanatory content of the theory as incompatible with the established philosophical system. In rejecting the explanatory content of a theory, this response also rejects its powerful predictive content. In the third response the philosophical community is so overwhelmed by the predictive content of a new theory that it fails to examine critically the explanatory content of the theory.

Recognition of the importance of the explanatory content of a new scientific theory leads to a fourth response. The fourth response critically examines the philosophical foundations of the new theory and asks if the explanation of the world which the new theory propounds is adequate. Often in the philosophy of science emphasis is placed only on the predictive content of science, since it is this aspect of the theory which is most easily tested empirically. For example, both the verificationist and falsificationist doctrines base the adequacy of a new theory on its predictive power.3 However, a scientific theory must also be judged on the adequacy of its explanatory power. Examination of the explanatory content of scientific theory is discouraged by the fact that conflicting theories usually predict different empirical results. In this situation, selection of the best theory can be made by examination of the predictive content alone. For example, Newtonian mechanics predicts that particles can be accelerated to infinite velocities, whereas relativistic mechanics predicts that there is an upper limit to velocities. However, it is possible for two conflicting theories to make the same empirical predictions, but to base these predictions on fundamentally different explanations of the world. In such cases, the adequacy of the conflicting theories cannot be based on verification or falsification alone. This situation highlights the alternative philosophical foundations upon which the opposing theories are constructed. Such is the situation in the conflict of Einsteinís and Whiteheadís theories for the four classical tests of relativity.

The Principle of Relativity 4 is a vivid example of the fourth response. Whitehead accepts the impact of the new predictive content of Einsteinís theory, but offers an alternative explanation of the foundations of special relativity and the law of gravitation. He writes an alternative metric law of gravitation, which predicts the same results as does Einstein, but which is modeled more closely to Newtonís law of gravitation (see 5:239 ff.) and electromagnetic phenomena. The differences between Whiteheadís theory and Einsteinís theory have been examined by Robert Palter (6:188 ff.) and Robert Llewellyn (4:225f). Both authors approach Whiteheadís theory from its mathematical nature, focusing particularly on its uniform metric structure.

While there has been some interest in the philosophical differences between Einstein and Whitehead, most of the discussion of the impact of relativity theory on process thought has been characterized by the third response. Process philosophers, accordingly, have been concerned with explicating aspects of process thought so as to make them conform to the demands of Einsteinís theory. Consequently, Einstein has dominated the discussion at the expense of Whiteheadís philosophical objections. Since process philosophers are working within a Whiteheadian framework, it seems important to revitalize Whiteheadís theory of relativity as an alternative to Einstein.5 In section two I discuss the explanatory content of Whiteheadís theory as an alternative to Einstein in order to redirect the discussion of the impact of relativity on process thought from an uncritical acceptance of Einsteinís interpretation to an appreciation of Whiteheadís theory as a philosophical alternative. Section three focuses on the consequences this study can have for process thought.

II

A. SPECIAL THEORY OF RELATIVITY

Whiteheadís approach to the theory of relativity is guided by the question: Is relativity theory consonant with our direct, immediate experience of nature? A fundamental feature of our immediate experience is the recognition of the contemporary world which is felt as simultaneous with us. Whiteheadís appeal to immediate experience of the contemporary world explains the nature of his objections to Einsteinís definition of simultaneity. Each of Whiteheadís arguments demonstrates a desire on his part to answer demands of our common experience.6 For Einstein, simultaneity is an operationally defined concept dependent on the transmission of light signals in a vacuum. Since this transmission depends upon causality, there can be knowledge only about the world as past, not about the contemporary world. Hence the contemporary world lacks all objective reality, since the contemporary region is only known in terms of the projection of the past world.

Following his demand to give an elucidation of our experience, Whitehead begins his investigation of relativity theory by examining our fundamental notions of time, rest, and motion. In dealing with the notion of time, Whitehead points to the fact that nature is given to us in sense awareness as now present. He writes:

Our sense-awareness posits for immediate discernment a certain whole, here called a Ďdurationí; . . . A duration is discriminated as a complex of partial events... A duration is a concrete slab of nature limited by simultaneity which is an essential factor disclosed in sense-awareness. (CN 53; emphasis mine)

In Process and Reality he speaks of this mode of awareness as "presentational immediacy," which "is our perception of the contemporary world by means of the senses" (PR 474). Presentational immediacy gives "no information as to the past or the future. It merely presents an illustrated portion of the presented duration" (PR 255).7 It is a physical feeling which displays the real extensiveness of the contemporary world. "It involves the contemporary actualities but only objectifies them as conditioned by extensive relations" (PR 494).8 Presentational immediacy has an eternal object in the contemporary world as its datum. This complex eternal object "is analyzable into a sense-datum and a geometrical pattern" (PR 475) which illustrates the presented duration. Since the presented duration defines the world as simultaneous, presentational immediacy functions to define a preferred meaning of simultaneity within one time system.

Using the concept of durations, Whitehead examines our notions of rest and motion. We have a feeling of the event which is the focus of our act of awareness as being both "here" and "now." Durations define the "now." "Cogredience" defines the "here" and explains the relation of an event of awareness (percipient event) to its associated duration. The sense of rest and motion helps us to differentiate durations. Whitehead writes:

the sense of rest helps the integration of durations into a prolonged present, and the sense of motion differentiates nature into a succession of shortened durations. As we look out of a railway carriage in an express train, the present is past before reflexion can seize it. We live in snippets too quick for thought . . . the immediate present is prolonged according as nature presents itself to us in an aspect of unbroken rest. (CN 109)

In terms of durations which are differentiated through cogredience, Whitehead propounds a doctrine of alternate time-systems, a doctrine which he recognizes is unacceptable to Einstein.9 A time-system, such as that of a personally ordered society, is defined in terms of its presented duration. Thus "a moment of time is said to be identified with an instantaneous spread of the apparent world. . . . A time system is a sequence of non-intersecting moments including all nature forwards and backwards" (R 69). Cogredience determines which duration is selected to be the presented duration;

amid the alternate time-systems which nature offers there will be one with a duration giving the best average of cogredience for all the subordinate parts of the percipient event. This duration will be the whole of nature which is the terminus posited by sense-awareness. Thus the character of the percipient event determines the time-system immediately evident in nature. (CN 111)

Similarly, in Process and Reality he writes:

An actual occasion will be said to be Ďcogredient withí or Ďstationary iní the duration including its directly perceived immediate present. . . . The actual occasion is included in its own immediate present; so that each actual occasion through its percipience in the pure mode of presentational immediacy . . . defines one duration in which it is included. The percipient occasion is Ďstationaryí in this duration. (PR 191)

Each time-system defines a Euclidean space, a series of presented durations being parallel. Each time-system is thus the analogy of Newtonian absolute space and time (see 5:239 ff). Alternative time-systems yield different definitions of absolute position and absolute time. The theory of relative motion is a result of the recognition of different definitions of absolute time and space "where motion is essentially a relation between some object of nature and the one timeless space of a time system" (CN 117).

Having established the concept of alternate time-systems, which may be defined as a family of parallel durations and moments, Whitehead proceeds to derive the Lorentz transformation equations through an analysis of the transformation of measurement between alternate time-systems. The Lorentz equations form the basis of the theory of relativity for both Einstein and Whitehead. In Einsteinís original publication of the Special Theory of Relativity (1905) these equations were given an algebraic interpretation involving the inertial motion of particles. Following the interpretation of Minkowski (1908), Einstein shifted to a geometrical interpretation of the Special Theory of Relativity which was later essential in his construction of the General Theory of Relativity. In the geometrical interpretation, the transformation equations describe rotations in spacetime, and are therefore directly related to a theory of measurement instead of a theory of uniform particle motion.10 Whitehead, writing in 1922, follows Minkowskiís interpretation. However, within this geometrical interpretation, Whitehead develops an alternative theory of measurement which is critical of Einsteinís operational theory.

For Whitehead, all measurement takes place in the mode of presentational immediacy, which defines the world as simultaneously now. Whitehead argues that our immediate experience of the world discloses a basis of uniformity. However, this uniformity applies only to geometric relations and not to the contingencies of the past actual world. That is, uniformity of nature applies only to cognizance by relatedness (or, in the vocabulary of Process and Reality, presentational immediacy). Cognizance by adjective (i.e., causal efficacy) refers to the contingent physical world which is not necessarily uniform.11 Whitehead believes that the uniformity of nature is necessary if we are to know anything. Accordingly, he believes that Einsteinís theory, as well as theoretical physics in general, is doomed to failure if it demands, at least in principle, that in order to know anything we must know the state of the entire contingent universe.

In order to explain Whiteheadís criticism, I must contrast his theory of measurement with Einsteinís, whose theory of measurement is based on operational procedures involving the transmission of light signals. For Einstein, measurements are made along the past facing light cone. Accordingly, measurement is made in the past world. Distances are calculated by multiplying the velocity of light by the interval of proper time. However, in the real world of particles (the General Theory of Relativity) the velocity of light is not a constant, but is affected by the presence of the gravitational field (matter). Thus the measurements, which involve the transmission of light, depend on the contingencies of the physical field. Thus Whitehead can write:

Einstein, in my opinion, leaves the whole antecedent theory of measurement in confusion, when it is confronted with the actual conditions of our perceptual knowledge . . . measurement on his theory lacks systematic uniformity and requires a knowledge of the actual contingent field before it is possible. (R 83)

For Whitehead, on the other hand, all measurement is made in the contemporary world in the mode of presentational immediacy. Hence, measurement in Whiteheadís theory is not affected by the contingencies of the physical world, as it is in Einsteinís theory.

The difference between their theories of measurement clarifies the difference in the meaning of simultaneity in Einstein and Whitehead. For Whitehead, simultaneity is defined precisely in terms of presentational immediacy which is given directly in immediate awareness of the contemporary world. For Einstein, simultaneity has only a calculative meaning; measurements of time and space are calculated in the past world along the past-facing light cone and are then projected into the contemporary world. Milic Capek cogently explains why this calculative definition of simultaneity leads to semantic obscurity:

relativists continue to speak about the simultaneity of distant events, although such simultaneity is a mere conceptual entity, created by definition, intrinsically unobservable, and when computed, different in different systems. It is questionable whether the continued use of such a ghostly and fictitious term is fruitful or even meaningful. It appears to be an effect of sheer semantic inertia, a simple concession made to our traditional and outdated linguistic habits. (1: 190)

Whiteheadís definition of simultaneity, based on his inductive approach, which gives importance to our immediate sense awareness, avoids the obscurity and ambiguity of Einsteinís definition.

With his theory of measurement Whitehead seeks to make a comparison of measurements in alternate time-systems. In order to make such a comparison, it is necessary to describe the relations between the two alternate time-systems, which demands the notion of congruence. Congruence is presupposed in any procedure involving measurement. "Congruence is founded on the notion of repetition, namely in some sense congruent geometrical elements repeat each other. Repetition embodies the principle of uniformity" (PNK 141). Whitehead must find a way to express the measurements of time and space in one system in terms of the measurements of time and space in another system, while preserving the principle of uniformity. He accomplishes this by appealing to our immediate awareness of motion. He examines the measurement of velocity (uniform motion) of one time-system in the space of another time-system. There are four arbitrary (undefined) constants which depend on the two systems and which are related to the measure of space in the two systems (two constants) and the measure of time in the two systems (two constants).

In order to find the values of these arbitrary constants so that a comparison of time congruence between alternate time-systems can be made, Whitehead appeals to our experience of kinematic symmetry.12 The Principle of Kinematic Symmetry has two parts: (1) The measures of relative velocities are equal and opposite; (2) Measurements perpendicular to the direction of motion are symmetric.13 Using this principle together with the "Transitivity of Congruence" (which states that if a time unit in time system a is congruent with a time unit in b, and b is congruent with c, then a is congruent with c), Whitehead is able to show mathematically that the four arbitrary constants are all interrelated (so that if one is known, the others can be calculated). Therefore, one only needs to find the value of one of the arbitrary constants, which is equal to the expression:

(1-v2 /k3)1/2 (PNK 157)

Whitehead then proceeds to examine this equation for possible values of k which will permit a comparison of measurement between two time-systems, preserving congruence. If k = 0 there is the nonsensical condition that the space units of time-system b would depend on the time-units of system a but not on the space units of a. If k is negative, "elliptic kinematics" results, which does not make a fundamental distinction between time and space and also in which the electromagnetic transformation equations are not invariant (see PNK 162 ff. or CN 140 f.). If k is positive, "hyperbolic kinematics" results, which Whitehead conveniently writes as k = c2, yielding the Lorentz equations. Whitehead defines c as a constant which preserves congruence relations between two time-systems. It so happens that in our cosmic epoch, c is most clearly realized in nature as the velocity of light.

Hyperbolic kinematics can be written in metric form:

dG2=c3dt2 - dx2 - dy3 - dz2

where dG2 is Whiteheadís definition of the metric structure of uniform background spacetime in terms of which measurements may be made which are invariant under transformation between alternate time-systems.

A mathematically equivalent expression is used by Einstein, but the metric dG2 is defined as ds2. Although mathematically equivalent, the metrics dG2 and ds2 embody different explanatory content. For Einstein, ds2 is associated with the "proper time" of a particle, describing geodesics, and consequently reflecting his theory of measurement based on the contingent facts of nature. For Whitehead, dG2 represents the uniform structure of a background Minkowski spacetime which describes the congruence properties between alternate time-systems.14 Thus, for Einstein, the metric embodies a physical content, while, for Whitehead, it embodies a geometrical content which is independent of the contingent physical world.

We are now in a position to review how Whiteheadís appeal to immediate experience and his corresponding definition of simultaneity function in the derivation of the Lorentz formulae and hence in the formulation of dG2, the first metric of his theory of relativity, and how this differs from Einsteinís Special Theory of Relativity.

Whiteheadís starting point in the derivation of the Lorentz equations was an awareness of a simultaneous present in the act of our direct experience of the world. From the definitions of durations and cogredience, which were dependent upon this felt simultaneity, Whitehead developed the concept of alternate time-systems. Each time-system defined a preferred meaning of simultaneity. The Lorentz transformations represented the congruence relationships between alternate time-systems, which depended upon our immediate awareness of relative motion. Consequently, the possibility of uniform translation between time-systems was constructed ultimately upon the notion of simultaneity. In summary fashion, we can state the foundational principles of Whiteheadís theory of relativity as:

1. Appeal to direct experience.

2. Recognition of the observable properties of relative motions between alternate time-systems, which demands an awareness of simultaneity for its basis.

Einsteinís Special Theory of Relativity is based on two different foundational principles which are:

1. Constancy of the velocity of light in a vacuum in all inertial frames of reference, independent of the velocity of the emitting source.

2. Independence of the laws of physics from the choice of the inertial system.

For Einstein, the Lorentz transformations and the definition of simultaneity depend on the postulate of the constancy of the velocity of light as an ultimate feature of physical reality. Einstein, accepting this counter-intuitive postulate, rejects the primacy of our felt experience of simultaneity. In contrast, Whitehead defends the immediate experience of simultaneity and uses this as the foundation of relativity.15

B. Law of Gravitation

The significance of Whiteheadís definition of simultaneity and his appeal to immediate experience is not confined to the first metric of his theory, but is equally important for his law of gravitation. In opposition to Einstein, Whitehead constructs his law upon the principle of uniformity embodied in the metric dG2 which defines Minkowski spacetime. For Einstein, uniform spacetime (Minkowski spacetime) is warped or curved in the presence of matter. For Whitehead, the uniformity of spacetime is not contingently warped. Physical contingencies do not affect geometrical relationships of extension in the contemporary world.16

Whiteheadís theory of gravitation is similar in many respects to the Newtonian model of gravitation (see 5:239 ff.). However, the Newtonian law of gravitation makes no mention of time (gravitational forces are propagated instantaneously) and makes no indication of who measures the spatial separation between the two bodies in question. These inadequacies of Newtonís theory motivated both Einstein and Whitehead to find a new law of gravitation. Following the demands of relativity theory, Whitehead searched for an expression of the spatio-temporal separation between the two bodies which is invariant. Since measurements must be made in the mode of presentational immediacy, the spatio-temporal separation must be measured when the two bodies are mutually simultaneous.

These principles of Whiteheadís law of gravitation may be shown diagramatically.17

In Figure 1, m propagates a gravitational force at P, which is felt by M at X. The line PN represents the path which m would follow if it continued with uniform velocity from point P. N represents where m

GRAPHIC HERE, P. 167

 

would be at the time that M is affected by the gravitational force propagated by m. The line NX represents the invariant separation of M and m when they are simultaneous. It can be shown mathematically that it is possible to find such a measurement which is invariant. It is important to notice in this diagram that NX represents a measurement made in the mode of presentational immediacy. In the case of uniform motion m will actually be at N in the future, in which case the strain locus" and presented duration will be equivalent. However, in the case of non-uniform motion, which is characteristic of the physically contingent world, m will not actually be at N in the future, in which case the strain locus defined by NX would not be equivalent to the presented duration which depends on the actual state of the world. With this argument I think it is proper to say that in Relativity Whitehead has made an implicit distinction between the presented duration and the strain locus. This distinction is not made in Concept of Nature, but it is made explicitly in Process and Reality (PR 491).

Perhaps more important than Whiteheadís theory of measurement with its demand for the principle of uniformity is Whiteheadís alternative explanation of the nature of gravitational forces. In Einsteinís theory gravity is not a "real force." Rather, it is an expression for spacetime curvature. Objects which are "falling in a gravitational field" are not being pulled by a force. Instead, they are following "grooves" in spacetime called geodesics. In contrast, Whitehead maintains a physical rather than a geometrical interpretation of gravity. Gravity is a real force which is propagated with a finite velocity. The difference between Einsteinís and Whiteheadís interpretations may be clarified by comparing their respective theories of motion. In Einsteinís "pseudo-force" explanation objects move along geodesics (i.e., straight lines in spacetime). Since they follow straight lines (not curved lines), no forces are required. However, this does not explain why the objects move rather than remain at rest. Whitehead, on the other hand, develops a causal theory of motion. Kinematic elements (elements making up a world-line) do not move. Rather, motion is derived from the transference of common Ďadjectives" along the path of motion (an historical route or world line). The character of this transference depends on the propagation of gravitational forces. In Figure 1, PX graphically represents the propagation of gravitational forces. The line PX is called the "causal future" in Whiteheadís theory.19 In Whiteheadís theory of motion the past has a retarded effect in the present. The similarity between this explanation and the theory of prehensions developed in Process and Reality should be obvious to readers of this journal.

Whiteheadís explanation of gravitational forces as real forces maintains the distinction between geometry and physics. Gravity is not an effect of geometry, but rather it is an expression of real causal relationships in the physically contingent world. The metric dG2 which represents the uniform structure of space-time has a geometrical content. In order to find a mathematical expression for the law of gravitation, Whitehead introduces a second metric, which embodies physical content. This metric, dJ2, represents the gravitational field of a particle and describes the way a particle pervades its future:

the regulation of future adjectives of appearance by past adjectives of appearance is expressed by this intermediate distribution of character, indicated by the past and indicating the future.

I call this intermediate distribution of character the "physical field." (R 71)

Similarly, in Process and Reality, the physical field is defined as the "interweaving of the individual peculiarities of actual occasions on the background of systematic geometry" (PR 507). This quotation is particularly important in characterizing the two-metric structure of Whiteheadís theory of relativity and pointing out that Whiteheadís work in Process and Reality reflects the same basic position of a two-metric theory propounded in The Principle of Relativity. The "individual peculiarities of actual occasions" represent the properties of the physical contingent world (dJ2) while the "background of systematic geometry" represents the metric of uniform background spacetime (dG2).

III

In section two I have examined the explanatory content of Whiteheadís theory of relativity, emphasizing the fundamental role of simultaneity and the notion of gravity as a real force. Having outlined the explanatory content of Whiteheadís theory as an alternative to Einsteinís theory, I now pose a question: What consequences does this analysis have for the discussion of the impact of relativity theory on process thought?

One illustration of the impact of relativity theory on process thought concerns the impact of relativity on temporalistic doctrines of God, which include both the view defended by William Christian and Lewis S. Ford that God is an actual entity and the view defended by Charles Hartshorne and John B. Cobb. Jr., that God is a society of occasions with personal order. Doctrines of God in which the temporalistic categories do not apply are not affected by the paradoxes of relativity. The discussion about God and relativity has centered on the viability of a divine definition of simultaneity and the problems involved in such a definition for process theism.

The main contributors to the discussion have been John T. Wilcox, Ford, and Paul Fitzgerald. However, each of these authors responds to implications derived from the explanatory content of Einsteinís relativity theory. There is no mention of Whiteheadís alternative explanation. The common concern underlying each authorís response is characterized in a statement by Fitzgerald: "If we assume that Einsteinís relativity theory is giving us something close to the truth about spacetime . . . then we must be sure that any form of process theology which we care to accept is tuned to harmonize with it" (2:254). Recalling the four patterns of response outlined in section one, we may identify the third pattern as that followed by each author. Accordingly, they have sought to make process theology conform to the demands of the explanatory content of Einsteinís theory. In so doing, they have grafted Einsteinís philosophy of nature onto their Whiteheadian roots. One might ask whether such a graft has any chance of survival.

Before dealing with this question, let us look at the Einsteinian context of their approach, which is apparent in the way each author poses his problem. Wilcox introduces the issue by reference to the problem which grows out of "Einsteinís theory of relativity . . . that under certain conditions there is no unique physical meaning of Ďsimultaneousí" (8:293). Ford develops the problem in Einsteinian terms much more forcefully and clearly than Wilcox. "The whole thrust of relativistic physics renders the notion of an absolute inertial system no more meaningful than the notion of an absolute center to space-time" (3:130). Similarly, Fitzgerald states that "special relativity modifies our concepts of space and time it implies the relativity of simultaneity" (2:252).

Temporalistic doctrines of God seem to deny the findings of Einsteinís relativity theory by asserting that Godís experience of the world establishes some preferred inertial system or absolute meaning of simultaneity. As Wilcox asks, "With whom does Godís knowledge agree? Does God utilize some unique space-time system, and are the other systems wrong?" (8:296). Ford expands the discussion initiated by Wilcox and utilizes the demands of Einsteinian relativity to support interpretations of God as a single everlasting concrescence as opposed to the view developed by Cobb in A Christian Natural Theology that God is an enduring society of actual occasions with personal order. Whether Ford or Cobb is right is not at issue in this paper, but it should be recognized that insofar as the actual entity view is temporalistic, it does not escape the problems raised by Einsteinís theory. Fitzgerald seeks a closer examination of "how the worldís temporality is reflected in Godís consequent nature" (2:251). He offers a series of very interesting alternatives, some concerning the view that God is an actual entity and others that he a living person.

It is clear that Wilcox, Ford, and Fitzgerald are operating in the context of Einsteinís theory of relativity. Yet all three claim to be concerned with Whiteheadís vision of reality. But are Einstein and Whitehead compatible? Can one graft Einsteinís philosophy of nature as embodied in the explanatory content of his theory onto Whiteheadís cosmology? Rather than making process thought conform to the demands of Einstein, would it not be more appropriate to accept Whiteheadís theory as a philosophical alternative.

In concluding this essay I shall describe three areas of conflict between Einstein and Whitehead in order to clarify the hitherto hidden dangers implicit in demanding that process thought conform to the explanatory content of Einsteinís theory. My argument is the following: since the explanatory content of Whiteheadís theory (i.e., his philosophy of nature) is congenial with his mature cosmology, process philosophers and theologians will avoid many problems by working within the context of the philosophy of nature of Whiteheadís theory of relativity.

(1) The Role of Experience -- Induction versus Deduction. As shown in section two, "experience" is the watchword of Whiteheadís approach to relativity theory. His description of simultaneity, his doctrine of the uniformity of nature, his doctrine of alternate time-systems, and his principle of kinematic symmetry all exemplify his appeal to our direct, immediate experience of nature. Experience is also the central method of his approach to problems in metaphysics. As he has written in Process and Reality,

Our datum is the actual world, including ourselves; and this actual world spreads itself for observation in the guise of the topic of our immediate experience. The elucidation of immediate experience is the sole justification for any thought; and the starting point for thought is the analytic observation of components of this experience. (PR 6)

In contrast, the key foundational principles of Einsteinís theory -- the constancy of the velocity of light and the equivalence principle -- are postulates which are the free creations of the mind and not open to immediate experience. This minimizing of the role of our actual experience is captured in Einsteinís epistemology. Notice the Kantian flavor in the following statement and compare it with the passage quoted above. "ĎBeingí, is always something which is mentally constructed by us, that is, something which we freely posit (in the logical sense). The justification of such constructs does not lie in their derivation from what is given by the senses" (7:669).

(2) The Theory of Perception, Whitehead defends a two-mode theory of perception, involving the interrelation of causal efficacy and presentational immediacy as described in terms of symbolic reference. This two-mode theory of perception represents Whiteheadís solution to the inadequacy of other theories of perception, especially Humeís. It must be remembered that presentational immediacy is not simply the projection of properties derived from causal efficacy onto regions in the contemporary world. Rather, presentational immediacy describes the vivid experience of the extensive relations of the contemporary region. Whitehead gives us a concrete example of his meaning when he writes, "If we are gazing at a nebula a thousand light-years away, we are not looking backward through a thousand years" (PR 495). Instead Whitehead would argue that we are experiencing an immediate region of external space. I think this aspect of presentational immediacy has been de-emphasized by many Whiteheadian commentators.

In Whiteheadian terms, the weakness of Einsteinís theory of measurement is that it limits perception to one mode -- causal efficacy. For Einstein, the only knowledge we have is confined to our awareness of the world as causally past. This point is overlooked in most discussions of the so-called paradoxes of the relativity of simultaneity. For Einstein, the problems of simultaneity in the contemporary world can only be analyzed after the fact -- after the events of the contemporary world have entered the causal past. If process philosophers accept Einsteinís interpretation of relativity and his corresponding operationalist definition of measurement, they will have to develop an adequate theory of perception to replace or modify Whiteheadís two-mode analysis.

(3) The Doctrine of Causality. The difference between Whiteheadís and Einsteinís respective explanations of the nature of causality is exemplified in the difference between their description of the nature of gravitational forces. According to Whiteheadís theory (see Figure 1), an event in the past (P) pervades its future. It may be described as having "a foot in two camps, for it represents the property of the future as embodied in the past" (R 75). This physical interpretation of gravity allows Whitehead to speak concretely about the causal influence of the past on the future. It is legitimate to see in this description of gravity the foreshadowing of Whiteheadís theory of prehensions (especially simple physical feelings) as developed in his mature thought. In describing the experience of the simplest grade of actual entity, Whitehead writes:

The experience has a vector character, a common measure of intensity. If we substitute the term Ďenergyí for the concept of a quantitative emotional intensity, and the term Ďform of energyí for the concept of Ďspecific form of feelingí, and remember that in physics Ďvectorí means a definite transmission from elsewhere, we see that this metaphysical description of the simplest elements in the constitution of actual entities agrees absolutely with the general principles according to which the notions of modern physics are framed. (PR 177)

In contrast to Whiteheadís physical interpretation of gravity, Einstein defends a geometrical interpretation involving the warped curvature of space-time. In the Special Theory of Relativity Einstein, as is well known, denied the ontological status of the "ether." But we must remember that in the General Theory Einstein shifted his position and reintroduced spacetime as having physical qualities and the ontological capacity to act. That is, the properties of the spacetime curvature cause objects to follow certain geodesic paths of motion. According to Whiteheadís "ontological principle" only actual entities can act -- actual entities are the only reasons. It seems dubious for a process philosopher to accept Einsteinís contention that spacetime (geometrical elements) can act, unless he is willing to give up the relational theory of spacetime and reinstate spacetime as an entity.

These three areas of conflict between the explanatory content (and hence the metaphysical positions) of Einstein and Whitehead warn us against too quickly accepting the principles of Einsteinís interpretation of relativity without first evaluating their impact on the basic structure of Whiteheadís cosmological scheme. This point may be generalized to include the relation between any scientific theory and philosophical system. We must not absolutize any particular scientific theory as being "true." Rather, we should evaluate the explanatory content of the theory and ask if it embodies an adequate and coherent philosophy of nature.

With this warning in mind, I now ask again, "Can we graft Einsteinís philosophy of nature onto our Whiteheadian roots?" I respond, "No, unless we are willing to rework Whiteheadís system at very critical points -- his use of experience, his theory of perception, and his doctrine of causality."

Instead, we should strive for a critical appreciation and understanding of Whiteheadís theory as a philosophical alternative to Einsteinís theory. Process philosophers should then reexamine the issue of the impact of relativity theory on process thought in light of Whiteheadís own theory of relativity.

 

References

1. Milic Capek. The Philosophical Impact of Contemporary Physics. New York: Van Nostrand Reinhold, 1961.

2. Paul Fitzgerald. "Relativity Physics and the God of Process Philosophy" PS 2/4 (Winter, 1972), 251-76.

3. Lewis S. Ford. "Is Process Theism Compatible with Relativity Theory?" Journal of Religion, 47/2 (April, 1968), 124-35.

4. Robert R. Llewellyn. Alfred North Whiteheadís Analysis of Metric Structure in Process and Reality. Unpublished dissertation, Vanderbilt, 1971.

5. Robert R. Lewellyn. "Whitehead and Newton on Space and Time Structure." PS 3/4 (Winter, 1973), 249-58.

6. Robert Palter. Whiteheadís Philosophy of Science. Chicago: University of Chicago Press, 1960.

7. Paul Arthur Schillp. Albert Einstein: Philosopher-Scientist. LaSalle, Illinois: Open Court, 1949.

8. John T. Wilcox. "A Question from Physics for Certain Theists." Journal of Religion. 40/4 (October, 1961), 293-300.

 

Notes

1 For a good discussion of Galileoís defense of the Copernican System see James Brophy and Henry Paolucci (eds.), The Achievement of Galileo (New Haven: College and University Press, 1962).

2 A similar distinction is made by Paul Feyerabend in his response to Thomas Kuhn. Feyerabend speaks of the "normal component" and the "philosophical component" in opposition to Kuhnís discussion of normal science and periods of revolution. The important point is that the two components exist simultaneously and are in constant interaction. See Paul Feyerabend, "Consolations for the Specialist," in Imre Lakatos and Alan Musgrave (eds.), Criticism and the Growth of Knowledge (London: Cambridge University Press, 1970), pp. 197-230.

3 The falsificationist principle of Karl Popper exemplifies this point of view. See his discussion of the criterion of demarcation in Conjectures and Refutations (New York: Harper and Row, 1963), p. 253f.

4 Although my emphasis is on The Principle of Relativity, The Concept of Nature and An Enquiry Concerning the Principles of Natural Knowledge are equally important in forming the basis of Whiteheadís theory of relativity. The latter two are concerned primarily with the first metric of his theory.

5 This task is important since Whiteheadís theory is empirically and mathematically equivalent to Einsteinís theory insofar as both yield the Schwarzchild metric, as demonstrated by Sir A. S. Eddington, "A Comparison of Whiteheadís and Einsteinís Formulae," Nature, 113 (1924), 192. A group of physicists has argued that Whiteheadís theory is inadequate regarding its prediction of geotidal effects. For a popular presentation of their work see Clifford M. Will, "Einstein on the Firing Line," Physics Today, 25 (October, 1972), 23-29 and the two essays in PS 4/4 (Winter, 1974),285-90.

6 See PNK 53f. The arguments are (1) Einstein gives light signals too prominent a place in our lives; (2) there are other means of sending messages; (3) Einstein does not take account of the agreement within one time-system of the meaning of simultaneity.

7 Perhaps Whitehead should also have mentioned "strain loci" in his definition in order to emphasize the geometrical significance of presentational immediacy. Strain loci provide the systematic geometry, while durations share in the "deficiency of homology characteristic of the physical field which arises from the peculiarities of the actual events" (PR 196).

8 In my discussion of presentational immediacy I have emphasized "extensiveness. Too many discussions of presentational immediacy overlook this aspect and focus only on the role of presentational immediacy as the projection of the causal past onto the contemporary world. Limiting it to this role undercuts Whiteheadís two-mode theory of perception.

9 Within the framework of the special theory the doctrine of alternate time-systems would be acceptable to Einstein. The significance of Whiteheadís statement (that his doctrine would be unacceptable to Einstein) is apparent only in terms of the divergence of their theories of gravity. For Whitehead the alternate time-systems form the basis of the uniform structure of spacetime. For Einstein there is only one spacetime structure which varies depending on the presence of matter.

10 Einsteinís equations for the general theory reduce to the special theory when the mass is zero. Thus it is appropriate to think of the special theory as describing the structure of spacetime in the absence of matter. Matter warps this uniform spacetime structure, producing curved spacetime. For this reason, the geometrical interpretation seems better suited to both the special and general theories.

11 The fact that uniformity applies only to cognizance by relatedness has been overlooked by many interpreters of Whiteheadís theory of relativity -- in particular, Synge and Will. The gravitational field and the propagation of light are both aspects of the physically contingent world and consequently are not necessarily uniform. Furthermore, the differentiation between uniformity (geometry) and contingency (physics) parallels the shift of emphasis between PNK/CN and R. In the first two works Whitehead was primarily concerned with the nature of uniformity as expressed in the first metric, dG2í. In R Whitehead moves from considerations of geometry to physics. Consequently R is an analysis of the physically contingent relations in nature which are expressed in terms of the second metric, dJ2. Notice that the movement from uniformity to contingency corresponds with a movement from the analysis of the contemporary region to an analysis of the relationship between the past and future.

12 Einstein has a similar principle. If velocities were not reciprocal, the velocity of light in different frames of reference could be different.

13 In fact measurement in the transverse direction is unaffected by motion.

14 Many authors argue that the first metric, dG2, defines a prior geometry. If "prior" merely means that geometry and physics are separate in Whiteheadís theory of relativity, then their interpretation is accurate. However, "prior" usually implies much more. Misner, et al., for example, state that the prior geometry of Whiteheadís theory leads to its disconfirmation, since the flat background metric (dG2) influences the propagation of gravitational forces. See Misner, Thorne, and Wheeler, Gravitation (San Francisco: Freeman and Co., 1973) p. 430. While it is true that Whiteheadís mathematical formula requires this restriction in the propagation of gravitational forces (and hence the formula is falsified), the restriction is not demanded by his philosophy of nature, which is built on the separation of geometry and physics. The conflict between the formula and the explanatory content of the theory can be reconciled if we clarify Whiteheadís intentions. The first metric defines geometrical relations. The second metric defines physical relations. Whitehead admits that if "space" means physical space, then physical space is contingently warped. Whitehead expresses this view when he states that "if space-time be a relatedness between objects, it shares in the contingency of objects, and may be expected to acquire a heterogeneity from the contingent character of objects" (H 58). Notice that the physical relations between events create physical objects which endure through time. A second point may further clarify the issue of prior geometry in Whiteheadís theory. In R Whitehead correlates the metric dG2 with kinematic elements rather than a background geometry (see R 78, 81, and 87). I believe that the distinction between geometrical and physical relations and the correlation of the first metric with the "abstract measures of spatio-temporal process" (R 87) indicate that in R Whitehead already has made the distinction between physical space and the extensive continuum which characterizes his treatment of these issues in PR.

15 The difference between Einsteinís and Whiteheadís approaches may be characterized as a difference in a basically deductivist approach to science by Einstein and an inductivist approach by Whitehead. For a discussion of induction in Whitehead see Ann Plamondon, "Metaphysics and ĎValid Inductions,"í PS 3/2 (Summer, 1973), 91-99.

16 In R, Whitehead deals with the propagation of gravitational forces along straight lines. However, there is no requirement in his philosophy of nature that gravitation be propagated in this fashion. In fact, as a physical contingency, the route of propagation could be contingently warped.

17 This diagram represents the approach to Whiteheadís theory taken by J. L. Synge, The Relativity Theory of A. N. Whitehead (Lecture Series 5, Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1951) p. 6.

18 Whitehead defines the strain locus as that which provides Ďthe systematic geometry with its homology of relations throughout all its regions" (PR 196).

19 For Einstein, the causal future means the entire hyper-volume inside the future light cone. This same region is termed the "kinematic future" by Whitehead (11 30).


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