Disconfirmation of Whiteheadís Relativity Theory -- A Critical Reply
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. 288-290, Vol. 4, Number 4, Winter, 1974. 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.
Robert Andrew Ariel has presented a concise and simplified account of Clifford Willís work "disproving" Whiteheadís theory of relativity. It is an accurate presentation of that work as well as of Willís interpretation of Whiteheadís theory. However, Arielís article lacks both a critical evaluation of Willís "empirical test" and a critical understanding of Whiteheadís theory. The purpose of this short reply is to correct these two weaknesses in Arielís article and to caution against too hasty a rejection of Whiteheadís theory of relativity (and with it his philosophy of nature) as a viable and living alternative to Einsteinís proposal. Accordingly, I will discuss (1) the physics of Willís test and (2) the philosophical aspects of the controversy.1
Arielís article leaves the impression that an actual physical experiment was performed. This is not the case. To find the experimental limit on the variations of the gravitational constant (anisotropy in G), Will interpreted existing gravimeter data, ignoring all accelerations too small to be related to the galactic center mass. Regarding this data, he states that "we have not attempted a detailed analysis of the tidal data or of models of the Earthís interior, and we have been somewhat cavalier in our treatment of uncertainties" (2:145). Although "cavalier," his interpretation of the existing data is reasonable.
The weakness of Willís approach lies in the simplified model of the universe which he uses in calculating Whiteheadís "prediction." The prediction depends on the model of the universe used. To calculate the local gravitational constant according to Whiteheadís theory, Will assumes that all the mass of our galaxy (1011 solar masses) is concentrated at a point 20,000 light-years from the earth -- the distance of the earth from the center of the galaxy. However, with a more realistic model in which the mass is smeared throughout the galaxy, Whiteheadís prediction is altered by a factor of 100, greatly diminishing the divergence between his prediction and Willís experimental limit. Also, if one takes account of the mass of the universe outside our own galaxy (such as Andromeda), Whiteheadís theory predicts a different result. This demonstrates that Whiteheadís theory, like Einsteinís, is sensitive to the cosmological model employed in making calculations. To settle the issue between the two formulae would require far more detailed work than has yet been done.
More important than the physics of Willís article is the philosophical interpretation of Whiteheadís theory. It was Whiteheadís purpose in The Principle of Relativity to offer an alternative interpretation of relativity equivalent to Einsteinís predictions; consequently, the real issue between Whitehead and Einstein is philosophical not physical. Whitehead anticipated that in the future, as in the past, given scientific theories would be superseded by more comprehensive theories:
If the above formula gives results which are discrepant with observation, it would be quite possible with my general theory of nature to adopt Einsteinís formula, based upon his differential equations, for the determination of the gravitational field. (R 84)
The crucial issue is Whiteheadís theory of nature. This theory may be applied equally well to other laws of gravitation. Whitehead offers, in fact, four such laws.
Will is not sensitive to the philosophical aspects of Whiteheadís theory. Willís interpretation of Whiteheadís law of gravitation is based on the work of Synge. While Synge presents a mathematically accurate translation of Whiteheadís theory, he misinterprets Whiteheadís philosophy of nature. Syngeís attitude is captured in the introduction to one of his lectures:
. . . if the philosophy is only a wrapping for physical theory, then the mathematical physicist can take a savage joy in tearing off this wrapping and showing the hard kernel of physical theory concealed in it. Indeed there can be little doubt that the oblivion in which this work of Whitehead lies is due in no small measure to the effectiveness as insulation of what a physicist can in his ignorance describe only as the jargon of philosophy. The account of Whiteheadís theory given in these lectures is emphatically one in which the philosophy is discarded and attention directed to the essential formulae. (1:2)
The interpretation of Whiteheadís theory is crucial in the context of Willís work, since the heart of his criticism against Whitehead is based on the supposed prior geometry embodied in Whiteheadís theory.
Whitehead, while maintaining a uniform geometry, did not claim that the geometrical structure is prior. Whitehead, in fact, emphasizes that geometry is an outgrowth of the relationships among actual events. That is, actual occasions are ontologically prior to geometry. According to the Will-Synge interpretation of Whiteheadís theory, gravitational forces are propagated along straight lines determined by the prior geometry, while electromagnetic waves are deflected by the contingencies of the universe. This restriction in the propagation of gravity produces the variations in the gravitational constant. While this is an acceptable interpretation of the mathematical formula of Whiteheadís law of gravitation, it does not express the demands of Whiteheadís philosophy of nature.2 For Whitehead, gravitational effects share in the contingency of nature. The uniformity of nature expressed in the geometry of Minkowski space-time applies only to "cognizance by relatedness" (presentational immediacy in PR). "Cognizance by adjective" (causal efficacy in PR) does not demand uniformity. Consequently, Whiteheadís philosophy of nature does not demand that gravity is propagated along the straight lines of a prior geometry, and hence the value of the gravitational constant is not a function of the prior geometry as Will and Ariel claim. This fact should be obvious from Whiteheadís separation of geometry and physics.
Since Whiteheadís formulae as they stand have not been disconfirmed and since Whitehead was quite prepared to adjust them to take account of new data, the real issues between Einstein and Whitehead are not physical but philosophical. No empirical test can decide the issue of the adequacy of Whiteheadís basic theory of relativity. This issue must be settled on other grounds. Currently there is considerable interest in correlating relativity theory with quantum mechanics. The efforts made in this direction tend to support Whitehead rather than Einstein.3
1. John L. Synge. The Eielativity Theory of A. N. Whitehead, Lecture Series 5. Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, 1951.
2. Clifford M. Will. "Relativistic gravity in the solar system, II: Anisotropy in the Newtonian gravitational constant." As-trophysical Journal, 169 (1971), 141-56.
1. I will be very brief concerning the philosophy. In a~,,~aper to, be published in a forthcoming issue of Proce.ss Studies I work through tehead s theory as a philosophical alternative to Einsteinís thought.
2. Perhaps Whiteheadís formula should be wntten to make this point clearer. However, ~vith the exception of Willís work, Whiteheadís theory is identical to Einsteinís in its predictions of the four tests of relativity.
3. See Suraj N. Gupta, "Einsteinís and Other Theories of Gravitation," &views of Modem Physics, 29/3 (July, 1957), 334-36. In this work, Gupta perforzns the quantization of Einsteinís gravitational field. The equations he derives are almost %entical to Whiteheadís formula. However, Guptaís method involves a more complex procedure for the summation of the effects of the gravitating particles.
4. It seems that Whiteheadís equation for gravitation has been disconflimed by Willís experiment. However, the disconfinnation is rooted in the assumption that implicit in Whiteheadís equation is the demand that gravity is propagated along the geodesics of the uniform structure of space-time. Since this demand is not a feature of Whiteheadís philosophy of nature, disconfirmation of the equation does not entail rejection of the theory as a whole.