Dean B. Fowler is completing his Ph.D. at the Claremont Graduate School with a dissertation on the impact of Einstein’s relativity theory on Whitehead’s 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.

### SUMMARY

The author seeks to correct some weaknesses in Ariel’s article (“Recent Empirical Disconfirmation of Whitehead’s Relativity Theory”) and to caution against too hasty a rejection of Whitehead’s theory of relativity (and with it his philosophy of nature) as a viable and living alternative to Einstein’s proposal. 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.

Robert Andrew Ariel has presented a concise and simplified account of Clifford Will’s work "disproving" Whitehead’s theory of relativity. It is an accurate presentation of that work as well as of Will’s interpretation of Whitehead’s theory. However, Ariel’s article lacks both a critical evaluation of Will’s "empirical test" and a critical understanding of Whitehead’s theory. The purpose of this short reply is to correct these two weaknesses in Ariel’s article and to caution against too hasty a rejection of Whitehead’s theory of relativity (and with it his philosophy of nature) as a viable and living alternative to Einstein’s proposal. Accordingly, I will discuss (1) the physics of Will’s test and (2) the philosophical aspects of the controversy.^{1}

Ariel’s 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 Earth’s 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 Will’s approach lies in the simplified model of the universe which he uses in calculating Whitehead’s "prediction." The prediction depends on the model of the universe used. To calculate the local gravitational constant according to Whitehead’s theory, Will assumes that all the mass of our galaxy (10^{11} 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, Whitehead’s prediction is altered by a factor of 100, greatly diminishing the divergence between his prediction and Will’s experimental limit. Also, if one takes account of the mass of the universe outside our own galaxy (such as Andromeda), Whitehead’s theory predicts a different result. This demonstrates that Whitehead’s theory, like Einstein’s, 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 Will’s article is the philosophical interpretation of Whitehead’s theory. It was Whitehead’s purpose in *The Principle of Relativity *to offer an alternative interpretation of relativity equivalent to Einstein’s 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 Einstein’s formula, based upon his differential equations, for the determination of the gravitational field. (R 84)

The crucial issue is Whitehead’s 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 Whitehead’s theory. Will’s interpretation of Whitehead’s law of gravitation is based on the work of Synge. While Synge presents a mathematically accurate translation of Whitehead’s theory, he misinterprets Whitehead’s philosophy of nature. Synge’s 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 Whitehead’s 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 Whitehead’s theory is crucial in the context of Will’s work, since the heart of his criticism against Whitehead is based on the supposed prior geometry embodied in Whitehead’s 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 Whitehead’s 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 Whitehead’s law of gravitation, it does not express the demands of Whitehead’s 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, Whitehead’s 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 Whitehead’s separation of geometry and physics.

Since Whitehead’s 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 Whitehead’s 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}

**References**

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.

**Notes**

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 Einstein’s thought.

2. Perhaps Whitehead’s formula should be wntten to make this point clearer. However, ~vith the exception of Will’s work, Whitehead’s theory is identical to Einstein’s in its predictions of the four tests of relativity.

3. See Suraj N. Gupta, "Einstein’s and Other Theories of Gravitation," &views *of Modem Physics, *29/3 (July, 1957), 334-36. In this work, Gupta perforzns the quantization of Einstein’s gravitational field. The equations he derives are almost %entical to Whitehead’s formula. However, Gupta’s method involves a more complex procedure for the summation of the effects of the gravitating particles.

4. It seems that Whitehead’s equation for gravitation has been disconflimed by Will’s experiment. However, the disconfinnation is rooted in the assumption that implicit in Whitehead’s 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 Whitehead’s philosophy of nature, disconfirmation of the equation does not entail rejection of the theory as a whole.