In 1922, some nine years after Einstein had published his first paper on General Relativity, Whitehead was compelled by the differences he had with Einstein’s view to come forward with his own work, The Principle of Relativity, in which he formulated a theory of gravitation more in keeping with his own philosophical outlook.
The resulting theory, though founded on quite different principles and developed in an independent fashion from Einstein’s theory, nevertheless gives predictions that are identical to the latter’s, within observable limits, for each of the four classic tests of gravitational theories (i.e., precession of the perihelion of Mercury, redshift of light emitted by a massive body, the bending of light-beams in a strong gravitational field, and the apparent slowing of the speed of light propagation near massive bodies). Whitehead’s theory not only agrees with Einstein’s and with observations in these crucial cases, it is also a mathematically simpler theory. Einstein’s gravitational equations are nonlinear, and the difficulty in solving them for even a simple problem are enormous. Whitehead’s linear theory is almost simple in comparison. Hence, if the two theories always gave identical predictions, Whitehead’s formulation would be the theory of choice (2:303). However, despite the similarity of prediction for the four "classic" tests, there are some differences between the two theories that can be exploited to disconfirm one or the other.
To understand the recently discovered evidence against Whitehead’s theory it is necessary to examine the Newtonian gravitational law in the light of Einstein’s and Whitehead’s /theories. We recall that Newton’s law for gravitational attraction between two bodies is given by: force=(Gm1m2)/r2, where m1 and m2 are the masses of two bodies, r the distance separating them, and G the gravitational constant which acts as a factor of proportionality. The value of G can be found experimentally: If two spheres of known mass are separated by a known distance, there will be a measurable force between them. Knowing the force and knowing the masses and distance involved, one can find G from the above force law. The question can now be asked: Is the value of the gravitational "constant" G, thus measured, truly constant and independent of the location or orientation of the two masses? The answer, in brief, is that on Einstein’s theory the value of G is constant, while on Whitehead’s theory it is not. In other words, on Einstein’s theory two given masses separated by a given distance will attract each other with the same force anywhere in the universe. On Whitehead’s theory the attraction between the two masses will vary slightly as a function of the position of other bodies in the universe.
The reason for this difference goes right to the heart of the two theories. Einstein’s theory is characterized by having no prior geometry, no prior structure to space; the geometry of space, its local curvature, is determined entirely by the location of masses within it. The attraction which we observe between objects is a manifestation of the motion of an object in the space that has been curved by the mass of another object. Now since curvature is the origin of attraction (Or, more accurately, curvature manifests itself as attraction), the only factor that determines the attraction between two bodies is the local curvature of space. Since there is no prior geometry, the only thing that determines the local curvature of space is the amount of "curving force," i.e. mass, that is present. For Einstein, the constancy of G is a consequence of the direct connection between the quantity of mass and the degree of curvature, for nothing else causes curvature aside from mass; there is no prior geometry that also contributes to the curvature.
In sharp contrast to Einstein’s theory, Whitehead’s demands a prior geometry for space. That is, it demands that space have some structure that is independent of the location of bodies within it. Whitehead felt that we needed a prior geometry, a uniform "structure for the continuum of events, . . . because of the necessity for knowledge that there be a uniform relatedness, in terms of which the contingent relations of natural factors can be expressed. Otherwise we can know nothing until we know everything" (H 29f). Thus it comes about that for Whitehead the attraction between two given bodies, which measures the value of G, is a function not only of the masses and the separation involved, but also of the prior geometry. Hence, if Whitehead were correct, it would be theoretically possible to perform an experiment to detect the variations in the force of attraction between two masses as the position and orientation of the masses varied. Though the masses involved in such an experiment would, of course, remain unchanged, fluctuations in G still should be observable, for the masses and their separation are not the only factors responsible for the observed attraction: the prior geometry enters the calculation as well (1:1121-25).
The detection of variations in G form the basis of the empirical test that was actually performed. In the experiment (3:141-56) one mass was the earth, and the other a gravimeter located on the earth’s surface. Variations in G would produce changes in the gravimeter’s readings. Calculations (3:141-56) based on Whitehead’s theory (2:303) showed that the orientation of the two masses relative to the center of the galaxy should produce a variation in the attraction between the two masses, and hence in the gravimeter’s readings: as the earth rotates, bringing the earth, gravimeter, and galaxy center alternately into and then out of line, Whitehead’s theory predicts that the attraction should likewise vary periodically, with period 12 hours (i.e., the galaxy center, gravimeter, and earth are in line twice a day.) Actual measurements found no variations in G with such a 12 hour period, not even in amounts as small as 1/200 the amount predicted by Whitehead’s theory. Accordingly, the theory must be judged to have been empirically disconfirmed.
References
1. Misner, Thorne, and Wheeler. Gravitation. San Francisco: Freeman and Co., 1973. The description of the differences between Whitehead’s and Einstein’s theories followed the discussion here, especially pp. 1121-25. See also pp. 429-31.
2. J. L. Synge. "Orbits and rays in the gravitational field of a finite sphere according to the theory of A. N. Whitehead." Proceedings of the Royal Society of London, 211A (1952), 303. The calculations employed in the experiment were based on Synge’s generalization of Whitehead’s original work.
3. C. M. Will. "Relativistic gravity in the solar system, II: Anisotropy in the Newtonian gravitational constant." Astrophysical Journal, 169 (1971), 141-56, and references cited herein.