Published in the July 1996 Physics Today
Letters Editor
Physics Today
Re: MS#10033
As a geophysicist, I appreciated Kenneth Nordtvedt’s remark that more detailed modeling of geophysics effects is essential to progress in the lunar-ranging tests of relativity theory (From Newton’s Moon to Einstein’s Moon, May 1996, page 26). Professor Helmut Moritz (1), emphasizing the cross-discipline interactions that are common in geophysics, pointed out that geophysical tidal data had been used to rule out the relativity theory of Alfred North Whitehead. This particular contribution requires an update. Whitehead’s theory of relativity (2) is philosophically distinct from Einstein’s, since it incorporates a nondynamical flat background metric, but it predicts the same values as Einstein's theory for most other observables, including black holes. It is a difficult theory to analyze, and much modified since its conception, but, as Professor Moritz said, it is the “exact tensor analogue of Maxwell’s vector equations for electromagnetism. ” It survived as a possibility until the early seventies, when researchers noticed that it apparently predicts a large gravitational anisotropy which would induce a sizable augmentation of certain Earth tides, with a sidereal half-day period. Such was not observed in the extensive tidal records, and Whitehead’s theory was eliminated as a valid theory of relativity (3).
The predicted anisotropy was proportional to M/r (where M is mass, and r is distance of that mass from the Earth), which of course was assumed to be dominated by our galactic (Milky Way) center. Even the famous “Hughes-Drever” experimental investigations of Mach’s Principle assumed that any effect which was proportional to M/r would be dominated by our galactic center. This common assumption is apparently false. Recent studies of the distribution of matter within the Universe have found structures among the stars that are massive enough to enable detection of their gravitational influence upon our galaxy and other galaxies. The Virgo Supercluster has an M/r ratio close to that for our galactic center, and the Great Attractor ratio appears to be very much larger, even allowing for uncertainties. There are other structures in the Universe that are also important in calculating M/r effects. The structures spread across large portions of the sky, as does the Milky Way itself, and the effect of one structure partially cancels the effects of others. Thus, the direction or magnitude of any anisotropy proportional to M/r is essentially indeterminate, especially if the M/r ratios continue to hold as the investigations reach out to the edges of the Universe.
The present indeterminacy of the M/r distribution of matter in the Universe does not necessarily resurrect Whitehead’s theory, but it does imply that there is interesting work yet to be done. The anomalous sidereal tides which do exist (4) could be analyzed with no a priori orientation. A statistical argument analyzing the variation in distribution of matter would probably argue against Whitehead. The basic question of what is the anisotropy in M/r, from the Earth’s point of view, may be unanswerable.
Sincerely,
Richard Mentock
Geology Department
University of North Carolina - Chapel Hill, NC
1. Moritz, H. in Quo Vadimus, G.D. Garland and J.R. Apel, eds., p.113 (American Geophysical Union, Washington, 1990).
2. Whitehead, A.N. The Principle of Relativity, p.190 (Cambridge University Press, Cambridge, 1922).
3. Will, C.M. Theory and Experiment in Gravitational Physics, p.380 (Cambridge University Press, Cambridge, 1993).
4. Warburton, R.J., and Goodkind, J.M. Astrophysical J., 208, 881-886 (1976).