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In theoretical physics, Whitehead's theory of gravitation was introduced by the mathematician and philosopher Alfred North Whitehead in 1922.BOOK, Whitehead, A. N.,weblink The Principle of Relativity: With Applications to Physical Science, 2011-06-16, Cambridge University Press, 978-1-107-60052-2, en, Alfred North Whitehead, 1922, While never broadly accepted, at one time it was a scientifically plausible alternative to general relativity. However, after further experimental and theoretical consideration, the theory is now generally regarded as obsolete.

Principal features

Whitehead developed his theory of gravitation by considering how the world line of a particle is affected by those of nearby particles. He arrived at an expression for what he called the "potential impetus" of one particle due to another, which modified Newton's law of universal gravitation by including a time delay for the propagation of gravitational influences. Whitehead's formula for the potential impetus involves the Minkowski metric, which is used to determine which events are causally related and to calculate how gravitational influences are delayed by distance. The potential impetus calculated by means of the Minkowski metric is then used to compute a physical spacetime metric g_{munu}, and the motion of a test particle is given by a geodesic with respect to the metric g_{munu}.JOURNAL, Synge, J. L., 1952-03-06, 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. Series A. Mathematical and Physical Sciences, en, 211, 1106, 303–319, 10.1098/rspa.1952.0044, 1952RSPSA.211..303S, 121363087, 0080-4630, Unlike the Einstein field equations, Whitehead's theory is linear, in that the superposition of two solutions is again a solution. This implies that Einstein's and Whitehead's theories will generally make different predictions when more than two massive bodies are involved.Following the notation of Chiang and Hamity, introduce a Minkowski spacetime with metric tensor eta_{ab}=mathrm{diag}(1, -1, -1, -1), where the indices a, b run from 0 through 3, and let the masses of a set of gravitating particles be m_a. It is the metric g that appears in the geodesic equation.

Experimental tests

Whitehead's theory is equivalent with the Schwarzschild metricJOURNAL, Eddington, Arthur S., Arthur Eddington, 1924, A comparison of Whitehead's and Einstein's formulas, Nature, 113, 2832, 192, 1924Natur.113..192E, 10.1038/113192a0, 36114166, free, and makes the same predictions as general relativity regarding the (:Category:Tests of general relativity|four classical solar system tests) (gravitational red shift, light bending, perihelion shift, Shapiro time delay), and was regarded as a viable competitor of general relativity for several decades. In 1971, Will argued that Whitehead's theory predicts a periodic variation in local gravitational acceleration 200 times longer than the bound established by experiment.JOURNAL, Will, Clifford M., Relativistic Gravity in the Solar System. II. Anisotropy in the Newtonian Gravitational Constant, The Astrophysical Journal, IOP Publishing, 169, 1971, 0004-637X, 10.1086/151125, 141, 1971ApJ...169..141W, JOURNAL, Gibbons, Gary, Will, Clifford M., On the multiple deaths of Whitehead's theory of gravity, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 39, 1, 2008, 1355-2198, 10.1016/j.shpsb.2007.04.004, 41–61, gr-qc/0611006, 2008SHPMP..39...41G, 17017857, Misner, Thorne and Wheeler's textbook Gravitation states that Will demonstrated "Whitehead's theory predicts a time-dependence for the ebb and flow of ocean tides that is completely contradicted by everyday experience".BOOK, Charles W., Misner, Thorne, Kip S., Wheeler, John Archibald, Charles W. Misner, Kip Thorne, John Archibald Wheeler, amp, Gravitation (book), Gravitation, San Francisco, W. H. Freeman, 1973, 978-0-7167-0344-0, {{rp|1067}}Fowler argued that different tidal predictions can be obtained by a more realistic model of the galaxy.JOURNAL, Bain, Jonathan, Whitehead's Theory of Gravity, Stud. Hist. Phil. Mod. Phys., 1998, 29, 4, 547–574,weblink 10.1016/s1355-2198(98)00022-7, 1998SHPMP..29..547B, Reinhardt and Rosenblum claimed that the disproof of Whitehead's theory by tidal effects was "unsubstantiated".JOURNAL, Reinhardt, M., Rosenblum, A., Whitehead contra Einstein, Physics Letters A, Elsevier BV, 48, 2, 1974, 0375-9601, 10.1016/0375-9601(74)90425-3, 115–116, 1974PhLA...48..115R, Chiang and Hamity argued that Reinhardt and Rosenblum's approach "does not provide a unique space-time geometry for a general gravitation system", and they confirmed Will's calculations by a different method.JOURNAL, Chiang, C. C., Hamity, V. H., August 1975, On the local newtonian gravitational constant in Whitehead's theory, Lettere al Nuovo Cimento, Series 2, en, 13, 12, 471–475, 10.1007/BF02745961, 121832243, 1827-613X, In 1989, a modification of Whitehead's theory was proposed that eliminated the unobserved sidereal tide effects. However, the modified theory did not allow the existence of black holes.JOURNAL, Hyman, Andrew, 1989, A New Interpretation of Whitehead's Theory,weblink dead, Il Nuovo Cimento, 387, 4, 387–398, 1989NCimB.104..387H, 10.1007/bf02725671, 122670014,weblink" title="web.archive.org/web/20120204224955weblink">weblink 2012-02-04, Subrahmanyan Chandrasekhar wrote, "Whitehead's philosophical acumen has not served him well in his criticisms of Einstein."JOURNAL, Chandrasekhar, S., Subrahmanyan Chandrasekhar, March 1979, Einstein and general relativity: Historical perspectives,weblink American Journal of Physics, en, 47, 3, 212–217, 10.1119/1.11666, 1979AmJPh..47..212C, 0002-9505,

Philosophical disputes

Clifford M. Will argued that Whitehead's theory features a prior geometry.JOURNAL, Will, Clifford, Einstein on the Firing Line, Physics Today, 1972, 25, 10, 23–29, 10.1063/1.3071044, 1972PhT....25j..23W, Under Will's presentation (which was inspired by John Lighton Synge's interpretation of the theoryBOOK, Synge, John, Relativity Theory of A. N. Whitehead, 1951, University of Maryland, Baltimore, JOURNAL, Tanaka, Yutaka, 1987, Einstein and Whitehead-The Comparison between Einstein's and Whitehead's Theories of Relativity,weblink Historia Scientiarum, 32, ), Whitehead's theory has the curious feature that electromagnetic waves propagate along null geodesics of the physical spacetime (as defined by the metric determined from geometrical measurements and timing experiments), while gravitational waves propagate along null geodesics of a flat background represented by the metric tensor of Minkowski spacetime. The gravitational potential can be expressed entirely in terms of waves retarded along the background metric, like the Liénard–Wiechert potential in electromagnetic theory.A cosmological constant can be introduced by changing the background metric to a de Sitter or anti-de Sitter metric. This was first suggested by G. Temple in 1923.JOURNAL, Temple, G., Central Orbit in Relativistic Dynamics Treated by the Hamilton-Jacobi Method, Philosophical Magazine, 1924, 48, 284, 6, 277–292, 10.1080/14786442408634491, Temple's suggestions on how to do this were criticized by C. B. Rayner in 1955.JOURNAL, Rayner, C., The Application of the Whitehead Theory of Relativity to Non-static Spherically Symmetrical Systems, Proceedings of the Royal Society of London, 1954, 222, 1151, 509–526, 10.1098/rspa.1954.0092, 1954RSPSA.222..509R, 123355240, JOURNAL, Rayner, C., The Effects of Rotation in the Central Body on its Planetary Orbits after the Whitehead Theory of Gravitation, Proceedings of the Royal Society of London, 1955, 232, 1188, 135–148, 10.1098/rspa.1955.0206, 1955RSPSA.232..135R, 122796647, Will's work was disputed by Dean R. Fowler, who argued that Will's presentation of Whitehead's theory contradicts Whitehead's philosophy of nature. For Whitehead, the geometric structure of nature grows out of the relations among what he termed "actual occasions". Fowler claimed that a philosophically consistent interpretation of Whitehead's theory makes it an alternate, mathematically equivalent, presentation of general relativity.JOURNAL, Fowler, Dean, Winter 1974, Disconfirmation of Whitehead's Relativity Theory -- A Critical Reply,weblink Process Studies, 4, 4, 288–290, 10.5840/process19744432,weblink 2021-09-22, In turn, Jonathan Bain argued that Fowler's criticism of Will was in error.

See also

• Classical theories of gravitation
• Eddington–Finkelstein coordinates

References

{{Reflist}}

Further reading

• BOOK, Will, Clifford M., Was Einstein Right?: Putting General Relativity to the Test, 2nd, Basic Books, 1993, 978-0-465-09086-0,

{{theories of gravitation}}{{Alfred North Whitehead}}