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Concept
Whitehead's theory of gravitation
Summary
In theoretical physics, Whitehead's theory of gravitation was introduced by the mathematician and philosopher Alfred North Whitehead in 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.
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 , and the motion of a test particle is given by a geodesic with respect to the metric . 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 , where the indices run from 0 through 3, and let the masses of a set of gravitating particles be .
The Minkowski arc length of particle is denoted by . Consider an event with co-ordinates . A retarded event with co-ordinates on the world-line of particle is defined by the relations . The unit tangent vector at is . We also need the invariants . Then, a gravitational tensor potential is defined by
where
It is the metric that appears in the geodesic equation.
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