13 - Alternative theories of gravity

Summary

From Chapter 5 until now we have confined our attention to Einstein's general theory of relativity. But general relativity is not the only possible relativistic theory of gravity. Even in the late 1800s, well before Einstein began his epochal work on special and general relativity, there were attempts to devise theories of gravity that went beyond Newtonian theory. Some attempts were modeled on Maxwell's electrodynamics. Some replaced ∇² with a wave operator in Poisson's equation of Newtonian gravity, in an attempt to formulate a theory that was invariant under Lorentz transformations. None of these attempts was very successful; for example, most theories could not account for the anomalous perihelion advance of Mercury. In 1913, before Einstein completed the general theory of relativity, Nordström proposed a theory involving a curved spacetime; the metric was expressed as g_αβ = Φη_αβ, with the scalar field Φ satisfying a Lorentz-invariant wave equation. But the theory automatically predicts a zero deflection of light, and ultimately it failed the test of experiment.

Alternative proposals appeared even after the publication of general relativity and the empirical successes with Mercury and the deflection of light. The eminent mathematician and philosopher Alfred North Whitehead formulated such an alternative theory in 1922. Troubled by the fact that in general relativity the causal relationships in spacetime are not known a priori, but only after the metric has been determined for a given distribution of matter, he devised a theory with a background Minkowski metric in order to put causality on a “firmer” ground.