The equivalence principle according to Mach

A prerelativistic Machian theory of gravitation in a relative configuration space of the type developed in Barbour and Bertotti (1977) is proposed, which fulfils the principle of equivalence in a natural way. This is accomplished by assuming that the basic interactions with which the dynamical Lagrangian is constructed are three-body and velocity dependent. Gravity arises between two bodies when other masses move-in particular when the universe expands (or contracts). The properties and physical consequences of this theory are very similar to the previous one; in particular the two-body problem has a small post-Newtonian correction leading to an advance of the periastron, and to the determination of the velocity of expansion of the universe. We find that the motion of test particles introduces naturally into the theory the restricted covariance group, in which any space transformation that preserves simultaneity is allowed. This permits us to define an inertial frame of reference, and to obtain the analog of the equation of geodesic deviation. Finally, we discuss the effect of the anisotropy of the universe on the mass.