MACH-EINSTEIN DOCTRINE AND GENERAL-RELATIVITY

It is argued that, under the assumption that the strong principle of e quivalence holds, the theoretical realization of the Mach principle (i n the version of the Mach-Einstein doctrine) and of the principle of g eneral relativity are alternative programs. That means only the former or the latter can be realized-at least as long as only field equation s of second order are considered. To demonstrate this we discuss two s ufficiently wide classes of theories (Einstein-Grossmann and Einstein- Mayer theories, respectively) both embracing Einstein's theory of gene ral relativity (GRT). GRT is shown to be just that ''degenerate case'' of the two classes which satisfies the principle of general relativit y but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation. These considerations lead to an interesting '' complementarity'' between general relativity and Mach-Einstein doctrin e. In GRT, via Einstein's equations, the covariant and Lorentz-invaria nt Riemann-Einstein structure of the space-time defines the dynamics o f matter: The symmetric matter tensor T-ik is given by variation of th e Lorentz-invariant scalar density L(mat), and the dynamical equations satisfied by T-ik result as a consequence of the Bianchi identities v alid for the left-hand side of Einstein's equations. Otherwise, in all other cases, i.e., for the ''Mach-Einstein theories'' here under cons ideration, the matter determines the coordinate or reference systems v ia gravity. In Einstein-Grossmann theories using a holonomic represent ation of the space-time structure, the coordinates are determined up t o affine (i.e., linear) transformations, and in Einstein-Mayer theorie s based on an anholonomic representation the reference systems (tetrad s) are specified up to global Lorenz transformations. The correspondin g conditions on the coordinate and reference systems result from the p ostulate that the gravitational field is compatible with the strong eq uivalence of inertial and gravitational masses.