The Incompatibility of Mach's Principle and the Principle of Equivalence in Current Gravitation Theory

Abstract

Both Mach's Principle and the Principle of Equivalence have been extensively discussed in the recent past. However, the compatibility of the Principle of Equivalence with Mach's Principle is a question which, for some time now, has received little explicit attention. To the present it has been assumed that if gravitational field equations could be found which globally yield no solution in an empty universe, Mach's Principle would be subsumed under these equations. (This was the opinion of Einstein which has widely prevailed to this day.) The object of this paper is to show that for the two principles to be compatible this condition on the field equations is merely a necessary, but not a sufficient condition and that, given accepted theories of gravitation, the two principles are incompatible. Mach's and the Equivalence Principles are well known, but, as neither has a succinct and generally held definition, let us now give definitions of these principles that will suffice for our purposes in the following discussion. Mach's Principle may be stated: the global distribution of matter in the universe (Mach's 'fixed stars') causally determines by itself the properties of the local inertial field and thus the inertial properties of local bodies and the local inertial frame of reference.' Note that we say the rather than a local inertial frame of reference. We make this distinction because recent criticism indicates convincingly that globally the principle of general relativity (as formulated by Einstein) does not hold. Specifically, the failure stems from the fact that there exists only one frame of reference at any given point in the universe in which the cosmic blackbody radiation appears isotropic.2 However, the unique frame of reference in which the universe appears isotropic with respect to all phenomena is that maintained by Mach to be at rest with respect to the local inertial field as defined by the 'fixed' stars. It is firmly established that Mach's Principle is empirically verified with significant accuracy. The Principle of Equivalence simply asserts that the effects of acceleration and gravitation are physically indistinguishable, or, that inertial and