Relativistic Theory of a Rigid Body

Abstract

GARDNER¹ has recently given a new relativistic theory of a rigid body, and Synge² has applied this theory to the earth considered as a rigid body in rotation. He predicts, on the basis of the Gardner theory, that the fringes in a Michelson interferometer with one arm inclined at 45° to the horizontal should shift on rotating the interferometer about a vertical axis—provided that the interferometer is rigidly attached to the earth. The fringe shift predicted is (E/c D/λ) sin θ, where E is the velocity of earth's rotation, D is the length of the arm of the interferometer and θ is the angle between the projection of the direction of the inclined arm on a horizontal plane and a line pointing north³.