Is Space-Time Flat?

Abstract

Lorentz transformations are developed between relatively accelerated systems, based on the assumption that there exists an inertial set defining absolute acceleration and on the supposition that the accelerated observer uses at each moment the member of this inertial set appropriate to his momentary velocity. The application of this transformation to a planetary observer shows that the system is non-affine; beyond a critical distance events occur in reverse order during half the year and stretch through longer than normal times in the opposite season. Actual appearances at the origin are not affected by this feature, since the velocity of light is reversed when time is reversed, and carries the original frequency unchanged to the observer. Rosen's method of avoiding this non-affine character of flat space is discussed, and shown still to require the existence of an absolute standard of uniformity of motion before the real field theory of gravitation can be maintained. It is not claimed that flat-space theory is false, but that in practice it would be an inconvenient method of description that can hardly be identified with that actually employed in astronomy and physics.