UNIFORMLY ACCELERATING REFERENCE FRAMES AND THE EQUIVALENCE PRINCIPLE

Abstract

In addition to the well-known Møller frame (or Rindler frame), we may construct another frame to describe the uniformly accelerating system. In the new frame, all "static" (i.e. spatial coordinates keeping constant) observers have the same proper acceleration but each has his own horizon. In contrast, the proper acceleration of a static observer in the Møller frame (or Rindler frame) depends on his position, but the horizon is (static-) observer-independent. We argue that the new uniformly accelerating reference frame is more suitable than the Møller frame to describe the system in an accelerating spacecraft. It is possible to distinguish the Møller frame and the new frame by high-precision experiments (such as arrival-time- and/or redshift-measurements) in an accelerating spacecraft. When the non-relativistic limit is taken, the second law of mechanics and Schrödinger equation in the new uniformly accelerating frame are all different from those in the Møller frame. The effects on the equivalence principle are discussed. We argue that even when the space–time curvature is ignored, it is still possible in some sense to distinguish gravity from acceleration at the next leading order.