On the Dynamical Approach to the “Clock Paradox”

Abstract

The problem of establishing a dynamical connection between the proper time rate of a standard clock and its physical environment is considered, and the relevance of this for the famous “clock paradox” controversy is discussed. In particular, the possibility of “explaining” this phenomenon as due to a physical interaction between the gravitational field and the clock, governing the rate of the latter, is investigated. We find that one may always introduce formally an “effect” by the field on the clock rate, and thus “resolve the paradox,” as has been done in the literature; however, this “effect” is physically trivial, arising from a conventional choice of coordinates, and can always be “normalized away,” irrespective of the field environment of the clock. It is argued that a nontrivial “dynamical resolution” of the clock paradox must yield a way of predicting the effect of the field on the proper time rate of a clock from local field observations, without observing this rate directly on the clock. It is shown that this requires a number of restrictions to be imposed on the gravitational field environment of the clock and that the field equations of standard relativity theory are not sufficiently restrictive in this respect. Hence, the clock paradox cannot, in principle, be explained as a genuine dynamical phenomenon within this theory.