The clock paradox in a static homogeneous gravitational field

Abstract

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars.

Revision: Posted with the caption included with the figures

References in corpus (1)

• An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity

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• The task of the relativistic oscillator in a non-inertial frame of reference