Acceleration and weight of extended bodies in the theory of relativity. [Doppler effect relation]

A spring weight used as an accelerometer and as a dynamometer is considered. It is shown that in the theory of relativity the force scale of a dynamometer moving in a gravitational field is conventionally changed with position and velocity. Investigating the acceleration and weight of extended bodies, it is concluded that this weight does not depend on the position of the supporting force on the body. The connection between this result and the relativistic interpretation of the gravitational Doppler effect, which implies that from a global point of view the energy of a photon moving in a gravitational field is constant, is emphasized. (AIP)