[Author ORCID: 0000-0003-1871-7803]
When an oscillating body is subjected to either relative velocity or a gravitational potential difference, it can experience a phase shift in its oscillations, which can be associated with an infinitesimal loss of wave energy.
However, the difference between the relative Doppler shift and the phase shift due to the potential difference is the relative energy difference between the propagating wave and the oscillating bodies in relative position, respectively.
Doppler shift considers the frequency change of a wave in propagation but gravitational potential difference considers the frequency change of the oscillating body'. Furthermore, propagating waves even become irrelevant in terms of velocity when the oscillating body itself is in motion.
