On the Interpretation of Gravitational Redshift: Local and Coordinate Frequencies

Gravitational redshift is a standard prediction of general relativity, yet its interpretation can remain conceptually puzzling for students. In particular, the relation $E=h\\nu$ may lead to the intuition that a photon must lose energy when its locally measured frequency decreases. Following the interpretive discussion of Okun, Selivanov, and Telegdi, this paper revisits the issue from an operational and pedagogical perspective. The distinction between frequencies measured with local proper times and a frequency defined with respect to a common Schwarzschild coordinate time is made explicit. For the static Schwarzschild spacetime, the latter is associated with time-translation symmetry and the corresponding conserved energy, whereas the former describes the actual local measurements made by clocks and frequency standards. This provides a simple framework in which gravitational redshift can be understood without attributing an energy loss to the propagating photon. More broadly, the example introduces a useful teaching principle: before asking how an energy changes, students should first identify the relevant time parameter and the spacetime symmetry underlying the conservation law. The treatment uses only standard general relativity and is intended as a pedagogical clarification of a familiar gravitational-redshift problem.