Volume 15: Pages 297-302, 2002
A Single Equation Encompassing Gravitational and Doppler Frequency Shifts
Departamento de Física, Universidade Federal do Paraná, CP 19044, CEP 81531‐990, Curitiba, Paraná, Brazil
We analyze the problem of the emission and absorption of photons, applying general energy‐momentum arguments obtained within an extension of the principle of relativity, where gravity is described as viewed from inertial frames of reference. This description of gravity unifies into a single equation the gravitational shift of frequency and the Doppler effect. In this case a difference in the gravitational potential is the cause of a shift in atomic spectral lines, which is in agreement with the known gravitational redshift and the “slowing down” effect of gravity on atomic beam clocks. Within this framework we suggest an experiment in order to check whether Einstein's principle of the inertia of energy also holds or not, when we consider the attribute of the gravitational mass of a body under the action of gravity. The main consequence of the possible enlargement of this principle is that the inertial mass (an attribute of inertia of matter) and the gravitational mass (an attribute of “gravitational charge” of matter) are equal. Indeed, the confirmation of this extension implies that we can discard the attempts to dispel this equality by appealing to experience; that is, it is not necessary to assume it as an “unexplained” true law of Nature, an equality that has been deduced by appealing to experience.
Keywords: inertia, energy, redshift, gravitational mass, Doppler effect, atomic clocks
Received: April 25, 2001; Published online: December 15, 2008