Abstract

Astronomers use the Doppler-shifted absorption (dark) lines in the spectra of moving astronomic bodies to measure their radial velocities respect to Earth. A dark line, however, is the absence of radiation. How, then, can it be red-shifted or blue-shifted in any sense? This paper investigates this problem trying to comply with QM, and with both, the classical Doppler effect and its relativistic version. For relativity this is the problem: the Doppler-shifted dark lines are produced by absorption in the atmosphere of the selfsame star that emits the radiation. So it looks like a Doppler shift without relative motion. For QM the problem is how to harmonize the frequency shift with Planck's quantum relation, E=hf, where the frequency f is uniquely defined by a given energy level of a given atom in a stationary frame of reference. How can it be Doppler-shifted, by the macroscopic motion of the atom?  Between 1918 and 1932, Bohr, Schroedinger, Dirac, and Fermi studied a similar problem, developing a quantum theory of the Doppler effect. They criticized and improved what each other said. Yet, in this paper preference will be given to the complete classical version of the Doppler formula, explained as a double Doppler effect with time difference between emission and reception. A ?bonus? prediction of the paper is a non-relativistic diffraction experiment in which the cosmic motion of the Earth might be detected.