Resonant Absorption between Moving Atoms due to Doppler Frequency Shift and Quantum Energy Variation

By taking both the Doppler frequency shift for electromagnetic wave and the quantum energy variation of matter wave into consideration, a resonant-absorption condition based on the local-ether wave equation is presented to account for a variety of phenomena consistently, including the Ives-Stilwell experiment, the output frequency from ammonia masers, and the Mössbauer rotor experiment. It is found that in the resonant-absorption condition, the major term associated with the laboratory velocity is a dot-product term between this velocity and that of the emitting or absorbing atom. This term appears both in the Doppler frequency shift and the transition frequency variation and then cancels out. Thereby, the experimental results can be independent of the laboratory velocity and hence comply with Galilean relativity, despite the restriction that the involved velocities are referred specifically to the local-ether frame. However, by examining the resonant-absorption condition in the Mössbauer rotor experiment to a higher order, it is found that Galilean relativity breaks down.