Resonance absorption between moving atoms due to Doppler frequency shift and quantum energy variation

[[abstract]]Consider the resonance absorption between source and absorber atoms moving at velocities vs and v_e, respectively. According to classical propagation, the transmitted and received frequencies due to the Doppler effect is f_t/f_r=1+u_es/c+v_e\cdot v _es/c^2, where v_es=v_e-v_s, u_es=u_e-u_s, u=v\cdot hatR_t, and unit vector hatR t points from source to absorber [1]. Furthermore, based on a wave equation, quantum energies and hence transition frequency f in an atom moving at velocity v decrease with speed by the mass-variation factor as f=f_0(1-v^2/c^2)^1/2, where f0 is that in the atom at rest [2]. By considering both the Doppler frequency shift and the quantum energy variation, we have the resonance-absorption condition: [ f_0e√1-v_e^2/c^2=f_0s√1-v_s^2/c^2 1-u_es/c-(v_e\cdot v_es-u_es^2)/c^2 , ] where f_0e and f_0s are the rest frequencies in absorber and source, respectively. If the absorber is stationary (v_e=0), then f_0e=f_0s(1-v_s^2/c^2)^1/2/(1-u_s/c). This agrees with the frequency shift of light emitted from fast-moving hydrogen atoms in the Ives-Stilwell experiment. If the source is stationary (v_s=0) and v e is parallel to ± hatR_t, then f_0e=f_0s(1-u_e/ c)/(1-v_e^2/c^2)^1/2. This agrees with the two-photon absorption in neon atoms moving collinearly with two counterpropagating laser beams from an identical source [3]. However, according to the local-ether model, one fundamental difference is that velocities vs and ve in these terrestrial experiments are referred to an ECI frame [1,2], although slight for high-speed atoms.[[fileno]]2030130010021[[department]]電機工程學