Testing fundamental physics with photon frequency shift

We propose a high precision satellite experimentto further test Einstein’s General Relativity and constrainextended theories of gravity. We consider the frequencyshift of a photon radially exchanged between two observerslocated on Earth and on a satellite in circular orbit in theequatorial plane. In General Relativity there exists a pecu-liar satellite-distance at which the static contribution to thefrequency shift vanishes since the effects induced by puregravity and special relativity compensate, while it can benon-zero in modified gravities, like in models with screen-ing mechanisms. As an experimental device placed on thesatellite we choose a system of hydrogen atoms which canexhibit the 1 s spin-flip transition from the singlet (unalignedproton-electron spins) to the triplet (aligned proton-electronspins) state induced by the absorption of photons at 21.1cm. The observation of an excited state would indicate thatthe frequency of the emitted and absorbed photon remainsunchanged according to General Relativity. On the contrary,a non-zero frequency shift, as predicted in extended theo-ries of gravity, would prevent the spin-flip transition and thehydrogen atoms from jumping into the excited state. Sucha detection would signify a smoking-gun signature of newphysics beyond special and general relativity