# Testing fundamental physics with photon frequency shift

## TL;DR

This paper proposes a satellite-based experiment using hydrogen atoms to measure photon frequency shifts, aiming to test Einstein's General Relativity and detect potential deviations predicted by extended gravity theories.

## Contribution

It introduces a novel experimental setup combining satellite photon exchange and hydrogen atom spin transitions to distinguish between GR and extended gravity models.

## Key findings

- Identifies a specific satellite distance where GR predicts zero frequency shift.
- Suggests non-zero shifts in extended theories could prevent hydrogen spin-flip transitions.
- Proposes a feasible method to experimentally detect deviations from GR using atomic transitions.

## Abstract

We propose a high precision satellite experiment to further test Einstein's General Relativity and constrain extended theories of gravity. We consider the frequency shift of a photon radially exchanged between two observers located on Earth and on a satellite in circular orbit in the equatorial plane. In General Relativity there exists a peculiar satellite-distance at which the static contribution to the frequency shift vanishes since the effects induced by pure gravity and special relativity compensate, while it can be non-zero in modified gravities, like in models with screening mechanisms. As an experimental device placed on the satellite we choose a system of hydrogen atoms which can exhibit the $1$s spin-flip transition from the singlet (unaligned proton-electron spins) to the triplet (aligned proton-electron spins) state induced by the absorption of photons at $21.1$cm. The observation of an excited state would indicate that the frequency of the emitted and absorbed photon remains unchanged according to General Relativity. On the contrary, a non-zero frequency shift, as predicted in extended theories of gravity, would prevent the spin-flip transition and the hydrogen atoms from jumping into the excited state. Such a detection would signify a smoking-gun signature of new physics beyond special and general relativity.