Test of Einstein's Mass-Energy Relation

The Einstein's mass-energy relation $E=mc^2$ is one of the most fundamental formulae in physics, but it has not been seriously tested by an elaborated experiment, and only some indirect evidences in nuclear reaction suggested that it holds to high precision. Manifestly, for a particle, different self potential leads to different energy-speed relation, which can be used as the fingerprints of them. In this letter, we propose an experiment to test this relation. The experiment only involves low energy of particles and measurement of speed, which can be easily realized. The experiment may shed lights on a number of fundamental puzzles in physics.