True dynamical tests of the weak equivalence principle for matter and anti-matter

Abstract

After a brief review of the evidence for the validity of the Weak Equivalence principle for anti-matter, I show that, contrary to general belief, the near equality of the Shapiro delay for photons, neutrinos and anti-neutrinos in the galactic gravitational potential is not a true test of the WEP for their intrinsic properties and quantum numbers due to the overwhelming contribution to the gravitational mass from the relativistic kinetic energy. Then I prove the remarkable result that particles that obey the Newtonian law of dynamics automatically respect the WEP due to the firm equivalence between the law of motion and the WEP in any relativistic scenario, through gravity of all the matter in the Universe. Thus a test of the validity of Newtons's law in any force field is a true test of the WEP and provides strong direct tests of WEP for anti-particles. This result opens up an entire new insight of conceptual and practical importance for the tests of WEP.