Do electrons obey the equivalence principle?

Abstract

In the realm of elementary particle physics gravity is negligibly small when compared to the other fundamental interactions. Notwithstanding, it is assumed as an obvious truth that electrons are affected by gravitational fields in the usual sense, i.e., obeying Einstein's equivalence principle. Experimental verifications of that fact are extremely difficult and sometimes inconclusive. Therefore, it is pertinent to further inquiry whether electrons are affected by gravity. In the present letter, quantum states of the hydrogen atom in a gravitational well are considered, but energy measurements require a precision in the range of 10−16 eV. From the classical Eötvös experiment it can be concluded that electrons do couple to the gravitational field as expected, setting upper bounds to the gravitational to inertial electron mass difference to |κ−1|<6.89×10−7.