Quantum equivalence principle without mass superselection

Abstract

The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important principle and quantum mechanics depends crucially on the imposition of a non-fundamental restriction. The objective of this work is show that, contrary to what the standard account holds, the compatibility between the principle of equivalence and quantum mechanics does not depend on the introduction of such a superselection rule. For this purpose, we consider the extended Galileo group, in which mass is treated as an operator, and show that within this scheme superpositions of different masses behave as they should in order to obey the equivalence principle.