  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.
