  The covariance of the Schr\"odinger equation under Galilei boosts and the
compatibility of nonrelativistic quantum mechanics with Einstein's equivalence
principle have been constrained for so long to the existence of a
superselection rule which would prevent a quantum particle from being found in
superposition states of different masses. In an effort to avoid this expedient,
and thus allow nonrelativistic quantum mechanics to account for unstable
particles, recent works have suggested that the usual Galilean transformations
are inconsistent with the nonrelativistic limit implied by the Lorentz
transformation. Here we approach the issue in a fundamentally different way.
Using a formalism of unitary transformations and employing quantum reference
frames rather than immaterial coordinate systems, we show that the
Schr\"odinger equation, although form variant, is fully compatible with the
aforementioned principles of relativity.
