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The covariance of the Schr\"odinger equation under Galilei boosts and thecompatibility of nonrelativistic quantum mechanics with Einstein's equivalenceprinciple have been constrained for so long to the existence of asuperselection rule which would prevent a quantum particle from being found insuperposition states of different masses. In an effort to avoid this expedient,and thus allow nonrelativistic quantum mechanics to account for unstableparticles, recent works have suggested that the usual Galilean transformationsare inconsistent with the nonrelativistic limit implied by the Lorentztransformation. Here we approach the issue in a fundamentally different way.Using a formalism of unitary transformations and employing quantum referenceframes rather than immaterial coordinate systems, we show that theSchr\"odinger equation, although form variant, is fully compatible with theaforementioned principles of relativity.

Galilei covariance and Einstein's equivalence principle in quantum reference frames