  Here we show that two Bloch states, which are energy eigenstates of a quantum
periodic potential problem, with different wavevectors can not be linearly
superposed to display quantum interference of any kind that captures the
relative phase between them. This is due to the existence of a superselection
rule in these systems, whose origin lies in the discrete translation symmetry.
A topological reason leading to such a superselection is found. A temporal
analogue of this superselection rule in periodically driven quantum systems is
also uncovered, which forbids the coherent superposition of any two
quasi-periodic Floquet states with different quasienergies.
