Post-quantum relativity

Special relativity puts constraints on clocks including atoms. So does quantum mechanics. Which theory gets the upper hand in case of conflict? It is suggested that redshifted atoms are bigger in all directions in accord with the quantum picture, even though special relatively makes the same prediction only in one direction. The resulting hypothetical “quantum relativity” is testable. It is related in spirit to ElNaschieʹs Cantorian unification of all forces.