Eliezer:I wouldn't be surprised to learn that there is some known better way of looking at quantum mechanics than the position basis, some view whose mathematical components are relativistically invariant and locally causal. There is. Quantum Field theory takes place on the full spacetime of special relativity, and it is completely lorentz covariant. Quantum Mechanics is a low-speed approximation of QFT and neccessarily chooses a reference frame, destroying covariance.

Hal Finney: The Schrodinger equation (and the relatavistic generalization) dictate local evolution of the wavefunction. Non-locality comes about during the measurement process, which is not well understood.