In this paper, I present a new analysis of the meaning of the phase in quantum mechanics. First, I give a simple but rigorous proof that the global phase is not real in $$\psi$$ -ontic quantum theories. Next, I argue that a similar strategy cannot be used to prove the reality of the global phase due to the existence of the tails of the wave function. Finally, I argue that the relative phase is not a nonlocal property of two regions (...) together, and adding a relative phase to one local branch of a superposition only changes the local properties at the boundary of the region of the branch. (shrink)