I'm surprised the article doesn't mention phases or the idea of projective Hilbert spaces. The QM formulation it gives is well known ambiguous: the condition <φ

I'm surprised the article doesn't mention phases or the idea of projective Hilbert spaces. The QM formulation it gives is well known ambiguous: the condition <φ|φ>=1 does not determine φ, because it's also satisfied by any other state ψ=exp(iλ)φ with λ real. So, the state of a physical system is really described by the ray (equivalent class) of all state vectors differing by a phase. I wonder if this has any consequence on their reasoning and conclusions.