Physical Meaning of Phase Ambiguity What is the physical significance of multiplying a quantum state $|A>$ by a phase factor $e^{i\theta}$. This does not have any effect on the normalization of the state so what is it physically? Does it have to do with the waves and their phase?
 A: There is no physical relevance of a phase in front of a phase vector, as this is unobservable, hence unphysical. In the geometric approach to quantum mechanics this can be viewed as a gauge freedom that can be used to reduce the total Hilbert space to the quantum phase space, i.e. the projective Hilbert space (equipped with a natural Kähler structure).
A: There's kind of an indirect meaning to it. Suppose you have a photon flying along. Photons seem to experience infinite time dilation and so there's no oscillating thing that the photon is "carrying with it" to have its particular frequency: rather that frequency comes via some sort of interaction with its surroundings. Phase factors are how that sort of wavey information enters the quantum theory. By itself, the photon/qubit/whatever cannot observe this phase factor; it has no meaning in the subsystem. But the moment you start to have two systems with a phase difference between them, you have interference effects with that phase.
With charged fields in addition the quantum phase becomes identified with the electromagnetic gauge symmetry, and actually leads to a conservation of electric charge term. So if you like, the physical meaning can also be "charge is a conserved quantity."
