If only the traced out shape and the direction of the rotation of (x (t), y (t)) is considered when interpreting the polarization state, i.e. only M ( | ψ ψ ⟩ ⟩ ) = { ( x ( t ) , y ( t ) ) | ∀ ∀ t } (where x (t) and y (t) are defined as above) and whether it is overall more right circularly or left circularly polarized (i.e. whether | ψ R | > | ψ L | or vice versa), it can be seen that the physical interpretation will be the same even if the state is multiplied by an arbitrary phase factor, since M ( e i α α | ψ ψ ⟩ ⟩ ) = M ( | ψ ψ ⟩ ⟩ ) , α α ∈ ∈ R and the direction of rotation will remain the same. In other words, there is no physical difference between two polarization states | ψ ψ ⟩ ⟩ and e i α α | ψ ψ ⟩ ⟩ , between which only a phase factor differs.