  According to quantum theory, pure physical states correspond to equivalence
classes of state vectors, where any two members of one class differ by a
complex factor. The point is that such a factor does not change the probability
for the occurrence of any measurement result as computed within the formalism
of quantum mechanics. In the formalism to be presented here, the state vector
does not only determine the probabilities for the occurrence of measurement
results, rather it determines the result itself. The information which guides
the selection process is obtained from the state vector in a way that is not
invariant against multiplication by a complex factor. It can be seen as a kind
of global phase of the state vectors. This global phase then is a perfectly
hidden variable. For this presentation of quantum mechanics we have a
remarkable parallelism to classical statistical mechanics: If we would know
exactly the initial state of a system, we could compute the outcomes for all
experiments to be done later on this system. In the quantum case the initial
state is to be represented by its state vector with specified phase, e.g. as a
concrete complex-valued wave function.
