  In quantum experiments the acquisition and representation of basic
experimental information is governed by the multinomial probability
distribution. There exist unique random variables, whose standard deviation
becomes asymptotically invariant of physical conditions. Representing all
information by means of such random variables gives the quantum mechanical
probability amplitude and a real alternative. For predictions, the linear
evolution law (Schrodinger or Dirac equation) turns out to be the only way to
extend the invariance property of the standard deviation to the predicted
quantities. This indicates that quantum theory originates in the structure of
gaining pure, probabilistic information, without any mechanical underpinning.
