  Newtonian and Scrodinger dynamics can be formulated in a physically
meaningful way within the same Hilbert space framework. This fact was recently
used to discover an unexpected relation between classical and quantum motions
that goes beyond the results provided by the Ehrenfest theorem. A formula
relating the normal probability distribution and the Born rule was also found.
Here the dynamical mechanism responsible for the latter formula is proposed and
applied to measurements of macroscopic and microscopic systems. A relationship
between the classical Brownian motion and the diffusion of state on the space
of states is discovered. The role of measuring devices in quantum theory is
investigated in the new framework. It is shown that the so-called collapse of
the wave function is not measurement specific and does not require a
"concentration" near the eigenstates of the measured observable. Instead, it is
explained by the common diffusion of a state over the space of states under
interaction with the apparatus and the environment. This in turn provides us
with a basic reason for the definite position of macroscopic bodies in space.
