 It is also extremely important to stress that, by resorting to the quantity (7) one can define an appropriate ‘distance’ between two states as the integral over the whole 3-dimensional space of the square of the difference of \(m(\boldsymbol{x},t)\) for the two given states, a quantity which turns out to be perfectly appropriate to ground the concept of macroscopically similar or distinguishable Hilbert space states. In turn, this distance can be used as a basis to define a sensible psychophysical correspondence within the theory.