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It is importance to note that in our generalization of the
projection postulate, as the result of a jump, not all of the old
state is forgotten. The new states depends, to some degree, on the
old state. Here EEQT differs in an essential way from the naive
von Neumann projection postulate of quantum theory. The parameter
becomes important. If  the case where
is a projection operator  the new state, after
the jump, is always the same, it does not matter what was the
state before the jump. There is no memory of the previous state,
no "learning" is possible, no "lesson" is taken. This kind of a
"projection postulate" was rightly criticized in physical
literature as being contradictory to the real world events,
contradicting, for instance, the experiments when we take
photographs of elementary particles tracks. But when is
just close to the value , but smaller than the
contradiction disappears. This has been demonstrated in the cloud
chamber model[9], where particles leave tracks much like
in real life, and that happens because the multiplication operator
by a Gaussian function does not kill the information about the
momentum content of the original wave function. Notice that
have the properties similar to those of Gaussian
functions, namely

(19) 
Next: 4. Geometrical meaning of
Up: 4. Notes
Previous: 2. Fuzzy projections
20020411