RockyMarciano
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AFAICS what you call "a properly understood statistical mechanics approach" doesn't seem to say much more about what constitutes a measurement(at least anything different from the classical measurements with commuting observables that classical statistical mechanics addresses) than the Born's postulate. Furthermore you blur any additional hint by declaring the ambiguity between classical and quantum uncertainty exploited for a statistical mechanics interpretation as something subjective and out of the formalism, so I honestly can't see how this approach improves on the Born's rule for elucidating the nature of the quantum uncertainty and measurements.A. Neumaier said:The quantum formalism is independent of knowledge. Subjective issues have no place in physics, except for judging the adequacy of the assumptions and approximations made.
A measurement of a microscopic system is a reading from a macroscopic device that contains information about the state of the microscopic system. The nature of the coupling and the dynamical analysis must tell which information is encoded in the measurement result, to which accuracy, and with which probabilities.
This definition of a measurement is operationally checkable since one can prepare the states and read the measurement results and can thus compare the theory with the calculations without any ambiguity of concepts.
The only interpretation needed is how the reading from the macroscopic device is related to its macroscopic properties. In the thermal interpretation, this poses no problem at all. The consequences for the microscopic theory are then a matter of deduction, not one of postulation.
Whereas Born's rule is very incomplete in that it doesn't say the slightest thing about what constitutes a measurement, so it is an uncheckable piece of philosophy not of science, unless you know already what measurement means. But this requires knowing a lot of quantum physics that goes into building high quality measurement devices for quantum objects. Thus foundations based on Born's rule are highly circular - unlike foundations based on a properly understood statistical mechanics approach.