In addition to these formal axioms one needs a rudimentary
interpretation relating the formal part to experiments.
The following minimal interpretation seems to be universally
accepted.
MI. Upon measuring at times t_l (l=1,...,n) a vector X of observables
with commuting components, for a large collection of independent
identical (particular) systems closed for times t<t_l, all in the same
state
rho_0 = lim_{t to t_l from below} rho(t)
(one calls such systems identically prepared), the measurement
results are statistically consistent with independent realizations
of a random vector X with measure as defined in axiom A5.
Note that MI is no longer a formal statement since it neither defines
what ‘measuring’ is, nor what ‘measurement results’ are and what
‘statistically consistent’ or ‘independent identical system’ means.
Thus MI has no mathematical meaning—it is not an axiom, but already
part of the interpretation of formal quantum mechanics.
[...]
The lack of precision in statement MI is on purpose, since it allows
the statement to be agreeable to everyone in its vagueness; different
philosophical schools can easily fill it with their own understanding
of the terms in a way consistent with the remainder.
[...]
MI is what every interpretation I know of assumes (and has to assume)
at least implicitly in order to make contact with experiments.
Indeed, all interpretations I know of assume much more, but they
differ a lot in what they assume beyond MI.
Everything beyond MI seems to be controversial. In particular,
already what constitutes a measurement of X is controversial.
(E.g., reading a pointer, different readers may get marginally
different results. What is the true pointer reading?)
I wouldn’t call it “orthodox”, but see this:
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