vanhees71 said:
I don't understand, what the content of Sect. 4.5 has to do with our discussion. I don't see, how you can come to the conclusion that the "pragmatic use" of the formalism contradicts the Born rule as the foundation.
I didn't claim a contradiction with, I claimed the nonapplicability of Born's rule. These are two very different claims.
vanhees71 said:
all these pragmatic uses are based on the probabilistic interpretation of the state a la Born.
You seem to follow the
magic interpretation of quantum mechanics. Whenever you see statistics on measurements done on a quantum system you cast the magic spell "Born's probability interpretation", and whenever you see a calculation involving quantum expectations you wave a magic wand and say "ah, an application of Born's rule". In this way you pave your way through every paper on quantum physics and say with satisfaction at the end, "This paper proves again what I knew for a long time, that the interpretation of quantum mechanics is solely based on the probabilistic interpretation of the state a la Born".
You simply cannot see the difference between the two statements
- If an ensemble of independent and identically prepared quantum systems is measured then ##p_k=\langle P_k\rangle## is the probability occurrence of the ##k##th event.
- If a quantum system is measured then ##p_k=\langle P_k\rangle## is the probability occurrence of the ##k##th event.
The first statement is Born's rule, in the generalized form discussed in my paper.
The second statement (which you repeatedly employed in your argumentation)
is an invalid generalization, since the essential hypothesis is missing under which the statement holds. Whenever one invokes Born's rule without having checked that the ensemble involved is actually independent and identically prepared, one commits a serious scientific error.
It is an error of the same kind as to conclude from x=2x through division by x that 1=2, because the assumption necessary for the argument was ignored.
vanhees71 said:
Also, as I said before, I don't understand how you can say that with a non-stationary source no accuracy is reachable, while the quoted Penning-trap experiments lead to results which are among the most accurate measurements of quantities like the gyro-factor of electrons or, just recently reported even in the popular press, the accurate measurement of the charge-mass ratio of the antiproton.
This is not a contradiction since both the gyro-factor of electrons and the charge-mass ratio of the antiproton are not observables in the traditional quantum mechanical sense but constants of Nature.
A constant is stationary and can in principle be arbitrarily well measured, while
the arbitrarily accurate measurement of the state of a nonstationary system is in principle impossible. This holds already in classical mechanics, and there is no reason why less predictable quantum mechanical systems should behave otherwise.
vanhees71 said:
Nowhere in your paper I can see, that there is anything NOT based on Born's rule, although you use the generalization to POVMS, but I don't see that this extension is in contradiction to Born's rule. Rather, it's based on it.
This is because of your magic practices in conjunction with mixing up "contradition to" and "not applicable". Both prevent you from seeing what everyone else can see.