atyy
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vanhees71 said:It's not in the Hamiltonian, because you choose not to describe it, but take the functioning of the measurement device for granted. Of course, as long as a theory (here relativstic local QFT) is not known to have limits of applicability (which for sure it has, but it's not known yet), I've all reason to believe that also the interaction between the measured object and the measurement device is ruled by the laws described by the theory. Hence, this interactions are the very same local interactions used in the Hamiltonian.
E.g., to describe the creation of a polarization-entangled photon pair with (in-medium) QED, you have to make a model Hamiltonian (as done by Hong and Mandel in the mid 1980ies) and see whether it correctly describes satisfactorily the observed (statistical!) facts about these pairs (which to my knowledge it does). As long as there is not an experiment showing that the creation of entangled photon pairs cannot be described by these standard QED local interactions, I keep it as the valid description. The same holds true for the theory of photon detection, which are also very well described using the standard local QED interactions.
If you believe that quantum theory makes sense with the Hamiltonian extending to the whole universe and having only unitary evolution with neither hidden variables nor many-worlds or something else, then you are mistaken. Also, you are not using the minimal interpretation.