Let's look at the measurement problem in the orthodox interpretation of quantum mechanics as an inconsistency between inner and outer treatment of the measurement apparatus. You can always push your boundaries of treating the evolution of your system as unitary further and further. You can say OK, the universe as a whole is evolving unitarily (let's not worry about information loss in a blackhole). So it's up to me to consider the boundary to see the evolution of my system and apparatus together or just my system. And I should be able to work out the reduced density matrix of my system equally in every treatment unambiguously! However, If you treat the apparatus externally, the evolution of the system would be:
$$a|\uparrow\rangle + b|\downarrow\rangle \to |\uparrow\rangle$$
with probability $|a|^2$ or
$$a|\uparrow\rangle + b|\downarrow\rangle \to |\downarrow\rangle$$
with probability $|b|^2$.
Whereas, an internal treatment of the apparatus would give
$$|\uparrow\rangle\otimes|\text{ready}\rangle\to U\bigl(|\uparrow\rangle\otimes|\text{ready}\rangle\bigr) = |\uparrow\rangle\otimes|\text{up}\rangle$$
and
$$|\downarrow\rangle\otimes|\text{ready}\rangle\to U\bigl(|\downarrow\rangle\otimes|\text{ready}\rangle\bigr) = |\uparrow\rangle\otimes|\text{down}\rangle$$
with $U$ a linear operator, $U(a|\psi\rangle + b|\phi\rangle) = aU|\psi\rangle + bU|\phi\rangle$, which evolves
$$\bigl(a|\uparrow\rangle + b|\downarrow\rangle\bigr)\otimes|\text{ready}\rangle$$
to
$$U\bigl[a|\uparrow\rangle\otimes|\text{ready}\rangle + b|\downarrow\rangle\otimes|\text{ready}\rangle\bigr] =a|\uparrow\rangle\otimes|\text{up}\rangle + b|\downarrow\rangle\otimes|\text{down}\rangle$$
However, pushing the boundary after the measuring apparatus gives a difference physics. This could be viewed as a problem with measurement in orthodox quantum mechanics (as opposed to realist or operational strategies to solve the measurement problem) But I was thinking it's not really an inconsistency within a theory. It's just an inconsistency between two different choices of the internal-external boundaries! I'm not asking about the role of decoherence theory. It sounds to me like the measurement problem wasn't really a problem in the first place! Am I right about that?
update: It has been pointed out that the question is not clear enough yet. Here is my last attempt: It's believed that for an adequate postulates for quantum mechanics, the inner and outer treatment of measuring apparatus shouldn't affect the physics of the system. Which for the orthodox interpretation of quantum mechanics does. For instance in the Bohm's model this has been resolved by denial of representational completeness. And in Operational interpretation it's bypassed by avoiding talking about physical state of the system. Here the question is Are we really allowed to change the boundaries? Because if you don't believe you can, the problem will never appear in the first place. I hope that explains what I'm asking. Because I don't think I can make it more clear :-)