Weinberg on the measurement problem

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vanhees71 said:
In the standard interpretation you trace out all details which are not resolved. You can do quantum statistics and quantum-many-body theory in the standard formulation very well and straight-forwardly.
My question was about the total system. What does the fact that the environment considered in total still has interference terms mean in the minimal statistical interpretation?
 
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It means that, if you could resolve enough microscopic details you should be able to observe the corresponding interference terms, but it's tough to get such details measured. There are, however, some examples, where macroscopic systems show quantum behavior, like two diamonds with entangled phonon modes.