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Well the Copenhagen interpretation traditionally requires the act of an 'observer'. I.e., you are not allowed to perform that act of summation on the set of orthonormal vectors in N dimensional Hilbert spaces until an "observer" observes. (That's where that stupid cat came into play and the 'uncertainty' of it being both dead and alive simultaneously until it's 'observed'.) Until this discrete event occurs, the wave function doesn't "collapse" and we're just living in statistical la-la land.

The disagreement lies in "I can mathematically apply the trace function, I'm just not quite sure when".

Alternatively, according to the Everett interpretation (to which I subscribe, and to which you seem to as well) quite a few reputed physicists do believe that the universe "splits" (though not in an actual literal sense, there's nothing ripping the universe physically in two) every time an "observation" occurs and there are lots and lots of occurring simultaneously taken from various frames of reference. This actually makes a lot of sense. Let Sean Carroll https://youtu.be/ZacggH9wB7Y convince (the plural) you.

The wave function never collapses. This is easily demonstrated with a simple thought experiment that is described in the first two references that I link to.

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