Obama has chosen his VP, the universe has decohered/collapsed

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Suppose an observer is located a few thousand km from Obama. If that observer has a box containing N molecules then, because the box doesn't keep the molecules isolated from the environment, the wavefunction of the N molecules is always in an entangled state with the environment. We can simply say that the N molecules are part of the environment that has decohered because of Obama's choice.

The question is how large must we choose N so that the wavefunction will be close to orthogonal for the few choices Obama has?
 
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turbo-1 said:
Biden's wave-form hasn't collapsed, though his environment is large. How will you figure this.

Well, we can't be consciously aware of our own exact wavefunction.

Anyway, we now have a situation like:

|VP_1>|environment_1> + |VP_2>|environment_2> + ...

The question is as follows. For what N is it possible to have an N particle operator acting on the environment states that
has the |environment_k> states as eigenvectors with different eigenvalues for different k? The N particles are chosen several thousand km from Obama.
 
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Put differently, in the operator A


A = sum over k of k |environment_k><environment_k|

what part of the environment do you really need to include here for A to have the desired property?