Some thoughts on the hidden variables interpertation

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HomogenousCow
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Hi, another thread talking sbout QM interpertations sparked my interest on the subject.
Now let's assume that we have electrons in a box, it could be anywhere inside.
And let us assume that the electrons do indeed have unique positions instead, that each electron has a set of three continuos hidden variables, giving each one a unique position, thus the illusion of porbability simply arose when we assumed that all electrons were the same.
Why three? Well if we had 2, all the electrons would lie on a surface, if we had only one they'd all lie on a curve.
Now if these variables truly exist, can someone think of a way to test for them?
 
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And to address the issue of probability densities being different in different points in space, perhaps this just tells us the propotions electrons are created in, and since all experiments with electrons involve trillions of them, we'd get the same mixture of them on average.