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I was just wondering.

Why does Heisenberg's principle of indeterminacy say that we can't know the position and velocity (momentum) of a particle with any precision, when a particle isn't point-like anyway? It's like the position of a car, it's arbitrary and all we can say about its position is that it occupies a space in which we can eventually interact with it.

So why don't we add within the principle the fact that the particle occupies a 3D space ... twice ?

I suppose i understand how we came to this principle because i have read about the tought experimentations that lead to the interpretation.

But i dont understand why when we talk about the position of a particle we do as if a particule would only have one position.

A non point-like particle occupy a space, so there are an infinity of position within continuous space (or at least because the quantum therory is right, there is a finite number of possible positions).

Did i missed some point ?

Thank you for your enlightenment.