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Suppose I have a ball of a certain radius inside a box (with the length bigger than the radius) such that the ball fits in the box. The ball has a large mass (1 Kg). Heisenberg uncertainty principle tells me that I cannot say for sure if the ball is moving or is at rest. If I'm interested in the probability that the ball is at some place, I suppose that this probability is uniform inside the box, since the ball has a large mass. But how about the speed probability? Is it uniform too? I think yes, but I'm not 100% sure beaucase I cannot write a proof.

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  • $\begingroup$ The problem that you have is that you can't treat the large body as a point mass, i.e. any attempt to measure its position with that kind of precision would be measuring internal degrees of freedom, instead (e.g. molecular vibrations). $\endgroup$ – CuriousOne Jun 16 '15 at 19:16
  • $\begingroup$ But I can measure the center of the ball for instance. Suppose the ball can only move to one direction in the box, and no translation is allowed, so the ball has 1 degree of freedom. $\endgroup$ – SebiSebi Jun 16 '15 at 19:18
  • $\begingroup$ While the theory suggests that you can, you can't do it in reality. In reality you would start seeing thermal excitations long before you ever reach the necessary precision to measure the quantum effect. At that point it becomes a non-question for you and for nature. It simply doesn't matter. That's not the case for all quantum effects. Many of them do survive the scaling of the system towards macroscopic size. Magnetism is an example of that. $\endgroup$ – CuriousOne Jun 16 '15 at 20:02
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Here is the Heisenberg uncertainty principle:

HUP

Here is h_bar 1.054571726(47)×10^−34 joulesecond

All it needs is some algebra to see that a kilogram ball moving at a micron per second and measurement accuracies of the order of a micron will still fulfill the HUP constraint as h_bar is a very small number. For classical dimensions h_bar is essentially zero and the HUP always holds.

When one goes to dimensions of less than nanometers and masses of the order of molecules then one is in the quantum mechanical regime and can start talking of uncertainties .

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  • $\begingroup$ Ok. I understood that. But as small as $\hbar$ is I cannot say with certainty if the ball is moving or is at rest, am I right? $\endgroup$ – SebiSebi Jun 16 '15 at 19:29
  • $\begingroup$ ". But as small as ℏ is I cannot say with certainty if the ball is moving or is at rest, am I right? " -- That depends on the state of the ball. $\endgroup$ – WillO Jun 16 '15 at 21:12
  • $\begingroup$ Yes, except the uncertainty is so tiny that it has no meaning in the everyday and down to microns context. $\endgroup$ – anna v Jun 17 '15 at 3:36

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