Heisenberg uncertainty principle applied to large bodies?

Question

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.

anna v · Answer

Here is the Heisenberg uncertainty principle:

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 .

Harshit · Answer

It cannot be applied to a large body in our classical universe. The larger the body is, the less kinetic energy it has and therefore very negligible wave function. So, we are more certain that it is at a particular position.

Answered by Harshit on June 1, 2021

Heisenberg uncertainty principle applied to large bodies?

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