Undergrad Heisenberg Uncertainty Principle and macroscopic objects

[wnvl2]

Is the Heisenberg Uncertainty Principle (HUP) applicable to macroscopic objects? A football, for instance, is composed of an enormous number of particles. Can the applicability of the HUP to a macroscopic object like a football be demonstrated through statistical methods, starting from the behavior of elementary particles? Are there any references or research that support this approach? Alternatively, should the principle be derived directly from the commutation relations between momentum and position, extended to macroscopic objects while accounting for all interactions between their constituent particles?

I understand that macroscopic behavior is generally not sensitive to quantum fluctuations, but I am curious about the theoretical justification and derivation of the HUP at this scale.

 

[gentzen]

Alternatively, should the principle be derived directly from the commutation relations between momentum and position, extended to macroscopic objects while accounting for all interactions between their constituent particles?

The de Broglie wavelength of a macroscopic solid body gives you the uncertainty of its center of mass. You can check that by transforming the system into center of mass and reduced coordinates. This is a linear canonical transformation of the spatial coordinats, and the Schrödinger equation of non-relativistic QM is invariant under those.

 

[Nugatory]

Is the Heisenberg Uncertainty Principle (HUP) applicable to macroscopic objects?

Yes, but you will find it interesting to calculate the uncertainty for a reasonable sized macroscopic object (say, a grain of sand that might have a mass of .1 milligrams).