Posted by Erick on Sunday, July 11, 2010 at 1:51pm.
If you use the Heisenberg uncertainty principle, the minimum error will be something like
sqrt[(h*R/(2 pi))/p]
where p is the nominal momentum at impact and R is the distance it falls.
You must be careful to recognized that the lateral position error depends upon the lateral momentum uncertaintly. You need to relate both to the angular deviation from a vertical fall.
It is more likely that the minimum position error will be governed by random turbulent eddy production in the wake of the marble, which has nothing to do with quantum mechanics. This goes beyond the scope of your physics question.
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