Ping pong ball bounces under quantum uncertainty constraints

[Allday]

I ran across an interesting problem in quantum uncertainty today. I'm working out the details right now, but I thought I would share. This might belong in brain teasers or something like that, but I know some people love problems like these (others consider them a complete waste of time)

Imagine dropping a ping pong ball of radius R onto an identical ping pong ball from a height of 10R. The balls undergo perfectly elastic collisions. What combination of delta x and delta p yield the most number of bounces while still satisfying the uncertainty relation delta x * delta p > hbar. Make any reasonable assumptions.

Now Classical physics allows perfect initial allignment and an infinite number of bounces if there are no pertubations. However there is a tradeoff in uncertainty of position (the farther away from center it hits the faster it will bounce off) and uncertainty in momentum (a bigger uncertainty there will lead to a "drift" of the ping pong ball away from the center, when we use quantum. How do we keep that durn ping pong ball on for as many bounces as physically possible.

I made some quick calculations and got about eight bounces

 

[DrClaude]

The uncertainty principle is about measurements. I don't see how the two balls colliding would count as a measurement.

I made some quick calculations and got about eight bounces

The fact that the result is independent of the size of the ball or its mass is very suspicious.