Maximizing Bounces in Quantum Ping Pong Ball Collisions | Brain Teaser

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SUMMARY

The discussion centers on maximizing the number of bounces in quantum ping pong ball collisions, specifically when a ping pong ball of radius R is dropped from a height of 10R onto an identical ball. The key focus is on the relationship between delta x and delta p, adhering to the uncertainty principle (delta x * delta p > hbar). Initial calculations suggest that eight bounces can be achieved, raising questions about the independence of the result from the balls' size or mass, and the implications of quantum uncertainty on collision dynamics.

PREREQUISITES
  • Understanding of quantum mechanics and the uncertainty principle
  • Knowledge of elastic collisions in classical physics
  • Familiarity with the concepts of delta x and delta p
  • Basic mathematical skills for calculations involving bounces
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  • Research elastic collision dynamics in classical physics
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Physics enthusiasts, quantum mechanics students, and anyone interested in the intersection of classical and quantum physics, particularly in understanding collision dynamics and uncertainty principles.

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

Allday said:
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.