A Bouncing Ball

We see a kid bouncing a ball. According to quantum mechanics, which applies to everything that happens, why does the ball bounce?

Answer

We present a simplified version of the complexities of this bouncing ball action. The compression of the ball (and the concrete being struck) sends phonons (quantum sound waves) running around telling the material that compression is occurring and that the increased energy density in parts of the ball can be reduced by expanding back to its normal size. Of course, the expansion overshoots and the ball “rings” as it leaves the concrete, each extended state also increasing the energy density in parts of the ball. One can model much of this behavior by assuming that the atoms and molecules are in a potential well somewhat similar to the parabolic well of the harmonic oscillator. However, instead of a potential energy for an atom versus the atomic separation distance being proportional to r² only, there must be additional terms proportional to r³, etc., where r is the distance from the equilibrium location.

Eventually the phonons help the ball get back into its normal shape, but the atoms and molecules never quite make their initial relative positions again, there being some residual distortion. Even the concrete being struck by the ball never quite recovers. Witness the eventual wear of a concrete highway by cars and trucks compressing the road, a more vigorous process but conceptually the same.