In real life, for a tennis ball to go through a wall, does it have to completely prevent the particles from interacting? (decoherence)

Question

In real life, for a tennis ball to go through a wall, does it have to completely prevent the particles from interacting? What would happen if we tried infinitely in the real world, where the interaction of particles could not be completely prevented? Because of quantum coherence, will the ball not pass through the wall even if it tries infinitely?

Answer 1

The problem is the tension here between "real life" and "infinitely". In "real life" we cannot do an experiment infinitely many times, and if we tried other factors like the erosion of the ball and wall for unrelated reasons would mess up the result.

The in-theory answer is of course that the ball can tunnel through the wall with a finite probability. We can estimate it (see equation 7.7.29 here), but the answer turns out to be vanishingly small. The relevant wavelength of the tennis ball wave packet is $1/\beta \approx h/mv = 2\cdot 10^{-34} $m for a tennis ball moving 50 m/s, making the transmission probability way smaller than $e^{-2\beta L}$; for a 10 cm wall I get something like $10^{-10^{32}}$. That is astronomically small: if you tried this every second until proton decay in $10^{36}$ years time, you will still almost certainly not see it happen.