Assume I place a tea cup on a table (say, about a centimetre thick). Quantum mechanics tells us that the wave function for the nuclei and electrons of the cup is not zero below the table (while being terribly small, though).
I'm constantly measuring that system. So, with a very small (but not zero) probability, the particles should be tunnelling through the table. Afterwards, measuring them will cause the wave function to collapse and the particles falling to the floor. So, I'd assume that if I leave the cup long enough on the table, it will eventually tunnel through the table. Completely.
Obviously, I wouldn't be around to witness it, given the small probability even a single particle has to fall through the table. But I'm wondering if it is truly a matter of (a lot of) time, for this to happen, or if it is truly impossible for the cup to gradually (!) make its way through the table. Assuming the cup, table, floor, building, earth, solar system, galaxy, and universe would survive an arbitrary timespan, what would happen?