Assume I place a tea cup on a table (say, about a centimetre thick). Quantum mec

Question

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?

Explanation / Answer

For the same reason that macroscopic objects do not display quantum mechanical behavior, except in very special setups, as in superconductivity etc. Macroscopic systems in general, due to Avogadro's number which is something like 10^23 molecules per mole, cannot be described by one quantum mechanical wave function .They are an incoherent superposition of this large number of individual wave functions.

Thus one can solve for one particle in a potential well, and that particle has a probability of tunneling through that potential well, but ~10^23 potential wells for ~10^23 particles ensure the total incoherence of all these wave functions, and the impossibility of a teacup tunneling whole through the table ( considering the table another ~10^23 potential wells).

Now googling I found electron tunneling in protein crystals, which shows some effects of tunneling measurable macroscopically.

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