Hi combjelly; Re: "Sigh. Someone else who is uncomfortable with infinity. Low probability, regardless of how low, is not zero.";
A sad fact of modern physics is that there is no quantum theory of gravity. This means that quantum mechanics is not complete. In particular, QM has no explanation for why my chair doesn't float away. And yet you think QM can be used to prove that "anything can happen". No, QM cannot be used to prove that and it's silly to think it can.
What's more, even within the theory of QM, as mentioned above, superselection sectors define regions in a Hilbert space which cannot be crossed by any unitary process. Thus the transition probabilities are zero and "it can't happen". Here's an arXiv paper, written by a physicist, on the subject of superselection rules:
In contrast, a SSR [superselection rule] is usually thought of as making a more rigorous statement. It not only forbids certain transitions through particular modes, but altogether as a matter of some deeper lying principle; hence the “Super”. In other words, transitions are not only inhibited for the particular dynamical evolution at hand, generated by the given Hamiltonian operator, but for all conceivable dynamical evolutions.
arxiv.org
-- Carl |
