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> e.g. quantum tunneling is the same as basically measure 0 events. It is not. Quantum tunneling is just an event with low probability, and when you notice tha

> e.g. quantum tunneling is the same as basically measure 0 events. It is not. Quantum tunneling is just an event with low probability, and when you notice that quantum tunneling doesn't happen (on a macro scale), you're just noticing that events with sufficiently low probability don't happen. The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. You need measure theory to talk usefully about measure zero events. You don't need measure theory to talk about quantum tunneling. Just ordinary probability.

mlevental 9y ago
> The probabilistic analogy is flipping a billion coins and having them all come up heads. Flipping a billion coins and having them all come up heads does not have measure zero. It has a positive measure. wut? 1. in each instance it's 1MM conditionally independent trials so i don't see the difference 2. any realization of any continuous random variable has measure zero >Contrast this to measure zero events. Flipping infinitely many coins and having them all come up heads has measure zero. you're playing fast and loose with the difference between a counting measure (no measure zero events) and a continuous/discrete measure. anyway my point was exactly that quantum tunneling is counterintuitive exactly for the same reason that measure zero events are counterintuitive