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There is a thread in Physicsforums.com which states due to Quantum Mechanics, if you wait long enough diamonds will appear in your pocket, it also states its possible for all your atoms to spontaneously re-arrange themselves so you turn into a Boeing airplane. Surely this is fiction?

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You don't even need quantum mechanics for this. In ordinary classical mechanics if you wait long enough every configuration that is compatible with the handful of conservation laws (energy, momentum, angular momentum, charge, etc.) is likely to occur. The probability for a configuration with entropy $S$ is proportional to $\mathrm{e}^{-S}$, so low entropy configurations are exponentially improbable. Conversely, you need to wait a time of the order $\mathrm{e}^{+S}$ for it be probable. These ideas come under what's called ergodic theory en.wikipedia.org/wiki/Ergodic_hypothesis – Michael Brown Jan 19 at 14:16
Er...but "long enough", expressed as the mean time until some event can easily exceed the current lifetime of the universe or even the expected time until local heat death or the big rip. Or many times those spans. Once it gets to that level, improbable because effectively congruant with impossible. – dmckee♦ Jan 19 at 19:30

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