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I have very little background in physics, and none in quantum physics, but I've been reading about how sub-atomic particles behave probabilistically, so I was wondering, is it possible (even though the probability would be unimaginably small) that all the particles which make up my body are located somewhere 100 light years away?

Or have I misunderstood the concept?

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I want to comment on Mike Dunlavey answer but I have no rep.

I think the same video is here (also I use Linux so I can't check)

Why not take a course by Leonard Susskind ?

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Let me suggest you watch Richard Feynman explain it:

Probability and Uncertainty - the quantum mechanical view of nature. The Character of Physical Law, part 6. The Messenger Lectures, Cornell University. BBC TV, 11/18/1964.

enter image description here

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Could you link to a non-microsoft silvelight site? Us Linux users can't watch the video. :( – Kitchi Feb 22 '13 at 19:46
Would you know the name of the talk? I can't even get a look at that. Once I've found that, I can Google it myself. – Kitchi Mar 5 '13 at 13:04
@Kitchi: I put it above. Actually wizzup found it at – Mike Dunlavey Mar 5 '13 at 14:57
Ah! Sorry, Mike, I didn't see your comment. I changed the link to YouTube, which should be viewable by anyone. – Emilio Pisanty Mar 5 '13 at 15:04
I would also recommend anyone with some hours to spare to watch all of the The Character of Physical Law lectures. Feynman at his best, I think. – Emilio Pisanty Mar 5 '13 at 15:05

In a naive way and Schrödinger picture: the probabilistic intrepretation of Quantum Mechanics, via Born's Rule, means that we have a prescription to calculate probabilities for certain events to happen, but this does not mean that every event has a non-zero probability. If you are studying the hidrogen atom there are certain positions in which you are never ever going to find an electron.

That probability density is given by $|\psi(x)|^2$ which needs to tend to zero in for arbritrary large distances, so you can't expect any of your atoms to be in the Andromeda Galaxy-.

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