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Is the Infinite monkey theorem helpful for determining the existence of the very same our universe somewhere else?

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closed as not constructive by Ebenezer Sklivvze, Manishearth Dec 29 '12 at 21:27

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I've once read a popular article wherein serious cosmologists were applying this theorem (although the name was not explicitely mentioned) to investigate if things we can observe inside our cosmic horizon could be repeated in our universe outside the cosmic horizon. I think when considering the question in such a context, it is legitimate and does not need to be closed. But maybe @Inquisitive you could clarify the context a little bit? –  Dilaton Dec 29 '12 at 11:35
    
This is rather open-ended in its current form. (as well as being about fictional physics, and not really clear) Please see the don't ask section of the faq. –  Manishearth Dec 29 '12 at 21:27

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No. Well, not really, though some amusement can be had by calculating how far you'd have to go to find an exact copy of your mother in law. However these calculations are not based on any rigorous science, so while they're fun take care with them.

The basic idea is that if you take some system (e.g. your mother in law) containing $n$ Planck volumes then the maximum number of configurations of this system is 2$^n$. So you need to look at about 2$^n$ such volumes to stand a reasonable chance of finding a duplicate of your mother in law. This is the origin of claims that an exact copy of the Earth must exist if you take a big enough region of the universe. Whether such claims have any physical validity is open to debate.

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John Rennie - Consider a universe of size 1cm^2 with only 1 atom(consider an atom as an indivisible particle) ,now doesn't that 1 atom has infinite number of possible arrangements?1)Due to the infinite number of possible orientation of atom. 2)Infinite number of possible arrangement of atom in the space? Planck volumes are something related to that? (I understood what you have written above except what means of Planck volumes) –  Inquisitive Dec 28 '12 at 19:51
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@Inquisitive: the idea is (remember this is all very speculative) that it isn't possible to measure position to an accuracy of better than a Planck length. Therefore the number of physically distinct positions for your atom is 1cm divided by the Planck length. –  John Rennie Dec 28 '12 at 20:54
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There is a related concept that says that although entropy is an increasing quantity, a finite system will eventually find its way back through an initial state within a poincaire recurrence time. Nevertheless, when applied to systems like "the universe", such timescales are inconceivably long. –  KDN Dec 29 '12 at 0:07
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@Inquisitive no. The walls create an interference pattern inside the volume which is the wave function solution. The number of such solutions is limited. An analogy is the position of an electron in an atom: it cannot occupy any orbit, but only just the permitted ones. This is the basics of quantum mechanics. –  Anixx Dec 29 '12 at 1:46
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@Inquisitive Yes there are continuum variables defining most systems, and yes, mathematically, you can never hope duplicate such things with a finite number of samples. However, John Rennie is implicitly constructing large equivalence classes of systems. If you jiggle all the atoms in your body by some random amount on the order of a Plank length, it really won't make you a different person in any conceivable way. –  Chris White Dec 29 '12 at 21:28

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