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Were the physical constants chosen randomly by the nature or it was determined by some source of… matter(?).

I really don't have idea. If you could help me it'd be awesome.

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IIRC this is a great unsolved problem of physics--they're able to boil everything down to a few constants but can't get past that. –  Manishearth Apr 24 '12 at 7:04
I was under the impression that we chose the constants depending on the units we choose. –  Antillar Maximus Apr 24 '12 at 11:56
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No-one knows the answer to this, so the best I can do is describe some of the ideas. Bear in mind this is all speculative so take it with a pinch of salt.

In our existing tried and tested theories the fundamental constants are put in by hand and there is no mechanism for them to vary. However the idea that constants might be variable goes back as far as Dirac.

Many experiments have looked for variation in the fundamental constants, but so far without success. Examples include the Oklo natural reactor and many astronomical studies looking for changes in the fine structure constant.

The most concrete proposal for variable fundamental constants comes from string theory. This requires six of the spatial dimensions to be compatified so we don't see them. This compactification can occur in many different ways, at least $10^{500}$ according to the landscape idea, and each different compactification will result in different fundamental constants. Whether this really describes our universe is currently a highly contentious issue.

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You should distinguish between the values of the five constants $c,hbar,G,k_B,\epsilon_0$ which are only set by our arbitrary unit conventions, and are essentially arbitrary numbers (they are determined by the Academy of Weights and Measures, not by nature), and the remaining dimensionless constants of nature, which are determined by something else. –  Ron Maimon May 1 '12 at 21:57
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