Throughout history people have been carrying out experiment after experiment to test many of the known constant, so I like to know if there are any oddities among the known fundamental constants. If not how come they don't exist?
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Do you mean whether the fundamental constants of Nature are correlated/dependent? If this is the case, then it is very broad question. – Benjamin Mar 19 '16 at 00:37
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3Part of the criteria for being a fundamental constant is to be independent of time and location. – tom10 Mar 19 '16 at 00:45
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The simple answer is "We don't know.". We don't know how many fundamental constants there are, if there are any, and we don't have sufficient evidence for theoretical mechanisms which could create them. We do have some rather tight physical and astronomical evidence that many of the constants had to be very constant during most of cosmological time. – CuriousOne Mar 19 '16 at 01:25
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Possible duplicate of What is the proof that the universal constants ($G$, $\hbar$, $\ldots$) are really constant in time and space? – ACuriousMind Mar 20 '16 at 01:42