Constraints on speed of light?

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The speed of light is fast but far from instantaneous. What constrains the speed of light to be what it is? e.g. c = f(xi)

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In the 1860's Maxwell found that c = \frac 1 {\sqrt {\epsilon_0 \mu_0} }

Where \epsilon_0 is the permitivity and \mu_0 is the permeability of free space.
 

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