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 Quote by hellfire Actually there are experimental ways to test theories with varying speed of light. One of the consequences of these theories is that the electromagnetic coupling constant $\alpha=e^2/2\epsilon_0 h c$ does also vary. This constant determines for example the spitting of the spectral lines of the hydrogen (the “fine-structure”). Comparing distant spectral lines with the ones of today might provide information about a varying $\alpha$.
for example;

http://arxiv.org/abs/astro-ph/0601264

on astro-ph today.