The fine structure constant, alpha, is a so-called dimensionless constant. This is defined as 2*pi*e^2/hc. If this "constant" changes over time, the conventional wisdom is that c, the speed of light, may not be a constant but variable. The fine structure constant causes absorption lines in spectra to be separated in specific ways. One experiment to see if the fine structure changes is to look at the spectra of quasars. This was done in 2001 and 2003. In both of these cases, there was a small change in the fine structure constant implying the speed of light was slowing down with time. This effect was slight, though, on the order of a difference of 1/1000 of a percent.
Now we have a newer and more rigorous survey that shows a non-changing fine-structure constant within 6/100000 of a percent. Variable speed of light theories took another blow as I described here.
The speed of light. It's not just a good idea, it's the law.
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