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Back in 2002 there was some research published hinting that $c$ may have been faster at some distant point. It was based on measurements of the fine-structure constant, $$ \alpha = \frac1{4\pi\epsilon_0} \frac{e^2}{\hbar c} \approx \frac 1{137}, $$ in light from distant (and thus ancient) quasars.

Has there been any recent developments on this? I know that at the time there was considerable doubt as to whether $c$ was inconstant. Have there been further measurements? Is it accepted now that alpha is changing? What's the current thinking on whether that means $c$ has changed?

http://www.theage.com.au/articles/2002/08/07/1028157961167.html

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    $\begingroup$ Just curious... why would a change in $\alpha$ indicate a change in $c$ specifically, and not in one of the other constants appearing in the formula? $\endgroup$ – Federico Poloni Oct 19 '16 at 8:54
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    $\begingroup$ @FedericoPoloni If I recall correctly, there were some other varying-$c$ ideas floating around during the early 2000s. However, given the role that $c$ plays in metrology, it doesn't really make sense to talk about its value changing. (And soon the same will be true of $e$ and $\hbar$.) The current literature is all about possbile change in α. $\endgroup$ – rob Oct 19 '16 at 13:05
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    $\begingroup$ The claimed changes in $\alpha$ are really tiny, we are talking about a variation at the $\frac{\Delta \alpha}{\alpha} = 10^{-5}$ level. Secondly even if this is physical (apposed to being due to a systematic in the observations) then this does not have to be due to a varying speed of light. This effect can be obtained by for example having a new scalar field $\phi$ coupled to the electromagnetic field strength $F_{\mu\nu}^2 \to (1+\phi/M)F_{\mu\nu}^2$. $\endgroup$ – Winther Oct 19 '16 at 13:34
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    $\begingroup$ $c$ is a defined number of metres per second. A change in $c$ cannot be measured using metres and seconds. $\endgroup$ – Rob Jeffries Oct 19 '16 at 23:27
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    $\begingroup$ @Qmechanic See arxiv.org/abs/1008.3907 and references therein. $\endgroup$ – rob Oct 20 '16 at 13:40
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That result has been controversial since the beginning. A comparable survey looking at a different part of the sky saw no effect, but the original authors and some new collaborators combined data from a most-of-the-sky survey and found hints that the fine-structure constant might be large in one direction of space and small in another.

One of the strengths of the quasar observation was that was based on spectroscopic observations of atomic transitions. Since a slight change to the fine-structure constant pushes some energy levels up and others down, there were transitions from the same sources which were both redder and bluer than predicted. This was the main argument against the effect being some sort of redshift miscalibration.

If the fine-structure constant is changing over time, or if Earth is moving through regions of space where the fine-structure constant has different values, those same sorts of energy-level shifts would occur on Earth. A long-running experiment has compared the atomic-clock transition in cesium, which should be relatively insensitive to changes in α, to a particular transition in dysprosium which should have enhanced sensitivity to changes in α. So far, no earthbound effect has been seen.

Conclusion: still an open question. Stay tuned.

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I have nothing to support my opinion but I believe that the speed ($c$) of electro-magnetic radiation (EM) has been slowing down since the Big Bang (BB).

My reasoning is:

1 - The impedance of space (Z) depends on the $E_o$ and $U_o$ parameters.
2 - As the Universe expands, Z increases. Therefore Z was smaller at the time of BB.
3 - The speed of EM is inversely proportional to Z ($c = 1/Z$), therefore the speed of EM was faster at the time of the BB.
4 - Therefore, the speed of EM ($c$) has been slowing down.

Since the "slowing down" is an exponential decay, after 13.5 billion years, the slow down rate is so small that it may take thousands of years to detect a measurable difference.

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