I read an article one time, and it might have bearing or enlightenment here on this topic. It was a Nobel Prize acceptance speech, I believe from one of the people that formulated weak interactions.
It was a very enlightening article. He (the author) talked about absolute quantities, like the speed of light, not as non-variating constants of nature, but as "non-observables" of symmetry breaking .. that is, we couldn't/didn't observe interactions that lead to that constant being broken in nature because of symmetry.
If anybody is interested, I could fish out the article, and cite a publication. It is a few pages long .. I couldn't post the whole article here. I could post it on a personal web site, but I'd have a hard time reproducing the formulas and special expressions/characters in it.