# Variable speed of light impact on spectral absorption lines in distance luminous objects?

There are many other arguments as to the constancy of the speed of light (or more precisely, c). One thing I have been curious is what would the impact be on spectral measurements from distant luminous objects.

Basically, we can get the relative speed (at the time the observed) light was emitted based on a red shift in spectral absorption lines. Stars have predictable chemical composition, and expected elements have multiple absorption lines that all shift together.

Quantum field theory, which explains those absorption spectra, relies on electrical charge force carriers to move at c (I think). If c were to change, what impact would that have on spectral absorption lines? Presumably, electron shell energy levels would undergo a lot of changes.

Two possibilities:

(1) Different elements absorption patterns would shift differently, definitively proving that either c is constant, or else our observations of light from distant objects are nonsense.

(2) Absorption lines should all shift the same, making this argument say nothing at all one way or the other about c.

Anyone understand this well enough to comment?

• The speed of light would have no impact on the spectra as far as its transmission trough the universe would be concerned. You can send light trough a piece of glass, the effective speed of light will be lower by the index of refraction and the frequency of the light will be exactly the same. The frequencies of spectral lines in atomic physics depend on the product of $c$ with $\alpha$, the fine structure constant, so most such analyses (and there many) focus on the constancy of $\alpha$. en.wikipedia.org/wiki/Fine-structure_constant. I don't know if this is a general degeneracy. – CuriousOne Jan 15 '16 at 17:42
• So what I'm thinking about is how c might affect electron shells and binding energies, which might or might not affect, for instance, how chemical bonds form. – Timothy Miller Jan 15 '16 at 18:23
• It's more common to look at $\alpha$. By the definition of $\alpha$, the product of $c\alpha$ doesn't contain $c$ any longer, but it still contains $\epsilon_0$. Intuitively this is clear from the definition of electromagnetic quantities. The vacuum permittivity is a fundamental physical constant while $\mu_0$ is not (it's just a choice of units e.g. for the unit of current in the SI system). If Maxwell's equations and QED are asymptotically (at low energy) correct theories, then one can probably "stuff" any variation in $c$ into $\epsilon_0$. Like I said, something may break this degeneracy. – CuriousOne Jan 15 '16 at 18:34