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Q & A: deriving speed of light?

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Most recent answer: 10/13/2014
Q:
is it possible to derive the speed of light from quantum electrodynamics (like it can be done from Maxwell's equations) or is that constant an assumption behind the theory? My understanding is that QED assign a mass zero to photons and so, assuming special relativity, they must travel at the speed of light. Based on this understanding don't we run into a circular contradiction? Special relativity was inspired by the constant speed of light that is predicted from Maxwell's equations. QED assumes special relativity BUT, at the same time, it replaces Maxwell's equations, therefore pulling the ground off special relativity.
- roberto conto (age 47)
new york, NY
A:

In quantum electrodynamics (QED) the speed of light just appears as a constant, not derived from anything deeper.

Your question about the circularity of the argument is great. Yes, special relativity was first obtained as a way of making Maxwell's equations work in any inertial frame. It still does that. Now Maxwell's equations have a somewhat different status than they did back then. They're the macroscopic low-frequency limit of the QED field equations. So you could imagine that some different space-time symmetry, not SR, would be needed. QED was constructed within the SR framework, however, so it turns out that SR survived that transition untouched. In fact, the ability of SR to serve as a guide for all the new components of particle theory that were entirely unknown when SR was developed is a very strong argument for the value of SR.

That doesn't mean that its applicability is universal. Including gravity required the broader theory, general relativity (GR). SR appears then as an approximation to GR on flat patches of spacetime. The sort of quantum issue you're worried about does show up, but not driven by QED. It's the issue of quantizing gravity, not electromagnetism, that leads to problems that seem to require some radical change, e.g. the higher-dimensional space of string theory.

Mike W.


(published on 10/13/2014)

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