Deriving speed of light from QED

[robcon]

Is it possible to derive the speed of light from quantum electrodynamics (like it can be done from Maxwell's equations) or is the fact that the speed of light in vacuum is constant and has a certain value an assumption in the theory?
My understanding is that QED assign a mass zero to photons and so, by assuming that special relativity describes space and time, photons must travel at the speed of light in vacuum.
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 presupposes that special relativity is true but, at the same time, it replaces Maxwell's equations, therefore pulling the ground off special relativity.

 

[DarMM]

Well QED as you said supposes Special Relativity is true, or rather it is a quantum theory living in Minkowski space (the model of spacetime in special relativity), so the speed of light, or any massless particle, is automatically constant. That's it really, it doesn't matter that Einstein used Maxwell's equations to figure out Special Relativity.

 

[dextercioby]

QED is the quantized Maxwell theory. It's a specially relativistic field theory, so that c is postulated finite and how the quanta's momentum and energy are linked through c (the same c as in Maxwell's theory) can be proven.

 

[robcon]

@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds. QED is an extension of Maxwell's equations but requires special relativity to make the same prediction. How can a more approximate theory make such an important deduction using fewer assumptions?
In addition, we also know that special relativity is an approximation of general relativity (GR) and that general relativity and quantum theories don't coexist well at the quantum level in their current formulations. This means that we can't really use GR to help QED derive the speed of light. Again, we have an important and correct deduction of a weaker theory that disappears in an extension of that theory.

 

[bhobba]

Obviously you can since Maxwell's equations are the classical limit of QED.

In fact a mathematical analysis shows gauge symmetry is the real essence of both QED and Maxwell,s equations, and inevitability leads to EM waves traveling at the invariant speed that appears in SR.

It's simply that the speed is frame independent which immediately implies its the invariant speed of SR. That's the case in QED or classical EM.

In Maxwell's equations its wave solutions are frame independent. In QED I think its tied up with the propagator - its the propagator of a massless particle - but don't hold me to that because my understanding of QED is not as good as I would like. If its massless - it must travel at the speed of light.

There is something in the back of my mind that all gauge bosons are massless - hence, since the photon is a gauge boson, it must be massless. Gauge bosons however can gain mass by interaction with the Higgs field. So the rock bottom essence of why QED predicts the speed of light is photons do not interact with the Higgs.

Thanks
Bill

 

[ChrisVer]

@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds. QED is an extension of Maxwell's equations but requires special relativity to make the same prediction. How can a more approximate theory make such an important deduction using fewer assumptions?
In addition, we also know that special relativity is an approximation of general relativity (GR) and that general relativity and quantum theories don't coexist well at the quantum level in their current formulations. This means that we can't really use GR to help QED derive the speed of light. Again, we have an important and correct deduction of a weaker theory that disappears in an extension of that theory.

I am not understanding your question very well. But...
Maxwell equation determines the speed of the electromagnetic wave [light]. The massless particles in SR or QED are not the electromagnetic waves, but the photons. The velocity eg in Maxwell's EM equations can change if you change matterial, the velocity of the photons however doesn't [it's always c because they are massless].
The "massless particles run at speed of light" statement of SR doesn't only refer to the photons, but any massless particle. So it's not that Maxwell equations contain any "large" information about this fact. I hope I made my point clear.

There is no reason to use GR in a QFT as long as the gravitational interactions can be neglected.

 

[DarMM]

@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds.

Not really, if you have Maxwell's equations and still keep Galilean transformations, then the speed of light is not constant and varies between frames, even Maxwell's equations require Special Relativity for light to have a constant speed in all reference frames.

 

[bhobba]

Not really, if you have Maxwell's equations and still keep Galilean transformations, then the speed of light is not constant and varies between frames, even Maxwell's equations require Special Relativity for light to have a constant speed in all reference frames.

Yep - true.

I forgot about that.

You have to invoke the POR for the speed of light to be the same in all frames.

Thanks
Bill

 

[robcon]

Thank you all