Light is faster than the speed of light

[the_pulp]

I was thinking about the QED lagrangian and renormalization and I thought something like this:
"There are three renormalizable infinites in QED so there should be three free parameters to adjust in order to obtain the low energy results. The three 'high energy' parameters are e, m and where is the third parameter? Let me see... Oh it should be c, the speed of light.
One of the Renormalizable diagrams is the vacuum energy. That is a photon travels from left to right, it suddenly turns into an electron and a positron and then they should turn again into a photon. If the speed of the 'electron-positron' is slower than light then the speed of the high energy photon should be higher than c, in order to get a speed of the low energy photon equal to c."
I don't know if I could express the idea in a clear way, but supposing this is a case:
Is the high energy photon faster than c? That is to say, is there, for high energy, a bare c that is higher than experimental c?

Sorry in advance if I couldn't express myself

 

[bhobba]

Let me see... Oh it should be c, the speed of light.

There are two - the electrons mass and charge.

The speed of light is not a free parameter - that an invariant speed exists and has a fixed value is implied by space-time symmetries:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Relativistic field theories like QED are formulated to have that built in from the start.

The other issue is, as has been discussed many times on this forum, virtual particles do not exist - they are simply shorthand for terms that appear in the Dyson series.
http://en.wikipedia.org/wiki/Dyson_series
http://en.wikipedia.org/wiki/Feynman_diagram

Thanks
Bill

 

[the_pulp]

Thanks bill. I know that virtual particle are mathematical artificial shortcuts. Expressed in this terms my question is:

As happens with bare charge and bare mass (that could be thought to be the mass and the charge of the artificial virtual particles invented to visualize the calculations) that their values are different than experimental mass and charge. Can we say that the speed of light (of the virtual light ie photon) is different (higher) than the experimental c??

My confusion comes because of a lot of papers and books that say things like the following (taken from wikipedia Renormalization Group):

"For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the "dressed electron" seen at large distances, and this change, or "running," in the value of the electric charge is determined by the renormalization group equation."

So, in terms of wikipedia words, as mass changes and charge changes seeing from shorter distances, can we say that c changes too? If not, what is the third thing that changes? (There should be three, in anywhere in qed renormalization appears the number three: counter terms, renormalizable diagrams, Z1 Z2 Z3...)

Thanks!

 

[bhobba]

So, in terms of wikipedia words, as mass changes and charge changes seeing from shorter distances, can we say that c changes too? If not, what is the third thing that changes? (There should be three, in anywhere in qed renormalization appears the number three: counter terms, renormalizable diagrams, Z1 Z2 Z3...)!

No. I don't know where you are getting 3 from.

The reason you need to do renormalisation is it turns out when you apply perturbation theory things blow up to infinity. A lot of things can cause that but what research found was it was a bad choice of what to perturb about. If one applied a cutoff to the theory then you got finite answers but as the cutoff went to infinity what you perturbed about went to infinity. Normally things you perturb about need to be small for it to work. If it was infinity that is a really really lousy choice and no wonder it failed. So here is the trick. What you do is choose something that doesn't go to infinity - but what. The solution was simple - if something existed that didn't blow up then the theory would give finite answers - so you simply find some value from experiment and write it in terms of what blows up to infinity so the equation is now in terms of this new value. These are called renormalised quantities. You perturb about that and because it doesn't blow-up as the cutoff goes to infinity, lo and behold, it works. In QED you only need two things to be fixed - electron mass and charge - they are called renormalised. The speed of light is not one of them, nor does it make sense for it to be since its not what you perturb about. But it turns out that the actual value of these renormalised quantities found from experiment depend on the energy scale you are probing. We normally don't probe very far so they are the values of low energy (or equivalently distances that are not short) - but in principle you could use values probed at higher energies (or shorter distances).

Here is the detail - but its advanced:
http://isites.harvard.edu/fs/docs/icb.topic1146665.files/III-5-RenormalizedPerturbationTheory.pdf

Note only the bare mass and charge need renormalisation.

Thanks
Bill

 

[Demystifier]

I was thinking about the QED lagrangian and renormalization and I thought something like this:
"There are three renormalizable infinites in QED so there should be three free parameters to adjust in order to obtain the low energy results. The three 'high energy' parameters are e, m and where is the third parameter? Let me see... Oh it should be c, the speed of light.
One of the Renormalizable diagrams is the vacuum energy. That is a photon travels from left to right, it suddenly turns into an electron and a positron and then they should turn again into a photon. If the speed of the 'electron-positron' is slower than light then the speed of the high energy photon should be higher than c, in order to get a speed of the low energy photon equal to c."
I don't know if I could express the idea in a clear way, but supposing this is a case:
Is the high energy photon faster than c? That is to say, is there, for high energy, a bare c that is higher than experimental c?

Sorry in advance if I couldn't express myself

Loop corrections may change the physical velocity of light, and sometimes it may even be larger than c. See e.g.
http://en.wikipedia.org/wiki/Scharnhorst_effect