Static Charge Photons: Frequency & Wavelength

[ObsessiveMathsFreak]

What is the frequency/wavelength of the photons which mediates the forces between static charges? Are they exclusively low frequency photons, or is there a distribution of some kind? Also, in a slightly related question, is there a lower bound for photon frequency?

 

[tiny-tim]

… where's my flak jacket … ?

Hi ObsessiveMathsFreak!

'spect I'll get shot down for this, but …

I think they're just in mathematicians' imaginations … they help to simplify the perturbative expansion of the field … they have all possible frequencies and speeds … they're virtual photons, and virtual means not real, so they don't exist!
​

… runs for cover … ​

 

[peter0302]

Wouldn't it depend on the energy that is actually exchanged in the interaction? For example, I think you could just determine the kinetic energy involved in the "collision" of two electrons, depending on their momentum, and using E=hf find the frequency of the virtual photon involved. Am I wrong?

Also, in a slightly related question, is there a lower bound for photon frequency?

I've wondered this myself, or rather, wondered about the opposite question - is there an upper bound? Would it be a photon with a wave length equal to a Planck length? That'd be a very high energy photon!

 

[tiny-tim]

For example, I think you could just determine the kinetic energy involved in the "collision" of two electrons, depending on their momentum, and using E=hf find the frequency of the virtual photon involved. Am I wrong?

Yes, you can do that - and the momentum of the photon is always larger than its energy, which means it's always faster than light.

In fact, in the centre-of-mass frame of reference, the photon travels infinitely fast (I think this is why people talk of the "exchange" of a photon)!

(Though I don't know how you'd work out the frequency. )

Another reason for my not believing in them!

 

[peter0302]

And yet we do know that the EM force is transmitted _at_ the speed of light. So there is indeed something that is exchanged at a finite speed.