# Do virtual photons Doppler-shift?

Just a casual thought I had, with no answer since I'm not well-versed in QFT:

Given two point charges, the force between them is given by Coulomb's law, $$\frac{1}{r^2}$$. I know this is only fully accurate when the particles are stationary. What I'm wondering, is that since the force is mediated by (virtual) photons, whether the effect of motion could be approximated as a Doppler-shift.

In other words, could you then approximate the Coulomb potential between two moving particles as:
$$V(r) = \frac{1}{r}\sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}\quad, v = \frac{dr}{dt}$$

I haven't put a lot of thought into this, so I might be completely wrong :) But it does feel intuitively correct to assume a stationary charge would 'feel' a greater force from a particle headed towards it than away from it.

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Gold Member
I don't know much about QFT so I can't answer your question, but Coulomb's law is a $$\frac{1}{r^2}$$ relation not $$\frac{1}{r}$$

The force is 1/r^2 the potential is 1/r. The first equation was a typo.