# Fine structure constant and energy scale

Hi all,

I have a rather naive question about the fine structure constant and the relationship between its value and the energy scale involved.

I understand the idea of the a charge being 'screened' by vacuum polarization (i.e., electron-position pairs popping in and out of existence), and that the value of the fine structure constant is approx. 1/137 for a 'dressed' charge at an infinite distance. What I don't understand is what exactly it means to 'increase' the energy scale.

If we were to simply accelerate, say, an electron, to a high velocity (without smashing it into anything), would we expect the electromagnetic interaction with a passing proton to be stronger, since the electron has more kinetic energy? This doesn't seem right, since velocity is relative. Or does the energy scale only matter in a collision?

I guess I'm not really clear on the meaning of energy scale; when other posts refer to the energy scale as increasing at shorter distances, does this mean the value of the fine structure constant would effectively be different when measured 'near' the electron?

Sorry if this has already been dealt with - I searched through the archives but wasn't able to find an answer to these specific questions.

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Certainly velocity is relative but if you are on a lab and you accelerate very much an electron, probably the protons will have a speed "similar" to the lab and therefore the relative velocity between the electron and the proton will be big. In that case, since the electron comes to the proton with a higher speed, the coulomb force needed to repel the electron will be greater and the interaction as well.

By the way, what has this to do with the fine structure constant??

The relevant energy scale is the invariant mass M² = P² where P is the sum over the 4-momenta of all particles involved in a process; http://en.wikipedia.org/wiki/Coupling_constant
Thanks Tom - I'm still a bit foggy though... from other reading, I surmise that as the energy scale increases, greater momentum transfer is involved. Does this mean that by using a higher energy probe, one gets closer to the 'bare' charge (i.e., there's less screening by vacuum polarization, since the interactions are occurring over shorter distances)? Not sure if that makes sense.

Thanks.