QED Explanation of Force Between Motionless Particles

[jjustinn]

The standard layman description of QED is that forces are no longer mediated by fields present at all points in space, but by particles that are (presumably?) at least somewhat localized, and carry some energy. Forces are then exchanged between two electrons by "exchanging photons" -- at the most basic level, it's usually at least implied that this works like momentum transferred between two people passing a ball back and forth, but there's usually a disclaimer that this "isn't exactly right".

However, the examples given inevitably deal with the very specific phenomena of radiation emission -- where classically energy is lost by the emitter (electron) and carried away by the field...if static fields are mentioned, they are quickly dismissed with a mention of "virtual photons".

So, my question: what is the QED explanation for the Coulomb force between two particles constrained to sit motionless in proximity of one another? E.g. Does modern understanding of QED really add anything to the description of the forces beyond classical one of force-carrying fields?

 

[Bill_K]

Hey, very good, jjustinn, I think it's the first time this week this question has come up!

two people passing a ball back and forth, but there's usually a disclaimer that this "isn't exactly right".

More like "almost totally wrong." Taken literally, this picture leads to a series of very logical-sounding followup questions, such as:

How many photons? How often are they exchanged? How can they cause unlike charges to attract? What happens if one of them misses?

Well here's the truth: photons have a polarization vector. And so there are two types of photons: longitudinal and transverse, depending on which way the polarization vector points. Transverse photons are useful for describing radiation, while longitudinal photons are associated with the Coulomb field but frankly are not all that useful. One of the first things you do in QED is to show that longitudinal photons can be eliminated and replaced by the familiar 1/r potential between the source charges. (Note: "virtual" photons is not the issue. Both transverse and longitudinal photons can be virtual.)

Does modern understanding of QED really add anything to the description of the forces beyond classical one of force-carrying fields?

Yes, what you get in QED in addition to the classical description is a foundation upon which higher order corrections can be built. The Coulomb potential is not exactly 1/r for example. This leads to small but observable effects in atomic energy levels like the Lamb shift.

 

[jjustinn]

Hey, very good, jjustinn, I think it's the first time this week this question has come up!

More like "almost totally wrong." Taken literally, this picture leads to a series of very logical-sounding followup questions, such as:

How many photons? How often are they exchanged? How can they cause unlike charges to attract? What happens if one of them misses?

I was worried about mentioning the hated force-exchange-as-Newtonian-game-of-catch metaphor for just that reason (e.g. that it would turn into a discussion about how it was wrong rather than the main question), but now I'm really confused--you deftly avoided the flamebait and succinctly answered the main question (eg "yeah, QED is just corrections to force-field theory"), but your "logical follow ups" seem a little too logical to me at the moment (save the one about attractive forces -- I *know* I've read that discussion here numerous times).

So...indulge me? With a photodetector, you can detect individual photons -- transverse ones at least -- so the question “how many/how often are they emitted/what if one misses" seems to be an elementary exercise (given a sensitive-enough detector and a weak-enough emitter, at least).

I can see how with a static force this becomes tricky, because in that case there's no "emitter" in the sense of a radiation field (since by definition when it's changing it's not static) -- but as you say, these longitudinal photons can be as real as transverse ones (obviously, since the transverse/longitudinal split exists in classical ED as well).

So -- what am I missing? Why are those questions not "very logical"? Apologies in advance for asking what must be a common question, but I couldn't find it in the last few pages of your post history, so maybe it will at least be a fun trip down memory lane to last week (or the week prior).