@DavidZaslavsky You made it up? Awesome!

well, that's kind of what writing a blog post is all about (and same for answers on PSE!)

@pcr hmm, but doesn't Chris' answer make sense as well?

Aah, right.. It looked like one of those famous quotes though

@pcr magnetic fields can apply torque on a loop. So they can do work.. \int\tau d\theta

Chris' answer makes sense, but he doesn't address the real problem here. The fact that the proton radiates doesn't dictate the fact that it goes clockwise. We already know that the proton goes clockwise from basic EM law (or if you want, Lenz law). And now, we're trying to force the m.B paradigm into our system -> which definitely won't work because we're not dealing with a permanent magnet.

@Manishearth "magnetic fields can apply torque on a loop. So they can do work.. \int\tau d\theta" -> Yes, but there also exists torque acting on the current, so that the total torque is still zero on the microscopic level.

@Manishearth "which definitely won't work because we're not dealing with a permanent magnet." -> but then the m.B paradigm is resqued by Feynman again.

(and I'm not sure if I can post my previous lines as an answer)

Hmm.. Now I'm thinking of a meta question on what to do when you get a profusion of contradictory answers...

@Manishearth if you had enough people to upvote/downvote them, the result would be clear

we got some thermodynamics questions today, yeah!

@Manishearth 'torque of the current' -> it acts to change the value of the current at different orientation of the rotation plane

@F'x I was the one who upvoted ur answer because it is sufficient to say that '-m.B' doesn't hold here. The correct explanation shouldn't be subjective.

Another EM question, if you want physics.stackexchange.com/questions/4147/… -> I was wondering if the long wavelength limit gives the same behavior as NMR's spin echo

@Manishearth alternatively, see griffiths electrodynamics page 210 (djvu ;)) for discussion related to "work" done by a magnetic field (I still prefer feynman's lecture).

@Fx Actually, i don't think it's subjective. It's a paradox, and while paradoxes(paradoxi?) have multiple explanations(at different levels), they all boil down to pretty much the same thing. I'd expected different explanations, though not conflicting ones. :P

@pcr Aah, I see.. Basically the work is recompensated in the change in current.

@pcr I will check Griffiths later.. I probably have the same djvu buried somewhere (I have a whole bunch of these books in djvu format, as well as hardcopies of a few)

@pcr yeah, in the end my original answer agrees with [F'x]'s answer (how does one use a possessive apostrophe when the username already has one? 0_O). The detailed answer about +m.B may be correct as well, but most of the arguments for and against both make (partial) sense, so I'll just wait

@F'x the issue is, all the answers have both upvotes/downvotes. 0 score != +2-2 score. The latter means that atleast 4 people took a look at it. :/

I'd posted it as a question for everyone to have some fun (paradoxi always are), but I had no clue that there was so much EM involved in it. So I get to have fun as well :). Of course, right now I'm more confused than having fun..

@Manishearth yeah, you've just rephrased it in a cleaner way. I think Emitabsorb's answer needs some cleanup too, to make it clearer.

"[F'x]'s answer (how does one use a possessive apostrophe when the username already has one? 0_O)" -> F'x probably knows more about this

@Manishearth "So I get to have fun as well :). Of course, right now I'm more confused than having fun.." -> the 2nd sentence is part of the experience of the 1st sentence :)

@ArnoldNeumaier My current understanding is that virtual particles appear only when we quantize at least 2 different kind of fields / 1 field with self interaction (or else we won't see internal loops). I have a slight confusion related to mat.univie.ac.at/~neum/physfaq/topics/virtcoul. Since we're dealing with a single tree diagram here, the EM field needs not to be quantized and yet we still get the superluminal coulomb interaction.

At least I know that the separation of the covariant propagator into transverse and longitudinal is artificial. Hence, is this an example of a classical version of virtual 'particle'?

"into transverse and longitudinal is artificial" -> equivalent to choosing different 'perturbation' scheme

@pcr; Tree diagrams give precisely the result of classical perturbation theory applied to classical field theory, where photons don't even exist. conceptually. This settles it all; the other stuff doesn't make sense though to make arguments one has to pretend it does. - My assertion was made on the basis that I keep the electron on-shell during the interaction with the e/m field (as it would be in nonrel. QM) Then 4-momentum conservation forces the photons to be superluminal.

But in fact a Coloumb field does not radiate, so there are no real photons around, the photons must be considered to emanate from a far away source (the only way to get an external field into QED proper), which makes them internal nodes. And my old argument was faulty as the electron is of course also virtual (an internal line) as soon as it crossed the first vertex.

...I updated the FAQ to mention this.

@ArnoldNeumaier The classical photons from a far away source you mentioned are considered classical source, right? Why does the electron has to be virtual when it interacts with the source?

Perhaps, this is the source of my confusion? Even a classical field can be "virtual" too. e.g. momentum space Feynman propagator in classical K-G field ( 1/(p^2 -m^2)) is different from on-shell propagator ( delta(p^2 - m^2))

more explicitly, (Feynman propagator) = (on-shell particle propagator) + (on-shell antiparticle propagator)

@pcr: Trying to reconcile virtual particles with something having properties one can talk about with some precision is opening a can of worms. One has to make lots of unjustified assumptions based on plausibility, and one can do that in different ways. it is too fuzzy a concept as to be able to get definite properties out.

external field = classical source. For feynman diagrams, see p.305 of Peskin-Schroeder - all photons end in a different crossed node - stating that it is a virtual photon emitted somewhere. From the interpretation as an internal line, the momentum of a virtual particle can be anything (integration over R^4), and all these contributions must be added (in a path integral-like fashion).

The electron is always an internal line except before interacting with the first photon and after interacting with the last photon, hence it is virtual. This has nothing to do with bare or not. With bare particles all contributions are infinite, and everything is meaningless. To have meaning, one must interpret all lines (external and internal) and vertices as renormalized.

Then the sum of feynman integrals corresponding to a fixed order is finite (but of course the individual contributions still may be infinite). Almost nothing makes sense once one goes into detail; so I'll stop this discussion at this point. Dropping the concept altogether is the best course of action. (If you are still unssatisfied, ask a new question, so that there is more space to reply.

@Manishearth by the way, don't @mention me; you really need to reply to a message of mine if you want me to read it (I know, I'm a diva)

@pcr F'x's is fine with me

@ArnoldNeumaier I see. 1. external field = classical source 2. "all photons end in a different crossed node - stating that it is a virtual photon emitted somewhere" -> I'll think more about this, still not sure. "Dropping the concept altogether is the best course of action" -> but then 'virtual' is useful to label the artificial terms/expansions in our calculation.

Thank you for your time. I'll post a new question later and hope that it is not redundant to the previous ones (most likely about the classical field).

As for now, I probably need to be more careful with any internal lines, even in 100% classical field theory where no renormalization is needed.