Picture a wire with current directed out of the page. The electrons in the wire emit virtual photons in all directions which mediate the produced magnetic field. What is the orientation of the momenta of the emitted virtual photons, or are they randomly oriented?

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    $\begingroup$ The question is really moot, as you can't treat virtual particles like real ones with definite momentum and position. They are really just mathematical tricks to help calculation $\endgroup$ – Triatticus Oct 16 '18 at 19:55
  • $\begingroup$ How I wish the term "virtual particle" was never invented. It's quintessentially not even wrong. Some textbooks, and even papers, perpetuate the confusion by deliberately trying to 'explain' what they are, but it's just beating a dead horse. Refer to what @Triatticus said above, and some other (good) Q/As on this topic, cf. physics.stackexchange.com/q/230113/133418 $\endgroup$ – Avantgarde Oct 16 '18 at 20:16
  • $\begingroup$ Then how does one explain experiments that cause virtual photons to instantiate with the addition of energy? I believe virtual photons are real in that they "exist" for too short a time to be measured. The more energetic the particle the shorter its life governed by delta E*delta t < h/2. They are not here long enough to measure but they are here long enough to influence "real" particles. My feeling is that the math shows an underlying reality but many claim it is just mathematical hand waving. phys.org/news/2011-11-scientists-vacuum.html $\endgroup$ – user209889 Oct 16 '18 at 20:25
  • $\begingroup$ @user209889 I skimmed through the paper. The word "virtual" occurs just 3 times, all within the first half of the first page. The calculations proceed without any Feynman diagrams (which is what virtual particles are ascribed to). $\endgroup$ – Avantgarde Oct 16 '18 at 20:51
  • $\begingroup$ @user209889 I meant that the calculation itself (which is what matters) does not proceed using virtual particles, so nothing changes if you never talk about virtual particles in the first place. Like I said before, please refer to some of the Q/As on virtual particles on this site. $\endgroup$ – Avantgarde Oct 16 '18 at 21:12

I disagree with the other answer. If the electrons are moving with a constant velocity (i.e. not accelerating), then there are no real photons emitted.

In the rest frame of the moving electrons, the electrons will set up an electric field (in this case a field that will point inwards and drop like a log of the distance from the line of charge). The Fourier transform of this field will give the direction of the momenta of the virtual photons.

  • $\begingroup$ So do you have any idea what that might look like? It would seem the symmetry of the magnetic field would suggest a symmetry of the momenta of the various virtual photons. Are their momenta directed in the same direction the electrons were moving when the virtual photon was emitted? This would make sense from a classical perspective, but I know things don't always work that way in quantum mechanics. $\endgroup$ – user209889 Oct 16 '18 at 19:53
  • $\begingroup$ The so called virtual photons are just the Fourier transform of the vector potential. They do not propagate and carry no energy or momentum. $\endgroup$ – my2cts Oct 16 '18 at 19:56

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