B What causes recombination of virtual particles?

[newjerseyrunner]

In a situation like this:

What causes the particle/antiparticle pair to recombine? They obviously will have opposite charge, is there a virtual photon being exchanged between them that's omitted from Feynman diagrams? That would imply that it's mathematically irrelevant, I know than these diagrams represent mathematical equations, not actual movement.

 

[Khashishi]

I'm no expert here, but there are other diagrams which include virtual photons inside that loop, and even more complicated diagrams with loops within the loops. So if you want to include the subtle effects between the virtual particles, then you need to include higher order diagrams in the calculation. The actual motion is calculated from all the diagrams together. It makes no sense to talk about something happening in one diagram.

 

[newjerseyrunner]

The actual motion is calculated from all the diagrams together. It makes no sense to talk about something happening in one diagram.

I know that, quantum electrodynamics is a perturbation theory. But it's only the diagrams that are valid and I'm wondering why the diagram that I posted is valid without an interaction between the antiparticles.

 

[Khashishi]

I'm not sure what the issue is. Why does something have to "cause" them to recombine? They recombine because they can.

 

[A. Neumaier]

The diagram is a perfectly valid 1-loop diagram for QED if you read it from bottom to top (as indicated by the arrows and the labels $e$). The momentum of the virtual particles takes all possible values, hence all directions.

The magic is in how they manage to coordinate their momenta to result in a perfect circular bend: They don't need to bother about momentum conservation because the Heisenberg uncertainty relation allows them to borrow for a short time momentum from the surrounding vacuum (whitespace in the diagram) if one pays it back sufficiently quickly. There are enough virtual accountants to enable the short-term loan, and enough virtual police to make sure that every particle late in paying back goes to prison.

So the particle/antiparticle pair will spontaneously emerge (pop into existence) from the vacuum as a vacuum fluctuation. Born at the same time by the same vacuum fluctuation, the twins smoothly bend along the circular path, borrowing some momentum. Although under heavy time pressure because of the loan, both emit a virtual photon at precisely the right moment and in precisely the right direction to hit the real particles and make them bend. Then they hurry to bend further without bumping into other particles that pop in and out of existence in the surrounding vacuum. It is no surprise that under this extreme stress they might have ignored the standard speed limit and proceeded with superluminal speed (which is allowed for virtual particles as long as they are not caught by an observation). Fearing prison like hell They make sure that they meet exactly and from opposite directions to annihilate within the allowed time. they also take care not to produce two photons (as a real particle-antiparticle pair would upon annihilation). Instead, in a true act of friendship of the twins, the antiparticle pays back the momentum loan of the particle, and conversely - both exactly the borrowed amount! Instead of going to prison for not having paid it back in time they are rewarded for their unselfish act by being allowed into Nirvana - they pop out of existence.

All this is true magic since, if momentum were conserved (as it is in the underlying math but ostensibly not in traditional virtual reality), or if it were real particles bending, they would have to interact with infinitely many virtual photons to bend the way they do. And the probability for doing so would have been zero.

Thus the diagram clearly demonstrates the magic properties of virtual particles. You should add an account of the bending magic to the wikipedia article, so that their phenomenology is complete! Note that anyone can edit the page. What is contributed is more important than the expertise or qualifications of the contributor. This ensures that wikipedia spreads an amount of nonsense proportional to that held in the general public. Many experienced editors are watching to help ensure that edits are cumulative improvements. Indeed, the number of page watchers is 135, as of today - this many cooks will surely spoil the broth. A clear sign of it is that in spite of 577 edits so far (and 13 in the last 30 days) it is classified as one of the ''Wikipedia articles needing clarification''. Your observation might just give it the finishing touch ;-)

 

[A. Neumaier]

I'm wondering why the diagram that I posted is valid without an interaction between the antiparticles.

The simple, unexciting reason for this is that one can use the Feynman rules to write down a corresponding multiple integral, and one finds (with a cutoff) a perfectly well-defined mathematical expression. This is the only physics behind the diagram.

Of course, the animation given in the previous post - consistent with the claims in the wikipedia article on the vacuum state (supported by references [3][4][5] to alleged ''reliable'' sources, one of which is a dead link) and on virtual particles - makes a much better story! So please excuse me for having given a popular science version (without any physical content) first!

 

[A. Neumaier]

The actual motion is calculated from all the diagrams together. It makes no sense to talk about something happening in one diagram.

No motion at all is calculated from the diagrams, only contributions to S-matrix elements. Therefore nothing happens even in all diagrams together.