Energy is borrowed from the vacuum /Virtual Particles

[Polyrhythmic]

"Energy is borrowed from the vacuum"/Virtual Particles

I know that there are countless threads on virtual particles (some of which I have participated in), but I don't think that this issue has been adressed yet.

One common handwaving argument for the existence of virtual particles is the Heisenberg uncertainty principle. It is said that virtual particles exist shortly enough so that the uncertainty principle applies and let's them "borrow energy from the vacuum".
My question is now: Does this argument have any actual theoretical/mathematical backing within the framework of quantum field theory? Because I don't see how this emerges as a consequence of anything in the theory. Virtual particles emerge as internal lines of Feynman diagrams, it is not clear to me how the uncertainty principle could be related to them.
Let's for now ignore the fact that energy/time uncertainty is a little different from other uncertainties (time does not have a corresponding hermitian operator). Don't let this grow into a "real vs not" discussion, please simply adress my specific question.

 

[maverick_starstrider]

I think the whole "borrowing" picture exists entirely in pop science stuff since, as you pointed out, virtual particles are just a mathematical artifact of perturbation theory and the energy-time uncertainty relation isn't really as fundamental as the x,p one.

 

[San K]

I know that there are countless threads on virtual particles (some of which I have participated in), but I don't think that this issue has been adressed yet.

One common handwaving argument for the existence of virtual particles is the Heisenberg uncertainty principle. It is said that virtual particles exist shortly enough so that the uncertainty principle applies and let's them "borrow energy from the vacuum".
My question is now: Does this argument have any actual theoretical/mathematical backing within the framework of quantum field theory? Because I don't see how this emerges as a consequence of anything in the theory. Virtual particles emerge as internal lines of Feynman diagrams, it is not clear to me how the uncertainty principle could be related to them.
Let's for now ignore the fact that energy/time uncertainty is a little different from other uncertainties (time does not have a corresponding hermitian operator). Don't let this grow into a "real vs not" discussion, please simply adress my specific question.

you cannot borrow energy from a vacuum
if you can, then its not a vacuum...;)

 

[jbrussell93]

you cannot borrow energy from a vacuum
if you can, then its not a vacuum...;)

Quantum Electrodynamic (QED) Vacuum :)

 

[tom.stoer]

Let's define 'virtual particle' as internal lines in a Feynman diagram, i.e. lines with two ends at two vertices.

In a Feynman diagram energy-momentum (and everything else like angular momentum, charge etc.) is conserved at every vertex; for virtual particles this means that they don't 'borrow energy from the vacuum'; all what they do is to violate the usual constraint p² - m² = 0 where p is the energe-momentum four vector.

So for a virtual photon energy-momentum conservation holds, but it represents something (attention: it's not a Fock-state!) with m² ≠ 0.