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According to QFT, virtual electron-positron pairs are created everywhere in the space, and more frequently near electric charges. Suppose that one such a pair is created in the proximity of an electron. Is it possible for the initial electron to annihilate with the created positron, leaving behind the created electron?

If so, the position of the created electron would not be the same as the initial electron, so this effect would change the position of the electron we observe in that region of the space, creating some kind of uncertainty in position. Is there any quantitative measure of such an uncertainty in position due to vacuum fluctuations?

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  • $\begingroup$ Electron position normally is uncertain, due to the HUP. And if you try to force its position to become more certain you increase the uncertainty in its momentum, so it will move somewhere else anyway. $\endgroup$ – PM 2Ring May 5 at 18:22
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    $\begingroup$ "According to QFT, virtual electron-positron pairs are created everywhere in the space, and more frequently near electric charges." [citation needed] This is a popular misconception about QFT because people take Feynman diagrams too literally as depicting actual processes. See e.g. physics.stackexchange.com/q/230113/50583 for a discussion of what virtual particles actually are $\endgroup$ – ACuriousMind May 5 at 18:35
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According to QFT, virtual electron-positron pairs are created everywhere in the space,

Vacuum loops in space have no meaning if there is no incoming or outgoing energy , an interaction, because they have zero energy by themselves, i.e. they are virtual, a mathematical construct.

and more frequently near electric charges

This "more frequently" should be "always" for the electromagnetic loops, see my answer here about vacuum fluctuations.

In calculations with Feynman diagrams higher order terms come with such loops of particle antiparticle which correct the energy levels, look at the Lamb shift..

In this sense the probability of finding an electron at (x,y,z,t), the orbital, is modified, but it is not a simplistic exchange of positions , it is a quantum mechanical calculable interaction.

Is there any quantitative measure of such an uncertainty in position due to vacuum fluctuations?

From vacuum fluctuation without interaction, no. From higher order loop corrections yes, as the orbitals change. It is all about quantum field theory and higher order corrections to the interactions.

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  • $\begingroup$ Is there a measure for "how much" the orbital changes? $\endgroup$ – Ali Lavasani May 5 at 19:18
  • $\begingroup$ Also, are vacuum fluctuations the only reason for the lamb shift? I had heard that electron's self-energy correction is also effective. $\endgroup$ – Ali Lavasani May 5 at 19:20
  • $\begingroup$ @AliLavasani the self energy corrections are also loops, but i cannot discuss lamb shift without looking with google , as I am not a theorist. I just used it as an easy example. $\endgroup$ – anna v May 6 at 3:41
  • $\begingroup$ the expectation value for the radius will change if there are energy level changes. see here hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html $\endgroup$ – anna v May 6 at 3:44

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