Virtual electron contribution to electron charge Renormalization, or "a dippy way to to sweep all this stuff under the rug", makes QED the most accurate science ever. I came across a value that explained the difference between the predicted electron charge and the measured, which verified the contribution of virtual electrons. I recorded it in my notes, made a big move, and cannot locate my source (in my library). Does anyone have those values at their fingertips? 
 A: I think you're looking for one of two things:


*

*The Uehling potential which essentially represents the lowest order modification to the electric field between point charges due to quantum fluctuations.

*A related concept (Also mentioned by @Artem Alexandov) called vacuum polarisation. The quantum vacuum can be thought of as full of virtual electron-positron pairs that are indirectly observable; yet when test charges or photons are incident on such a vacuum the virtual pairs can participate in interactions with real particles.


Both of these effects are derived in quantum field theory. Other concepts include the "Euler-Heiesnberg Lagrangian" that describe the non-linear dynamics of photon propagation due to interaction with the virtual particles in the vacuum.
Finally it occurs to me that you may be thinking of the electron's Anomalous magnetic dipole moment, the so called $g-2$. Classical mechanic predict the electron magnetic moment should be $g = 1$, the Dirac equation gives $g = 2$ but higher order loop corrections after quantisation imply that $g - 2 \neq 0$. This has been calculated to Four loop order in a spectacular 10 year near-solo effort and there are various numerical results at Five loop order. This is one of the most precise predictions ever and agrees to an insane accuracy with experimental results. 
