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This question is similar to one asked if virtual electrons exist outside the nucleus, but please note, my question says virtual particles. It is not a duplicate. I read so often that matter is mostly empty space and the electron is some fantastically large distance from the nucleus that matter is mostly empty space. We know there is actually an electron cloud that fills the nucleus that reflects the probability of finding the electron. Are there virtual particles and anti particles popping in and out of existence in any of the spaces surrounding the nucleus? The same ones that produce the energy of the vacuum. I ask because there many textbooks that insist we are all mostly made of empty space since there is so much of it surrounding a nucleus.

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    $\begingroup$ Which question are you referring to? What difference does it make if the virtual particles are electrons? Possible duplicate of Do virtual particles actually physically exist? $\endgroup$
    – sammy gerbil
    Commented Nov 23, 2016 at 4:11
  • $\begingroup$ In re your last sentence: physics.stackexchange.com/q/126512 $\endgroup$
    – Kyle Kanos
    Commented Nov 23, 2016 at 11:55
  • $\begingroup$ please, see this answer of mine. In a nutshell, no: there are no virtual particles in the vacuum (which is clearly a tautology). $\endgroup$
    – AccidentalFourierTransform
    Commented Nov 23, 2016 at 17:22
  • $\begingroup$ More related questions/possible duplicates: physics.stackexchange.com/q/146003/50583, physics.stackexchange.com/q/205674/50583 $\endgroup$
    – ACuriousMind ♦
    Commented Nov 23, 2016 at 18:00
  • $\begingroup$ With all due respects I am just going by what other people in the field have written. Off the top of my head , Scientific American questions and answers , Gordon Kane , Director of Michigan Center for Theoretical Physics. Experimental evidence seems to suggest they actually exist. He sites experiments ( plural ) at CERN not the Casimir effect , apparently overwhelming evidence in other measurements support their existence. $\endgroup$
    – user86411
    Commented Nov 24, 2016 at 3:45

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"The same ones that produce the energy of the vacuum."

in mainstream physics theories the vacuum has zero energy, and feynman diagram loops representing creation and annihilation of particle pairs are non existent without an incoming real particle traversing the vacuum.

do virtual particles pop in and out of existence in the space just outside the nucleus?

A nucleus can be treated quantum mechanically with feynman diagrams as a real input line in a diagram , and thus loop corrections can be envisaged between the interactions of the nucleus with the lowest electron orbital field. So in this sense yes, virtual particle antiparticle loops are possible, except they are such higher order corrections that the powers of 1/137 that will enter in the calculations , make it a futile effort as a correction.

For the total atom, the Lamb shift is the effect of such vacuum loops modifying calculations.

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  • $\begingroup$ Just thinking out loud. You say. "The vacuum has zero energy". Gee and all this time I thought there was a big stink over the cosmological constant being so much smaller than the predicted vacuum energy of QFT. Must be a different vacuum I was reading about. Now that could be part of my problem. $\endgroup$
    – user86411
    Commented Nov 24, 2016 at 3:52
  • $\begingroup$ The QFT vacuum is a different story than General Relativity , which has not been consistently quantized and QFT can only be used in flat space where the cosmological constant is irrelevant. When one applies field theoretical mathematics to other systems, nuclear for example, it is the quantum mechanical ground state that takes the part of the vacuum on which fields exist and creation and annihilation operators operate. We are not at that stage in QFT $\endgroup$
    – anna v
    Commented Nov 24, 2016 at 5:38