# What causes virtual particle pair production to not occur in the space occupied by matter?

Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is there a shell surrounding an atom or maybe I should call it a boundary beyond which particle pair production occurs, and within the boundary it does not, I have wondered if the different orbitals around an atom are affected (set)by the influence of the virtual particles.

Virtual particles are mostly the name given to a category of mathematical expressions (contained in Feynman diagrams): while virtual particles are mathematically associated to real, physical particles (virtual electron, etc.), they have no reason to exist physically. Essentially, the name is somewhat of a misnomer.

Now, there is a point of view in which virtual particles do have an influence. Your example of an atom is one such case: if you first model the atom as being a set of electrons that only interact with the nucleus via the (relativistic) equation of Dirac, you can refine this theory by adding the possibility for energy to create particles (that's basically Quantum Electrodynamics [QED], a Quantum Field Theory). When you correct the energies of your simple atomic model with QED, electrons can interact with each other, and the energy levels of your atom coincide with experiment (up to this day…). Now, within this theory (QED), the interaction between electrons (and between the nucleus and electrons) can be approximated with more and more precision through Feynman Diagrams; these diagrams contain mathematical quantities (propagators) that describe the propagation of a "virtual particle" from one point to another (in space-time). Such treatments correctly predicts the "Lamb shift" of atomic levels, for instance.

However, I don't see any reason to believe that such virtual particles (mathematical expressions) have a physical counterpart. In fact, as far as I know, they only come up through approximations (expansions in a small parameter) of the theory. You can also do QED without these approximations; in this case, I don't think that virtual particles are a concept that plays a role. So, to summarize, virtual particles are mostly a mathematical device that comes from approximations, and they have no reason to be particles.

That said, one can find many descriptions of vacuum as being full of "vacuum bubbles" and "particle pairs" that are produced from energy (via $$E=mc^2$$) and annihilate each other (matter goes back to energy). My position on this is that this image has nothing to do with the physical reality, but has everything to do with the mathematical treatment by approximations that physicists often rely on.

Virtual particles influence physics at every point of space, whether or not there is a nearby atomic nucleus or orbital. All electrons in an atom receive energy shifts analogous to the Lamb shift (from virtual photons), aside from other quantum corrections. In fact, the influence of the virtual particles only becomes truly measurable if there are some nearby particles that feel the effect.

There is a counterpart of the Pauli principle for virtual fermions: one may get some cancellation between Feynman diagrams for various special quantities. However, one shouldn't interpret the Pauli exclusion principle for virtual particles in the same way as for real particles because virtual particles are not real particles.

Virtual particles are properties of real particles, it is indication on the real particles being compound systems with many internal degrees of freedom. As a model, let us consider a charge coupled to the electromagnetic field, the latter is described as a set of oscillators. Let us simplify our system to one oscillator. You may imagine it as two balls on a spring, one of them is charged, the other neutral, and the whole system has the global variables and internal motion variables. The global variables are the center of mass (CM) position and velocity, and the internal variables are the relative distance and velocity of the two balls. When we push the charge (one ball of the two), we transmit the energy to the whole system which is split between the CM and internal energy. This is how we produce photons which are excitations of the oscillator. Now, in the ground state in QM there is always non trivial motion leading to smearing positions of the balls in the oscillator, like clouds of electrons in atoms. This makes the system fluctuate and these fluctuations affect the charge interaction with other charges.

If our charge is strongly bound in atom, the leading force acting on the charge is the atomic one. For the oscillator it means a driving force that imposes its own frequency and the resulting effect is determined with the interplay between the two couplings acting on the charge. If our oscillator frequency is very low, it is completely driven by the motion of the charge in the atom. If the oscillator frequency is much higher than the atomic one, the oscillator is strongly attached to the charge and causes only small "jitter" of its motion in orbit.

In reality there are many oscillators with different frequencies so their total effect is producing many photons when the electron gets acceleration and the Lamb shift when the electron is bound in atoms. The latter case was described by T. Welton in 1948.