How often do virtual particles pop out of the vacuum and annihilate each other? And do they have relative motion?

Question

You all know quantum foam or zero point energy or virtual particles (same thing). It says matter and anti-matter pop out of the vacuum and immediately annihilate. At what rate do this occur per volume in the vacuum? How many particles per volume per second?

Another question is: do virtual particles have relative motion? You know how we are constantly moving and for those particles that pop out of nowhere, they must have a relative motion compared to us. Like, how will they know our motion before they pop out?

Answer 1

The concept of virtual particles and their pair annihilation belongs to elementary particle physics interactions, which are mathematically modeled with Feynman Diagrams . To understand the mathematical meaning of "virtual particle" see this

Only lines entering or leaving the diagram represent observable particles. Here two electrons enter, exchange a photon, and then exit. The time and space axes are usually not indicated. The vertical direction indicates the progress of time upward, but the horizontal spacing does not give the distance between the particles.

This question and answer here shows a loop, of particle creation and annihilation. This loop exists only within the complicated integral that the Feynman diagram represents , and within the limits of its integration. The reason the internal lines have the names of particles is because of the quantum numbers that identify them, as electrons or taus or ... in order not to violate conservation laws and have the correct interactions.

A loop in a complete vacuum would violate energy conservation so cannot happen. A vacuum loop can happen next to a virtual particle line , the energy conserved by the incoming and outgoing particles. It is a very complicated mathematical theory that "vacuum loops" refer to. See for example here.