Trying to visualize virtual particle behavior near "real" particles

Question

I hope this isn't too clumsy a question, but I'm trying to figure out if my way of thinking about virtual particles is reasonably OK or completely wrong. This question got me thinking about it though I've thought about this before.

Say you have a virtual pair creation, an Electron and a Positron and a near by atom with an electron near by. (yes, I know, Heisenberg says knowing how near is kind of tricky), but theoretically, the Electron around the atom should be able to hit the virtual Positron and disappear and the virtual particle should be able to replace the Electron.

My hobbyist understanding of quantum physics leads me to think this kind of thing happens all the time. It provides a method by which particles can apparently teleport instantaneously. My primary question is whether this is a bad way to look at it, if this needs correction or if it's accurate enough?

A secondary/related question is, is there any measurable difference if a "real" particle is replaced by a virtual particle in this way. My guess would be that there's no measurable change, since it happens all the time.

Thanks.

Answer 1

A virtual particle is like a sticky note. It reminds you to do something. In this case it reminds you to do an integral.

So every time you see a mention of a virtual particle it means you have to do an interval over a whole region of momentum space with a vertex factor and a bunch of math. It reminds you to do that and can help you avoid accidentally doing it twice, so it helps you compute number for predictions.

It is not a thing that starts here and ends up there.

If you had an atom and you wanted to bring up virtual particles you have to: First, decide to compute something. Second, decide to approximate it with perturbation theory. Third pick an order for the approximation. Fourth write down every diagram up to the order that matches the input and output states, grouped up to topological similarity. Fifth, do an integral for each diagram over all the possible momentums for each virtual particle at that vertex.

That's it. It's about doing a calculation and each of those integrals is going to include continuum many totally different momentums, hence infinitely many totally different particles. So whenever you worry about one, you worry about a bunch, because it's a reminder to do an integral.

It isn't a thing.