exponent137 said:
a.) One electron emits one real photon and it hits another electron.
b.) One electron emits one virtual photon and it hits another electron. (Repulsion because of charge repulsion)
What is gradual transition between cases a. and b. ? Or maybe, does it not exist?
Sometimes, I think of the virtual state as being a type of polarization. In my advanced QM courses, they talk about the polarization of a virtual photon. The virtual nature of the photon enters the mathematical description in the same variables that includes the polarization.
Here is how I visualize the four polarization states of an electromagnetic photon moving in a certain direction with a certain energy.
First, I imagine the photon as being composed of a wavevector and a polarization vector attached at the same point. The wave vector gives the direction and energy of the photon.
The polarization vector of an electromagnetic wave in a vacuum has to be perpendicular to the wave vector. So there are two transverse polarization states of a photon in optics. One can call these two states "horizontal" and "vertical". These two types of photons are "real" photons.
The polarization vector of a static electromagnetic field can be parallel to the wave vector. You could call this a longitudinal polarization state. However, there are two types of longitudinal states. One can have a longitudinal state describing a static electric field. One can have a longitudinal state describing a static magnetic field.
Hence there are two longitudinal polarization states of an electromagnetic field: electric and magnetic. Photons which are in one of these two longitudinal states are referred to as "virtual photons".
So in my view, "real photons" have "transverse polarization" and "virtual photons" have "longitudinal polarization". The "virtual photons" spontaneously disappear at short distances from an electric charge, although they can also disappear if they collide with an electric charge. The "real photons" persist until they collide with another electric charge.
This is just my visualization to help with the Feynman diagrams. In my view, the squiggle in the Feynman diagrams stands for longitudinal polarization. How seriously you want to take this is up to you.
String analogy time. I present a heuristic picture using an analogy between a vacuum and a string.
A lot of teachers use the waves on a string as an analogy to light waves. The waves on a taunt string that everyone visualizes are transverse. Just pluck a taunt string and you can see them. However, longitudinal waves can also carry down a taunt string. This is children can talk to each other using tin cans attached by a taunt string.
Consider the example of a taunt string. The transverse waves can carry down a string even if it isn't taunt. However, the longitudinal waves don't travel very far if the string isn't taunt. One can make an analogy between a string which isn't taunt and a vacuum. The vacuum state isn't taunt enough to carry a longitudinal wave very far down the string.
Call the quantized excitations of a string the "stringons". When children jump rope, they see the "real stringons" as transverse vibrations on the rope. When children talk to each other using a string connecting two tin cans, they are using the "virtual stringons".
The children don't care whether which "stringons" are "real" or "virtual". Each refers to a different type of energy transfer.
I don't have the software for posting the corresponding equations. However, I hope this analogy is useful.