# Do virtual particles follow worldlines (spacelike, timelike, lightlike)?

When we talk about static force fields, we use virtual particles to describe the interaction of such fields with other particles. These virtual particles are not real particles, they are a mathematical model.

Let's say that the Sun moves away from us, this should cause a change in gravitational force, when will this change be noticed by us?

Does static gravity follow spacelike geodesics?

Now since we are describing force fields with them, and force fields are created by a real object (like an electron for EM, or a star for gravity, quarks for strong, weak force) the virtual particles somehow propagate (at least theoretically) from the object to where the near field reaches.

Now in theory, virtual particles are off mass shell, and do not obey SR, speed of light.

There are though three worldlines as per SR:

1.spacelike

2.timelike

3.lightlike

Now in the case of gravity, there is a center of gravity, usually an object (with stress-energy), and these virtual gravitons exist everywhere in the gravitational field.

In the case of EM, there is a center object, a charge, that creates the EM field.

These virtual particles at least theoretically must mediate the forces from the object to the positions in the field wherever the field interacts with a particle.

Does SR somehow describe these virtual particles in terms of speed or worldline?

Question:

1. Now do we at least theoretically have a worldline for these virtual particles?
• There are no worldlines for quantum particles, either real or virtual. Commented Jul 26, 2019 at 16:18
• @G.Smith do you mean that a photon is not following a geodesic? see here en.m.wikipedia.org/wiki/World_line , look for "quantum" Commented Jul 26, 2019 at 17:36
• @annav I should have said that a quantum particle does not follow a particular worldline. In the Feynman path integral formulation, it follows all possible worldlines. I do not think this what the OP had in mind. Commented Jul 26, 2019 at 18:56