# How is the EM force exchanged over long distances?

The Situation

Imagine we place two charged objects a very far distance apart, essentially making them point charges. How does the EM force interact between the two point charges if virtual photons cannot exist for long periods?

What I know

According to particle theory, the EM force is "activated" by the exchange of virtual photons. According to QM and the Uncertainty Principle: ΔE*Δt > h (approx). Virtual photons can only come about if they exist for a very, very short amount of time because the error in the energy becomes very large, and thus the conservation of Mass and Energy is not violated. If we place the two point charges very far away, the time component becomes very large, thus making the energy component have a small deviation, narrowing it down to a specific energy.

Thought Experiment

Place two point charges 1 light year apart, and give the two points equal charges such that the total electrostatic force is 1 newton between them. In order for the force to be exchanged, the "virtual particles" must now live for 1 year (Δt = 3.15569e+7 seconds), giving each photon a very specific energy and thus a very specific wavelength. If we look at the space in between these two objects, will we see light in that void?

Tying it all together

Sorry for the block of text, but this is how I thought of this problem.

So in conclusion:

1. Can the EM force be exchanged by real photons and NOT virtual photons?

2. Can virtual photons change into real photons?

3. Over long distances, will we see radiation from the photons coming from the electromagnetic force?

• If they are virtual, they are not on shell in which case they can be involved in an interaction a light year apart in a less than a year, however the farther off shell the more the amplitude is suppressed. Of course the amount of phase space available is a factor as well. In general you should expect the electromagnetic interaction to get weaker the farther apart things are. So this is reasonable. Image not sure I'd put much quantitative stock by the time energy tradeoff, it is usually how far off shell that is the true factor of interest. – Timaeus Jul 30 '15 at 6:05

## 1 Answer

Virtual particles are not real. They come, as I've said in many answers on this site, from a naive interpretation of Feynman diagrams which should not be taken as an actual, exact description of how the physics works.

The actual description of an interaction in the quantum field theory is more complicated than "photons are exchanged". In particular, "virtual particles" are perturbative "objects", since they are associated to lines in a Feynman diagram, which are mnemonic devices to remember which integrals are to be taken in what fashion. They are not how a force is defined in the quantum field theory, and not its fundamental, exact mode of transferral (such a thing does not exist because the quantum notion of force is not easily connected with the classical notion of force).

Nevertheless, on long ranges and at low energies, we may recover the classical electromagnetism, and, for instance, Coulomb's law from the quantum field theory (and in particular from the diagram that means "a virtual photon is exchanged") as I briefly outline in this answer. Hence, it is actually perfectly feasible to speak of an "exchange of virtual photons" also at long distances, if you also speak of it at short distances (I would advise against using this terminology at all). But these still are virtual photons, not actual photons, so you won't see any radiation, because nothing detectable, as far as we know, is actually "exchanged". Real photons do not mediate the electromagnetic force, they are light.