# Speed of electromagnetic interactions

We know that electromagnetic waves fly with the speed of light, but my question not about waves. Consider a very strong electromagnet that creates a substantial field 3 meters away. Then we send a proton accelerated to near the speed of light to fly by. The proton interacts with the field of the magnet and is deflected.

The field is generated by the electrons in the wire of the electromagnet. The interaction of the proton with the field is a quantum exchange of energy, momentum, etc. between the proton and these electrons. Whether we label these exchanges as "mediating virtual photons" or not is not really important here. My question is about the speed of these exchanges.

What are the current views on the timing of these exchanges? Are they instantaneous or limited by the speed of light? If instantaneous, would they not violate casualty by transferring information and energy faster than light?

If the exchanges happen at the speed of light, a number of problems arise. First, the exchanges must be directional. Say, if an electron in the wire emits "a virtual photon" toward the proton, then the proton would be 3 meters away from that position by the time "the virtual photon" arrives. So the electrons would have to aim at the future position of the proton to hit it. This makes no sense and probably is one of the reasons why the "virtual particle" model is not in favor. Secondly, a virtual photon would have to exist for a nanosecond that would severily limit its energy per the uncertainty principle.

Can someone please clarify the actual physics behind the electromagnetic interactions from the timing standpoint? By physics here I mean physical observables, something we can measure. Using quantum fields of mathematical probabilities if fine as long as they are linked to observable values.

If the field is initially off, then it has to be turned on at least $d/c$ seconds before the proton arrives, where $d$ is the distance from the electromagnet to the proton's path through the field and $c$ is the speed of light. When the electromagnet is turned on, the field it creates will be established at a point after a delay due to the speed of light.