Relativistic 3rd Law Question?

[blainiac]

This is not a homework question, but I read elsewhere that questions for self-study were required to be placed in this section.

I had a question that pertains to the non-instantaneous transfer of information (limited at the speed of light, c) and how it would work in a thought-experiment.

Thought:

Imagine we had two powerful electromagnets, separated by a distance, d. Arbitrarily, when anything happens to one electromagnet (turned on, shut off, destroyed, etc.), the event won't be known to the other electromagnet until t = d/c.

So, imagine at t = 0 that electromagnet A is switched on for a duration of d/c, and then it is shut off and disconnected (open circuit or something). For the lifetime of electromagnet A, it feels no net force in any direction since it's electromagnetic field propagated in all directions equally without interacting with anything before being disconnected.

At t = d/c, we switch electromagnet B on, which should be just now be seeing electromagnet A's electromagnetic field. Since electromagnet B is now on and in its frame of reference sees electromagnet A is currently on also, it will interact with this field and feel a force in some direction.Questions:

Is the equal and opposite reaction to the force on electromagnet B applied to the electromagnetic field?
It seems to imply that a strong propulsion device reacting against EM fields is possible? What am I missing here?
It seems that the electromagnets will see and interact with the past version of the electromagnet, is this true?

 

[mfb]

Is the equal and opposite reaction to the force on electromagnet B applied to the electromagnetic field?

Yes. For this experiment to work the separation has to be larger than the possible switching times, which means B only sees electromagnetic radiation from A. It absorbs some of this radiation.
The force on B will be tiny, and its momentum is balanced by a now imbalanced radiation field.

 

[blainiac]

mfb,

Thank you for taking the time to reply. Your answer makes a lot of sense. I was just confused for a while as it seemed weird having non-instantaneous action / reactions. It seems the electromagnetic field makes it possible.