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A charge is at rest in an inertial reference frame.

Consider this situation:

From the point of view of an observer who is accelerating relative to the charge. Would the observer observe electromagnetic waves generated by the charge?

A few thoughts on this question recently in response to the link given below by joshphysics:

Assuming energy conservation, and considering classical physics, it seems the observer will observe no EM waves -- Since in inertial frame all the energy the charge gets is from its electric field - and it is proportional to $\int\limits_{\text{all space}}(\frac{1}{r^2})^2 \, \mathrm{d}v$ , which is some value/bounded (assuming no point charge), meanwhile assuming there exist EM waves in accelerating frame, the EM waves will have arbitrary energy, as it totally depends on the observer.

If there is EM waves in accelerating frame, Where does the energy come from? It is indeed strange if you input energy to the observer, somehow the charge get the energy and emits it instead.

So I will guess probably no. Once no EM waves in inertial frame, then no EM waves in accelerating frame. (okay, I admit it is kind of appealing to ignorance.)

Pierre Polovodov
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Shing
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    Related: http://physics.stackexchange.com/q/21830/ – joshphysics Aug 08 '14 at 08:37
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    In an absolutely accelerating frame, all celestial bodies have apparent acceleration component of the opposite sign and some of them would be getting immense kinetic energy due to this. This just shows the law of conservation of energy does not apply, in general, to description of motion of bodies referring to non-inertial frames. One can introduce fictitious forces in the non-inertial frame, and then bodies get kinetic energy due to work of those fictitious forces. This can be applied to charged body as well. – Ján Lalinský Mar 15 '23 at 22:44
  • It is interesting that the the vector magnetic and electric potential depend on velocity of the particle. But if the particle is at rest and the observer is in relative motion, it seems like that case has the observer receive transformed $\vec B$ and $\vec E$ in opposite velocity. Does this answer the question fully or if what not, what still needs to be stated? – Stephen Elliott Aug 14 '23 at 11:26

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As you accelerate toward the charge you would observe a time changing electric field which would generate a time varying magnetic field and so on. You can measure this by interacting with the fields using something like an antenna. So yes, in a sense you would observe energy between the charge and your measuring device which is accelerating.

Alex
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  • It is not that simple. assuming two observer A & B. they will say, "hey I see photons!" if they observe so. Then will A heard of B says that, given: A accelerating, and B is not (in A's eye, B should receive photons)? – Shing Aug 02 '15 at 20:28
  • Just as moving observers experience magnetic fields which stationary observers do not, an accelerating observer can "see" photons which a stationary observer cannot. – Alex Aug 02 '15 at 20:29
  • Also keep in mind that the observer who is accelerating will observe a charge being accelerated. Just as a moving charge that generated a magnetic field can consider itself to be at rest and observe other charge particles as the ones moving and emitting a magnetic field. – Alex Aug 02 '15 at 20:31
  • True. See Unruh radiation https://en.wikipedia.org/wiki/Unruh_effect – Bob Wildfong Feb 11 '22 at 17:04
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    How does this relate to the radiation reaction of an accelerated charge, if technically in this new reference frame, I am the one accelerating and not the charge, will the charge in my reference frame experience this radiation reaction what about the poynting vector from this charge where is the energy coming from? As if I accelerate, I will observe that this charge radiates energy( I think) which normally comes from the force being applied to the charge, but in this case, the force is being applied to ME – jensen paull Feb 12 '22 at 12:41
  • thought experiment: if I e.g 1000 lyr away, accelerate, will the charge in my reference frame appear in my perspective to radiate energy IMMEDIATELY, and if it does, does that mean that energy is transfered faster than light? As the actual "energy" making it radiate is coming from me, 1000lyr away? I assume not as I am not in a inertial reference frame and energy conservation only applies in 1 single frame – jensen paull Feb 12 '22 at 12:41
  • Simpler wording: Energy in one point in space, is transfered as work to an object causing it to accelerate.In this objects frame of reference, charges, infinitely far away radiate energy. Which I would intuitively assume would collectively radiate more energy than the work being done on the object to begin with. Although this energy is only present in the accelerating frame and is not inertial, can anyone explain this – jensen paull Feb 12 '22 at 12:44