Why don't constant motion charges produce waves?


Solution 1

For any charged particle in uniform motion there is an inertial frame in which that particle is at rest, and vice versa. So if the particle shed energy as EM waves due to uniform motion you would have the odd situation that a motionless particle would also have to shed energy as EM waves. Likewise if a motionless particle doesn't create EM waves then neither can one in a state of uniform motion.

Solution 2

One difference that might help you is the following. A moving charge certainly has fields that move along with it, so I understand why you might think it would produce waves. But these fields (the electric field, at least) decay as $1/r^2$, just like the field of a static charge. They also "propagate" at the speed of the charge, because they're following it. But the crucial point is that these fields don't carry energy away, or else the charge would slow down.

If you have a charge at rest and you kick it so it starts moving at constant speed, there will be a ripple in the field that goes away at the speed of light and decays as $1/r$. This wave does carry energy, which is taken from your kick. If you give the same impulse to an uncharged an a charged particle, the uncharged one will move faster as a result of this.


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Anti Earth
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Anti Earth

Updated on April 15, 2020


  • Anti Earth
    Anti Earth over 2 years

    I'm a little confused about the origin of electromagnetic waves. Although I can understand their origin mathematically, I get a little confused about the physical intuition of...

    Information transfer is restricted to the speed of light; a local change in a field can only perturb distant regions once a light sphere has reached said regions

    This makes perfect sense, but I can't understand then why only accelerating bodies product EM waves, and not any motion which would affect a local field (such as linear, constant motion).

    Of course, I realise constant motion is entirely relative and by producing EM waves, I'm suggesting the experience of light entirely subjective. But that's not the case, right?

    How then does constant motion not produce EM waves, but also disturb a local field and not violate the speed limit on field propagation?

    Also, besides appearing in an entirely separate physical model and mathematical framework, does the origin of gravitational waves (and the lack thereof for constant motion mass) follow a similar explanation?

    Any and all input is appreciated!

    • CuriousOne
      CuriousOne almost 7 years
      A charge in constant motion does produce a field disturbance that transfers energy to a medium that breaks the Lorentz invariance of the vacuum. As soon as there is even one "receiver" in play, that Lorentz invariance is broken, even for a charge moving in vacuum, so the answer to your problem is that it doesn't exist. A charge moving at constant speed relative to an observer does radiate.
    • Anti Earth
      Anti Earth almost 7 years
      Doesn't radiation imply energy loss, slowing the charge? Wouldn't that suggest different observers can see different, disagreeing evolutions?
    • CuriousOne
      CuriousOne almost 7 years
      Yes, the coupling between a charge and an observer will slow the charge, relative to that observer down, although in many cases that will be either irrelevant or imperceptible.
    • EigenDavid
      EigenDavid almost 7 years
      Take a look at this question, the different answer might help you: physics.stackexchange.com/questions/186361/…
  • Anti Earth
    Anti Earth almost 7 years
    This is what I reasoned in the comments; your suggestion that this eliminates the possibility is contrary to what CuriousOne suggests.
  • KF Gauss
    KF Gauss over 5 years
    This does not eliminate that possibility. There is no guarantee the second particle is at rest in the first particle's inertial frame, except in the degenerate case of both particles moving with the same velocity.
  • Antonios Sarikas
    Antonios Sarikas over 3 years
    only em waves are travelling with speed of light ? if we have a point charge in space the electric field in a point P would emerge instantaneous ?