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Accelerated electrons emit electromagnetic waves, but those at rest do not. So accelerated electrons emit energy and those at rest do not. (At rest hypothetically, I know it is not permissible according to uncertainity principle)

But lets assume that we keep an electron at rest and start accelerating ourselves pretty fast, now even though we do not move the electron, it seems to move and produce EM waves, we should get these waves, and if we do get these waves then the electron must have released these waves or energy.

However someone standing near the electron should not see these and hence must not say that electron is emitting energy.

Why are the two observations differing ? Although energy is not conserved across frames, what else can be the source of light in one frame other than the electron which seems to move.

If my thought experiment that electron does emit energy is correct, then why doesnt the standing observer see it ? And even if he does see it in some other form, does this imply that particles continuously lose energy ?

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In your first paragraph, do you mean accelerated or accelerating electrons? There is a big difference between the two. –  Kvothe Apr 10 at 20:46
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Pay attention to the postulates of special relativity here. You can only assume that the laws of physics apply to your observations if you are in an inertial frame. –  dmckee Apr 11 at 1:46
    
@dmckee : do you mean to say that laws of physics are not valid in non-inertial frame ? I have never heard so. I assume that I am misunderstanding your comment, so please explain. –  Rijul Gupta Apr 11 at 3:57
    
The laws of physics as they are usually written down (like "accelerating charges radiate") only apply in inertial frames. There are mathematical prescriptions that allow you to produce the laws that apply in non-inertial frames, but they do not always have the same form and content as the ones we usually talk about (i.e. a rotating frame has centrifugal and coriolis pseudo-forces). You are trying to apply the untransformed laws to a non-inertia frame. That's an error. It's not valid to compute the electron's acceleration based on it's distance from you without subtracting your acceleration. –  dmckee Apr 11 at 4:27
    
@dmckee : That is very helpful. So, is the law "accelerating charges produce em waves" valid for non-inertial frames, the acceleration being with respect to the observer present in said frame ? If not, does electrons or charges which seem to accelerate in frames do not produce em waves ? Does it also mean that if we see an accelerated electron from its frame we would not see any em waves ? –  Rijul Gupta Apr 11 at 10:20

1 Answer 1

Let's focus on radiating EM waves first and forget about energy. When you jump into accelerating train and see charge accelerate away from you, this is all in a non-inertial frame. In this frame, electromagnetic theory has to be formulated with modified equations and new appropriate boundary conditions. That being said, nothing forbids static field in inertial frame to have time-dependent and wave-like component in non-inertial frame.

With energy it is similar. Whether energy is propagating through the field or not may in general depend on which frame is used to describe it; energy is frame-dependent quantity. Conservation of energy will be satisfied in all frames, even in non-inertial frame, because total energy can be defined in such a way that increase in the energy of the particle and the field will be compensated by decrease of potential energy of the system in the field of acceleration force (pseudo-gravity).

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This does not answer the question (does it actually emit EM?). –  Kvothe Apr 10 at 22:10
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If it did emit a photon (EM), it would accelerate in the opposite direction. This is an effect visible to all observers. So, no, one accelerating observer cannot make an electron at rest emit a photon. –  MSalters Apr 11 at 23:28

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