# Different frames of reference

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## Main Question or Discussion Point

Ok I have a really basic question.

Say you and I are floating in space and there is a single electron in front of us stationary to our frame of reference.

Now I start hopping up and down.
I see the electron accelerate up and down from my hopping frame of reference.
I see a EM wave be emitted....you do not.
Which is true? I'm missing something, sorry for the simple question.

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Dale
Mentor
Your frame of reference is not inertial.

Nope....but the question is, is a EM wave emitted? When I stop hopping, does a EM wave exist?
Say I hopped for 4 seconds, a emwave has traveled quite far in that time, does it cease to exist when I stop hopping?

Dale
Mentor
My comment wasn't a question. It was a statement. Your reference frame is non inertial.

Maxwell's equations don't take their usual form in your reference frame because it is non inertial.

ok, I'm not sure about that, just curious if a em wave gets generated by the moving electron (my frame of changing reference) and if it does, does it still exist when I stop hopping?

Nugatory
Mentor
Nope....but the question is, is a EM wave emitted? When I stop hopping, does a EM wave exist?
No, there is no EM radiation emitted by the charge (which is mostly common sense, as the charge shouldn't know or care about whether you're hopping around while you're watching it). Consider also that in both frames an accelerometer connected to the charge will read zero, so this isn't really an accelerated charge situation at all.

Note that although speed is relative, acceleration is not. We can use accelerometers to determine the true -in-all-frames fact that you are accelerating and the charge is not.

I know its frustrating to have someone who's not up on maxwell's equations etc, but either 1 of three things must be true....
1. I hop up and down and see a wave get emitted, and the stationary observer does too
2. I hop up and down and nothing gets emitted at all (this is my guess), even though the electron accelerates and decelerates over and over from my FR
3. A wave gets emitted while I hop but disappears when I stop
4??
Just wondering which is true?

No, there is no EM radiation emitted by the charge (which is mostly common sense, as the charge shouldn't know or care about whether you're hopping around while you're watching it). Consider also that in both frames an accelerometer connected to the charge will read zero, so this isn't really an accelerated charge situation at all.

Note that although speed is relative, acceleration is not. We can use accelerometers to determine the true -in-all-frames fact that you are accelerating and the charge is not.
AHHH I get it, so my frame of reference is invalid because I'm accelerating

Is being in a gravitational field the same as accelerating? Perhaps thats another question.
Though I wonder are two frames of reference the same if both are accelerating at the same rate?

Dale
Mentor
AHHH I get it, so my frame of reference is invalid because I'm accelerating
It is not that it is invalid, just different. You would have to carefully define the frame mathematically, then derive the correct form of Maxwell's equations in that frame, then solve those equations. Once you did all of that it would be perfectly valid, just complicated.

@Nugatory sounds pretty confident, and his statement would be what I would guess also, but I don't know for sure having not worked it out myself.

Nugatory
Mentor
AHHH I get it, so my frame of reference is invalid because I'm accelerating
It's not exactly invalid.... However, many formulas/equations/laws take on a much more complicated form in non-inertial frames, and a common mistake is to try applying the straightforward inertial-frame formulas in a non-inertial frame. That's what Dale was getting at when he said "Maxwell's equations don't take their usual form in your reference frame because it is non inertial".

Mister T
Gold Member
even though the electron accelerates and decelerates over and over from my FR
Nugatory's point is that it doesn't accelerate in your rest frame. If there were an accelerometer in the electron's rest frame, and you viewed it from your rest frame, you'd see the accelerometer always reading zero. However, your accelerometer would reveal that you are accelerating.

I think the reason that Maxwell's equations was mentioned is because if the electron were moving relative to you you'd observe both magnetic and electric fields, but if the electron were at rest relative to you you'd observe only an electric field. In the case of relative motion, it makes no difference if it's the electron that's moving or it's you that's moving. But this is only the case if the motion is inertial. That is, an accelerometer would always read zero because it can't distinguish between a state of rest and a state of steady motion. Both are considered inertial motion, and in both cases an accelerometer reads zero. One of the foundations of physics is that there's no way to distinguish between a state of rest and a state of steady motion.

I'm still a little confused (not being a physicist I assume this is normal :-), that my accelerometer shows a steady 9.8m/s downward, yet a electron at 'rest' with me does not seem to radiate anything,
So I guess if I was in space accelerating at 1G in +X direction and a electron is also accelerating along side me at 1G in the +X I would not see any emission of em if our acceleration was caused by a gravity field vs some other means?? Or would it radiate, but stop if we both decelerated by 'landing' on the surface of the object causing the gravity?
It seems gravity isn't quite the same as acceleration in this case? Man I'm confused.
Thanks for taking the time with my weird questions

Dale
Mentor
Locally, constant acceleration is the same as uniform gravity. But again, you would have to work it out in detail to know what measurements to expect.

One thing that most people forget when trying to "Intuit" this stuff is to accelerate both the charge and the detector when they are thinking about the accelerating case. That would be equivalent to a detector in free fall passing a charge at rest in a gravity field.