[mxplxxx (OP)]

Two charged particles, A & B, are moving at the same speed. According to commonly accepted physics dogma, both are generating Electromagnetic (EM) fields. But from particle A's perspective, particle B is stationary and cannot be generating an EM field and vice versa. How is this seemingly unresolvable paradox resolved in physics?

[evan_au]

When we say that something is moving, the theory of relativity always asks "relative to what?"...
Both of these statements are true:  (a) it generates a magnetic field, (b) it doesn't generate a magnetic field - but in different frames of reference.

[mxplxxx (OP)]

Thanks ... so in one frame of reference the EM field has triggered a fault in a missile launcher resulting in a nuclear holocaust and in the other it is just business as usual. I must admit I have heard of frames of reference but I never considered that they could result in alternative realities. But, I guess, this is all in the realm of quantum superpositions.

[chiralSPO]

I don't think quantum superpositions has anything to do with it. If the EM field-sensitive trigger is in the missile, it is the trigger's frame of reference that determines whether the trigger fires. From another frame of reference in which there appears to be an EM field that should trip the trigger, it would look like the missile should have exploded, but misfired for some reason.

[burning]

OK, lets look at this in detail.  A charged particle has an electric field.  This is true in all frames of reference.  If you look at the charge particle from a frame of reference where it is in motion, it will also produce a magnetic field.  The electromagnetic field is transformed between relatively moving frames of reference.  However, when you take this into account with everything else that gets transformed, observers in the different frames of reference will still have consistent observations.

If we have two particles with charges of equal magnitude but opposite sign, if we look in the frame of reference where they are motionless (or if they aren't constrained where their motion is solely due to their mutual attraction) the electric field will be very weak far away from the particles because their effects cancel.  If we look at them in a frame where they are comoving, they do produce a magnetic field, but again a very weak one because we now have two opposite "currents."

If we have charges of the same sign, the electric field is stronger because the effects don't cancel and the magnetic field is also stronger because the currents also have the same sign.

If we are asking whether the two particles can fire the trigger, the easiest way is to figure out what would trip it in the triggers rest frame and then figure out what field the particles are producing in this frame.

If we then change our frame of reference, it will be true that the electromagnetic field of the particles will be transformed, but we need to remember that the trigger is now in motion as well and we need to consider how the electronics in the trigger behave moving through the new electronmagnetic field.  We can't act as if it is stationary in that field, because it isn't.  If you crunch through the details, there will be no paradox.  All observers will agree whether the trigger should be tripped or not.

[JP]

burning is absolutely correct.  The paradox is resolved when you look at the results of any experiment you carry out.  The electric force only cares about the field "seen" by a particle and that particle's charge, not by how the particle is moving.  The magnetic force is deeply dependent on the motion of the particle. 

But the electric and magnetic fields emitted by some object are also deeply dependent on the motion of that object.  So if you switch reference frames, you will see the charge receiving the force change its apparent velocity with respect to you, but you will also see the electric and magnetic fields emitted by the source change.  When you calculate the force on the particle, you will see that it does not change, because the particle's motion in the new reference frame exactly compensates for the changes in the electric and magnetic fields due to motion.

This is actually an amazing point and means that the laws of electrodynamics (unlike Newton's laws) have special relativity built in.  These laws are the same and predict the same outcomes in all inertial reference frames.

[mxplxxx (OP)]

Let me illustrate the paradox with another example. A person on the space station (s) observes a person on earth (e). Because the earth is moving, from s's point of view, e will be generating considerable amounts of light as a result of this movement and s can observe this. e however thinks he/she is stationary and, because there is no movement involved, can observe no light emanating from him/herself. Both can measure the result they observe and compare notes at which point they will be amazed to find that there are two realities involved. Very obviously this cannot happen (or can it!) so the idea of an em wave (light) being generated as a result of the movement of a charged particle would seem to be incorrect.   

[JP]

Particles traveling with constant velocity do not radiate, so changing from one inertial reference frame to another will not cause radiation to appear.

However, accelerating charges do radiate, and accelerating fields will be measured as radiation, so if you are in an accelerating with respect to the charge, you will see it as accelerating and the fields as accelerating and so will measure radiation. 

It's somewhat counterintuitive, but we're very used to this effect for non-electromagnetic effects.  If I'm in a car that's traveling in any inertial reference frame, I will say I feel no forces (other than gravity) pushing me into the seat.  If the car is accelerating, I will say from the perspective of  my reference frame) that there is a force pushing me into my seat.  So in one reference frame there's no force and in another there is a force.  There's no problem with this since one frame is not inertial. 

Fields are more abstract concepts, but the basic idea is the same: if you move from non-inertial to inertial, quantities can appear in your reference frame.

[mxplxxx (OP)]

Of course the earth is accelerating when it turns, so my example still holds. An observer observes an effect on the observed but the observed does not observe the effect.

[evan_au]

Because the earth is moving, from s's point of view, e will be generating considerable amounts of light as a result of this movement

Perhaps there is some confusion here about electromagnetic fields and electromagnetic radiation?

• Electromagnetism, as the name suggests, studies electric and magnetic fields and the forces they create.
  
• A charged particle will generate an electric field, as seen from the same frame of reference. This will not radiate any energy away from the particle.
  
• A charged particle will also generate a magnetic field, as seen from a different frame of reference. This will not radiate any energy away from the particle, either.
  
• A hot particle (high temperature) will radiate electromagnetic radiation which will carry energy away from the hot particle, allowing it to cool down. This thermal radiation will be visible to people in the same or different frames of reference (only a moving observer will see the spectrum red-shifted or blue-shifted).

So...

• Electromagnetic radiation carries energy away from the source, over a potentially infinite distance.
  
• Electromagnetic radiation consists of oscillating electric and magnetic fields. We call these packets of energy Photons.
  
• Static electric and magnetic fields do not allow energy to propagate infinitely far from the source, and so there is no violation of conservation of energy when you switch between frames of reference. 

[JP]

Of course the earth is accelerating when it turns, so my example still holds. An observer observes an effect on the observed but the observed does not observe the effect.

Yes, your example still holds, but your conclusions are wrong.  Seeing an effect in one reference frame and not seeing it in another isn't a problem in physics.  In particular, we expect to see different forces and fields in accelerating reference frames from non-accelerating ones.

What you would need to check is if the laws of physics hold in these two reference frames, e.g. conservation of energy, momentum and so on.  You should find that these laws hold if you properly account for acceleration. 

[acsinuk]

Which reference frames are EM photons measured in? and which ones dont apply. Why?
CliveS

[evan_au]

Because the earth is moving [rotating], from s's point of view, e will be generating considerable amounts of light

If there were a charge separation on opposite sides of the Earth, then the rotation of the Earth would create electromagnetic radiation. The wavelength of this radiation is about 10 times the width of the Solar System, and you would need an antenna at least the diameter of the Solar System to pick up this signal efficiently. Photons of this wavelength have extremely low energy, so there would be a considerable number of them, but they are almost undetectable with our current technology.

Natural charge separation happens all the time on the Earth - and it is quickly equalised by means of lightning bolts, which produce photons at much higher frequencies, including radio waves, visible light and gamma rays.

I think that any radiation caused by the rotation of electric charges on Earth's surface would be swamped by radiation from the Sun, Jupiter, and Earth's own magnetosphere.

[mxplxxx (OP)]

Come to think of it, is their such a thing as an Einstein "frame of reference" given that seemingly everything in the universe is being accelerated all the time? Earth turns, Solar System turns, Galaxy turns etc..

[PmbPhy]

Two charged particles, A & B, are moving at the same speed. According to commonly accepted physics dogma, both are generating Electromagnetic (EM) fields. But from particle A's perspective, particle B is stationary and cannot be generating an EM field and vice versa. How is this seemingly unresolvable paradox resolved in physics?

I didn’t see this when I first came back to the forum so I’ll start from the beginning. I’m going to assume you mean velocity because if you didn’t then it becomes more complicated, e.g. they could have the same speed but be moving in the opposite direction, etc.
You wrote are moving at the same speed which means that there is a frame of reference relative to which the particles have the speed v. Let’s call that frame S. So in S there is both an electric field and a magnetic field. In the mutual rest frame of the particles, which we’ll call S’ there is no magnetic field and only an electric field. The charges must be held where they are because the mutual electric force is trying to get them to accelerate. Notice that in S there is a no magnetic field but in S’ there is. That’s because the value of the electric and magnetic fields change from one frame to another using the Lorentz transformation for the EM field. See http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity [Links inactive - To make links active and clickable, login or click here to register]

Thanks ... so in one frame of reference the EM field has triggered a fault in a missile launcher resulting in a nuclear holocaust and in the other it is just business as usual.

No. That can’t happen. If you were to actually sit down and carefully study the exact situation then you’d find that there’s no paradox at all. Each scenario/design (e.g. a particular kind of nuke triggering mechanism) requires an entirely different mechanism and an entirely different analysis. The mechanism will work the same way from both frames. The only difference will be the physical reasons. E.g. in one frame it might be an electric field exerting a force and in the other frame it could be just the electric field doing the work. Or something like that. As I said, it depends on the exact design.

Come to think of it, is their such a thing as an Einstein "frame of reference" given that seemingly everything in the universe is being accelerated all the time? Earth turns, Solar System turns, Galaxy turns etc..

No. Not that I'm aware of. I've never heard of such a thing and can't see how it'd be special in any way, shape or form.