# Conflict between electrodynamics and classical relativity?

1. Jul 3, 2007

### michael879

Id just like to start by saying I believe relativity is 100% at least in macroscopic terms. However, I'm having trouble seeing what the conflict was between electrodynamics and relativity.

Electrodynamics in a nutshell states that light goes a constant c. relativity states that physical laws are the same in every inertial reference frame. These don't necessarily conflict do they? Yes, if light went c with respect to some global reference frame, they would conflict. However, what if the speed of light was just c with respect to the emitter's reference frame? Wouldn't that fit both theories? It would be like a particle that is always emitted at the same speed relative to the emitter. Is there anything I'm missing that is fundamentally wrong with that?

2. Jul 3, 2007

### country boy

Some thoughts to test your suggestion:

What about if c was the same in all reference frames, as relativity states? Is there a conflict then?

If the emitter is going at c and emits a photon in the forward direction, how fast will it be going?

3. Jul 3, 2007

### Integral

Staff Emeritus
Didn't know that there was or ever has been a conflict between Relativity and Electrodynamics. Historically the conflict was between Newtonian Physics and Electrodynamics. The conflict arises in 1867 when Maxwell expressed the relationships between the fundamental electrical laws in form of a wave equation. This was when the speed of electromagnetic waves was found to be a fundamental constant. The idea of a fixed speed of an electromagnetic wave violated the idea of addition of speeds. Einstein, developed Relativity to reconnect Newtonian Mechanics to Electrodynamics. In doing so he showed that Newtonian physics was a approximation to Special Relativity.

4. Jul 3, 2007

### JesseM

Classical E&M predicts that light travels at c regardless of the velocity of the emitter, so if in my frame an emitter traveling at 0.5c sends out an electromagnetic wave which moves at 1.5c in my frame, Maxwell's laws don't work in my frame.

5. Jul 8, 2007

### michael879

ok first, I was referring to classical relativity, not special relativity.

second, does E&M actually predict that c is constant regardless of the emitters speed? If thats true it answers my question, thanks.

6. Jul 8, 2007

### JesseM

What do you mean by classical relativity? Galilean relativity?
It predicts that electromagnetic waves always move at c regardless of the emitter's speed, yes.

7. Jul 9, 2007

### Mentz114

JesseM said :
Maxwell predicts the speed of light to be
$$c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$$

but I don't think that the constancy of c regardless of the emitter/receiver relative velocity can be deduced from this. That idea came with SR. If you apply Gallilean relativity to EM, you get discontinous field lines and other nasties. That was one of Einstein's motivations for SR.

8. Jul 9, 2007

### JesseM

It has nothing to do with applying Galilean relativity. If you pick a single frame where Maxwell's laws hold, you can analyze the behavior of an emitter which is moving in that frame--there's no need to consider any other frames, like the rest frame of the emitter.

9. Jul 10, 2007

### country boy

Only if you add the requirement that the E&M equations be invariant among inertial frames. If classical E&M had predicted that c was independent of the emitter, Michelson and Morley may not have been surprised by their result.

10. Jul 10, 2007

### Mentz114

I'm not sure I understand this - but it does nothing to change my view. If there is an emitter moving relative to a receiver - one has to apply some rule of velocity addition, which is where the problems start.

Yes, thank you CB.

11. Jul 10, 2007

### JesseM

No, you don't need velocity addition! You just have the object's velocity in your frame, and you apply Maxwell's laws to it--Maxwell's laws are certainly capable of dealing with objects that have a nonzero velocity in the frame you're using, the entire phenomenon of magnetism is based on moving charge after all!

12. Jul 10, 2007

### JesseM

Classical E&M does predict that c is independent of the emitter, but only in a frame where Maxwell's laws hold exactly. Michelson and Morley (along with other physicists at the time) thought Maxwell's laws would only hold exactly in the rest frame of the aether, and that in other frames they would have to be modified by a Galilei transformation. M&M thought that the Earth would have a different velocity relative to the aether at different points in its orbit, so if they repeated their interferometer experiment at different times of year they would see a deviation from Maxwell's laws at some point, in the form of light traveling at different speeds in different directions.

Last edited: Jul 10, 2007
13. Jul 10, 2007

### Mentz114

Even so, I would take the velocity c to be wrt the emitter. Pre SR I would then apply a velocity addition law. I do not agree that the first principle of SR can be deduced from Maxwell's equations.

14. Jul 10, 2007

### JesseM

But that would be wrong. Just as the theory of vibrations in the air predicts that all sound waves move at the speed of sound as measured in the rest frame of the air, regardless of the velocity of the emitter, so Maxwell's laws predict that all electromagnetic waves move at c in the frame where Maxwell's laws hold--there are no valid solutions to Maxwell's equations that describe a traveling wave moving at any other speed, and an oscillating charge will produce waves traveling at c regardless of its own average velocity. This is why people imagined that electromagnetic waves were vibrations in a "luminiferous aether", analogous to sound waves which are vibrations in the air, and they imagined that Maxwell's laws would only hold exactly in the rest frame of the aether, just as sound waves only move at exactly the same speed in all directions in the rest frame of the air.

This page also gives some mathematical detail to show that if you have a frame where Maxwell's laws hold and you do a Galilei transform on it, Maxwell's laws will be violated in the new frame (look at the section 'Proof of Galilean non-invariance').
I didn't say they could, although SR can be deduced from the assumption that all laws of physics, including Maxwell's laws, must obey the same equations in every inertial frame.

Last edited: Jul 10, 2007
15. Jul 11, 2007

### Mentz114

Thanks, JesseM. I will study this.
[some time later ...]
I've done a simple calculation. Writing the equation of a plane wave travelling in the x-direction with wave number k and phase velocity s = w/k ( w for omega) thus

$$\phi = Ae^{i(kx-\omega t)}$$

Now I make a Gallilean boost x -> x' = x + vt to a frame moving at speed v in the x direction. Substituting x' for x in the wave equation immediately gives the Doppler change in frequency and a phase velocity s' = s - v.

Does this mean the speed of the wave is now measured as a different value, despite always being emitted at a constant speed wrt the medium ?

Last edited: Jul 11, 2007
16. Jul 12, 2007

### JesseM

If you make a Galilean boost, naturally the velocity of the wave will change by v. But Maxwell's laws will no longer hold in the frame you've boosted to, as explained in the second link from my last post. If you want to know what Maxwell's laws predict about a moving emitter, you pick a frame where Maxwell's laws hold, and see what they predict about the waves sent out by an emitter which is moving in that frame, there's no need for any sort of boost.

Do you understand that in general, when calculating the behavior of moving objects, there is no need to use multiple frames? For example, would you agree that when calculating the results of an elastic collision in classical mechanics, you can use the equations of classical mechanics to find the outcome in a frame where both objects are moving, there's no need to transform into either object's rest frame?

17. Jul 12, 2007

### pervect

Staff Emeritus
OK, at the request of some of the posters, I've split this thread into two parts, since it took off in a different direction. See "relative speed of a photon - mk2" for the split-off part.

Last edited: Jul 12, 2007