# Is electromagnetic wave theory correct?

#### Nickelodeon

The following statement came out of Wikipedia

"Maxwell's correction to Ampère's law was particularly important: In 1864 Maxwell derived the electromagnetic wave equation by linking the displacement current to the time-varying electric field that is associated with electromagnetic induction. This is described in A Dynamical Theory of the Electromagnetic Field, where he commented:

The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws."

What I find difficult to understand is that light, or any em wave, cannot be bent or distorted by a magnetic or electric field in a vacuum.

Now, get some iron filings, sprinkle them round a magnet and get another magnet and the iron filings will change their pattern indicating that the field has been distorted. I would have thought that light being an 'electromagnetic disturbance propagating through the field according to electromagnetic laws' would be seriously effected by an adjacent magnetic or electric field.

So the question is, 'why isn't it?'

Nick

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Staff Emeritus
The best answer is "because experimentally, it is observed to be this way".

If you want a more theoretical answer, it's because electric and magnetic forces act on charges and electromagnetic radiation is uncharged.

#### Nickelodeon

The best answer is "because experimentally, it is observed to be this way".

If you want a more theoretical answer, it's because electric and magnetic forces act on charges and electromagnetic radiation is uncharged.
I know that it is observed that way and I have no doubt that magnetic forces have no effect whatsoever on the passage of light. But wouldn't you have thought it should as magnetic forces can act on other magnetic forces apart from, obviously, moving charged particles.

#### weichi

I know that it is observed that way and I have no doubt that magnetic forces have no effect whatsoever on the passage of light. But wouldn't you have thought it should as magnetic forces can act on other magnetic forces apart from, obviously, moving charged particles.

Nick
But magnetic forces *don't* act on other magnetic forces. As V50 pointed out, they act on *charged particles*.

In your magnet example, a better way to think about it is that the magnetic fields from the two magnets are added together, so that the total magnetic field is the sum of the two fields. This follows from the linearity of maxwell's equations.

In the case where an EM wave passes through a region where there is "pre-existing" E or B field, the EM field in that region *will* be different than outside the region. But once outside the region the wave is back to "normal" again. Also a consequence of linearity.

#### Nickelodeon

In the case where an EM wave passes through a region where there is "pre-existing" E or B field, the EM field in that region *will* be different than outside the region. But once outside the region the wave is back to "normal" again. Also a consequence of linearity.
This infers that if you passed a laser beam through an area of a strong magnetic field you would see it go all fuzzy then come out straight and normal again. I don't think it would (not go fuzzy).

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#### Phrak

What I find difficult to understand is that light, or any em wave, cannot be bent or distorted by a magnetic or electric field in a vacuum. Nick
Light is an electromagnetic effect. Do you see light bending in the presence of light?

#### Nickelodeon

Light is an electromagnetic effect. Do you see light bending in the presence of light?
I don't think I'm getting my point across.
No one doubts that light is not bent or distorted by magnetic fields. My point is that, because light is purported to be a mutual supporting combination of electric and magnetic field then I have difficulty understanding why it can't be momentarily interfered with as it passes through an area of strong magnetic field.
Looking at it another way, converging transverse waves on water produce turbulence in the area they meet then come out the other side fine. How is it that with a laser beam through a strong magnetic field you cannot see this area of turbulence?

#### vanesch

Staff Emeritus
Gold Member
Looking at it another way, converging transverse waves on water produce turbulence in the area they meet then come out the other side fine. How is it that with a laser beam through a strong magnetic field you cannot see this area of turbulence?
The reason is that the equations that describe the propagation of EM radiation in space (the Maxwell equations) are *linear* equations, while the equations that govern the propagation of surface waves on water have non-linear terms.

A linear set of equations has as a defining property that if A is a solution, and B is a solution, then A + B is also a solution. This is not the case for an equation that has non-linear parts.

If you take as "A" the initial traveling wave, and as "B" your "perturbing" field (another wave, a strong magnetic field etc...) then you see that the presence or not of B has no influence on A in the case of a linear set of equations, but does so in the case of a non-linear set, because then A + B is no solution anymore, but something like A' + B', with A' a modification of A and B' a modification of B (although we don't care about that last one).

#### Dale

Mentor
To expand on what vanesch said. An equation which is linear (like Maxwell's) is said to obey the principle of http://en.wikipedia.org/wiki/Superposition_principle" [Broken].

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#### weichi

This infers that if you passed a laser beam through an area of a strong magnetic field you would see it go all fuzzy then come out straight and normal again. I don't think it would (not go fuzzy).
I didn't say anything about fuzzy ! You would get the sum (superposition as DaleSpam said) of the EM wave and the "pre-existing" magnetic field. This is not the same as saying that the light would get "fuzzy.

It means that if you put, say, a light detector in the region then it's behavior would be determined by the "total" field. If the detectors is unaffected by a constant magnetic field (which is true of many, though perhaps not all, detectors of light), then you would get the same response as outside the region. So not fuzzy.

On the other hand, if you put a test particle into the region, it's behavior *would*be different than outside the region, because it feels the effect of both the constant magnetic field and of the EM wave.

#### Phrak

Pure propagating electromagnetic fields, free of matter, combine in the simplest possible way, but the fields act back on their derivatives, such as $\nabla \cdot E$.

#### vanesch

Staff Emeritus
Gold Member
Pure propagating electromagnetic fields, free of matter, combine in the simplest possible way, but the fields act back on their derivatives, such as $\nabla \cdot E$.
Well, "derivative" is also a linear operation: if A is a field, then $\nabla \cdot A$ is its divergence, and if B is a field, then $\nabla \cdot B$ is its divergence, and if we now have the combined field C = A + B, then $\nabla \cdot C =\nabla \cdot A + \nabla \cdot B$

So in whatever linear equation we have A (including its divergence) as a solution, and B is also a solution, then A + B remains also a solution.

If A is a wave, propagating to the north, and B is a strong field in some domain, that means that outside of that domain, the solution A is valid, and we can add, or not, the field B, it won't change the field outside of that domain (which remains A). In other words, on the "receiving side" we will just see A (if we are outside of B's domain), and this will not change, whether we "switch on" B or not.

#### Phrak

We have nothing to discuss, Mr. Vanesh. Period.

#### vanesch

Staff Emeritus
Gold Member
We have nothing to discuss, Mr. Vanesh. Period.
I didn't know what you meant with your comment, and I interpreted this that you might be suggesting that the fact that derivatives are present in electromagnetic theory might cause one field to influence the derivative of the other or something of the kind. Not that you said this explicitly, but otherwise I don't understand what you wanted to say in the frame of this discussion.
(of course the derivative of a field depends on the field itself...but what does it have to do with this discussion ?)

#### Nickelodeon

Thanks for everyone's input.

I've sort of been left with the conclusion you can't have an omnidirectional transverse wave because you run out of dimensions. That's why it is impossible to visualise.
Waving lengths of string, especially in a circular motion, as previously described in this thread and elsewhere points nicely to another solution to the nature of light.

Take one hydrogen atom and excite it just long enough to produce one photon. What I suggest you will see is a unidirectional, or maybe bidirectional, twinkle with a wavelength proportional to the energy required to produce it. This small wavelength packet carries on its way until it bumps into something.

So take lots of hydrogen atoms and excite them to produce photons and what you experience now is a cacophany of twinkles in all directions, following on behind and adjacent to each other, but separate.

The good thing is that 'twinkles' can have the transverse wave characteristics, the helical correlation between a magnetic and electric field, for example. Another bonus is that waving a magnet in the vicinity of a packet will have little effect as the packet is essentially bipolar.

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#### Shackleford

We have nothing to discuss, Mr. Vanesh. Period.
Uh-oh. I detect some animosity.

#### Topher925

To expand on what vanesch said. An equation which is linear (like Maxwell's) is said to obey the principle of http://en.wikipedia.org/wiki/Superposition_principle" [Broken].
Perhaps I'm not completely understanding the question, but I think DaleSpam said all that needed to be. The magnetic fields in your iron filings experiment aren't being modified or transformed by each other, they are simply being superimposed and they will interfere with each other. For an example that involves light, think of interferometry.

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#### Dale

Mentor
Thanks Topher925, I also agree with that assessment, but I am obviously biased!

#### Bitzy7

I think the Iron filings that you are speaking of are not in fact showing evidence of a distortion of the magnetic fields upon eachother, but just how a ferrous material is reacting to the two seperate fields.??

#### Nickelodeon

I think the Iron filings that you are speaking of are not in fact showing evidence of a distortion of the magnetic fields upon eachother, but just how a ferrous material is reacting to the two seperate fields.??
That's a very interesting point and a bit difficult to figure out whether the fields are actually separate or combined. Personally, I think they are combined because a magnetic field round a magnet is not a wave as such (could be a standing wave I suppose).

#### Dale

Mentor
That is kind of the point of the principle of superposition. You can consider it as one total field or the sum of multiple separate fields. The results are the same.

#### Phrak

That is kind of the point of the principle of superposition. You can consider it as one total field or the sum of multiple separate fields. The results are the same.
Interesting. Of course, I know this already. The interesting part is that superposition works for a space-like slice, R^3, rather than all, or some part of spacetime, where a superposition fails when there is charge present.

It's rather peculiar, if you think about it. Superpostion works for every inertial frame, v<c, at all points in spacetime---any boost, any rotation and any translation of coordinates. It works perfectly well on a (3,1) pseudo Riemann manifold (because the field equations are manifestly covariant). Yet it doesn't work on the manifold as a whole.

Does it work in v>c? Dunno.)

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#### cragar

Light is an electromagnetic effect. Do you see light bending in the presence of light?
Can't 2 light beams attract towards each other or maybe you meant something else.

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