# Electromagnetic Waves and Fields

Hi,

This may ultimately be an opinion question:

When thinking about electromagnetic waves semi-classically, how appropriate is it to describe the waves as propagating through an electromagnetic field? If it is appropriate, how appropriate is it to describe the electromagnetic field as a medium through which electromagnetic waves propagate?

In terms of your specific question, EM waves are waves *of* the EM field, not waves *in" the EM field. I.e., an "EM wave" is a region of space where the EM field has properties that we associate with waves (harmonic oscillations in space and time).

But you are getting really close to asking whether there is an "aether" or "medium" that EM waves move through. I think it's safe to say that nearly all professional physicists agree that there is *not* an aether, and that it is not correct or helpful to think of EM waves as moving through a medium.

However, you should be aware that this view is extremely controversial among some laymen, and I'm sure there are numerous threads here on physicsforums where this is debated ad nauseum.

Thanks for the reply. I am a bit confused by the "of" v. "in" distinction though.

What about a wave on a rope? Why is a wave on a rope a wave "in" the rope, but an electromagnetic wave is a wave "of" the electromagnetic field?

But you did answer my question perfectly on a practical level. When describing an electromagnetic wave, I should NOT describe it as traveling through the medium of an electromagnetic field.

Electromagnetic waves propagate through space, and space has a permeability u0 = 4 pi x 10-7 Henrys per meter and a permittivity e0 = 8.85 x 10-12 Farads per meter.

Sqrt (u0/e0) = 376.730 ohms (impedance of free space), and

1/sqrt(u0 e0)= 2.997924 x 108 meters per sec

Thanks for the reply. I am a bit confused by the "of" v. "in" distinction though.

What about a wave on a rope? Why is a wave on a rope a wave "in" the rope, but an electromagnetic wave is a wave "of" the electromagnetic field?

I think there's an aspect of this question that is just semantics, but it's not completely semantics

All (?) of the waves we have direct experience of are mechanical, like your rope example. Also sound waves, water waves. In these cases some material object(s) is *moving*, and we speak of that object(s) as the "medium through which the wave moves" (rope, air, water).

Abstracting away from the specific cases, one thing that all these phenomenon have in common is a harmonic dependence on space and time (*). And of course phenomena like interference and diffraction (which occur in, e.g., water waves) are consequences of this harmonic dependence.

The tricky thing about EM waves is that nothing is moving: there is no medium. So the analogy to rope waves breaks down in this sense! This makes EM waves very difficult / impossible to visualize (did you see my post on Feynman's view of this?).

But there *is* a harmonic dependence on space and time: the magnitudes of the fields have this harmonic dependence. This justifies the description of the electromagnetic phenomenon that we call "light" as a "wave". And of course the phenomenon of light interference and diffraction is a consequence of this harmonic dependence.

Not sure if this is clear, maybe someone else with have another way to think about it.

(*) By "harmonic" I mean sine and cosine. If you want to be more accurate I guess you could say "periodic" dependence, since waves on a rope aren't going to be *exactly* harmonic, but they will be "pretty close". It doesn't really matter for the purposes of this argument.

Integral
Staff Emeritus