# I Are electromagnetic waves sine waves?

#### Jeff Root

Light is said to consist of photons or electromagnetic waves.
I'm not asking which view is correct, what conditions make one
of each view. I am assuming the two views are compatible to
the extent that the wave character of light can be described
in quantum electrodynamics.

I'm also assuming that someone here can explain some aspects of
how quantum electrodynamics describes electromagnetic waves in
a way I can understand. Like, without calculus.

Electromagnetic waves are generally depicted as sine waves.
The carrier waves of artificial radio transmissions are usually
sine waves. Sine waves are a very common occurrance in nature,
due to harmonic oscillation. There are many ways harmonic
oscillation can arise naturally, so it would not be surprising
if electromagnetic waves are in fact sine waves.

I know, of course, that most light sources give a mixture of a
range of wavelengths/frequencies, so the waves are not coherent.
Even in monochromatic light, the waves aren't necessarily in
phase and with the same polarization.

But in general, for ordinary light sources...

Are electromagnetic waves sine waves?
If so, how was that determined?
If not, what are they?
If the answer is not known, why not?
If the answer depends, what does it depend on?

-- Jeff, in Minneapolis

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#### PeterDonis

Mentor
Light is said to consist of photons or electromagnetic waves.
More precisely, it is said to be photons in the early quantum theory of light, and it is said to be electromagnetic waves in the classical theory of light. But in quantum electrodynamics, the more modern quantum view of light, light is a quantum field; neither of the terms "photon" or "electromagnetic wave" are correct for a quantum field, although there are particular approximations in which one of those terms is useful.

I am assuming the two views are compatible to
the extent that the wave character of light can be described
in quantum electrodynamics.
This assumption is false. The approximations in which "photon" is a useful term are not the same as those in which the term "electromagnetic wave" is a useful term. The two kinds of approximation are not compatible.

I'm also assuming that someone here can explain some aspects of
how quantum electrodynamics describes electromagnetic waves in
a way I can understand. Like, without calculus.
I don't see how any useful description of electromagnetic waves could avoid calculus. You labeled this thread as "I" level, meaning undergraduate, so calculus is well within scope.

If you are interested in the description of light as electromagnetic waves, this thread belongs in either the Classical Physics forum or the Relativity forum, not here. Any aspects of light that show properties normally considered "quantum" would not fit within the model of light as electromagnetic waves.

If you are interested in the quantum electrodynamics description of light, then asking about electromagnetic waves is really off topic. You will need to figure out what particular quantum aspects of light you are interested in.

#### Nugatory

Mentor
Electromagnetic waves are generally depicted as sine waves.
Sine waves (actually their generalization as complex exponentials, but it comes down to the same thing) are one of the solutions of the differential equation we get from Maxwell’s equations which describe classical electromagnetism. This differential equation is linear, meaning that if $A$ and $B$ are solutions then $A+B$ is also a solution. Thus, we can take sine wave solutions and add them to get solutions that aren’t sine waves; conversely any electromagnetic wave can be rewritten as a sum of sine waves.

Because any arbitrary electromagnetic wave can be written as a sum of sine waves, once we can calculate the behavior of the sine waves we can calculate the behavior of any wave form - and it turns out that the sine waves are especially easy to calculate with. Thus, a college-level physics program will introduce Maxwell’s equations, derive the wave equation from them and find the sine wave solutions; then introduce the mathematical techniques used to write more complex waveforms as sums of sine waves; and then use these to solve many seriously interesting problems (like how radio transmission really works). This sequence is covered by, for example, the second and third books in the Berkeley Physics Course.

Photons are altogether unrelated to any of this stuff. You won’t meet them for another year or so after you’ve been through classical electromagnetic waves.... and although you won’t take this advice, the best thing you could do now is to forget that you ever heard the word “photon” until you get to quantum electrodynamics.

#### vanhees71

Gold Member
If you are interested in the quantum electrodynamics description of light, then asking about electromagnetic waves is really off topic. You will need to figure out what particular quantum aspects of light you are interested in.
Well, this pours the baby out with the bath ;-)). I'd say one of the most profound applications of QED with huge impact of everyday life is the invention of the laser. Of course, laser light is described by QED. It's a socalled coherent (or nowadays even more generally squeezed) state of the electromagnetic field. QED does not only consist of dealing with a few charged particles and single photons as in high-energy particle physics but also applies in the huge realm of quantum optics!

"Are electromagnetic waves sine waves?"

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