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I understand longitudinal waves. For example, I've got a clear mental modal of air waves: a slice of air becomes overcompressed, then the slice next to it becomes overcompressed and the first slice becomes undercompressed. The air itself does not travel, but the overcompressed and undercompressed regions do travel, and that's a wave:

2d longitudinal wave 2d longitudinal wave

I also understand transverse waves. For example, ripples on the water surface. The surface is a 2D field, the ripples oscillate in the third dimension (thus, water waves are a 3D structure). But transverse waves can also exist on a true 2D plane without the third dimension, here's an example:

2d transverse wave 2d transverse wave

But as for radiation waves, I fail to find a mental model for them. The closest one seems to be a rope: if you wobble a wire holding it by its end, it will oscillate in a sine-like pattern. I see it as a 1D field oscillating in a second dimension (thus, a wobbling wire is a 2D structure):

EM wave
(these are an electric and a magnetic wave, the two are different waves that travel in different fields, they just happen to always appear in pairs)

Note how B and E arrows on the above animation demonstrate how the field wobbles without travelling.

I also know that light waves can be radially polarized and they are depicted as a spiral. This also corresponds to the wobbling rope metaphor:

EM wave -- radially polarized

But the electric and magnetic fields are 3D, yet light is not spatial like air is. When a light wave travels through its field, it looks like it occupies an 1D line of a 3D field, and this line wobbles either in one extra dimension (linear polarization) or in two extra dimensions (radial polarization).

This does not make sense to me. A wobbling rope could be a great depiction of a light wave, but it's a poor metaphor: the medium of a rope wave is a rope itself, and a rope is kinda 1D (in a sense that it's a line). But the medium for a light wave is an electirc field, and the field is 3D, it's spatial.

So how can 3D spatial field be a medium for string-like non-spatial waves? And is there a human-world analogy for this phenomenon?

PS This must have something to do with the wave-particle duality, but I don't understand that either.

UPD I no longer understand what is a transverse wave and what is a longitudinal wave.

Water ripples are transverse, right? The waves spread parallel to the water surface but the oscillations happen perpendicular to the water surface. Thus, transverse.

But if you look at the flat water surface from above (from the third dimension), it will not look like the transverse animation. It will look exactly the longitudinal one! What happens here?

Do light waves appear longitudinal when observed from a fourth dimension? Mind: blown.

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    $\begingroup$ Possible duplicate: physics.stackexchange.com/questions/160042/… Also related: physics.stackexchange.com/questions/184381/… $\endgroup$ – dmckee Jul 2 '15 at 22:48
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    $\begingroup$ I think it is important for someone to say that the visualization you are showing show a single "ray" of light (which is why you are talking about it as a 1D structure), but real EM waves are spacing filling entities. The "ray" visualization is a tool for understanding where the energy flows are going, not a literal description of the structure of light. $\endgroup$ – dmckee Jul 2 '15 at 23:05
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    $\begingroup$ Photons don't follow any lines. They are emitted in one place and absorbed in another, between that there is quantum electrodynamics, which certainly doesn't have anything resembling "lines". $\endgroup$ – CuriousOne Jul 2 '15 at 23:20
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    $\begingroup$ There is a piece of advice about learning E&M that I give a lot: don't try to understand light in both the classical and quantum picture at the same same time. Pick one and learn it well. Then you can learn the other one on its own merits and without reference to the first. Then look at how they connect to one another. Trying to mix them is a recipe for misunderstanding until you understand both theories. $\endgroup$ – dmckee Jul 2 '15 at 23:25
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    $\begingroup$ You won't be able to develop proper mental models without understanding at least the basic phenomenology, which obviously takes some effort. If it helps, one can develop a reasonable understanding of the basics without going trough the entire theory, if you are willing to take a lot of details as a matter of trust in the theorists. $\endgroup$ – CuriousOne Jul 3 '15 at 0:39
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When a wave travels through a rope, the rope goes up and down, the position of all the 'rope-particles' changes, they oscillate and this makes up the wave.

With light, it is indeed the electromagnetic field oscillating, but you shouldn't think of the arrows that represent that field in your first picture of light as 'extending into the rest of the space'. They are not spatial, they just represent the magnitude and direction of the electric/magnetic field at that point.

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  • $\begingroup$ So radio waves do not wobble? They travel in straight 1D lines, and each point on the line just kinda strengthens and weakens? Then why the segment size of an antenna or a Faraday cage depends on the wavelength to capture? $\endgroup$ – lolmaus - Andrey Mikhaylov Jul 2 '15 at 22:53
  • $\begingroup$ I'm sorry, but can you please upvote my question? I need +10 rep to answer another question. $\endgroup$ – lolmaus - Andrey Mikhaylov Jul 2 '15 at 22:53
  • $\begingroup$ Hmm, the wavelength means the distance between two humps of a rope. The height of each hump depicts amplitude. And the hump can be very tall even for a very short wavelength. So I do understand that sine-like rope this is a merely a metaphor for a radio wave, but the Faraday cage question from my previous comment still stands: if all radio waves are straight, why can a shorter wave pass through a Faraday cage but a longer wave can't? $\endgroup$ – lolmaus - Andrey Mikhaylov Jul 2 '15 at 23:04
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    $\begingroup$ For the Faraday cage: physics.stackexchange.com/questions/141562/… $\endgroup$ – Dries Jul 3 '15 at 22:29
  • $\begingroup$ Dries, as I understood from dmckee and CuriousOne, Faraday cage shields from spread waves because every point of the wave interacts with nearby points. Photons do not travel individually, the travel in a front that bounces off a mesh. $\endgroup$ – lolmaus - Andrey Mikhaylov Jul 4 '15 at 23:33
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But the medium for a light wave is an electirc field, and the field is 3D, it's spatial.

The medium for the light wave motion is not the electric field . There are two points here:

1) Light is described by Maxwell's equations which are lorenz invariant, i.e. four dimensional, classical waves appear as a solution of the equations and they fit the data

2) The second point is that the Michelson Morley experiment showed that there is no medium on which light propagates, thus the animations you show depict the mathematics of the Maxwell equations which describe light as sinusoidal variations of electric and magnetic fields propagating in vacuum with velocity c.

When going to the underlying quantum mechanical level, light is composed by an enormous number of photons (elementary particles) which in synergy build up the classical electromagnetic wave.In a sense photons are the medium on which the classical wave rides. How this happens is a matter of understanding quantum field theory.

Maybe this picture can give you a feeling.

photspin

So it is more complicated than your visualizations.

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  • $\begingroup$ "The medium for the light wave motion is not the electric field" -- well, what field it is then? $\endgroup$ – lolmaus - Andrey Mikhaylov Mar 12 '17 at 20:13
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    $\begingroup$ As I tried to explain "light" and "electric fiedl" are classical models very useful macroscopically, but it so happens nature is at the basic level quantum mechanical and the classical light emerges from the underlying quantum mechanical level of zillions of photons with wavefucntions and probabilities in superposition to form the classical electric field. Field theory in quantum mechanics proposes an operator field for each standard model particle, and thus the photons appear from creation operators on the photon field, and then the classical emerges from the photons. $\endgroup$ – anna v Mar 13 '17 at 4:58
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    $\begingroup$ You can find the mathematics here motls.blogspot.com/2011/11/… but you have to know quantum field theory basics to understand it. $\endgroup$ – anna v Mar 13 '17 at 4:58
  • $\begingroup$ I think this is unhelpful, as you do not need to understand quantum mechanics to understand electromagnetic waves. The same way you don't need QFT to understand water waves. $\endgroup$ – Daniel Nov 30 '18 at 11:07

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