Difference between a light wave in space and a wave in a pond

Question

Apart from their nature and the medium utilized, what are the differences between an EM wave and a wave we see in a pond?

When we throw a stone into a pond, can we imagine we are observing light propagating through space or are we missing something?

Answer 1

Both the surface wave in water, and light waves in space, obey a wave equation: there's some sense in which a time-delay and a spatial distance displacement both are cyclic (the time-delay giving a frequency of repetition, and the spatial displacement giving a wavelength). Aside from that, they're completely different. The ripple in the water is peculiar to the water surface and always an up/down direction. Underwater you get also longitudinal-motion "P waves", the surface "S waves" are transverse-motion waves (movement is perpendicular to wave travel direction, with some fluid rotation).

Water waves are different in shallow water and in deep water. Gentle swells in deep water turn to breaking surf in shallow water, partly because of the fluid rotation coupled to the surface movement.

Light waves in space have transverse character (two different polarizations). The E and B fields are always orthogonal to the propogation direction.

It gets complicated in nonisotropic materials, the electromagnetic fields in a piece of calcite (Iceland spar) do NOT obey a wave equation: there's a complex quantity, called the 'Ewald vector' that does, however, and the result is a double wave equation, one for 'ordinary rays' and the other for 'extraordinary rays'.

So, there are similarities (time and space cyclic repetition), and differences (everything else). Wave propogation is a very deep subject, spreading over multiple disciplines, including oceanic movement and X-ray crystallography and traffic blockages.

Answer 2

An electromagnetic wave is more like an oceanic swell wave than a circular spreading ripple in a pond. If you've ever been on a ship you'll know what I mean. A swell wave is maybe two metres in height, two hundred metres in wavelength, and five hundred metres wide. It's this big hump of water barrelling across the ocean at maybe ten knots, going in a straight line, without dissipating. Of course this isn't an ideal analogy for an electromagnetic wave, because space doesn't have a surface, but IMHO it gets you part-way there. Have a look at wind waves on Wikipedia. See the animated gif with the red dots? If you cut and paste that, you can remove the surface to emulate a wave in space, like this:

Original GNUFDL image by Kraaiennest, see Wikipedia Commons

As for the exact nature of the wave in space, it's surprisingly difficult. If you were to ask What is a photon? you won't get a clear consensus answer. But I personally would take a tip from E=hc/λ and Maxwell's transverse undulations, and say this: when a seismic wave travels through the ground, the ground waves. When a swell wave travels through the ocean, the ocean waves. And when an electromagnetic wave travels through space, space waves. Some will say this is archaic or downright wrong. But if you take a look at LIGO, they're talking about the arms of the interferometer changing length. That sounds an awful lot like space waves. Of course electromagnetic waves aren't the same as gravitational waves, but they're still waves in space.

Note that electromagnetic waves don't propagate because a changing electric wave creates a magnetic wave and vice-versa. That's a bad-science myth. An electromagnetic wave is an electromagnetic wave, wherein the sinusoidal "electric" waveform is the spatial derivative of electromagnetic four-potential, and the magnetic waveform is the time-derivative. See Wikipedia. It's like the underlying potential is the real wave, and the sinusoidal electric wave is merely a plot of its slope, like this:

Answer 3

What I am seeing in most of the Physics are exploratory models, which we can use to explore on the different conformations of the considered subject.

Extract from Poincare's Science and Method:

"But analogy with the phenomenon which these laboratories enable us to reach may nevertheless serve as a guide to the astronomer. The Milky way, for instance, is an assemblage of suns whose motions appear at first sight capricious. But may not the assemblage be compared with that of the molecules of a gas whose properties we have learnt from the kinetic theory of gases?"

We should use comparisons only for explorations and not for reasoning, in the same way, here, I think it is better that kinetic theory be used as only and exploratory idea rather than the real one for milky way case. We should be alert with these types of theories while reading.

In most of the cases, we can't say anything to be of a particular structure, unless we observe it in reality. So, by default it seems better to say, "according to electromagnetic exploratory model" the light may have certain picture in analogy with water waves.