# Is light amplitude spatial?

In diagrams I often see light waves depicted as little sine waves that travel through space. And often when describing polarizers, the explainer will angle their hand to show the angle of polarization and bob it up and down in a sine wave action, apparently emulating the amplitude of the wave.

My questions is, is the amplitude of light really like this? Where it moves up and down or side to side in space? Or, is the sine wave relationship just an analogy?

• The light "wave" is in fact a mere straight line, in line with the principle of least action. All "gymnastics" of your teachers are referring to the electromagnetic wave character which is not represented in spatial dimensions. – Moonraker Jan 18 '15 at 8:49
• – dmckee --- ex-moderator kitten Feb 16 '15 at 18:02

If the person drawing the graph bothers to label the axes you'll see that the thing that "goes up and down" is not displacement as it is in a wave on a string but electric field strength.

So, no, nothing is moving off the line of the ray, but the because electric field is a vector the oscillation does have a direction associated with it (and therefore polarization makes sense).

• If a radio wave does not wobble and is a straight line (that kinda has strengthened and weakened regions) then why do segment sizes of antennas and Faraday cages depend on wavelength? – lolmaus - Andrey Mikhaylov Jul 2 '15 at 22:55
• The antenna bit for two reasons: (A) the wave is not a "straight line", it is a space-filling oscillation of the field. and (B) because the response of the field depends on motion of electrons in the antenna to efficiently reproduce the time dependence of the wave. For the Faraday cage the reason is primarily because of Huygens' Principle: you need the retarded and un-retarded wave fronts entering the cage to have a lot of variation on scales less than the wavelength. – dmckee --- ex-moderator kitten Jul 2 '15 at 23:01
• Hmm, the wavelength means the distance between feet of a hump. The height of a 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. – lolmaus - Andrey Mikhaylov Jul 2 '15 at 23:02
• "the wave is not a "straight line", it is a space-filling oscillation of the field" -- D'oh! So does a wave wobble like a rope or not? Is this animation a true depiction of a wave or it's merely a graph of tension vs time? en.wikipedia.org/wiki/Electromagnetic_radiation#/media/… – lolmaus - Andrey Mikhaylov Jul 2 '15 at 23:09
• No. There is no material thing or stuff that moves in any direction in a pure EM wave. Waves are traveling disturbances. The thing that is disturbed in a ripple on a pond is the position of a lot of water molecules. The thing disturbed in a EM wave is the value of the electric and magnetic fields. That's it. Full stop. – dmckee --- ex-moderator kitten Jul 2 '15 at 23:11

There is a pretty picture in wikipedia

Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together

On the axis is the direction of the plane wave. What is increasing and decreasing in space are the electric and magnetic fields. As the energy that the wave carries is proportional to the average electric field squared, what is increasing and decreasing in this polarized wave is related to the energy.

In non polarized light the rays have random polarizations so the wave is not organized macroscopically but a lot of directions can be visualized, in the plane perpendicular to the direction. The energy carried is still proportional to the average electric field squared, but cannot be drawn in a pretty diagram.

Here's an animated flux diagram, a cross section of the e-field pattern radiated by a short dipole emitter, from the MIT physics 8.02 course.

Here's a 3D flux pattern frozen in time. (Also lots more cool stuff from MIT 8.02)

Notice, no sine waves. Just expanding blobs (they'd be donut-shaped in 3D,) with the maximum wave-emission being broadside, and a zero node on the vertical axis. Near the EM source, the field pattern looks like expanding tori with the e-field wrapped around poloidially. Farther away from the dipole source we'd see it more as thin, expanding sphere waves with holes at the poles, with e-field and b-field flux lines "drawn upon the sphere," and at right angles to each other. The flux lines always close upon themselves to form squashed, outward-moving circles.

I suspect that these hand-waving sine-wave explanations (and even textbook explanations about "transverse waves") date to many decades ago, back when all light was "Transverse Waves In The Aether." Light is not a transverse wave, not like a shaking rope or shear-wave acoustic vibrations in solids. But it's very hard to make physics textbook authors change their language (search SJ Gould and the Fox Terrier clone problem.) The luminiferous aether was struck down, yet few authors stopped using the vibrating-string analogy for polarization, or stopped teaching us that EM radiation is "transverse wave."

• The sine waves have nothing to do with aether; they are the correct description of plane waves which are useful because (1) they are easily shown to be solutions to Maxwell's equations, (2) they are the limit of your dipole waves at large radius when you examine only a small solid angle, and (3) by completeness they can be used as a basis for describing all solution to Maxwell's equations. – dmckee --- ex-moderator kitten Jan 19 '15 at 3:08

Light is also called electromagnetic radiation. Electric and magnetic fields are a vector quantity. For example an electric field determines in which direction a charged particle will be accelerated. So light/photons do not oscillate spatially, but its electro and magnetic field changes amplitude.