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I am familiar with the Faraday Effect, but I remain confused as to why the electric and/or magnetic components of light do not naturally align themselves with a magnetic or electric field (in a vacuum) and thereby become polarized.

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I suspect the answer to this is because electromagnetic waves are linear. i.e, light doesn't interact with electric and magnetic fields; light passes through light, light passes through electric fields and magnetic fields. –  QuantumDot Feb 1 '13 at 6:07
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Just by superposition of waves: if you have an electric or magnetic field on a region of space and light goes through it, within that region the fields will sum to each other, and be the same as in the beginning when the leave that region. –  MyUserIsThis Feb 4 '13 at 0:05

5 Answers 5

The Faraday effect is dispersive, so it is coherent and reversible. It tweaks the evolution of the light but doesn't cause "relaxation". In general, a system cannot reach a ground state, like becoming aligned to a magnetic field, without some sort of dissipation (e.g., absorption).

The linear algebra way to think about this is as follows: consider orthogonal states of light, such as $H$ and $V$ linear polarizations. After coherent evolution, they remain orthogonal, or else the evolution would not be reversible (given the final state, the initial state can be uniquely determined). This logic shows us the range of possible options for coherent evolution. The polarization can rotate (like the Faraday effect), it can go from linear to elliptical or circular (like a quarter waveplate), or it can undergo a mirror reflection (like a half waveplate). Of course, any combination of those options is also valid. But it can't align without ''losing information'', which would require a absorptive polarizer. (What I've just described is the $U(2)$ group of unitary matrices on $2\times 2$ complex vectors.)

Note: when I say "reversible", I mean coherent or unitary. I'm not referring to time reversal symmetry, which the Faraday effect breaks.

Edit If we're looking for a way for light to align to the magnetic field, we need the information on the original polarization of the light to be lost. The Faraday effect is off-resonant and cannot achieve that. One way to realize this is through dichroism, where one polarization (usually circular) of light is absorbed. This process is clearly not coherent/unitary because it erases the information on what the incoming polarization is. After absorption, with the right setup, the light can become aligned with the magnetic field. (I can give an explicit example with atoms, if you'd like.)

Sorry if this repeats my comment.

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I guess the next logical question is: why does polarization require dispersion? –  JoeHobbit Feb 4 '13 at 2:31
    
What do you mean by "relaxation"? –  JoeHobbit Feb 5 '13 at 1:48
    
The Faraday effect in particular is an off-resonant excitation, hence it's only dispersive. Dichroism is a related effect in which the light polarization it changed or rotated through absorption -- this is what I mean by "relaxation". Incidentally, dichroism is an excellent example where the light becomes aligned with the magnetic field: one ciruclar polarization is absorbed and the other one remains. "Information" about the original state is lost. To distinguish these effects, I'm referring to the way that light can be dissipitated, absorbed, or incoherently scattered. –  emarti Feb 5 '13 at 8:35

I think the crux of the matter lies in your :

why the electric and/or magnetic components of light do not naturally align themselves

What does "align" mean other than an interaction?

So the question "do photons interact with an electric or magnetic field in vacuum"? has to be answered first before going into the details of the type of interaction.

The answer to this last is "yes, with very very small probability". It is called Delbruck scattering and has been experimentally observed.

It is a QED only effect, it does not exist in classical electromagnetic theory and the measurements are used as an experimental confirmation of QED. It is evidence of vacuum polarization in the strong electric fields of nuclei.

So the photons do interact with the fields through higher order QED diagrams, and not simple higher order, the lowest order allowed is sixth order, which makes this interaction very improbable. It is small in the strong fields around nuclei, it is infinitesimal in the distant coherent fields of atoms, which is what an electric or magnetic field is in vacuum. To have any fields you need the electric and magnetic sources of atoms.

The "infinitesimally low probability of interaction" is what negates the "natural" in your question. A beam of photons does not align its electric or magnetic field to the direction of electric and magnetic fields in vacuum because the interaction probability is practically non existent.

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You are right anna, such effects are possible and measurable. However, they have been mentioned in the discussion by John, in the context of vacuum polarisation. I feel your detail gains you +1. –  JKL Feb 7 '13 at 11:16

Light does become polarized in the presence of a magnetic field. That is how some 3-dimensional maps of the magnetic field lines above certain surface structures of the Sun are recovered, by means of observing the direction of polarization of light of a specific infra-red line, that arrives from the photosphere. I remember it was a paper in Nature by Krupp and Collados and others. It is a relatively recent technique (from the last decade, I think) because it was technically difficult to observe the polarization of light from the Sun until recently.

See this link for the paper (it is really a letter). A popular description of the technique can be found here.

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It is unclear from my brief scanning of the article whether the magnetic field was measured for within solar flares. According to the other answers it must have been within the solar flares. –  JoeHobbit Feb 5 '13 at 2:51

@QuantumDot You seem to be close to the answer to this question. Neither the electromagnetic field Lagrangian nor the gauge theories of fundamental interactions include interactions between photons and electric or magnetic fields. An electric or magnetic field, on their own, represent very low energy photons. To say that a photon interacts with a magnetic or an electric field would suggest that photons interact among themselves. Photon-photon interactions are possible via two fermion 'square' loops, like e- e+ for example. Furthermore photons have neither electric nor magnetic dipole moment. Hence your suggestion that photons pass through an electric or magnetic field undisturbed is right. I have increased your comment by 1.

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Are you saying that a magnetic dipole and/or an electric monopole is required to interact with an electric or magnetic field? How can magnetic fields (in EM waves) exist without dipoles? –  JoeHobbit Feb 5 '13 at 1:56
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@JoeHobbit That is correct. The electromagnetic force (that is magnetic and electric fields) couple only to electric charges or magnetic poles in the form of dipoles such as the magnetic compass for example. This is why neutrinos are hard to detect as they do not interact with the electromagnetic field. Also thing of the way charged particles such as e+ and e- are detected in bubble chambers, taken by the strong magnetic field in opposite circular motion and give the famous V-shape tracks. I hope this helps? –  JKL Feb 5 '13 at 12:58
    
One thing separated your answer from the others: Yours mentioned that a dipole/monopole, which is lacking in light, is required to interact with an electric or magnetic field. I almost chose anna v's answer for clarity regarding the exceptional event of Delbruk Scattering. –  JoeHobbit Feb 9 '13 at 7:44
    
@JoeHobbit Many thanks for that. The point is that we are all learning something, and that is by far more valuable. –  JKL Feb 9 '13 at 13:44
    
@John, if we're discussing the Faraday effect, it's completely incorrect to say that there's no interaction. The whole point is that you can use materials to couple DC magnetic fields and optical fields. If you restrict yourself to a vacuum, you miss most of the interesting phenomena in electromagnetism and I'd be out of a job. –  emarti Feb 10 '13 at 21:12

I think, from a viewpoint of photonics, light, or photon, can only interact through charge and gravity. View light as bosonic vibration of space-time. Charge is the source for such vibrations and responsible for scattering, absorption as well. Gravity affect light because gravity is the curvature of space-time itself.

From a pure wave picture, any effect of light is tracked down to the effect of wave-interference: The scattering is the wave generated by dipoles inside matter excited by incident wave; absorption is simply the scattered wave out of phase with respect to incident one, nonlinearity is anharmonic scattering, etc, etc. Wave themselves simply add up by principle of interference without changing each other's internal property. Polarization is such a property. Hence light add up with another light will not change either's polarization, although they may form a standing wave or beat.

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Er...no. A "vibration of space-time" would be a gravitational wave and if you wanted to view it in quantum terms you would look for gravitons. A photon is an excitation of the electromagnetic field. –  dmckee Feb 7 '13 at 2:38
    
yet what is a "electromagnetic field".Explaining photon as electromagnetic field firstly, can't explain why EM wave and Gravity waves have the same speed invariant of space-time; secondly, it is simply a circular argument, essentially explaining nothing. By thinking of photons as bosonic vibration on space time (similar to that of string theory), helps at least on an intuitive basis to understand its superposition, and propagating nature. For the full theory, Check xiaogang wen's spin net theory. (at MIT) –  Bo Zeng Feb 7 '13 at 4:31

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