#1




Polarization can be defined for each photon, right? And the energy of a single photon is dependent on the wavelength. Now let's take a polarizer filter with the polarization in the X axis (i.e. X polarized light is transmitted, Y polarization is absorbed). Now take a single photon polarized 45 degrees from the X axis. Shoot this photon at the polarizer. What happens? Normally, one would say that the Y component of the electrical field is absorbed, and what passes through is Xpolarized light with half the original intensity. However, if a single photon lost half its energy, its wavelength would change, which contradicts observations. So where am I making an invalid assumption?

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#4




I would hazard an educated guess that this counts as a measurement of a quantum phenomenon. The photon will either go through or not, with approximately a 50% chance of each. If it does go through it will be unaffected upon reaching the other side.
Now Chronos will tell you why I'm wrong. 
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Maybe the polarization of each photon is not an absolute number but a probability distribution  but the above example seems to rule that out as well. 
#6




TheNerd is correct. scr4 is making a fundamental mistake. The error lies in "the Y component of the electrical field is absorbed, and what passes through is Xpolarized light with half the original intensity". The polarizer does not absorb part of the field; that's what's predicted by Maxwell's model, which gives correct answers for large numbers of photons and is not a description of what's really going on. When you want to speak of small numbers of photons, you must use Quantum Mechanics. Quantum mechanics (which appears to be an almost inconceivably excellent model but not explanation of what is going on) speaks only of probabilities. Also, "what passes through is Xpolarized light with half the original intensity" is only true for light consisting of a large number of photons.
Given a single photon emitted with random polarization, before it passes through the polarizer, for each possible polarization there is a nonzero probability of that polarization. There is no polarization for which the probability is one. When it goes through the polarizer, the distribution of probabilities changes (there are other ways of describing this situation, but the "Copenhagen Interpretation" describes it this way). Either it goes through or it doesn't. If it goes through, then the probability of it being polarized parallel to the polarizer after, not before passing through is one, and its energy is unchanged.. If it does not go through, then the probability of it being polarized perpendicular to the polarizer is zero. If you repeat the experiment with a large number of photons that were not biased towards some polarization, half of them will pass through and half of them will not. If you have a beam of light or a single photon that is polarized at 45 degrees relative to the polarizer, then you must have made a measurement earlier in the experiment to find out or set that polarization, and the probabilities are different. For the singlephotonat45degrees case, the probability of that individual photon going through the polarizer will be 1/2 ... but the individual photon will either go through or it won't. No halfmeasures. For a beam of many photons polarized at 45 degrees, half of them will go through and half of them won't. The energy of the photons that do not pass through is absorbed by the polarizer, and reradiated as photons with wavelengths that depend on the temperature of the polarizer. If you want to know what's really going on when that photon hits the polarizer .. sorry, nobody knows. There are quite a few theories, but no proof. Finally, it's fairly eay to prove in, the privacy of your own home, that the model proposed by scr4 in the OP is incorrect. All you need is three polarizing filters. Observe a source of nonpolarized light through two of them, oriented at 90 degrees to each other, and observe that essentially no light goes through (depending on the efficiency of the polarizers). Now insert the third polarizer between the first two, oriented at 45 degrees. Much more light passes through; 1/8 of the original light. If the first polarizer absorbed all of one component of a filed, the third polarizer would make no difference. 
#7




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Friedo Ignoramus Primus ^{"And a singularly consistent investigation you have made, my dear Watson. I cannot at the moment recall any possible blunder which you have omitted."  Sir Arthur Conan Doyle, The Disappearance of Lady Frances Carfax } 
#8




Thanks, JohF  actually just asking the question here got my thoughts organized enough to see that that's the only possible explanation. I got confused because polarizers are always described as letting correct polarization light "pass through." So the right way to think is: a polarizer absorbs all incoming photons and with a certain probability reemit an identical energy photon. The reemitted photons all have the same linear polarization. The probability of reemission is dependent on the polarization of the incident radiation.
However, I disagree about that classical threepolarizer demonstration; it can easily be explained by Maxwellian thinking. The first polarizer absorbs the Y component, then the second (45degree) polarizer absorbs the 135degree component of that, so the emitted light has a 45degree polarization. Since it's at 45 degrees it has a nonzero Y component, and some light passes through the third polarizer. 
#9




Sorry, The Nerd, I don't tell folks they're wrong on quantum there's plenty of others on the board who know more quantum than I. I'm just checking in here to point out something about scr4's post:
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