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#1
07-01-2000, 12:10 AM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,120
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 X-polarized 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?
#2
07-01-2000, 12:18 AM
 tcburnett Guest Join Date: Apr 2000 Location: 19.508901 N, 154.923135 W Posts: 949
Quote:
 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 X-polarized 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?
But I'm a little rusty on quantum thingies, but when you look in the box The cat will either be dead or alive. If your assumption contradicts observations it is not an assumption. It is a fuck-up. Ask me about SCUBA diving instead.
#3
07-01-2000, 12:25 AM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,120
Quote:
But which of my assumptions is incorrect, and why? I thought the whole point of a thought experiment was to try to find exactly what is the cause of the obviously wrong conclusion. Are you suggesting my assumptions are so ridiculous that they are not worth thinking about?
#4
07-01-2000, 12:27 AM
 TheNerd Guest Join Date: Aug 1999 Posts: 1,620
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.
#5
07-01-2000, 12:33 AM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,120
Quote:
 The photon will either go through or not, with approximately a 50% chance of each.
That was my first thought as well. But if that was the case, a 45-degree photon has a 25% chance of passing through a pair of crossed polarizers, when in reality a crossed pair is totally opaque.

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
07-01-2000, 07:59 AM
 JonF Guest Join Date: Dec 1999 Posts: 946
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 X-polarized 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 X-polarized 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 non-zero 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 single-photon-at-45-degrees 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 half-measures. 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 re-radiated 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 non-polarized 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
07-01-2000, 08:14 AM
 friedo Guest Join Date: May 2000 Location: Brooklyn Posts: 23,588
Quote:

Quote:
 The photon will either go through or not, with approximately a 50% chance of each.
That was my first thought as well. But if that was the case, a 45-degree photon has a 25% chance of passing through a pair of crossed polarizers, when in reality a crossed pair is totally opaque.
No...when a 45 degree photon goes through an X polarizer, it comes out as an X-polarized photon on the other side, meaning there is a 0% chance of getting through a Y-polarized filter.
#8
07-01-2000, 08:50 AM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,120
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 re-emit an identical energy photon. The re-emitted photons all have the same linear polarization. The probability of re-emission is dependent on the polarization of the incident radiation.

However, I disagree about that classical three-polarizer demonstration; it can easily be explained by Maxwellian thinking. The first polarizer absorbs the Y component, then the second (45-degree) polarizer absorbs the 135-degree component of that, so the emitted light has a 45-degree polarization. Since it's at 45 degrees it has a nonzero Y component, and some light passes through the third polarizer.
#9
07-01-2000, 12:39 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 74,397
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:
Quote:
 So the right way to think is: a polarizer absorbs all incoming photons and with a certain probability re-emit an identical energy photon.
That's one way to think about it, but since photons are bosons, and hence indistinguishable one from the other, it's equally valid to say that those photons don't get absorbed at all, just rotated. It falls into the category of "don't know, and doesn't matter".

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