Nature of probabilistic measurement

[zonde]

I have a question regarding probability of quantum measurement.
Consider polarized photon beam that is going through polarizer. Let's assume that beam intensity is very low so that we can consider it as separate photons going through polarizer one by one.
Now if we consider any single photon from ensemble probability that it will pass the polarizer is cos^2(theta) where theta is relative angle between polarization axis of photons and polarization axis of polarizer.
But now if we consider two successive photons from ensemble. Does passing or absorbing of the first photon affect probability for the next photon? Say if first photon passed polarizer does next photon have lover probability that it will pass?

 

[SpectraCat]

I have a question regarding probability of quantum measurement.
Consider polarized photon beam that is going through polarizer. Let's assume that beam intensity is very low so that we can consider it as separate photons going through polarizer one by one.
Now if we consider any single photon from ensemble probability that it will pass the polarizer is cos^2(theta) where theta is relative angle between polarization axis of photons and polarization axis of polarizer.
But now if we consider two successive photons from ensemble. Does passing or absorbing of the first photon affect probability for the next photon? Say if first photon passed polarizer does next photon have lover probability that it will pass?

I don't think so ... if the photons going through the polarizer are really properly considered as separate events as you say. It seems to me that there would be a larger chance of the absorption of a photon changing the properties of the polarizer such that it slightly changed the probability of the next event. However any such effect can be minimized/eliminated by increasing the delay between the photons.

 

[jtbell]

Does passing or absorbing of the first photon affect probability for the next photon?

No, it does not.

 

[zonde]

I don't think so ... if the photons going through the polarizer are really properly considered as separate events as you say. It seems to me that there would be a larger chance of the absorption of a photon changing the properties of the polarizer such that it slightly changed the probability of the next event. However any such effect can be minimized/eliminated by increasing the delay between the photons.

It is not clear that these are properties of polarizer that are changing.
Consider simplest polarizer - wire-grid polarizer.
If wires are horizontal then horizontal component of photons electric field vector is absorbed. So we split electric field vector in two orthogonal components so that one is horizontal other is vertical. Transmitted is only vertical component but it does not have original energy of photon. To restore full energy of photon we resupply (or we don't) missing energy from nowhere (not from wire because in wire electric field vector can be only horizontal).

No, it does not.

Do you use just your intuition or have you some other reasons to say so?
Even if it's only your intuition maybe you can try to approximately formulate why do you say so?

 

[SpectraCat]

It is not clear that these are properties of polarizer that are changing.
Consider simplest polarizer - wire-grid polarizer.
If wires are horizontal then horizontal component of photons electric field vector is absorbed. So we split electric field vector in two orthogonal components so that one is horizontal other is vertical. Transmitted is only vertical component but it does not have original energy of photon. To restore full energy of photon we resupply (or we don't) missing energy from nowhere (not from wire because in wire electric field vector can be only horizontal).

Ok, I don't think what you say above is correct, but I cannot provide a detailed explanation why ... all I can say is that your statement above "Transmitted is only vertical component but it does not have original energy of photon." cannot be completely correct, because the energy of the photon is proportional to its frequency, and polarizers do not change the frequency of the light that they transmit.

And now I understand the subject line of your question a little better ... you are asking how the observed cosine-squared transmission probability for single, linearly-polarized photons going through a polarizer can be derived at a very low level, considering the interaction of the polarizer with the photons, right? Ok .. I don't know the answer to that, and I would be interested to see it myself.

My guess is that it has to do with the fact that linearly polarized light can be written as a superposition of left and right circularly polarized light, and the transmission probability has something to do with the probability that the phase angle of the polarization vectors lines up with the "allowed" direction for transmission. If I have time I will try to prove this using classical fields to describe the photons.

 

[DrChinese]

But now if we consider two successive photons from ensemble. Does passing or absorbing of the first photon affect probability for the next photon? Say if first photon passed polarizer does next photon have [lower] probability that it will pass?

Echoing what jtbell already said: no, there is no such effect. There have been stochastic attempts to model such an effect, but it actually makes absolutely no sense when you think about it closely.