# Why do photon polarization experiments show similar outcomes in different situations?

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• gohu
gohu
TL;DR Summary
Why does the same formula cos⁡2(θ) apply in different situations, one where photons are sequentially modified by polarizers, and the other where entangled photons pass through separate polarizers simultaneously without prior modification?
I'm trying to make sens of the dirac's three polarizer experiment (Moderator's note: link removed) and the epr experiment and bell's inequalities, and i have a loooots of questions, but here i will focus on one first. (I have read some of the long and very interesting threads on the subject that are already on this forum, but I missed some I guess because i cannot understand this).

in the three polarizer experiment, photons pass through a first 0° polarizer, THEN a second one at 45° angle for example. The number of photons that has pass through both filters is, I believe, calculated with the formula cos²(45 - 0). And it's important to notice that the photons are modified after the first filter, their polarization align with 0°.

but in the epr experiment, a pair of entangled photons pass SIMULTANOUSLY (i'm not yelling :p i just emphasize) in two polarizer distant in space, one at 0° angle and the other at 45° angle (to be consistent with my previous example), and the amount of photons that pass through the two filter is also, I believe, calculated with the formula cos²(45 - 0). And this time, the photons are not modified by the filter. Well i mean they are of course, but the photons that pass through the 45° polarizer were not previously modified by the 0° polarizer. Or were they ? if they were, i will have other questions then !

so, what's going on ? Why do we use the same formula ?

I found a beginning of an answer in this post by jesseM :

Perhaps by "same law" you just mean that the classical Malus' law for polarized light and the law for entangled particles both involve a cos^2? The problem is that although the equation can be written in a similar form for both laws, the physical meaning of the symbols is completely different, so from a physical perspective they cannot be called the "same". If you write cos^2(a-b) in the classical context a would be the polarization angle of the light, b would be the angle of a single polarizer, and cos^2 would be giving the reduction in intensity of the light as it passes through the polarizer; but if you write cos^2(a-b) in the quantum context, a and b would both be polarizer angles, there would be no term for the polarization of the light, and cos^2 would be giving the probability that both photons give the same binary result (both passing through their polarizers, or neither).

It explains how they differ, but not why they look the same.

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gohu said:
I'm trying to make sens of the dirac's three polarizer experiment (Moderator's note: link removed)
I have removed the link because that site has a lot of misinformation. What is says in this particular case is not bad, but the conclusion (no quantum "weirdness") doesn't work when one reduces the experiment to single photons.

gohu said:
but in the epr experiment, a pair of entangled photons pass SIMULTANOUSLY (i'm not yelling :p i just emphasize) in two polarizer distant in space,
Note that there is no need for the measurements to be simultaneous. You will find many posts talking about how the results are compatible with special relativity, including the relativity of simultaneity. (Note that there are formatting tools at PhysicsForums that allow to emphasize in other ways than all-caps.)

gohu said:
one at 0° angle and the other at 45° angle (to be consistent with my previous example), and the amount of photons that pass through the two filter is also, I believe, calculated with the formula cos²(45 - 0). And this time, the photons are not modified by the filter. Well i mean they are of course, but the photons that pass through the 45° polarizer were not previously modified by the 0° polarizer. Or were they ? if they were, i will have other questions then !

so, what's going on ? Why do we use the same formula ?
To put it simply, because this is what the math leads to. I don't think you'll find a satisfactory answer until you try to calculate these things yourself.

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Thank you for your answer @DrClaude :)

I have removed the link because that site has a lot of misinformation

well, I'd rather you left it please. I'm talking about two experiment, and while the epr experiment is famous enough to not need a presentation I suppose, I think this one needs a link to explain it better. I can gladly add a note saying this is not a reliable website if you will ? Or, I can use another link that explain what I'm talking about, like this one :

(link removed by mentor - DO NOT repost the link)

doesn't work when one reduces the experiment to single photons.

I know that, and in the same time it will be another question that I will post on this forum later when I'm done with this one, because even with single photons we can explain the experiment with local hidden variables, I think, so I may have more questions about it ;)

there is no need for the measurements to be simultaneous. You will find many posts talking about how the results are compatible with special relativity, including the relativity of simultaneity.

Ok ? I will look for that. And,can you elaborate ? If there is no need for simultaneity, what is required in the measurement ? In order to not be able to explain it with local hidden variables ? Now that I think about it, I indeed don't think that "simultaneous" is the appropriate word for what i'm trying to understand : that would rather be the fact that filters do not follow each other, so photons passing through the second filter are not already modified by the first one. So the point is not simultaneity, you are right, it is rather "independance", maybe ? "non-causality" ?

because this is what the math leads to

I have no doubts about that :p

I don't think you'll find a satisfactory answer until you try to calculate these things yourself

I will have very hard time doing that ! I'm wondering if there is a way to understand it better even if I don't have the mathematical knowledge for it ?

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Motore and PeroK
Thread is closed temporarily for Moderation...

After deleting some unacceptable links, the thread is reopened provisionally.

ok, so here is a description of the three polarizer experiment i was talking about :

You need three polarizing filters. The experiment takes place in two stages. The first step will be performed with 2 filters superimposed, and the second with 3. First, position a first filter by orienting it vertically (in fact, any orientation gives the same result). Then you add a second filter between you and the light source, initially oriented like the first, and the more you rotate it, the more it stops the light. Once it's oriented at 90° to the first filter, no light passes through (for perfect filters anyway). The second step is to add a third filter, between the first 2. Orient it at any intermediate angle between the other two, e.g. 45°, and you'll see that, counter-intuitively, some light does get through.

It's very easy to do at home, and polarizing filters can be found on computer screens, for example.

Please don't repost content the Mentors have deleted. It makes them unhappy.

Second, this has nothing to do with quantum mechanics (or quantum woo, or hidden variables) or even photons. This is purely a property of classical light and vectors. The projection of a vector A along B and then along C is not the same as the projection of A along C.

Please don't repost contemt the Mentors have deleted. It makes them unhappy.
I didn't repost, I asked if another link was better, but I should have asked in private I suppose. Eventually, to avoid any links, I simply explained the experiment in a new post. If I could edit my first post, I would even not talk about the experiment at all, I just need to talk about the Malus' law for the calculation of light passing through two consecutive polarizers.

Second, this has nothing to do with quantum mechanics
yes you are right, that quantum mechanics is not necessary to explain and calculate the output of this experiment (and my first deleted link didn't use it, so there was no confusion about this fact), and by the way this is not what my question is about ;) although, as noticed by DrClaude, the explanation with purely classical light and vectors "doesn't work when one reduces the experiment to single photons".

What I'm wondering, is why the calculation is the same for two situations that seems really different for me : when light passes through two consecutive filters, and when entangled photons passes through two different filters not consecutively ? Is it pure chance, that the calculation is the same, or is there similarities between the two phenomena ?

gohu said:
is there similarities between the two phenomena ?
Yes, there are.

For one photon passing through two consecutive filters, the first filter prepares the photon in a particular polarization state, and the second measures its polarization in a different direction.

For two entangled photons, assuming that by "entangled" you mean a "parallel polarization" state, where if both photons are passed through filters at the same angle their probabilities of transmission are the same, it must be the case that the calculation is the same as for the one photon case above. The filter for one photon corresponds to the preparation by the first filter in the case above, and the filter for the other photon corresponds to the measurement by the second filter in the case above. The correspondence is enforced by the entanglement between the photons.

PeroK
gohu said:
If there is no need for simultaneity, what is required in the measurement ? In order to not be able to explain it with local hidden variables ?
The pair of photons being entangled is enough. The actual QM prediction is the same regardless of when the measurements are made (of course they both have to be made after the entangled photons are created and sent off to their respective measurement points).

PeterDonis said:
For two entangled photons, assuming that by "entangled" you mean a "parallel polarization" state, where if both photons are passed through filters at the same angle their probabilities of transmission are the same, it must be the case that the calculation is the same as for the one photon case above. The filter for one photon corresponds to the preparation by the first filter in the case above, and the filter for the other photon corresponds to the measurement by the second filter in the case above. The correspondence is enforced by the entanglement between the photons.
thank you, your explanation is really clear !

It makes more sense now :) I understand the implications of the bell's inequalities like this :

if ( hidden-variables && locality )
then ( inequalities )

But I was focused on the hidden-variables condition, I was thinking : if != inequalities, then hidden-variables are impossible. Instead, we can say if != inequalities, then locality is not respected.

In other words, you say that the entangled photons are modified by the polarizer as much as the photons in the dirac's experiment, but non-locally. So no need for pure chance ( pure chance = no hidden variables ).

gohu said:
TL;DR Summary: Why does the same formula cos⁡2(θ) apply in different situations, one where photons are sequentially modified by polarizers, and the other where entangled photons pass through separate polarizers simultaneously without prior modification?

...

so, what's going on ? Why do we use the same formula ? It explains how they differ, but not why they look the same.
Of course, everything said by the Mentors and Advisors above is completely correct. But there is math available to explain HOW the entangled statistics get to the generic cos^2(theta) formula you are asking about. It is a little complicated, and you can read about it in the following reference:

Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory
(Dehlinger & Mitchell, 2002)

If you look at their (10), you will see that the formula for the probability of a VV match is 1/2(cos^2 (α - β)). The formula for a HH match is likewise 1/2(cos^2 (α - β)). So the total likelihood for a VV or HH match is the total of those, cos^2 (α - β). Of course (α - β) is theta. QED.

You can read their full derivation in the paper. For anyone studying entanglement, this paper covers almost every aspect* of theory and experiment in a very short and concise format. I highly recommend it as a minimum for general understanding of this phenomena.

*Pun intended... Alain Aspect shared the 2022 Nobel for his groundbreaking work on entanglement.

Lord Jestocost

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