A Did rotating polarizer show violations of Bell's Inequality?

[PeterDonis]

if you rotate both detectors in what you assign as the A+B- experiment, you are repeating the A+B- experiment, and indeed you get the same answer. To call it B+C- is simply an assertion.

No, your claim that it is "repeating the same experiment" is simply an assertion (and an unsupported and unfounded one). The experimental fact is that the detectors were rotated, and the experiment after the rotation was a separate experiment from the original one before the rotation. Recording the data from the two separate experiments as separate data is just being honest about what you actually did when the experiments were done.

Using rotational invariance to argue that the correlations from both experiments will be the same is a theoretical prediction, which then has to be compared with the actual experimental facts to see if it holds. You can't assert that they are "the same experiment", because that isn't what rotational invariance says anyway. Rotational invariance does not say that the two experiments, one before rotating the detectors and one after, are "the same experiment". It just says that those two separate experiments will give the same correlations.

 

[PeterDonis]

I was under the impression that the observed counts at the detectors, i.e. the count at detector 1, and the count at detector 2 arriving within x ns of a click at detector 1, were used to evaluate joint probabilities. These are simple measurements, with no theoretical model required.

That is correct, yes; the observed correlations that are then compared with theoretical predictions are obtained this way (at least that's my understanding). And those observations are made (at least in experiments that are intended to test inequalities like CHSH) with 3 different pairs of angles, which Bell takes to be 0 and 45 degrees, 45 and 90 degrees, and 0 and 90 degrees. The fact that two of these three pairs are predicted (by both theoretical models in view) to give the same correlations (but with different numerical values for the correlations in the two different models), because of rotational invariance, does not change the fact that there are three distinct experimental runs, each of which gives its own measured correlation that then has to be compared with theoretical predictions. Rotational invariance, as I said in post #52 just now, is simply one of the theoretical predictions (and of course is found to hold).

 

[Ian J Miller]

Bell starts out describing it that way, but he then points out that exactly the same logic that the socks model applies to socks, can be used to build a model of spin measurements at different angles, of the kind that are made in EPR experiments. So the properties of the socks model can also be used to derive predictions about correlations in such spin measurements. And, as he points out, those predictions are different from the QM predictions; the "socks model" predictions obey inequalities that the QM predictions violate.

That is literally the primary point of the paper you referenced. I am flabbergasted that you don't realize that since it is absolutely essential to understanding what Bell was talking about.

Of course I realize the sock model obeys the inequality, and the QM model does not, BUT the QM model only disobeys the inequality because the rotation of the polarizers in a set configuration when the source is rotationally invariant is allowed to introduce two new variables, when the only frame of reference, the angle between the two detectors, has also been rotated. My point is that if the source is polarized, i.e. it defines a fixed external frame of reference, the inequality is complied with. How can that happen, other than in one of the two cases something has gone wrong?

 

[Ian J Miller]

No, your claim that it is "repeating the same experiment" is simply an assertion (and an unsupported and unfounded one). The experimental fact is that the detectors were rotated, and the experiment after the rotation was a separate experiment from the original one before the rotation. Recording the data from the two separate experiments as separate data is just being honest about what you actually did when the experiments were done.

Using rotational invariance to argue that the correlations from both experiments will be the same is a theoretical prediction, which then has to be compared with the actual experimental facts to see if it holds. You can't assert that they are "the same experiment", because that isn't what rotational invariance says anyway. Rotational invariance does not say that the two experiments, one before rotating the detectors and one after, are "the same experiment". It just says that those two separate experiments will give the same correlations.

If simply rotating the detectors against a rotationally invariant background generates the two new variables then you have provided your answer to the original question. Thank you.

 

[PeterDonis]

if the source is polarized, i.e. it defines a fixed external frame of reference, the inequality is complied with.

What is your basis for this claim?

 

[PeterDonis]

If simply rotating the detectors against a rotationally invariant background generates the two new variables then you have provided your answer to the original question. Thank you.

Um, what? Seriously? That was the issue? And now, from that one simple statement, you're convinced it's no longer an issue?

 

[Ian J Miller]

What is your basis for this claim?

I thought I put that up earlier, however, if this is a repeat, forgive me. There is no experiment as far as I know because nobody has tried it, but:

Assume a source that provides entangled photons, all of which are polarized in one plane. Align the A+ detector with this plane, and, as with Aspect, assign B as a rotation of 22.5 degrees and C as a rotation of 45 degrees. If so, A+ has a probability of 1 (assuming everything is perfect)- B- a probability of sin squared 22.5 and C- sin squared 45 degrees. In short, (A+)(B-) and (A+)(C-) are now the same as calculated for the Aspect experiment, however, (B+) now has a probability of cos squared 22.5 degrees, and C- is the same as above. Inserting these values into our derived inequality and we get

1 x 0.146 + 0.8536 x 0.5 should be ≥ 0.5.

which comes out to 0.573 ≥ 0.5,

 

[Ian J Miller]

Um, what? Seriously? That was the issue? And now, from that one simple statement, you're convinced it's no longer an issue?

I was hoping to end the discussion.

 

[PeterDonis]

Assume a source that provides entangled photons, all of which are polarized in one plane.

There is no such thing. If you restrict the polarization to one plane, there is no way to get an entangled state.

Of course if you ran this experiment, the correlations would not violate the Bell inequalities. But that is because of the lack of entanglement. You need quantum entanglement in order to obtain correlations that violate the Bell inequalities.

 

[PeterDonis]

I was hoping to end the discussion.

Does that mean that the issue you were concerned about is no longer an issue?

 

[Ian J Miller]

Does that mean that the issue you were concerned about is no longer an issue?

It means I do not wish to continue

 

[Nugatory]

Assume a source that provides entangled photons, all of which are polarized in one plane….

Which of course is impossible. If it were possible then violations of Bell’s theorem would be the least of our problems - superluminal communication would be possible and we would have to deal with operational tachyonic antitelephones.

 

[Steve4Physics]

...we would have to deal with operational tachyonic antitelephones.

For which the owner's workshop manual is available here: https://www.redbubble.com/i/noteboo...Owner-s-manual-by-moviemaniacs/41343252.RXH2R

 

[Ian J Miller]

Which of course is impossible. If it were possible then violations of Bell’s theorem would be the least of our problems - superluminal communication would be possible and we would have to deal with operational tachyonic antitelephones.

Which is impossible why? I do not know whether that can be done now, but I am very skeptical of assertions that something is technically impossible without some very strong proof. Consider a down converter. The crystal acts occasionally to produce two photons with half frequency and opposite polarisation. Why is it impossible that some day a crystal might be found that sends the photons out along crystal planes? (I am unaware of how current crystals produce their polarised photons and I would be interested if someone could explain.

Then where did this superluminal transmission come from? It is usually discounted from non-local systems that violate Bell's inequality, so where does something that complies with Bell's inequality suddenly make superluminal communication possible?

Suppose the photons go through a polarization filter that is aligned with A+. Are you saying that by going through the filter, they are no longer entangled? Why? Because somehow they have interacted with the filter, where the others have been filtered out? Then let us assume they are no longer entangled as you say, and construct the parallel filters on each side of the source. Bell's inequality is now complied with. Now, rotate the filters at high speed maintaining the parallel axes. Now Bell's inequality will be violated, by the standard interpretation, yet according to you they are no longer entangled. You can switch on and off whatever property you think such violations entail.

You may argue the filter removed the superposition possibilities, but how do you know there ever were such possibilities? How do you know in the Aspect experiment that an electron with a specific spin did not generate a photon with one only polarization when it collapsed? There is no observational evidence for the superposition as a physical entity, as opposed to the "I don't know what it is" when predicting probabilities.

In the above when I said "I was hoping to end the discussion," I was trying to be polite. The discussion had reduced to whether moving a set configuration with no change of constraints produced new results or was merely reproducing the first. When it was stated that this did produce new results, that was the crux of the matter, but it was not explained. I was considering the system was invariant to rotation, so any such rotation was a repeat of the first. The response was that it was not a repeat. Since there is no way to settle that, as far as i can see, I wished to withdraw.

If you wish to answer the above questions, please do so with observational evidence. You cannot confirm a theory by citing another theory unless there is clear observational support for it.

 

[PeterDonis]

Which is impossible why?

Because, as I said in post #59, there is no such thing as an entangled state of photons whose polarizations are all restricted to a single plane.

I am very skeptical of assertions that something is technically impossible without some very strong proof.

The proof is simple: an entangled two-photon state is a state that cannot be written as a product of two single-photon states. The Hilbert space of single-photon polarization states is two-dimensional, i.e., it has two basis vectors. Restricting polarization to a single plane limits you to just one of those two dimensions, and hence just one basis vector. And it is impossible to write a two-photon state using just one single-photon basis vector that is not a product of two one-photon states. Why? Because with one basis vector, there is only one possible two-photon state, the product of that basis vector with itself. (Sure, you can multiply this product by a complex number, but that does not change the physical state; physical states are rays in the Hilbert space.)

 

[PeterDonis]

You cannot confirm a theory by citing another theory unless there is clear observational support for it.

Apparently you are unaware of the huge amount of observational support for the QM model of photon polarizations that, for example, I made use of in post #65 just now, and that I strongly suspect @Nugatory had in mind when he made his post that you responded to. Refusing to consider arguments using that theory is not a reasonable position to take.

 

[DrChinese]

1. Which is impossible why? I do not know whether that can be done now, but I am very skeptical of assertions that something is technically impossible without some very strong proof. Consider a down converter. The crystal acts occasionally to produce two photons with half frequency and opposite polarisation. Why is it impossible that some day a crystal might be found that sends the photons out along crystal planes? (I am unaware of how current crystals produce their polarised photons and I would be interested if someone could explain.

2. Suppose the photons go through a polarization filter that is aligned with A+. Are you saying that by going through the filter, they are no longer entangled? Why? Because somehow they have interacted with the filter, where the others have been filtered out? Then let us assume they are no longer entangled as you say, and construct the parallel filters on each side of the source. Bell's inequality is now complied with.

3. Now, rotate the filters at high speed maintaining the parallel axes. Now Bell's inequality will be violated, by the standard interpretation, yet according to you they are no longer entangled. You can switch on and off whatever property you think such violations entail.

It hurts us all when you ask questions (and deny established science) that are beyond your understanding of entanglement. Hopefully you are here to learn so, here are a few specific answers to your questions above:

1. Entangled photons can be polarized along a specific plane. However, such photons are not *polarization* entangled. Any pair of photons that have known polarization will *not* be polarization entangled. This is axiomatic, and should be obvious, as they are in separable states. (Photons exiting a common laser are polarized the same, but are not entangled.)

2. The same is true of polarization entangled photons AFTER they pass through a polarizer. Once polarization is known, they are no longer entangled. You know this because they won't any longer show perfect (anti)correlations (at all matching angles). That's how experimenters know they have a good source of entangled photon pairs; they calibrate to get as close to perfect correlation as possible. Only entangled pairs have this property at identical angle settings.

3. You can rotate the measurement polarizers very rapidly (keeping Alice's and Bob's settings parallel as the photons pass through), and they WILL show perfect (anti)correlation as you would expect. Variations on this are performed in 2 of the references below.

4. There are plenty of sources to learn about parametric down conversion. Here is one that explains this as part of their overall objective of performing a Bell test.

a. https://arxiv.org/abs/quant-ph/0205171

Further, there are many ways to entangle a pair of photons other than down conversion (which is one of the easiest and cheapest to study). Here is one of the earliest and most famous Bell tests, co-written by 2022 Nobel winner Alain Aspect:

b. https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.47.460

And in fact, entangled photons can be produced that DON'T come from a common source! They can be produced by independent sources that are outside each other's light cones (i.e. the entangled photons are never in a common light cone). This makes it very difficult to assert that there is some kind of element that restores conventional locality (I am not sure if you are asserting that or not). This is co-written by another 2022 Nobel winner, Anton Zeilinger.

c. https://arxiv.org/abs/0809.3991

Good luck!

-DrC

 

[Ian J Miller]

It hurts us all when you ask questions (and deny established science) that are beyond your understanding of entanglement. Hopefully you are here to learn so, here are a few specific answers to your questions above:

1. Entangled photons can be polarized along a specific plane. However, such photons are not *polarization* entangled. Any pair of photons that have known polarization will *not* be polarization entangled. This is axiomatic, and should be obvious, as they are in separable states. (Photons exiting a common laser are polarized the same, but are not entangled.)

2. The same is true of polarization entangled photons AFTER they pass through a polarizer. Once polarization is known, they are no longer entangled. You know this because they won't any longer show perfect (anti)correlations (at all matching angles). That's how experimenters know they have a good source of entangled photon pairs; they calibrate to get as close to perfect correlation as possible. Only entangled pairs have this property at identical angle settings.

3. You can rotate the measurement polarizers very rapidly (keeping Alice's and Bob's settings parallel as the photons pass through), and they will show perfect (anti)correlation as you would expect. Variations on this are performed in 2 of the references below.

4. There are plenty of sources to learn about parametric down conversion. Here is one that explains this as part of their overall objective of performing a Bell test.

a. https://arxiv.org/abs/quant-ph/0205171

Further, there are many ways to entangle a pair of photons other than down conversion (which is one of the easiest and cheapest to study). Here is one of the earliest and most famous Bell tests, co-written by 2022 Nobel winner Alain Aspect:

b. https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.47.460

And in fact, entangled photons can be produced that DON'T come from a common source! They can be produced by independent sources that are outside each other's light cones (i.e. the entangled photons are never in a common light cone). This makes it very difficult to assert that there is some kind of element that restores conventional locality (I am not sure if you are asserting that or not). This is co-written by another 2022 Nobel winner, Anton Zeilinger.

c. https://arxiv.org/abs/0809.3991

Good luck!

-DrC

1. What I meant was entangled photons polarized along a specific plane. I apologize if it did not come out that way. I don't understand your alternative, but since you say it is impossible, and I didn't mean it, no need to go further.

2. I am not sure I know what you are saying here. Are you saying once you know the polarization they no longer give the Bell correlations? If not, what correlations do you mean?

4. I mentioned down-conversion because it involved a crystal. I did not mean to imply that was the only way to do it; merely that it was an option. Thank you for the links. The first one answered one of my questions. Finally, I was not asserting there was switching between locality and non-locality

Again, thank you for your repsonse.;

 

[Ian J Miller]

Because, as I said in post #59, there is no such thing as an entangled state of photons whose polarizations are all restricted to a single plane.The proof is simple: an entangled two-photon state is a state that cannot be written as a product of two single-photon states. The Hilbert space of single-photon polarization states is two-dimensional, i.e., it has two basis vectors. Restricting polarization to a single plane limits you to just one of those two dimensions, and hence just one basis vector. And it is impossible to write a two-photon state using just one single-photon basis vector that is not a product of two one-photon states. Why? Because with one basis vector, there is only one possible two-photon state, the product of that basis vector with itself. (Sure, you can multiply this product by a complex number, but that does not change the physical state; physical states are rays in the Hilbert space.)

I am afraid we disagree again. Physical states may be represented mathematically as rays in Hilbert space, but the photons, in my opinion, remain in standard three-dimensional space, or if you wish, 4-dimensional spacetime. In the Aspect experiment, both photons have the same polarization as seen by detectors. As for a sequence of entangled photons in one polarization plane, I cannot produce them, but I would be very surprised if they are never produced. I had never heard of photons produced over extended time being considered as one state, so I am learning, albeit slowly.

 

[Nugatory]

Suppose the photons go through a polarization filter that is aligned with A+. Are you saying that by going through the filter, they are no longer entangled?

Yes, and I am resisting the temptation to say "Yes, of course". Any measurement, any interaction that collapses the wave function, any interaction that leads to decoherence, any interaction with anything that fixes the polarization plane of one photon, .... (these are different ways of saying the same thing) will break the entanglement.

Why? The entangled state is (by the definition of entanglement) the superposition $\frac{1}{\sqrt{2}}(|\alpha\beta\rangle\pm|\beta\alpha\rangle)$ where $\alpha$ and $\beta$ denote the two possible polarization states along the axis we have chosen and the position of the labels within the ket selects which particle. An interaction that yields the result $\alpha$ at the left-hand detector will leave the post-measurement state $|\alpha\beta\rangle$; an interaction that yields the result $\beta$ at the left-hand detector will leave the post-measurement state $|\beta\alpha\rangle$. Neither of these is an entangled state.

 

[PeterDonis]

Physical states may be represented mathematically as rays in Hilbert space, but the photons, in my opinion, remain in standard three-dimensional space, or if you wish, 4-dimensional spacetime.

Sorry, but you don't get to just use your opinion.

At this point you are verging on personal theory and therefore on receiving a warning. You don't get to just make up your own physics.

In the Aspect experiment, both photons have the same polarization as seen by detectors that are oriented in the same direction.

See the bolded qualifier, which is crucial.

With the qualifier, the statement is true, but this polarization is not restricted to one plane. The two detectors will always show the same polarization no matter which direction they are oriented, as long as the two detectors are both oriented in the same direction. The entangled photon state that produces these results is not at all the same as a two-photon state that is produced by restricting the polarization to one plane at the source. The latter state is not and cannot be an entangled state.

As for a sequence of entangled photons in one polarization plane, I cannot produce them, but I would be very surprised if they are never produced.

Then you should indeed be very surprised, because the argument I have already given for why they cannot be produced makes use of the same QM model of photons that, as I have said, already has a huge amount of experimental support. That's why nobody has produced such a state: because it's impossible, and everyone in the field knows it.

 

[berkeman]

After a Mentor discussion, this thread is now closed. @Ian J Miller -- please check your PMs in a few minutes...