Did rotating polarizer show violations of Bell's Inequality?

[Ian J Miller]

The model involves the sin squared relationship. It is equivalent in this circumstance to the Malus law, which applies to a polarized wave.

The sin squared 22.5 and 45 degrees was used by Bell in the second equation of p 10.

I explained my reason for multiple values. Take C-. If you ran C+ and C-. then C- = 0. If you run B+ and C-, C- takes the value 0.146. If you run A+ and C- then C- takes the value 0.5. That means that C- is a function, b ut in the derivation it occurs several times as a single term.

My problem was most simply seen by looking at A+.B- and B+.C- . These are the same results, and all that has happened is we have rotated both detectors by 22.5 degrees, so the angle between them is constant (leaving aside the question of exactitude). Now, according to Noether's theorem, that is merely one result repeated. The answers here say Noether's theorem does not apply, without saying why it doesn't.

I am sorry I asked this question. It relates to what the terms actually mean. Experimental tests are not relevant if the terms used are not clearly defined. The derivation of the inequality I gave requires the terms to take one value under one set of circumstances. Yes, the difference between socks and photons occurs because you add up socks to get probabilities. For photons, there is the wave aspect, wherein conservation of energy arises because cos squared plus sin squared equals 1 so the difference between orientation of polarised wave detectors is one of the two trig functions, depending on what you are projecting onto.

I think it might be better if we terminate this discussion now because we are not discussing the same thing. Thank you for your time.

 

[PeterDonis]

The model involves the sin squared relationship.

The quantum mechanical model does, yes.

But the "Bertlmann's socks" model that is used to calculate the Bell and CHSH inequalities does not.

If you have not grasped this simple fact, you have not read the paper you referenced very carefully.

It is equivalent in this circumstance to the Malus law, which applies to a polarized wave.

No, as has already been pointed out, the QM model is not equivalent to Malus' law. That law is a classical approximation. You should not expect classical approximations to work for these experiments.

The sin squared 22.5 and 45 degrees was used by Bell in the second equation of p 10.

Yes, because there he is calculating the quantum mechanical predictions for the correlations. Nothing he says that involves the sin squared function has anything whatever to do with deriving any inequalities. He is just showing that the QM prediction violates them.

Again, if you have not grasped this simple fact, you have not read the paper very carefully.

C- is a function, b ut in the derivation it occurs several times as a single term

What derivation? Where is this in the paper you referenced?

I think it might be better if we terminate this discussion now because we are not discussing the same thing.

Whether you want to post any further is of course up to you. But it seems to me that the reason for the difficulties in this thread is that you have insisted on using your own idiosyncratic derivation and notation that nobody else can understand, despite the fact that you referenced an actual paper. You could have given explicit equation numbers and quotations from text in that paper. But you didn't. The only time you have even talked about such things is when I forced you to by referencing them myself. And even then you only did it for a little bit, and then reverted to your former failed strategy, so that I have had to pose a follow-up question to you above that I shouldn't have had to pose at all.

 

[PeterDonis]

according to Noether's theorem, that is merely one result repeated.

No, that's not Noether's theorem, that's just rotational invariance. Noether's theorem says that, because the laws of physics are rotationally invariant, angular momentum is conserved.

Even with this correction, however, your claim here is wrong. Rotational invariance does not say that if run 2 of some experiment looks just like run 1 rotated by some angle, then they are really the same run. But that is what you are arguing here.

 

[PeterDonis]

Experimental tests are not relevant if the terms used are not clearly defined.

The terms used in the inequalities are perfectly well defined: they are the actual observed correlations between the two measurements, for different settings of the measurement angles. If this wasn't well defined, how could the experimenters even collect and analyze the data?

 

[PeterDonis]

The derivation of the inequality I gave requires the terms to take one value under one set of circumstances.

Why should I, or anyone actually doing these experiments, care about your derivation?

The people who actually do these experiments don't have any trouble understanding what the terms in the inequalities mean, or how the inequalities were derived, or how to calculate the numerical values from their data. If you are correct, they must all be doing something obviously wrong. What is that thing?

 

[Ian J Miller]

The quantum mechanical model does, yes.

But the "Bertlmann's socks" model that is used to calculate the Bell and CHSH inequalities does not.

If you have not grasped this simple fact, you have not read the paper you referenced very carefully.No, as has already been pointed out, the QM model is not equivalent to Malus' law. That law is a classical approximation. You should not expect classical approximations to work for these experiments.Yes, because there he is calculating the quantum mechanical predictions for the correlations. Nothing he says that involves the sin squared function has anything whatever to do with deriving any inequalities. He is just showing that the QM prediction violates them.

Again, if you have not grasped this simple fact, you have not read the paper very carefully.What derivation? Where is this in the paper you referenced?Whether you want to post any further is of course up to you. But it seems to me that the reason for the difficulties in this thread is that you have insisted on using your own idiosyncratic derivation and notation that nobody else can understand, despite the fact that you referenced an actual paper. You could have given explicit equation numbers and quotations from text in that paper. But you didn't. The only time you have even talked about such things is when I forced you to by referencing them myself. And even then you only did it for a little bit, and then reverted to your former failed strategy, so that I have had to pose a follow-up question to you above that I shouldn't have had to pose at all.

The Bertlmann socks does not use the sin squared because there are no waves involved.

You say the QM model is not equivalent to the Malus law, but it counts joint probabilities with the same function.

I never said the sin squared was involved in deriving the inequality; I said that it was not. This is further evidence that you are not understanding what i wrote. That is your right.

 

[Ian J Miller]

No, that's not Noether's theorem, that's just rotational invariance. Noether's theorem says that, because the laws of physics are rotationally invariant, angular momentum is conserved.

Even with this correction, however, your claim here is wrong. Rotational invariance does not say that if run 2 of some experiment looks just like run 1 rotated by some angle, then they are really the same run. But that is what you are arguing here.

Let me ask you this, then. If you did an experiment on one end of the bench and translated it to the other end, can you call that a new set of results, or are you reproducing the first result?

 

[Ian J Miller]

Why should I, or anyone actually doing these experiments, care about your derivation?

The people who actually do these experiments don't have any trouble understanding what the terms in the inequalities mean, or how the inequalities were derived, or how to calculate the numerical values from their data. If you are correct, they must all be doing something obviously wrong. What is that thing?

When you say, what is that thing? what do you think the above discussion is about? As an aside, I am not saying they are wrong; I am asking you why you and others think they are right.

I have explained my problem to the best of my ability. So far, nobody seems to understand the question I am putting, so i think this is no longer useful to me or anyone else.

 

[PeterDonis]

The Bertlmann socks does not use the sin squared because there are no waves involved.

Wrong. It doesn't use the sin squared because it is not a quantum model, it is a local hidden variable model.

You say the QM model is not equivalent to the Malus law, but it counts joint probabilities with the same function.

For this particular case, perhaps. That still doesn't mean you can expect to apply classical reasoning to a quantum model.

I never said the sin squared was involved in deriving the inequality

Then I fail to see why you keep talking about it, since your point, to the extent you have a coherent point, appears to be that there is something about the way the inequalities are derived that makes them somehow not apply the way they are claimed to apply to the experiments that are supposed to test them.

If you did an experiment on one end of the bench and translated it to the other end

Do you mean, move to the other end of the bench and then do another experiment that has (to within experimental error) the same initial conditions and measurements?

In what follows, I'll assume that the answer is yes.

can you call that a new set of results, or are you reproducing the first result?

Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.

What is your point with all this?

When you say, what is that thing? what do you think the above discussion is about?

I have no idea. That's why I keep asking you to actually quote equations and text from the paper you referenced in order to make whatever point you are trying to make. I understand the paper you referenced, so if you are quoting equations and text from that, I will at least be able to start from a point that I understand, in order to try to grasp whatever point you are trying to make. When you insist on trying to make your point using your own idiosyncratic notation and your own made up derivations, on the other hand, I have no point to start from at all, since I can't make sense of either your notation or your derivations.

I am asking you why you and others think they are right.

Um, because I and others (including the theorists and experimenters themselves) understand the derivations and equations and arguments they are using and agree that they are correct?

Everything is laid out right there in Bell's papers. What's wrong with his arguments? In my opinion, and apparently in the opinion of the theorists and experimenters in this field who have spent several decades now doing more and more accurate experiments and confirming everything Bell said, nothing. Isn't that a good enough reason to think they are right?

I have explained my problem to the best of my ability.

I strongly doubt that. I strongly doubt that it is beyond your ability to quote some actual equations and text from the paper you reference that will illustrate whatever point you think you are trying to make.

More precisely, I strongly doubt that would be beyond your ability, if you had an actual coherent point to make. So the fact that you have not done this obvious thing just indicates to me that you do not.

So far, nobody seems to understand the question I am putting

I have already explained why that is, multiple times now. See above.

 

[PeterDonis]

Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.

What is your point with all this?

To sharpen the question I ask at the end of this quote, let me run with the implied analogy you made here. In the case of the experiments described in Bell's Bertlmann's socks paper, we have two sets of runs where the difference in angles is the same, 45 degrees: we have runs where one measurement is done at 0 degrees and one is done at 45 degrees, and we have runs where one measurement is done at 45 degrees and one is done at 90 degrees. Rotational invariance says that, to within experimental error, the correlations observed in both sets of runs should be the same.

But rotational invariance does not tell us what those correlations should be, numerically. For that, we need a theoretical model. And both theoretical models that Bell uses in his paper, the QM one and the Bertlmann's socks one, satisfy rotational invariance: both of them predict that the correlations in both sets of runs described above should be the same. But they predict different numerical values for those correlations: the QM model predicts a correlation of $\sin^2 22.5 / 2$, or $.0732$, for both sets of runs, while the Bertlmann's socks model predicts a correlation of $22.5 / 180$ (since we're using degrees, the denominator is $180$ instead of $\pi$), or $.125$, for both sets of runs. Rotational invariance gives us no help at all in deciding between these theoretical models. So what's the point of bringing it up?

 

[vanhees71]

Maybe it would tremendously help, if the OP would read a good textbook's treatment of the Bell inequalities. Bell's papers are sometimes not so easy to understand, because he has a quite special language of his own and is a bit too much inclined towards philosophy rather than pure physics.

A very clear philosophy-free treatment of Bell's inequalities and their violation according to QT can be found in

S. Weinberg, Lectures on Quantum Mechanics, Cambridge
University Press, Cambridge, 2 edn. (2015),
https://www.cambridge.org/9781107111660

 

[Ian J Miller]

Wrong. It doesn't use the sin squared because it is not a quantum model, it is a local hidden variable model.

For this particular case, perhaps. That still doesn't mean you can expect to apply classical reasoning to a quantum model.Then I fail to see why you keep talking about it, since your point, to the extent you have a coherent point, appears to be that there is something about the way the inequalities are derived that makes them somehow not apply the way they are claimed to apply to the experiments that are supposed to test them.Do you mean, move to the other end of the bench and then do another experiment that has (to within experimental error) the same initial conditions and measurements?

In what follows, I'll assume that the answer is yes.Both. I am generating a second set of results, which, given the identical initial conditions and measurements and the fact that the laws of physics are translation invariant, I expect to be identical, to within experimental error, with the first set of results.

What is your point with all this?I have no idea. That's why I keep asking you to actually quote equations and text from the paper you referenced in order to make whatever point you are trying to make. I understand the paper you referenced, so if you are quoting equations and text from that, I will at least be able to start from a point that I understand, in order to try to grasp whatever point you are trying to make. When you insist on trying to make your point using your own idiosyncratic notation and your own made up derivations, on the other hand, I have no point to start from at all, since I can't make sense of either your notation or your derivations.Um, because I and others (including the theorists and experimenters themselves) understand the derivations and equations and arguments they are using and agree that they are correct?

Everything is laid out right there in Bell's papers. What's wrong with his arguments? In my opinion, and apparently in the opinion of the theorists and experimenters in this field who have spent several decades now doing more and more accurate experiments and confirming everything Bell said, nothing. Isn't that a good enough reason to think they are right?I strongly doubt that. I strongly doubt that it is beyond your ability to quote some actual equations and text from the paper you reference that will illustrate whatever point you think you are trying to make.

More precisely, I strongly doubt that would be beyond your ability, if you had an actual coherent point to make. So the fact that you have not done this obvious thing just indicates to me that you do not.I have already explained why that is, multiple times now. See above.

The socks is a hidden variable model? What is the hidden variable? The number of socks is clearly defined, the temperatures are measured, the length of the socks, say is measured. All is explicit. You may not know why the socks shrink, but that is not a hidden variable - it is an unexplored reason, probably due to protein folding and reorganization, which we expect to unravel with techniques like an electron microscope. As I understand it, a hidden variable is something you cannot measure. For example, in Bohm's pilot wave, the position of the particle is a hidden variable (as is presumably his quantum potential).

The connection between classical and quantum physics is that if sufficient data are obtained that you can get expectation or average values, then these expectation values follow the relationships of classical physics. (Ehrenfest, P. 1927. Bemerkung über die angenäherte Gültigkeit der klassichen Machanik innerhalb der Quantenmechanik Z. Physik. 45: 455 – 457.) I have assumed we have collected sufficient photons to get the expectation values in their relationships, in which case the Malus Law should apply.

The sin squared relationship is the expectation relation for the probability that the second detector will count the entangled partner counted at the first detector and is hence a theoretical prediction. Providing you keep count properly, this is also measured.

My point with the translational experiment is suppose you measured something you label as A+B- at one end of the bench, and moved it to the other end, you are simply repeating the experiment and you are still measuring what you call A+B-. By the same reasoning, 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. For the A+B- test, because you are only counting the second particle of an entangled pair, it is not a B at all, but a subset of A.

You wrote: "In my opinion, and apparently in the opinion of the theorists and experimenters in this field who have spent several decades now doing more and more accurate experiments and confirming everything Bell said, nothing. Isn't that a good enough reason to think they are right?" It is most certainly good enough to say the experiments gave the recorded results. That is without doubt. But if it is that right, why am I having so much trouble getting an explanation as to why simply rotating the detectors generates the third variable? Especially since moving the experiment within a symmetric environment has never done that elsewhere.

You wrote: "I can't make sense of either your notation or your derivations". The reason for using the inequality I did is that the question I am asking relates to the nature of the actual terms arising from the individual detectors. Most papers of which I am aware start with something like the CHSH inequality, that starts by assuming joint probabilities, in other words, the problem that is bothering me has already been assumed to be irrelevant. However, if you cannot follow the derivation I gave previously I can see why you are not understanding my question because it depends critically on what the terms actually mean.

 

[Ian J Miller]

To sharpen the question I ask at the end of this quote, let me run with the implied analogy you made here. In the case of the experiments described in Bell's Bertlmann's socks paper, we have two sets of runs where the difference in angles is the same, 45 degrees: we have runs where one measurement is done at 0 degrees and one is done at 45 degrees, and we have runs where one measurement is done at 45 degrees and one is done at 90 degrees. Rotational invariance says that, to within experimental error, the correlations observed in both sets of runs should be the same.

But rotational invariance does not tell us what those correlations should be, numerically. For that, we need a theoretical model. And both theoretical models that Bell uses in his paper, the QM one and the Bertlmann's socks one, satisfy rotational invariance: both of them predict that the correlations in both sets of runs described above should be the same. But they predict different numerical values for those correlations: the QM model predicts a correlation of $\sin^2 22.5 / 2$, or $.0732$, for both sets of runs, while the Bertlmann's socks model predicts a correlation of $22.5 / 180$ (since we're using degrees, the denominator is $180$ instead of $\pi$), or $.125$, for both sets of runs. Rotational invariance gives us no help at all in deciding between these theoretical models. So what's the point of bringing it up?

Now I am more confused. Bertlmann's socks were washed at three different temperatures. The degrees are degrees C, or K, not angles.

As far as theoretical models go, 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. The sin squared relationship is from the theory, but is only used to see if the observed results follow expectation.

The point of bringing up the rotational invariance is how does rotating a fixed configuration generate two new variables when the symmetry of the source indicates it should be considered simply the same experiment.

I believe I showed above that if you use a polarized source, where all the pairs are polarized in one plane and there is no rotational symmetry, then the inequality is complied with, at least if the Malus Law applies. So if it is only when the source is rotationally invariant that we get the violations (of course the statement could be checked by experiment) why is everyone so sure that simply rotating both detectors by the same amount generates new variables?

 

[PeterDonis]

Bertlmann's socks were washed at three different temperatures. The degrees are degrees C, or K, not angles.

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.

 

[PeterDonis]

The connection between classical and quantum physics is that if sufficient data are obtained that you can get expectation or average values, then these expectation values follow the relationships of classical physics. (Ehrenfest

No, that is not what Ehrenfest's theorem says. The equation he derived for expectation values only follows the same relationships as classical physics for certain expectation values under certain conditions. The claim you are making here is much stronger than that.

 

[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.