Can grandpa understand the Bell's Theorem?

[miosim]

It will shift it by 45 degrees, corresponding to the wave plate.

It means that the entangled photons may exhibit independence of their entangled characteristic. It is well within EPR paradigm but I thought that this is prohibited within QM and Bell’s paradigm; otherwise it would open the huge jar of worm-like questions.
Just couple of them are:
1. How you define entangled property (other than in the EPR terms) if they can be changed independently for each particle.
2. Does the change at one entangled photon is reflected in the wave function? If not, is QM wave function is complete description of events?

And of cause this should undermine the initial conditions of Bell’s theorem and interpretation of Aspect’s experiment that are based on the notion that “… correlations predicted by QM depends only on the orientations of polarizers …” (Bell’s Theorem : The Naive View Of an Experimentalist (page 14).

 

[DrChinese]

It means that the entangled photons may exhibit independence of their entangled characteristic. It is well within EPR paradigm but I thought that this is prohibited within QM and Bell’s paradigm; otherwise it would open the huge jar of worm-like questions.
Just couple of them are:
1. How you define entangled property (other than in the EPR terms) if they can be changed independently for each particle.
2. Does the change at one entangled photon is reflected in the wave function? If not, is QM wave function is complete description of events?

And of cause this should undermine the initial conditions of Bell’s theorem and interpretation of Aspect’s experiment that are based on the notion that “… correlations predicted by QM depends only on the orientations of polarizers …” (Bell’s Theorem : The Naive View Of an Experimentalist (page 14).

1. I have defined this any number of times: they are in a superposition of states. You can change the velocity (direction) of one without changing the velocity of the other as well. How is that any different?

2. The QM description is an complete as it gets. Otherwise, you would exceed the limits of the HUP. Which is what Bell tests demonstrate.

The correlations depend solely on the relative orientations of the polarizers (theta). What about this is hard to follow? Are you trying to say that the presence of a wave plate changes this statement somehow? You may as well say that whether or not my hand is blocking the detector on one side is a factor too. It would be helpful if you would use more common scientific terminology rather than trying to stretch the ordinary meaning of jargon. In controlled experiments, no other underlying physical variables have ever been detected other than theta. The QM correlation prediction depends on the wave state being produced, which of course changes when a wave plate is present. Or when my hand is present to disrupt things.

 

[miosim]

I have defined this any number of times: they are in a superposition of states. You can change the velocity (direction) of one without changing the velocity of the other as well. How is that any different?

If you do this for the velocity-entangled particles, do they LOSE their ENTANGLEMENT?

The QM description is an complete as it gets. Otherwise, you would exceed the limits of the HUP. Which is what Bell tests demonstrate.

In my opinion, the result of Gedanken Experiment you predicted severely damage the initial conditions of Bell’s theorem and the interpretation of Aspect’s experiment.

The correlations depend solely on the relative orientations of the polarizers (theta). What about this is hard to follow?

This “flies in the face” of the result of Gedanken Experiment you predicted, because a wave plate (and who knows what else) also affects the correlation

 

[DrChinese]

1. If you do this for the velocity-entangled particles, do they LOSE their ENTANGLEMENT?

2. In my opinion, the result of Gedanken Experiment you predicted severely damage the initial conditions of Bell’s theorem and the interpretation of Aspect’s experiment. This “flies in the face” of the result of Gedanken Experiment you predicted, because a wave plate (and who knows what else) also affects the correlation

1. Depends on whether you learn sufficient information about that velocity (momentum is the observable). HUP rules, that is as simple as I can say it. That is why entangled particles exhibit non-LR characteristics.

2. As to your opinion: it is clearly not based on the relevant science, as that has already been expressed to you many times in this thread. It makes me laugh to imagine you telling this to Bell, Aspect, or any other scientist (as if you discovered an important new fact that they failed to consider in their haste). But hey, otherwise good luck with that.

 

[Jonathan Scott]

There's a pair of photons which are in a combined unknown state, as a pair.

If you do anything to either one of them which does not involve resolving the state into a pure state, such as rotating it, reflecting it or whatever, then that operation acts on that half of the pair but does not affect the other one and doesn't tell you anything about the state. If however you do anything which definitely does resolve the state, such as putting it through a polarizing filter or a beam splitting device then observing it with a photo-detection device, then that also means that the state at the other end is now also known.

Obviously if you rotate or reflect a photon before observing it, then when you've resolved its state you have to backtrack through those operations to deduce the original state and hence the state of the other photon.

 

[SpectraCat]

I mean the angle between observable photons’ polarization (parallel, antiparallel or anything in between).

I just realized that I made a mistake that causes a major confusion.
While asking about observable polarization of the photon’s pair after one of them passed 90 deg wave plate I thought that antiparallel polarization means 180 degree, while 90 degree represents the middle point between parallel and antiparallel polarization. But I was wrong because 90 degree is difference between parallel and untiparalell polarization so 45 degree is a middle point.

I am sorry for this confusion.

Let me correct my previous question. What happens if one of the entangled photons passed 45 deg wave plate? Would the observable polarization of this photon's pair remain antiparallel or will be shifted by 45 degree?

This question is ill-defined. All that you can talk about are the following experimental parameters:

1) The settings of the detectors at A & B (i.e. the angle at which you set your polarizer).

2) Manipulations of the beams going to A and/or B (i.e. optical elements, including those that may rotate the polarization)

3) Statistics of detection events, either detector-local (i.e. only considering the detection statistics at A or B individually) or coincident (i.e. considering the correlations between time-coincident detections at both detectors).

The language that you use suggests that you think it makes sense to talk about "the polarization of an entangled photon" in between the point where it was generated, and the point where it was detected. In my opinion, such statements have no scientific basis.

So, let's modify your gedanken experiment. Let's talk about a setup where the "detectors" at A & B are actually polarizing beam splitters, each with two detectors that detect the polarization states |H> and |V>. Let us further assume that these are 100% efficient, so that each of the photons coming through is guaranteed to be detected at one of the detectors. Our entangled pairs are being generated by type II parametric down conversion, so that the polarizations of the two photons are anti-correlated in the |H> and |V> basis, corresponding to the entangled wavefunction:

$$\Psi=(|H_A>\otimes|V_B> + |V_A>\otimes|H_B>)$$

We start our experiment with both the A & B detectors aligned to detect in the same basis (i.e. |H>=|H_A>=|H_B>, etc.). In this configuration, we will find that each individual detector sees a 50-50 split between |H> and |V> detection events, and there is perfect anti-correlation between the coincidence measurements ... that is, if for a particular entangled pair the |H_A> detector clicks, then the |V_B> detector will also click, and vice-versa.

Now say that we put a 45 degree rotation on the polarization of the A beam. The statistics of the individual detections will not change .. i.e. each detector will still see a 50-50 split between |H> and |V>. However the coincident statistics for pairwise detection will be drastically different. In fact, you will find NO correlation for coincident detections. In other words, when |H_A> is detected, you will have an equal chance of observing |H_B> or |V_B> for that pair. This is in agreement with the predictions of Q.M., and with Malus' Law.

It is important to note that the loss of correlation in the coincidence statistics in the above example is due to the specific choice of 45 degrees as the rotation angle. If you choose a different rotation angle, you will measure coincidence statistics that are somewhere between perfectly anti-correlated and uncorrelated (i.e. random), with the precise coincidence rate given by Malus' law, with theta as the difference between the rotation angle, and the angle of the polarizing beam-splitter.

I suspect that most of this has already been laid out in this thread, but perhaps not in this form, and at the very least not for several pages . Hopefully this will help clear up some of the confusion.

 

[DrChinese]

Thanks SpectraCat & Jonathan! Your comments add a lot.

 

[miosim]

”… The language that you use suggests that you think it makes sense to talk about "the polarization of an entangled photon" in between the point where it was generated, and the point where it was detected. … In my opinion, such statements have no scientific basis….

I understand that within QM the polarization of entangled photons doesn’t make sense.
I also understand and agree with your description of your gedanken experiment (that I think isn’t differ from mine in the post #326). I also I agree with your prediction of the result of this experiment that matches with the prediction of DrChinese in post #327 (that time he ignored mistake with 90 degree (instead of 45 deg), but he understood what I ment).

Looks like we are on the same page and ready to move forward.

The reason I proposed this gedanken experiment is because I tried to falsify Bell’s and QM paradigms that, as I thought, would prohibit any changes of one of entangled particle without affecting another. Actually, as you pointed correctly, even asking the question what happens with photon that passes the wave plate prior to a wave function collapse would be an ill-defined question within the scope of the empirical QM theory that have nothing to offer about what happens with photon prior to a measurement.

So my question is how we can assume that a wave plate can rotate the polarization of an entangled photon if this is an ill-defined process within the scope of the QM? Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

 

[SpectraCat]

I understand that within QM the polarization of entangled photons doesn’t make sense.
I also understand and agree with your description of your gedanken experiment (that I think isn’t differ from mine in the post #326). I also I agree with your prediction of the result of this experiment that matches with the prediction of DrChinese in post #327 (that time he ignored mistake with 90 degree (instead of 45 deg), but he understood what I ment).

Looks like we are on the same page and ready to move forward.

The reason I proposed this gedanken experiment is because I tried to falsify Bell’s and QM paradigms that, as I thought, would prohibit any changes of one of entangled particle without affecting another. Actually, as you pointed correctly, even asking the question what happens with photon that passes the wave plate prior to a wave function collapse would be an ill-defined question within the scope of the empirical QM theory that have nothing to offer about what happens with photon prior to a measurement.

So my question is how we can assume that a wave plate can rotate the polarization of an entangled photon if this is an ill-defined process within the scope of the QM? Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

We say that the polarization is rotated because that is what is observed for non-entangled photons with well-defined polarizations. However, that is not supposed to imply that we somehow know what is going on with the entangled pairs. Rather, what we are saying is that, we know that if detect before the waveplate, we detect either |H> of |V>, AND we know that the waveplate rotates photons with well-defined polarization |H> to have well-defined polarization |H'> (and |V> to |V'>). It is thus more accurate to say that we are rotating the detection basis for the measurement, which is how I have tried to reflect things in my past few posts, although the idiomatic language implying that there is rotation of the polarization of the photon itself can be hard to avoid.

Basically you are worrying about the internal aspects of a process for which QM and experiment can only provide *definitive* answers about inputs and outputs. I know that it is unsatisfying to treat the rest of the process as a black-box, but the sad truth is that there are several interpretations of QM which propose models for "what actually happens" to the system internally, but so far there are no experimental tests that can tell us which of these interpretations is correct, and NONE of them can give us the complete story yet (at least not as far as I know).

That is why Mermin quipped, "Shut up and calculate!" ... I don't quite agree with that, because I still find it useful to ponder some of the interesting paradoxes that arise when aspects of interpretations are discussed, but I don't fool myself into think any of those interpretations provide anything approaching a complete description of reality.

 

[DrChinese]

...Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

The mathematical formalism IS the explanation. Same is true for relativity. We, as humans, want something that is not going to be supplied. So that is why interpretations were invented. Which is partially why they are all somewhat unsatisfying. They don't REALLY explain anything at all.

There is nothing really difficult about the idea that a superposition can be rotated. Each component of the superposition H + V is transformed: to H' + V'. And in fact, you can even separate those components and do different things to each. With suitable precision (this is extremely difficult in practice), you could later recombine them after having them go different paths.

 

[miosim]

As I understand nobody here see the contradiction between the dogma of QM and the prediction of the discussed above Gedanken Experiment; and it is fine with me. Let’s move on and try the Gedanken Experiment #2.

This is the classical Aspect’s experiment with one exception: the source of entangled photon is replaced with UNTANGLED twin photons that maintain untiparallel polarization.
What is your prediction for this experiment?

 

[SpectraCat]

As I understand nobody here see the contradiction between the dogma of QM and the prediction of the discussed above Gedanken Experiment...

That's because there isn't one ... and it's not just a Gedanken experiment ... Aspect and Zeilinger and others have done precisely that experiment many times (with the exception that they don't have "perfect" detection efficiencies), and they always obtain results that are consistent with the predictions from QM . So I really don't understand what your point is ...

This is the classical Aspect’s experiment with one exception: the source of entangled photon is replaced with UNTANGLED twin photons that maintain untiparallel polarization.
What is your prediction for this experiment?

Assuming that the new source produces counter-propagating beams with random polarizations, the statistics for the individual detector readings at A & B will be precisely the same (50-50 between |H> and |V>), and the coincidence statistics will be completely uncorrelated for any choice of detector settings and any setting of the "polarization rotation device".

 

[harrylin]

There's a pair of photons which are in a combined unknown state, as a pair.

If you do anything to either one of them which does not involve resolving the state into a pure state, such as rotating it, reflecting it or whatever, then that operation acts on that half of the pair but does not affect the other one and doesn't tell you anything about the state. If however you do anything which definitely does resolve the state, such as putting it through a polarizing filter or a beam splitting device then observing it with a photo-detection device, then that also means that the state at the other end is now also known.

Obviously if you rotate or reflect a photon before observing it, then when you've resolved its state you have to backtrack through those operations to deduce the original state and hence the state of the other photon.

Exactly; and there is nothing fantastic about us deducing that state. As I already remarked, this example demonstrates that the hypothesis that the measured photon magically and in no time communicates its state to its entangled photon is flawed, as that alone could not do the trick. Also information about its history would need to be communicated, which in turn would have needed to be remembered somewhere, which makes such a hypothesis increasingly implausible.

 

[Jonathan Scott]

Exactly; and there is nothing fantastic about us deducing that state. As I already remarked, this example demonstrates that the hypothesis that the measured photon magically and in no time communicates its state to its entangled photon is flawed, as that alone could not do the trick. Also information about its history would need to be communicated, which in turn would have needed to be remembered somewhere, which makes such a hypothesis increasingly implausible.

Given that entanglement violates locality anyway, you only need to assume that the particles are physically connected via their shared history (which is a connection back in time on one side and forward on the other). There is no need for a separate record of the history.

You could alternatively assume that the particles communicate via a spacelike connection along the traveled path, where the connection is subject to the same operations (rotation, reflection etc.) as the original photon, but I think that this idea may have been undermined by Aspect's experiments using a high frequency switch to select between alternative observations.

 

[miosim]

That's because there isn't one ... and it's not just a Gedanken experiment ... Aspect and Zeilinger and others have done precisely that experiment many times (with the exception that they don't have "perfect" detection efficiencies), and they always obtain results that are consistent with the predictions from QM . So I really don't understand what your point is ...

First, I don’t know any Aspect or Zeilinger experiment that “… have done precisely that experiment many times…” meaning installing the wave plate on one side. This experiment is intended to challenge the Bell’s theorem indirectly by demonstrating that QM entanglements and changes to one particle only are incompatible. This was the main point of my Gedanken experiment #1. However I could be wrong.

Assuming that the new source produces counter-propagating beams with random polarizations, the statistics for the individual detector readings at A & B will be precisely the same (50-50 between |H> and |V>), and the coincidence statistics will be completely uncorrelated for any choice of detector settings and any setting of the "polarization rotation device".

As I understand, you prediction is based on the Bell’s paradigm according to which to achieve the cos^2 correlation the photons need to be entangled (to preserve their superpositions by action over the distance). However the way I understand this experiment, the EPR correlated photons (that are untangled, but maintain antiparallel polarization) should produce the same cos^2 correlation without any action over the distance. Now we have a tangible disagreement.

How difficult is to perform this experiment?

 

[SpectraCat]

First, I don’t know any Aspect or Zeilinger experiment that “… have done precisely that experiment many times…” meaning installing the wave plate on one side. This experiment is intended to challenge the Bell’s theorem directly by demonstrating the QM entanglements that in my opinion is sort of the “conservation of momentum” that couldn’t be violated without braking the entanglement. This was the main point of my Gedanken experiment #1. However I could be wrong.

I think that you are wrong. The Aspect and Zeilinger experiments use polarizing beam splitters (PBS) for their detection. For practical reasons, it is easiest to work with such devices when all the detection beams are parallel to the table. Therefore, I am pretty sure that the way that they "set the detection angle" for their detectors is to put a polarization rotator in front of each PBS, rather than physically rotating the PBS.

I also don't understand what you mean by the "conservation of momentum argument" ... could you please elaborate? Also, as Dr. Chinese said .. do you really expect to find something so simple that was missed by all of these extremely good and well-respected scientists? Not to mention all of the reviewers who have critiqued their work before accepting it for publication.

As I understand, you prediction is based on the Bell’s paradigm that to achieve cos^2 correlation the photon need to be entangled (to preserve their superpositions by action over the distance). However the way I understand this experiment, the EPR correlated photons (that are untangled, but maintain antiparallel polarization) should produce the same cos^2 correlation without any action over the distance. Now we have a tangible disagreement.

How difficult is to perform this experiment?

Hmmm .. I may have misunderstood your second gedanken experiment initially ... I guess I should have asked some clarifying questions before answering. As I now understand it, you are proposing a hypothetical source with the following characteristics:

1) It emits counter-propagating beams of paired (i.e. time-coincident) photons A & B.

2) The polarization of photon A is always randomly chosen to be |H> or |V>

3) The polarization of photon B is always guaranteed to be anti-parallel to that of A

If that is what you are proposing, then I don't see how that is any different than entanglement. In other words, the wavefunction written in terms of the detector states will be exactly the same as in the previous case. Thus I would expect that you see precisely the same results as for the first example.

As for doing the experiment, I am not sure how that could be accomplished. When you say the two beams have characteristics 1 through 3 above, but are UNENTANGLED, I guess you mean that they come from independent sources, or something like that? I cannot see how you could accomplish this experimentally ... the sticky point is condition 1) .. i.e. the photon pairing. I don't know how you can guarantee that two photons can be emitted at the same time from two different sources. If you are using lasers, you could synchronize the timing of pulses to very high accuracy, but each pulse contains a huge number of photons, and there is no well-defined relationship between any pair of photons in different pulses.

I guess your point is that there is nothing mystical about entanglement per se, and any source that has the characteristics of 1-3 will produce the same behavior as for entangled photons created by parametric down conversion. I think I agree with that ... remember what I have been telling you from the start ... all we can specify experimentally is what goes in (i.e. conditions 1-3 above), and the detector settings. The only issue I see is that it is not clear to me how we could satisfy conditions 1-3 without using entangled photons. However, having said that, I don't think it matters that the source you describe uses photons ... if you set up the same experiment with classical objects, the detection statistics would be the same.

Consider the following set up:

1) you have a machine that produces pairs of boxes with lightbulbs on them, A & B

2) the lightbulb on box A is randomly chosen to be on or off

3) the lightbulb on box B is always guaranteed to be in the opposite of box A

4) the state of the light bulb on box A can be "rotated" by passing it through a device that has some probability of flipping the state according to a user-specified "angle". The probability relationship is designed to be analogous to Malus' law for photons.

I am not 100% certain, but I believe the classical device described above will produce identical measurement statistics to the entangled photon experiment we have been discussing. I would appreciate it if someone more deeply familiar with these experiments (are you there, Dr. Chinese?) would verify this please. Obviously, if I am wrong about this, then I have a critical misunderstanding somewhere .. and I would like to rectify that.

 

[miosim]

I think that you are wrong. The Aspect and Zeilinger experiments use polarizing beam splitters (PBS) for their detection. …

Indeed I was wrong. If no other, more important issues, I would try to understand why changing the polarization in one entangled particle doesn’t considered as a violation of entanglement. I may come back to this at another time.

I also don't understand what you mean by the "conservation of momentum argument" ... could you please elaborate?

This is just an analogy with the classical physics. Nothing important.

As to your opinion: it is clearly not based on the relevant science, as that has already been expressed to you many times in this thread. It makes me laugh to imagine you telling this to Bell, Aspect, or any other scientist (as if you discovered an important new fact that they failed to consider in their haste). But hey, otherwise good luck with that.

Also, as Dr. Chinese said .. do you really expect to find something so simple that was missed by all of these extremely good and well-respected scientists? Not to mention all of the reviewers who have critiqued their work before accepting it for publication.

I don’t belief in authority. I also have a very little respect to the “well-respected scientists” who insist on the greatness of QM. Personally I’m not impressed with this theory at all. Actually I don’t think that QM is a theory, but application only. According to Wikipedia “…A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content...” As far as I am concerned QM doesn’t have meaningful semantic component.
Regarding other scientists I respect Einstein (who in my opinion was born too yearly to be fully understood) and Schrödinger. I like John Bell’s bold thinking, but I wouldn’t hesitate to tell him what I think about his theorem.
I think that I provided enough material to ridicule my self-assurance.

Hmmm .. I may have misunderstood your second gedanken experiment initially ... I guess I should have asked some clarifying questions before answering. As I now understand it, you are proposing a hypothetical source with the following characteristics:

1) It emits counter-propagating beams of paired (i.e. time-coincident) photons A & B.

It is correct, more specifically this beam consists of the the former entangled photons that were “striped” from their entanglement and become EPR photons.

2) The polarization of photon A is always randomly chosen to be |H> or |V>
3) The polarization of photon B is always guaranteed to be anti-parallel to that of A

It is correct.

If that is what you are proposing, then I don't see how that is any different than entanglement. In other words, the wavefunction written in terms of the detector states will be exactly the same as in the previous case. Thus I would expect that you see precisely the same results as for the first example.

I agree with you and this is my main argument against Bell’s theorem; he compared the behavior of the real QM model with the fake deterministic EPR model and find that “fake” model gives different prediction.
If the fake deterministic EPR model is replaced with the real EPR model it would be no inequity.
In the proposed experiment we would use the correlated (but not entangled) photons and would achieve the same result without any action over the distance. However according to Bell it is impossible:
“…It cannot be done, so long as action at a distance is excluded…” (from Bertlmann’s Socks And The Nature Of Reality.)

So if this could be done the Bell’s theorem is dead.

As for doing the experiment, I am not sure how that could be accomplished. When you say the two beams have characteristics 1 through 3 above, but are UNENTANGLED, I guess you mean that they come from independent sources, or something like that? I cannot see how you could accomplish this experimentally ...

I think that we may use the same source as in the Aspect’s experiment but with beams passing through the media that causes the wave function collapse, but preserves the untiparallel polarizations. I see other potential solutions to achieve a similar result, but if you agree with me on the outcome of Gedanken Experiment #2 I see no need to perform this experiment.

I will respond on the rest of your comments later.

 

[miosim]

I guess your point is that there is nothing mystical about entanglement per se, and any source that has the characteristics of 1-3 will produce the same behavior as for entangled photons created by parametric down conversion.

It is correct

I think I agree with that ... remember what I have been telling you from the start ... all we can specify experimentally is what goes in (i.e. conditions 1-3 above), and the detector settings. The only issue I see is that it is not clear to me how we could satisfy conditions 1-3 without using entangled photons.

Why would you need entangled photons if the Gedanken Experiment #2 (that doesn’t use entangled photons) would yield the same result?

However, having said that, I don't think it matters that the source you describe uses photons ... if you set up the same experiment with classical objects, the detection statistics would be the same
Consider the following set up:

1) you have a machine that produces pairs of boxes with light bulbs on them, A & B …

I am having problem with the expaining the physical phenomenon, that is far from being understood, in terms of analogy. Analogy is a simplification of phenomenon and therefore is distortion of this phenomenon. However if this phenomenon is fully understood the analogy could be selected to insure that at least the critical element of the phenomenon we try to explain isn’t distorted.
Therefore I can’t accept any illustration of Bell’s theorem in terms of light bulbs, coloring balls, socks, etc that oversimplified and further distorts already distorted by simplified reality portrayed in the Bell’s theorem where QM events are described in terms of algebra and Yes/No results. I also found unacceptable that Bell provides his interpretation of “what Einstein had in mind” by using a naive classical picture. I am not surprised that eventually Bell comes with the abstract EPR model which prediction contradicts with the empirical QM. I wish Einstein would slap Bell’s hand and remind him that EPR argument wasn’t about how QM predicts, but how it interprets results. If Bell believed that the EPR interperation indeed contradicts with the prediction of QM (and if Einstein isn’t around to defend him self) Bell must show that his interpretation of EPR is correct or at least Bell must collaborate this interpretation in more details.
The ovrsimplifying the reality and sloppiness in justification of initial conditions for Bell’s theorem discourages me from learning more about Bell’s paradigm and his definition of reality (if you let me to redefine a reality I can prove/disprove anything). Majority probably find my ignorance as non justifiable, but I wouldn’t spent more time to prove it, because a talk is cheap.
It is why I should better focus on the Gedanken Experiment #2 to conform or refute the Bell’s paradigm experimentally. If this experiment conforms the Bell’s paradigm I will buy a beer for DrChinese.

As I understand there may be a difficulty to produce the source of the EPR correlated photons. If there isn’t the optical media that would collapse the wave function and in the same time preserve untiparallel polarization of photons, we may use a different approach as follows:
We may produce the EPR correlated photons by using the two polarizers set in parallel and placed at the opposite sides from the light source of entangled photons. This will produce the corelated photons in one particle angle. Rotation of these polarizers in tandem will produce the the polarized correlated photons pairs of any chosen angle and the Aspect-like experiment will be performed for the any number of chosen angles. Would it work?

P.S.
Actually, do we really need rotating polarizers to produce untangled photons pairs or stationary would work as well for this experiment?

 

[harrylin]

[..] if you set up the same experiment with classical objects, the detection statistics would be the same.

Consider the following set up:

1) you have a machine that produces pairs of boxes with lightbulbs on them, A & B

2) the lightbulb on box A is randomly chosen to be on or off

3) the lightbulb on box B is always guaranteed to be in the opposite of box A

4) the state of the light bulb on box A can be "rotated" by passing it through a device that has some probability of flipping the state according to a user-specified "angle". The probability relationship is designed to be analogous to Malus' law for photons.

I am not 100% certain, but I believe the classical device described above will produce identical measurement statistics to the entangled photon experiment we have been discussing. I would appreciate it if someone more deeply familiar with these experiments (are you there, Dr. Chinese?) would verify this please. Obviously, if I am wrong about this, then I have a critical misunderstanding somewhere .. and I would like to rectify that.

If I correctly understand your example, there is a flaw there: the light bulb on box B is supposed to be always opposite to that what box A would have if it were not altered by your operation no.4. Just now (in post #364) Jonathan proposed "only" a "connection back in time" for that issue.

I have now come to regard Bell's Theorem as just another paradox; with paradoxes the devil is often in the details as they say. :tongue2: For example, relativity theory has paradoxes based on "perfectly stiff" objects.

Something similar may be the problem here. As I mentioned in a parallel thread, according to Tim Maudlin's "Quantum non-locality and relativity", "real laboratory conditions at best allow some approximation of perfect agreement or disagreement".

Obviously, in order for such a classical example to reproduce an entangled photon experiment, the same level of approximation must be created.

Harald

 

[SpectraCat]

If I correctly understand your example, there is a flaw there: the light bulb on box B is supposed to be always opposite to that what box A would have if it were not altered by your operation no.4.

Yes, that is indeed what I meant. I should have added

5) the result for box B is determined PRIOR to the operation on A performed in number 4.

Just now (in post #364) Jonathan proposed "only" a "connection back in time" for that issue.

As I understand it, time for photons is different from time as we experience it, because photons don't have a frame. So perhaps that is not as strange as it might sound.

I have now come to regard Bell's Theorem as just another paradox; with paradoxes the devil is often in the details as they say. :tongue2: For example, relativity theory has paradoxes based on "perfectly stiff" objects.

Those are not paradoxes .. those are misunderstandings of relativity .. at least the ones I am aware of are. Personally, I think paradoxes are ALWAYS misunderstandings, and we as humans are prone to them because of the inherent bias associated with the development of our intellect and consciousness in an environment that is, at least ostensibly, governed by Newtonian mechanics.

Something similar may be the problem here. As I mentioned in a parallel thread, according to Tim Maudlin's "Quantum non-locality and relativity", "real laboratory conditions at best allow some approximation of perfect agreement or disagreement".

Obviously, in order for such a classical example to reproduce an entangled photon experiment, the same level of approximation must be created.

Harald

Right, the way this is typically dealt with is that you make the "no conspiracies" assumption. In that case, the imperfections in the detection arrangements appear as random noise, which has the effect of suppressing statistical correlations, rather than enhancing them. Therefore it should always work against experimental demonstrations of Bell violations.

 

[Joncon]

Hmmm .. I may have misunderstood your second gedanken experiment initially ... I guess I should have asked some clarifying questions before answering. As I now understand it, you are proposing a hypothetical source with the following characteristics:

1) It emits counter-propagating beams of paired (i.e. time-coincident) photons A & B.

2) The polarization of photon A is always randomly chosen to be |H> or |V>

3) The polarization of photon B is always guaranteed to be anti-parallel to that of A

If that is what you are proposing, then I don't see how that is any different than entanglement. In other words, the wavefunction written in terms of the detector states will be exactly the same as in the previous case. Thus I would expect that you see precisely the same results as for the first example.

Sorry but wouldn't this be very different than entanglement?

Example using unentangled photons with anti-parallel polarizations:
Both detectors are set vertical. Photon A is polarized at 30 degrees from vertical, so photon B is at 120 degrees.
Photon A (if I understand Malus' law correctly) has a 75% chance of passing through the detector. So if it does pass through, photon B still has a 25% of passing through its respective detector.

But with entangled photons, if photon A passes through its detector then photon B is instantly determined to be at 90 degrees, which means it has no chance of passing through the detector.

Have I missed something?

Oh, hello all BTW. I'm very much a layman on this subject so please be gentle if I've got anything wrong! :)

Jon

 

[harrylin]

Yes, that is indeed what I meant. I should have added

5) the result for box B is determined PRIOR to the operation on A performed in number 4.

Usually photons are detected after operations such as no.4

As I understand it, time for photons is different from time as we experience it, because photons don't have a frame. So perhaps that is not as strange as it might sound.

Photons have an infinite number of frames... probably you meant that they have no rest frame. For a photon time stands still; but that is irrelevant. Physical theory relates to our experience of time, as measured with "perfect" material clocks. And such clocks only run forward.

Those are not paradoxes .. those are misunderstandings of relativity .. at least the ones I am aware of are. Personally, I think paradoxes are ALWAYS misunderstandings, and we as humans are prone to them because of the inherent bias associated with the development of our intellect and consciousness in an environment that is, at least ostensibly, governed by Newtonian mechanics.

Paradox 1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. - http://dictionary.reference.com/browse/paradox

Right, the way this is typically dealt with is that you make the "no conspiracies" assumption. In that case, the imperfections in the detection arrangements appear as random noise, which has the effect of suppressing statistical correlations, rather than enhancing them. Therefore it should always work against experimental demonstrations of Bell violations.

If that is true is perhaps part of the debate that is discussed in parallel threads as well as in the physics FAQ. However, I merely replied to your question "if the classical device described above will produce identical measurement statistics to the entangled photon experiment we have been discussing". Apparently your own answer here is that it won't.

 

[SpectraCat]

Usually photons are detected after operations such as no.4

Who said anything about detection? I was describing *exactly* the objection you raised in your previous post. You said that "the light bulb on box B is supposed to be always opposite to that what box A would have if it were not altered by your operation no.4.". My addition of 5) was to clarify that.

Paradox 1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. - http://dictionary.reference.com/browse/paradox

Of course I know the definition of paradox .. don't be condescending. Re-read what I wrote ... the first part of my I was expressing my doubts that relativity paradoxes you mentioned are actually paradoxes when fully thought through by someone with a deeper understanding of physics (see http://en.wikipedia.org/wiki/Ehrenfest_paradox" for the resolution of the rigidity problem you mentioned). The second part was about my opinion that paradoxes are actually artifacts of human consciousness.

However, I merely replied to your question "if the classical device described above will produce identical measurement statistics to the entangled photon experiment we have been discussing". Apparently your own answer here is that it won't.

No, what makes you say that? I have said that I think it *will* produce identical measurement statistics ... once we have clarified its operation according to the last few posts. Of course I might be *wrong* with that prediction, but so far I can't see why this wouldn't produce identical results.

 

[harrylin]

Who said anything about detection? I was describing *exactly* the objection you raised in your previous post. You said that "the light bulb on box B is supposed to be always opposite to that what box A would have if it were not altered by your operation no.4.". My addition of 5) was to clarify that.

Detection is measurement; commonly photons are measured after one of them passes through a wave plate. Your addition 5):
"the result for box B is determined PRIOR to the operation on A performed in number 4."
I wonder if that corresponds to the quantum description which has that the result of the measurement is only determined at the time of measurement (as also suggested by tests with ultra fast changing detectors).

Of course I know the definition of paradox .. don't be condescending. Re-read what I wrote ... the first part of my I was expressing my doubts that relativity paradoxes you mentioned are actually paradoxes when fully thought through by someone with a deeper understanding of physics [..]. The second part was about my opinion that paradoxes are actually artifacts of human consciousness.

I had already re-read what you wrote and was merely trying to be polite: First you made the erroneous claim that I was mistaken to call them paradoxes while they are paradoxes by definition, and immediately thereafter you invalidated that claim as you expressed agreement with the standard definition of "paradox".

Note: You are talking to "someone with a deeper understanding of the physics" concerning such SR paradoxes (I even published a corrected solution to another paradox in a main physics journal), and that's why I gave that SR example. From my experience with SR paradoxes and the similarities I am optimistic that this nut will also be cracked (if it did not already happen!).

No, what makes you say that? I have said that I think it *will* produce identical measurement statistics ... once we have clarified its operation according to the last few posts. Of course I might be *wrong* with that prediction, but so far I can't see why this wouldn't produce identical results.

I can see no reason why a classical example that in principle has no precision limit would exactly reproduce the QM precision limitations that I cited, and you seemed to agree. There may also be other objections; let's wait for drChinese!

 

[SpectraCat]

Detection is measurement; commonly photons are measured after one of them passes through a wave plate. Your addition 5):
"the result for box B is determined PRIOR to the operation on A performed in number 4."
I wonder if that corresponds to the quantum description which has that the result of the measurement is only determined at the time of measurement (as also suggested by tests with ultra fast changing detectors).

I understand your objection, the word "result" was perhaps a poor choice, but I don't think the distinction is an issue for this explicitly classical simulation. However, perhaps a better way to phrase 5) so that it is consistent with QM is to say the following instead:

5) The state of the lightbulb on box B is always opposite to that of A for specific setting (say 0º) of the "rotation" device described in 4).

Actually, I think I really already said that, because I specified that the rotation device obeys the analog of Malus' Law for this example.

I had already re-read what you wrote and was merely trying to be polite: First you made the erroneous claim that I was mistaken to call them paradoxes while they are paradoxes by definition, and immediately thereafter you invalidated that claim as you expressed agreement with the standard definition of "paradox".

Hmmm ... I don't know ... I guess I read that definition differently that you do. To me a paradox is no longer a paradox once it has been resolved, but I guess I see your point. Also, it is true that these things retain the name "paradox" after they have been explained (e.g. Twin's Paradox, Zeno's Paradox), so I guess that is consistent with your usage as well. It sounds like we agree about the important part: namely that they are usually (and perhaps always) artifacts of human consciousness, rather than real contradictions.

Note: You are talking to "someone with a deeper understanding of the physics" concerning such SR paradoxes (I even published a corrected solution to another paradox in a main physics journal), and that's why I gave that SR example. From my experience with SR paradoxes and the similarities I am optimistic that this nut will also be cracked (if it did not already happen!).

Sorry .. which "nut" are you referring to? The original EPR Paradox?

I can see no reason why a classical example that in principle has no precision limit would exactly reproduce the QM precision limitations that I cited, and you seemed to agree.

My point before was, if you allow the "no conspiracies" assumption, then noise will only attenuate the correlations, rather than increasing them. Extra random noise can always be artificially added to systems where it is absent ... it is the opposite trick that is difficult :wink". So, although I didn't say it explicitly before, I think that you could induce an artificial precision limit in my classical example to match experimental reality.

There may also be other objections; let's wait for drChinese!

I definitely agree that he will likely be able to clarify whether my classical model will indeed produce statistics consistent with QM entanglement.

 

[harrylin]

[snip our agreement about several things]
Sorry .. which "nut" are you referring to? The original EPR Paradox?

For me Bel's Theorem is a "nut to crack". Indeed I forgot that already EPR's paper is called a paradox, but I forgot why. :uhh:

My point before was, if you allow the "no conspiracies" assumption, then noise will only attenuate the correlations, rather than increasing them. Extra random noise can always be artificially added to systems where it is absent ... it is the opposite trick that is difficult :wink".

I'm aware (perhaps not fully) of the difficulties that those people are facing who try to create local realist models models. :tongue:

So, although I didn't say it explicitly before, I think that you could induce an artificial precision limit in my classical example to match experimental reality. [...]

Good . I guess that with such a device your example can exactly simulate a quantum device - any other objections?

Cheers,
Harald

 

[SpectraCat]

For me Bel's Theorem is a "nut to crack". Indeed I forgot that already EPR's paper is called a paradox, but I forgot why. :uhh:

I'm aware (perhaps not fully) of the difficulties that those people are facing who try to create local realist models models. :tongue:

Lord, I hope you're not calling me a local realist! :rofl:

Good . I guess that with such a device your example can exactly simulate a quantum device - any other objections?

I just want to make it clear that I think that it will only work for this particular example. The point I wanted to make to miosim that somehow appears to have gotten lost in all of this is that, if you add a SECOND "rotation" device (like the one described in 4) to the B stream, whose setting can also be arbitrarily chosen, then the results for coincidence measurements will be DIFFERENT from the predictions of QM, and from the experimental statistics with entangled photons. I thought I had put that into my earlier responses, but somehow it seems to have gotten left out.

 

[SpectraCat]

It is correct

Why would you need entangled photons if the Gedanken Experiment #2 (that doesn’t use entangled photons) would yield the same result?
...
It is why I should better focus on the Gedanken Experiment #2 to conform or refute the Bell’s paradigm experimentally. If this experiment conforms the Bell’s paradigm I will buy a beer for DrChinese.

Well, there is an important point about your Gedanken experiment that we have been neglecting so far. Namely, as designed, it cannot lead to a Bell violation (at least I don't think it can). In order to make an experimental test of Bell's theorem, you need to be able to choose the detector settings at both sides of the experiment. So for your Gedanken's you would need to have a second polarizer for the B photon, which could be set to an angle independently of the polarizer for the A photon.

Now, in that set up, you would find very different results for the two gedanken experiments. For gedanken experiment #1, you would find perfect anticorrelation of the measurements any time the detectors were set to the same angle, so if you set them both to 45º, you would see perfect anti-correlation. For gedanken experiment #2, the you will only see perfect anti-correlation when the detection basis is identical to the basis in which the photons were polarized from their sources. If you were to set both the A and B detectors to 45º, you would see no correlation between the two sets of measurements.

Again, I am not 100% certain of this, but I recently went back and re-read some of the original papers linked from Dr. Chinese's website, and I believe this is correct.

As I understand there may be a difficulty to produce the source of the EPR correlated photons. If there isn’t the optical media that would collapse the wave function and in the same time preserve untiparallel polarization of photons, we may use a different approach as follows:
We may produce the EPR correlated photons by using the two polarizers set in parallel and placed at the opposite sides from the light source of entangled photons. This will produce the corelated photons in one particle angle. Rotation of these polarizers in tandem will produce the the polarized correlated photons pairs of any chosen angle and the Aspect-like experiment will be performed for the any number of chosen angles. Would it work?

No, I don't think this would work, because the photons will not be properly paired.

P.S.
Actually, do we really need rotating polarizers to produce untangled photons pairs or stationary would work as well for this experiment?

As I said above, you need to be able to change the settings at both detectors if you want to test a Bell inequality.

 

[DrChinese]

As I understand nobody here see the contradiction between the dogma of QM and the prediction of the discussed above Gedanken Experiment; and it is fine with me. Let’s move on and try the Gedanken Experiment #2.

This is the classical Aspect’s experiment with one exception: the source of entangled photon is replaced with UNTANGLED twin photons that maintain untiparallel polarization.
What is your prediction for this experiment?

This is the situation when you use a single Type I PDC crystal with a V> laser source: You get HH> all the time (never VV>).

It is also the case when you use a type II source with V> input: you get HV> all the time and never VH>.

In both of these cases, the photons are entangled but not on the polarization basis. So you end up with Product State statistics. There are perfect correlations at some special angle settings. In general do NOT follow the cos^2 rule except when one of the settings is H or V.

 

[DrChinese]

I don’t belief in authority. I also have a very little respect to the “well-respected scientists” who insist on the greatness of QM. Personally I’m not impressed with this theory at all. Actually I don’t think that QM is a theory, but application only. According to Wikipedia “…A formal theory is syntactic in nature and is only meaningful when given a semantic component by applying it to some content...” As far as I am concerned QM doesn’t have meaningful semantic component.
...
I think that I provided enough material to ridicule my self-assurance.

Finally, something I can sink my teeth into!

Hey, there is nothing wrong with questioning authority (I do constantly, though not so much in this forum). But the flip side is that it is useful to have a common language to discuss things. The reason scientific authority arises is from the UTILITY of the theory. It is not the person. That is just a label for an idea that can be applied and lead to something we can build upon further. That is why Bell was so important.

I wish that Einstein were alive to see Bell. I think he would have been astounded by that result.

 

[Gordon Watson]

Finally, something I can sink my teeth into!

Hey, there is nothing wrong with questioning authority (I do constantly, though not so much in this forum). But the flip side is that it is useful to have a common language to discuss things. The reason scientific authority arises is from the UTILITY of the theory. It is not the person. That is just a label for an idea that can be applied and lead to something we can build upon further. That is why Bell was so important.

I wish that Einstein were alive to see Bell. I think he would have been astounded by that result.

..
A quick 2c: I am sure he'd be astounded that anyone believes it!

He'd simply run a sound Gedankenexperiment, like https://www.physicsforums.com/showpost.php?p=3259676&postcount=127, and get back to real physics: The experimental science that tests our theories; Bell's theorem being nowhere confirmed in our quantum world, except classically.

So, please, seriously:

1: What in the above experiment would Einstein object to?

2: Or Bell, for that matter? Given that Bell [1964: eqn (14)] acknowledges that:

B(lambda, b) = – A(lambda, b),

and its equivalent is to be found in the above Gedankenexperiment on a single (pristine, entangled) photon.
..

 

[Gordon Watson]

..
A quick 2c: I am sure he'd be astounded that anyone believes it!

He'd simply run a sound Gedankenexperiment, like https://www.physicsforums.com/showpost.php?p=3259676&postcount=127, and get back to real physics: The experimental science that tests our theories; Bell's theorem being nowhere confirmed in our quantum world, except classically.

So, please, seriously:

1: What in the above experiment would Einstein object to?

2: Or Bell, for that matter? Given that Bell [1964: eqn (14)] acknowledges that:

B(lambda, b) = – A(lambda, b),

and its equivalent is to be found in the above Gedankenexperiment on a single (pristine, entangled) photon.
..

..
[My apologies for being on the fringe of PF at the moment; due other priorities.]

Grandpa has replied to the above:

"PS: There is an objection each would make, I'm sure! There is a mistake in my wording at https://www.physicsforums.com/showpos...&postcount=127 ! IT SHOULD READ:

7. Now, Alice; with added confidence in your retrieve-and-restore technique: Test and re-test retrieved-and-restored V1', at orientation b, many times: THE OUTCOME IS (say) b+; every time! But now test and re-test at b, many other "equivalent" particles; "equivalent" in that they too give a+ when first tested at a:

8. Outcome: P(b+|V1', b) = cos^2 (a, b). P(b–|V1', b) = sin^2 (a, b).

[NB: What if you had been working with a different photon-pair; say V1" and V2". And (say) V1" at orientation a had given the result a–? No problem. That a– notation says that the post-test polarization of V1" is orthogonal to orientation a. Then the multi-test outcomes of that photon's many "equivalents" at orientation b would yield:

P(b+|V1", b) = sin^2 (a, b). P(b–|V1", b) = cos^2 (a, b).]

Sorry, etc. I trust it's all correct this time."

Me too.
..

 

[miosim]

… In order to make an experimental test of Bell's theorem, you need to be able to choose the detector settings at both sides of the experiment. So for your Gedanken's you would need to have a second polarizer for the B photon, which could be set to an angle independently of the polarizer for the A photon.

In my Gedanken experiment there are two independently rotated polarizers A and B, the same as in the Aspect’s experiment. The only difference is that instead of entangled photons there are EPR correlated photons.

… For gedanken experiment #1, you would find perfect anticorrelation of the measurements any time the detectors were set to the same angle, so if you set them both to 45º, you would see perfect anti-correlation…

I am not sure what the “anti-correlation” refer to. The correlation varies only from 0 to 100%; I thing you mean “untiparallel polarization.
In this case, according to the gedanken experiment #1 all entangled photon pairs have 0% correlation when detectors set untiparallel.

… For gedanken experiment #2, you will only see perfect anti-correlation when the detection basis is identical to the basis in which the photons were polarized from their sources. If you were to set both the A and B detectors to 45º, you would see no correlation between the two sets of measurements.

Again it is hard to interpret what “anti-correlation” means, otherwise according to Bell, there is no difference between entangled and EPR photons at angles 0º and 45º. (see figure at post #1)

… the photons are entangled but not on the polarization basis. So you end up with Product State statistics. There are perfect correlations at some special angle settings. In general do NOT follow the cos^2 rule except when one of the settings is H or V

If I understand you correctly, the correlated (vs polarization-entangled) photons in the gedanken experiment #2 do NOT follow the cos^2 correlation while per my understanding of EPR phenomenon they SHOULD follow the cos^2 correlation. This could mean that the gedanken experiment #2 may falsify the Bell’s theorem. Do you think that it is worth to try this experiment?

 

[SpectraCat]

In my Gedanken experiment there are two independently rotated polarizers A and B, the same as in the Aspect’s experiment. The only difference is that instead of entangled photons there are EPR correlated photons.

Please explain what distinction you are drawing between entangled photons and "EPR correlated" photons .. you probably explained that before, but I have lost track. It was my understanding that the original EPR gedanken dealt with entangled pairs. Are "EPR correlated" photons local realistic, where the polarization angles are determined by local hidden variables?

I am not sure what the “anti-correlation” refer to. The correlation varies only from 0 to 100%; I thing you mean “untiparallel polarization.

perfect correlation = coincident measurements on A & B reveal that they always have the same polarization state ... this is the case for Type I PDC entangled states when the detectors at A and B are set to the same angle.

perfect anti-correlation = coincident measurements on A & B reveal that they always have opposite polarization states ... this is the case for Type II PDC entangled states when the detectors at A and B are set to the same angle.

uncorrelated = coincident measurements on A & B show that, if A is in one state, |H> or |V>, then B has an equal probability of being in either |H> or |V>

The first two cases allow us to know the state of both photons from a measurement on only one of them. In the last case the measurements are independent; measuring A gives you no information about B, and vice versa.

I don't like to talk about "0%" correlation, because it can mean either the second or the third case above, depending on context. In fact, I think various people on this thread have used it in both of those ways at different times.

In this case, according to the gedanken experiment #1 all entangled photon pairs have 0% correlation when detectors set untiparallel.

You have to be careful .. if you have specified a Type I PDC entangled state, then rotating one side by 90º (as in your gedanken #1) will result in anti-correlated statistics when the detector angles are parallel.

If you have a Type II PDC, then your statement is correct.

Again it is hard to interpret what “anti-correlation” means, otherwise according to Bell, there is no difference between entangled and EPR photons at angles 0º and 45º. (see figure at post #1)
If I understand you correctly, the correlated (vs polarization-entangled) photons in the gedanken experiment #2 do NOT follow the cos^2 correlation

Sort of ... what I said was that you CAN get the cos^2 correlation for gedanken #2, but ONLY for one choice of detection basis, namely the original polarization basis for the photons. In other words, if you keep the A detector set at 0º relative to the original polarization basis (the |H> and |V> polarization defining the entangled state as it was emitted from the source), then you will get cos^2 as you rotate the B detector angle from 0º to 90º. However, if you start with A and B both at the same random angle (say 79º) with respect to the original polarization basis, and then rotate B from 79º to 169º then you will not get a simple cos^2 relation anymore. The coincidence statistics will reflect both the relative angle between the detectors, AND the angle of the detection basis with the original polarization basis.

However for gedanken #1, you ALWAYS get cos^2 correlation for ANY detector settings, whatever the polarization basis might be. For example, if you start with both A and B at an angle of 79º with respect to the original polarization basis, and then rotate B relative to A, you will get the same statistics as if you started with both A & B at 0º, or any other initial angle (provided they start out equal). You cannot FAIL to get cos^2 correlation.

... while per my understanding of EPR phenomenon they SHOULD follow the cos^2 correlation. This could mean that the gedanken experiment #2 may falsify the Bell’s theorem. Do you think that it is worth to try this experiment?

It won't falsify Bell's theorem ... because they won't show a cos^2 dependence for any choice of detector angles, as I explained above.

 

[miosim]

Please explain what distinction you are drawing between entangled photons and "EPR correlated" photons .. you probably explained that before, but I have lost track. It was my understanding that the original EPR gedanken dealt with entangled pairs. Are "EPR correlated" photons local realistic, where the polarization angles are determined by local hidden variables?

I guess, you can say that for EPR photons the polarization angles are determined by “local hidden variables”.
According to EPR paper (1935) both correlated particles (having antiparallel polarization) after separation “… no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system… thus it is possible to assign two different wave functions… to the same reality …” . My understanding of EPR particles is based on that description.
While within QM mechanics there two types particle pairs: entangled and untangled (produced after wave function collapse), I don’t believe in existence of entangled over distance particles.
My gedanken experiment #2 intends to demonstrate that there is no difference between “entangled” and “untangled” photons by producing the same cos^2 correlation.

... what I said was that you CAN get the cos^2 correlation for gedanken #2, but ONLY for one choice of detection basis, namely the original polarization basis for the photons. In other words, if you keep the A detector set at 0º relative to the original polarization basis (the |H> and |V> polarization defining the entangled state as it was emitted from the source), then you will get cos^2 as you rotate the B detector angle from 0º to 90º. However, if you start with A and B both at the same random angle (say 79º) with respect to the original polarization basis, and then rotate B from 79º to 169º then you will not get a simple cos^2 relation anymore. The coincidence statistics will reflect both the relative angle between the detectors, AND the angle of the detection basis with the original polarization basis.

I don’t fully understand |H> and |V> polarization and the difference between Type I PDC and Type II PDC. I need to do some homework on my own prior to continue.