EPR paradox

[Nereid]

The EPR (Einstein Podolsky Rosen) paradox was, when created, a thought experiment. John Bell showed that it was possible to test whether 'hidden variables' could be a resolution to this paradox. Experiments were done, on the Bell inequality, and the results are pretty darn unambiguous - the universe is a very, very strange place.

I have started this thread so we have a single place in BAUT where we can discuss this topic. It is a topic which is, it seems, widely misunderstood (e.g. this heusdens post seems to imply a hidden variable solution is possible). It is also a topic with relevance to those who come at science with a classical view (e.g. ErdExpMann and ColdCreation - I'll add links later).

There are many excellent explanations of this topic on the web, and several places where you can discuss it, to whatever technical or philosophical depth you are comfortable with. If there is sufficient interest, I will add links to some of these.

[Ken G]

It's a pretty fascinating topic, but tough sledding to figure it out. Can anyone start off with a simpler piece, which is the answer to this:
When you have a particle in a spin eigenstate, and you make a perpendicular spin measurement, does the resulting change in momentum have to show up in the observing instrument? If so, one might be tempted to assert that the measurement has imparted spin to the particle, which is a piece of the Bell inequality that I didn't understand.

[peteshimmon]

I am probably impossible stuck in classical
feet in clay attitudes but I do try. I will
start with an observation that Bells work seems
to show something similar to the falloff in
transmission of two polarizors as one is
rotated wrt the other, ie 45 degrees lets
0.707 of the photons through. The inequalty is
about the difference between 0.5 and 0.707 and
thev rest of the curve is it not? Secondly,
The Dancing Wu Li Masters by Gary Zuukav
reviews the 3 polaroid trick and implies the
photon is detected or not according to the
instantaneous positions of the three polarizors.
Which suggests an easy experiment in the lab
to check.

[heusdens]

The simple fact is just that only *after* observing one particle we can tell something about it's state. The QM interpretation is that the act of observing the particle, causes the wave function to collapse.
That observation, acc. to this explenation, would cause the other particle's wave function to collapse also instantaniously (even when that particles has traveled milion of light years).
I don't fully trust this explenation, since it would invoke some form of "instantanious action at a distance" to occur.

But look at the conditions of the experiment.
We know the particles are created in a simultanious experiment.
Like for instance, if energy is converted into particles, we know that this experiment always obeys certain conservation laws (like for instance conservation of electric charge).

If the experiment involved in fact the creation of a electron/positron pair, nobody would argue that upon examining one of this particle, and discover that it has a positive charge, that observation would all of a sudden cause the other particle to become a positron.
This because the simple fact that the particles were created in an event that conserves the electric charge, means that the amount of electric charge must be zero (as it was zero before), and if we know the electric charge of one particle, we automatically know the charge of the other, without even observing that particle.

Since we don't mention some kind of "hidden instantanious force" acting on the other particle in this case, why would we need to do that in the EPR experiment?

[DrChinese]

I don't fully trust this explenation, since it would invoke some form of "instantanious action at a distance" to occur.

But look at the conditions of the experiment.
We know the particles are created in a simultanious experiment.
Like for instance, if energy is converted into particles, we know that this experiment always obeys certain conservation laws (like for instance conservation of electric charge).

If the experiment involved in fact the creation of a electron/positron pair, nobody would argue that upon examining one of this particle, and discover that it has a positive charge, that observation would all of a sudden cause the other particle to become a positron.
This because the simple fact that the particles were created in an event that conserves the electric charge, means that the amount of electric charge must be zero (as it was zero before), and if we know the electric charge of one particle, we automatically know the charge of the other, without even observing that particle.

Since we don't mention some kind of "hidden instantanious force" acting on the other particle in this case, why would we need to do that in the EPR experiment?

Well, that wouldn't really be a good example because the explanations are in fact identical.

Every quantum observable follows the same basic logic when there are entangled particles. A positron-electron creation event will too. Just as spin is conserved, so is momentum and charge (and color, etc.). All of these observables are in a superposition of quantum states until a measurement is performed (exactly as you say). Then there is the collapse of the wave function.

I cannot say exactly what the collapse of the wave function is as a process - no one really knows that. Is it local or non-local? That is definitely something that fuels a lot of debate.

You definitely do not need to accept non-locality as a condition of accepting the results of EPR/Bell experiments. If you object to a violation of relativistic cause and effect, you have another choice: reject the existence of hidden variables. That is a popular alternative.

[DrChinese]

When you have a particle in a spin eigenstate, and you make a perpendicular spin measurement, does the resulting change in momentum have to show up in the observing instrument? If so, one might be tempted to assert that the measurement has imparted spin to the particle, which is a piece of the Bell inequality that I didn't understand.

To my knowledge, there is absolutely no connection between momentum of a photon and its spin. These observables are completely independent. When a photon's spin changes, there is no discernible change in momentum from the measuring device. (I am not certain that holds true for an electron.)

For example, you could make a perpendicular (90 degree) measurement of a photon with a polarizing lens. The lens will absorb the photon 100% of the time. (Presumably you might be able measure that event.) If you make a measurement with a polarizer at 45 degrees, the lens will absorb the photon 50% of the time. The other 50% of the time, there is nothing happening at the polarizer which can be measured whatsoever. Yet the photon has had its spin twisted 45 degrees.

[Ken G]

To my knowledge, there is absolutely no connection between momentum of a photon and its spin.

Oops, typo, I meant "angular momentum"!

But both DrChinese and heusdens are addressing my question. Maybe the best way to set this up is to have a left circular polarizer, followed by a linear polarizer, followed by a right circular polarizer. Some photons can go through all three, despite the need to invert the polarization. From DrChinese's comment, it sounds like in that case there would be no effect at all on the polarizers, yet the inverted polarization signifies an angular momentum change. Statistically, this change is made up in all the cases where photons and their angular momentum is absorbed in the apparatus. But I did not realize that conservation laws were that statistical, I thought that only held for the uncertainty principle. Then again, the uncertainty principle for angular momentum is pretty funky anyway, so that's probably the resolution here.

[DrChinese]

Oops, typo, I meant "angular momentum"!

... Statistically, this change is made up in all the cases where photons and their angular momentum is absorbed in the apparatus. But I did not realize that conservation laws were that statistical, I thought that only held for the uncertainty principle. Then again, the uncertainty principle for angular momentum is pretty funky anyway, so that's probably the resolution here.

Photon spin is quantized, of course. So the question eventually becomes: how does a photon in a particular eigenstate change to be in a different eigenstate? I don't think there is any observable transfer between the photon and the measuring device that explains this.

[Ken G]

And the reason one does not have to explain it is apparently that statistically, such transfer never accumulates to macroscopic levels. The discrepancies that appear are always at the quantum level, and I suspect are manifestations of the uncertainty principle, but I can't prove it without a lot more thought. Like, the kind of thought that Nereid is trying to encourage with this thread!

[ngeo]

What exactly is meant by the 'spin' of a photon when it is a wave? Also, a picture of the path of a photon (as a wave) shows a spiral path (with linear exception). What problem does this cause?

[Ken G]

Photons have spin 1, which corresponds classically to their two polarization states, left-hand or right-hand circular. (The third polarization state implied by spin 1 apparently only exists in the photon rest frame, which doesn't exist at all). There is angular momentum associated with these polarization states. Don't ask me why. A photon is not a wave, it is a particle whose motion is determined by wave mechanics.

[ngeo]

Is an unmeasured photon supposed to exist in both spin states?

[Ken G]

Yes, a photon can be in a superposition of both circularly polarized states. Note that any such superposition is just another polarization state, perhaps linearly polarized, for example.

[ngeo]

If a photon 'can be' in a superposition, does this mean a photon can be produced that is known to be not in a superposition?

[Ken G]

No. However, a population can be in a "mixed state", which means, they are all in randomly distributed superposition states (with no phase correlations between these states).

[ngeo]

In the 'EPR' tests, are single photons 'picked out' by the detectors? I wonder how a single photon can be transmitted in two directions. (In other words, I must be asking what are the two detectors measuring?)

[Ken G]

There are two photons, but they are coupled by some kind of conservation law. I forget the details, better look it up.

[heusdens]

Well, that wouldn't really be a good example because the explanations are in fact identical.

Every quantum observable follows the same basic logic when there are entangled particles. A positron-electron creation event will too. Just as spin is conserved, so is momentum and charge (and color, etc.). All of these observables are in a superposition of quantum states until a measurement is performed (exactly as you say). Then there is the collapse of the wave function.

I cannot say exactly what the collapse of the wave function is as a process - no one really knows that. Is it local or non-local? That is definitely something that fuels a lot of debate.

You definitely do not need to accept non-locality as a condition of accepting the results of EPR/Bell experiments. If you object to a violation of relativistic cause and effect, you have another choice: reject the existence of hidden variables. That is a popular alternative.

{i assume this last remark is a type, and you meant to say: accept (instead of reject) hidden variables, since either the experiment is explained as non-local (instantanous action at a distance) WITHOUT any hidden variables, or as local WITH hidden variables}

I think the terminology used ("collapse of wave function", etc) mystifies these quantum events.
In the simple case of a electron/positrion pair being emitted by some process (one particle heading left, the other to the right), wether or not the particles that moves left is an electron or positron, is not known unless we observe the particle.
Wether, before the act of observing (which is a physical interaction), the quantum state of the particle is fixed or a superposition of states, is outside of knowledge. I does not contradict observations to explain that the particle already was in a fixed quantum state (instead of a superposition of states), since we do not know WHICH quantum state, unless we observe the particle.

[peteshimmon]

Lets reiterate my query. Bells workings (which
I do not doubt) indicated a linear falloff in
photon detection between 0 and 90 degrees of
rotation of a polarizor if there were a hidden
variable but an excess if quantum theory was
correct. But the same curve arises when a
polarizor is rotated wrt another polarizor in
front of an unpolarised light source. Hope my
puzzlement is clear!

[DrChinese]

{i assume this last remark is a type, and you meant to say: accept (instead of reject) hidden variables, since either the experiment is explained as non-local (instantanous action at a distance) WITHOUT any hidden variables, or as local WITH hidden variables}

It sometimes gets confusing with all the negatives and either/ors. I think I said it right, AND you said it right!

If you accept the results of Bell tests (nothing much left to question at this point), you can accept any of the following and be consistent:

1. Accept Quantum Mechanics (QM).

2. Hope for a different theory which mimics the predictions of QM and has explicitly non-local hidden variables.

3. Hope for a different theory which mimics the predictions of QM and is explicitly local but contains no hidden variables (I call any theory that rejects hidden variables a non-realistic theory).

4. Hope for a different theory which mimics the predictions of QM and is explicitly both non-local and non-realistic.

You will find a mixture of attitudes among scientists regarding the above. Most scientists actually hold a mixture of 1., 2. and 3.: QM has been supported, non-local "effects" have been demonstrated and the hidden variable program is over. But technically that is a bit more than is justified.

There have been attempts to introduce theories that match up to 2. and 3. above. Bohmian Mechanics is non-local realistic. The Many Worlds Interpretation is local non-realistic. However, these are not fully developed and are not generally accepted.

[DrChinese]

Lets reiterate my query. Bells workings (which
I do not doubt) indicated a linear falloff in
photon detection between 0 and 90 degrees of
rotation of a polarizor if there were a hidden
variable but an excess if quantum theory was
correct. But the same curve arises when a
polarizor is rotated wrt another polarizor in
front of an unpolarised light source. Hope my
puzzlement is clear!

Not sure if I understand your comment. So I will pass this on:

1. Local Realistic theories (which are contradicted by Bell tests) essentially show a linear roll off going from 0 to 90 degrees as you describe. (This is in the coincidence rate for entangled pairs.)

2. QM predicts that for Bell test: the roll off from 0 to 90 degrees follows the familiar cos^2(theta) relationship (which of course is NOT linear). The cos^2(theta) formula is also the same as Malus' Law (1809), which applies in the case of the polarizer rotated wrt another polarized source as was described. There is a direct correspondence between Malus' Law and the QM prediction.

[hhEb09'1]

The EPR (Einstein Podolsky Rosen) paradox was, when created, a thought experiment. John Bell showed that it was possible to test whether 'hidden variables' could be a resolution to this paradox. Experiments were done, on the Bell inequality, and the results are pretty darn unambiguous

That's not quite true.

It is a topic which is, it seems, widely misunderstood (e.g. this heusdens post seems to imply a hidden variable solution is possible).

As others have mentioned, it was local hidden variables that were ruled out by experiment--and I don't think EPR was even concerned with them. So, in that sense, EPR was supported.

[ngeo]

Ken G, I agree that last question of mine looks rather stupid (especially in light of the ongoing debate), which is why I generally try to avoid instant discussions and write things down first. As I read about the EPR/Bell’s tests in Wikipedia, it indicates that pairs of “photons” (?) are produced by “atomic cascade”. This sounds like it needs a very technical setup but it doesn’t seem to describe a precise measurement of individual photons. I guess the question is whether these pairs are supposed to become entangled as a ‘single photon‘, then ‘disentangled’ and each measured instantaneously by separate detectors, or whether the whole process is statistical. Reading the posts above it sounds statistical but encryption indicates precision.

Going by these posts, I have to wonder whether an artificial conundrum has been set up which illustrates only the limit on what can be directly measured.

[Grey]

As others have mentioned, it was local hidden variables that were ruled out by experiment--and I don't think EPR was even concerned with them. So, in that sense, EPR was supported.

I think that EPR were assuming locality, and hoping to use that to show that there had to be hidden variables, thus showing that quantum mechanics was incomplete. Since it now looks like locality does not hold, whether or not there are hidden variables, I think Einstein would have been quite unhappy with the resolution.

[Nereid]

The EPR (Einstein Podolsky Rosen) paradox was, when created, a thought experiment. John Bell showed that it was possible to test whether 'hidden variables' could be a resolution to this paradox. Experiments were done, on the Bell inequality, and the results are pretty darn unambiguous

That's not quite true.

I meant that there isn't, today, much doubt about what the results are - systematic effects have been identified, the expected 'classical' result is many, many sigmas outside the data, etc.

The interpretation of those results is, as we are discussing, quite a different thing!

It is a topic which is, it seems, widely misunderstood (e.g. this heusdens post seems to imply a hidden variable solution is possible).

As others have mentioned, it was local hidden variables that were ruled out by experiment--and I don't think EPR was even concerned with them. So, in that sense, EPR was supported.

Yes, my wording was sloppy; I should have said that heusdens' post seems to imply a local hidden variable solution is possible.

I'll leave it to others (esp DrChinese) to say more, but I thought the EPR paradox was, in fact, all about local hidden variables (the 'instantaneous' collapse of entangled states is just as 'spooky', and seemingly inconsistent with relativity as the non-existence of hidden variables, surely).

IIRC, DrChinese has collected (PDFs of) the seminal papers (inc the original EPR ones) into a single webpage, so it should be easy to check what E, P, and R regarded as paradoxical (and which experimental results have now confirmed).

[Nereid]

Ken G, I agree that last question of mine looks rather stupid (especially in light of the ongoing debate), which is why I generally try to avoid instant discussions and write things down first. As I read about the EPR/Bell’s tests in Wikipedia, it indicates that pairs of “photons” (?) are produced by “atomic cascade”. This sounds like it needs a very technical setup but it doesn’t seem to describe a precise measurement of individual photons. I guess the question is whether these pairs are supposed to become entangled as a ‘single photon‘, then ‘disentangled’ and each measured instantaneously by separate detectors, or whether the whole process is statistical. Reading the posts above it sounds statistical but encryption indicates precision.

Going by these posts, I have to wonder whether an artificial conundrum has been set up which illustrates only the limit on what can be directly measured.

What's so darn unsettling ngeo is that no one has been able to come up with an alternative explanation that is even half-way consistent with all the other results we have (esp wrt QM) ... initially there were many criticisms of the experimental setups (this systematic effect couldn't be ruled out, that measurement's error bars should have been larger, etc, etc, etc). I think you'll find that these, often well-justified, criticisms have now all been answered, by (among other things) new and different experiments.

[Grey]

I'm going to repost what I said here, since it seems fairly relevant.

I wouldn't have thought that entangled particles "communicate".
As an example I thought it was like- a woman has three pairs of shoes, red,green and blue. She wears the red ones but packs her suitcase early in the morning with one of the other pairs, in the dark(so she doesn't wake her husband). She then gets on the plane in London and flys to NewYork perhaps you could say that the pair of shoes in the woman's suitcase and the pair she left back in London are entangled but neither she or her husband know what shoes are where. The husband comes home later that day and discovers the green shoes in the cupboard- the uncertainty has collapsed and he knows that when his wife opens her suitcase in NewYork she will find the blue shoes.

If there are many universes all branching off from each other, while there is some uncertainty,there is also some uncertainty as to which universe they are in. Collapsing uncertainty just resolves which universe they were in all along.

at least that's my theory.

It's not actually that simple, and depends on the limits of quantum information. Quantum entanglement and measurement is much more complex than your example with the shoes, where the question is just one of lack of classical knowledge. This is going to be fairly lengthy, and in some sense is a digression. But in another sense, it gets at the very heart of what quantum mechanics has to say about the nature of reality that underlies what we see. Let me lay some important groundwork.

Suppose I have a photon, and I'm measuring it's spin. Now, it turns out that if I measure the spin in any given direction, call it x, I'll find the photon to be either aligned with that direction (call it x+), or aligned in the opposite direction (call it x-). Now, it turns out that the spins measured for any orthogonal directions are incompatible observables, just like position and momentum for single particle. If I measure the spin in the x direction, I have no idea what the spin in the y or z direction are. We can actually test this. If I take a stream of photons, and set up a filter that strictly removes any photons that are x-, I'll have a stream of photons that are all x+. If I pass them through the same kind of filter, all of them will pass through, since only the x+ ones are left. If I pass them through the same kind of filter rotated 90 degrees, to instead allow only spin y+ photons through I'll find that half of them will make it, and the other half will be blocked. The thing is, that you might think that the photons left after this second filter are all x+, y+ photons, but it turns out that measuring the spin in the y direction completely destroys any information I had about the x direction. If I measure the x spin again, I'll find that half of the photons are x+ and half are x-. Presumably, the act of measuring the spin in one direction, no matter how carefully done, destroys the information about the spin in the other direction. What if I redefine my axes, and tilt them 45 degrees (let's call this direction x') instead of 90? Quantum mechanics predicts, and experiment bears out, that there will be some amount of correlation (I won't get just half and half like I did when I rotated the filter 90 degrees), but it won't be complete. In fact, I can work out exactly what the probability that a photon I know is x+ will be aligned with any other direction, given the angle between the two directions.

Now, Einstein, Podolsky, and Rosen used this, along with the notion of entanglement, to try to show that quantum mechanics was not wrong, but incomplete. It's possible for two photons to be emitted by a source in such a way that they are spin correlated. That is, if one is down in the x direction, the other must be up in the x direction, and vice versa. Now, you take such a pair of photons, and wait until they're a long way away from each other, so there's no chance that they can interact. You measure the spin in the x direction for one of them, and find that it's (say) x+. You measure the spin in the y direction for the other one, and find that it's y+. But you know that the second photon has to also be x-, since it has to be opposite the spin of the first one in the x direction, and "obviously" that first measurement can't have affected the spin of the second one in any way (you could have waited until the photons were light years apart before making the measurements). So now you know the spin in two different directions for these photons (one is x+, y- and the other is x-, y+), more information than quantum mechanics says you can have. EPR claimed this showed that quantum mechanics was incomplete. Each photon must "really know" which way its spin is aligned in each direction. And actually, my choices of x, y, and z were arbitrary; I could have chosen different axes, so technically each photon knows which way it will respond to a measurement of spin in any direction at all. These photons would then be like the shoes: they have specific attributes, we just don't know what they are.

So let's follow this assumption, that photons are ordinary objects with real (though possibly unknown) attributes, and see where it leads us. Bell's equality says that, for any collection of objects with any three attributes, A, B, and C, N(A, not B) + N(B, not C) >= N(A, not C), where N(A, not B) is the number of objects that have trait A but not trait B, N(B, not C) is the number of objects that have trait B but not trait C, and so forth. The attributes can be linked or not, but the inequality holds so long as these are real attributes. Let's see why. First, we know that

N(A, not B, C) + N(not A, B, not C) >= 0

This is just the statement that either there are no objects that would satisfy one of these conditions or there are some that do. I can move from there to here, just by adding the same thing to both sides of the equation.

N(A, not B, C) + N(not A, B, not C) + N(A, not B, not C) + N(A, B, not C) >= N(A, not B, not C) + N(A, B, not C)

Now, if these are real attributes, then an object either has some trait, or doesn't have some trait. So N(A, not B, C) + N(A, not B, not C) is just the same as N(A, not B). That is, if you count the objects that have trait A but not trait B, that will be the same as adding up the objects that have trait A, do not have trait B, and have trait C along with those that have trait A, do not have trait B, and do not have trait C. All objects either have trait C or not. Similarly, N(not A, B, not C) + N(A, B, not C) can be replaced by N(B, not C) and N(A, not B, not C) + N(A, B, not C) is just the same as N(A, not C). This gives us Bell's inequality:

N(A, not B) + N(B, not C) >= N(A, not C)

I'd suggest you go back over that and convince yourself that I haven't made any mistakes here. If you're still not convinced, you might come up with a concrete example (say, a classroom of people, with your traits as being female, having blue eyes, and having dark hair), and check yourself that, however many members of the set there are and which ones have or do not have various traits, this inequality holds.

Done with that? Good.

So, now we go try to measure this on some photons. We're going to test whether N(x+, x'-) + N(x'+, y-) >= N(x+, y-). We run into a problem, though. We can't measure the spin in two directions for a single photon, because we know that the measurement in the first direction will mess up the measurement in the second direction. But we can use the trick EPR suggested for using entangled photons to find this out. We measure the spin in the x direction on one of them, and in the x' direction (this was tipped at some angle less than 90 degrees, remember) on the other one, and then we must know both spins for each particle. If we perform the experiment, though, we find out that the inequality is broken. The right side is actually greater than the left. This is also exactly what quantum mechanics predicts, but the fact that experimental results also seem to bear out the result means that even if someday quantum theory is superseded by some deeper theory (as EPR imagined it might), that theory will have the same problem.

How can this be? Well, we really only made a few assumptions in our work above. One is that we used basic rules of logic. It's hard to imagine that those are flawed. Another is that we assumed that these photons actually had definite real attributes, we just didn't know what they were. Another is the assumption that our measurements on the photons (separated possibly by light years) did not affect each other. It turns out that, regardless of whether we assume the attributes were real before we measured them, we can't get around the influence question. That is, to explain the results we see, one photon has to "tell" the other one, instantaneously regardless of distance, what it's results were, and the results of the measurements on the second one will be affected by this.

Let's revisit the woman and her shoes, with a slight change. Let's say she owns hundreds of shoes, all red, green, or blue, in equal proportion. She always packs one at random. If she does this many times, there will be a 1 in 3 chance for each color. Her husband always picks one of the boxes that she left behind at random and looks at the color. There's always a 1 in 3 chance for him to find each color. But, if they both open their boxes with them oriented the same way (either both vertically or both horizontally), there's a 1 in 2 chance that they picked the same color, whatever it was, while if they open their boxes holding them oriented differently, there's only a 1 in 6 chance that the colors match. The only way for that kind of correlation is if the act of opening the box is instantly communicated to the other pair of shoes somehow, and it has the possibility of changing its color in response. But also note that, since each measurement alone just gives a straight 1 in 3 chance for each color, just as we'd expect, there's no way to see this correlation, or to know which way the other person was holding the box (or even if they've opened it yet), until the woman comes back and they compare the results.

[DrChinese]

As I read about the EPR/Bell’s tests in Wikipedia, it indicates that pairs of “photons” (?) are produced by “atomic cascade”. ...

Going by these posts, I have to wonder whether an artificial conundrum has been set up which illustrates only the limit on what can be directly measured.

Initially, it was atomic cascade (in Aspect, for example). In recent years, almost all tests use spontaneous parametric down conversion (PDC or SPDC). This allows much more control and produces a more reliable stream of entangled photons. In PDC, a single photon is split into 2 entangled photons by passing it through a non-linear crystal. The resulting pair has half the frequency of the initial photon. This process has been used to confirm the QM particle nature of light to over 100 standard deviations (something that you might think was already proven but had not been rigorously). So PDC provides great insight into quantum optics at several levels. With the PDC technique, a lot of questions about entanglement have become more clear.

[ngeo]

What strikes me first about Grey’s description is the fact (I take it) that photons apparently previously eliminated by one filter can ‘reappear’ when passed through another filter. The first reaction to that is that maybe a photon doesn’t have a ‘permanent’ spin. So its ‘spin position’ when it passes through the first filter isn’t necessarily its ‘spin position’ at the second filter. So I wonder whether it is possible to produce a single photon with a known specific ‘permanent’ spin, or whether (as in DrChinese‘s post) there is only a ‘correlated’ existence of two photons, produced by a specific method, whose spins are opposite (I presume?).

The next striking thing is that some possible spin combinations are left out of the “A, not B, C” problem, which (beside the impression above) carries over to the x+, y- problem. It seems like the problem is being set up in a certain way to limit the available information (although maybe the information is limited by the physics). It is hard for a small non-logical brain to figure out whether this is logic or not.

I am coming at this from a point of view of a photon as possibly a spatial region spinning on three axes (eight combinations, four sets of mirror images). Maybe the half-frequency entanglement described by DrChinese splits the photon into two mirror images.

[DrChinese]

The first reaction to that is that maybe a photon doesn’t have a ‘permanent’ spin. So its ‘spin position’ when it passes through the first filter isn’t necessarily its ‘spin position’ at the second filter. So I wonder whether it is possible to produce a single photon with a known specific ‘permanent’ spin, or whether (as in DrChinese‘s post) there is only a ‘correlated’ existence of two photons, produced by a specific method, whose spins are opposite (I presume?).

There ARE in fact ways to create photons with a known spin. A laser creates all photons with identical spin, for example. And there are definitely ways to change a photon's spin in a relative manner - you can twist it 90 degrees using a half wave plate or twist it 45 degrees using a quarter wave plate.

In fact, it may surprise you to learn that even entangled photons can (and often are) created with known spin. As a general rule, you can't do a lot of cool stuff with such photons - so you know what is done? They mix beams at one angle with beams at another so the spin knowledge is lost. When that happens, you can do cool things again.

Let me give a common experimental setup using type I parametric down converted (PDC) photons. In type I, an entangled photon pair is produced with identical spin which is perpendicular to the spin of the input photon after being run through a Barium Borate crystal . To adjust for the known and certain spin of the output beam, two crystals are used which are themselves perpendicular and the output beams are focused together. The input beam is set at 45 degrees relative to the 2 BBo crystals. The result is a stream of pairs with identical but unknown spin because there is a 50-50 chance it went through one crystal and a 50-50 chance it went through the other.

Here is a reference which has a good description of how this is accomplished: Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory. See Figure 2.