Can grandpa understand the Bell's Theorem?

[jed clampett]

Thanks, Zonde. I thought you were agreeing with me, and was a little confused when Dr. Chinese implied you were agreeing with Jesse M.

I'm under the impression that some if not all of the experiments which produce singlet state entangled photons also produce triplet state entangled photons; and that the triplet state photons do not violate Bell, giving a correlation of 50% at best; and that one of the difficulties of verifying Bell is to separate the statistics of the singlet state from the triplet state.

This is just speculation on my part and I'm wondering if anyone could comment on it.

 

[miosim]

jed clampett (and you) was specifically talking about what to expect from "classical" photons.
This of course can not be discussed without reference to other types of experiments where photons behave classically.

What is a classical" photon?

 

[zonde]

Thanks, Zonde. I thought you were agreeing with me, and was a little confused when Dr. Chinese implied you were agreeing with Jesse M.

Yes, I agree with you. And I think that constructing correlations that you would expect from "classical" photons is half of the answer about what's going on in these entanglement experiments.

Look if you take Type I PDC source with one crystal you get say H-H pairs of photons and you observe such correlations:
$$P(\alpha,\beta) = cos^{2}\alpha\, cos^{2}\beta$$

Then you take Type I PDC source with two crossed crystal and you get H-H and V-V pairs of photons mixed together.
And you observe correlations like that:
$$P(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta + cos^{2}\alpha\, cos^{2}\beta$$

Now to produce polarization entangled photons you put walkoff compensators in both photon beams and you get correlations like that:
$$P(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta + cos^{2}\alpha\, cos^{2}\beta + \frac{1}{2}sin 2\alpha\, sin 2\beta = cos^{2}(\alpha-\beta)$$
This third term that appeared is called interference term and it depends from indistinguishability of H-H and V-V pairs in detectors.

So the question is about physical nature of this interference between H and V modes.

I'm under the impression that some if not all of the experiments which produce singlet state entangled photons also produce triplet state entangled photons; and that the triplet state photons do not violate Bell, giving a correlation of 50% at best; and that one of the difficulties of verifying Bell is to separate the statistics of the singlet state from the triplet state.

This is just speculation on my part and I'm wondering if anyone could comment on it.

It is unclear to me what do you mean with singlet state entangled photons and triplet state entangled photons.

 

[zonde]

What is a classical" photon?

Let's say it's photon that has property "polarization" at all times not only when it's measured.

 

[harrylin]

Let's say it's photon that has property "polarization" at all times not only when it's measured.

Isn't that already a restricted class of realist/classical possibilities? For example, one can imagine that "polarization" is the result of the measurement of a hidden variable, right?

 

[DrChinese]

Yes, I agree with you. And I think that constructing correlations that you would expect from "classical" photons is half of the answer about what's going on in these entanglement experiments.

Let's get back to reality here. You don't get any useful new insights from the classical picture of a photon ("polarization exists independent of observation, etc."). Bell opened up a huge area for entanglement-related experiments and these all flush the classical photon down the toilet.

And just a reminder to everyone reading this thread that might have some doubts about entanglement as a non-classical state:

a) You can entangle photons that have NEVER existed in the same light cone (so there is no joint point of origin) and therefore there is no classical mechanism to build from;
b) You can freely choose to entangle photons AFTER they have both been detected, violating the classical cause-effect sequence;
c) And finally, you can do BOTH a) and b) in the same experiment, which should be enough to throw any classical explanation out the window.

My point being that a lot of people try to salvage a classical viewpoint from a re-analysis of Bell. And jump through hoops only to come up against a wall. Meanwhile, the rest of the scientific community has moved so far past Bell (because they embrace it) that it is really silly.

It is always a good idea to question, and try to understand deeper - no issue there. But to throw out the powerful Bell logic "because it doesn't feel right" when the experimental evidence is overwhelming... well...

 

[miosim]

...It is always a good idea to question, and try to understand deeper - no issue there. But to throw out the powerful Bell logic "because it doesn't feel right" when the experimental evidence is overwhelming... well...

There are plenty of examples in the history of science when the powerful logic eventually failed. The closest example is EPR argument which undeniable logic dominated discussion in QM for decades.

Regarding the overwhelming experimental evidences in favor of “non-locality” - only a theory “knows” what these experiments really mean. QM is notoriously famous with mutually exclusive interpretations and therefore it should not be a surprise that a search for an ultimate meaning of these experiments is continuing.

 

[DrChinese]

There are plenty of examples in the history of science when the powerful logic eventually failed. The closest example is EPR argument which undeniable logic dominated discussion in QM for decades.

This is an inaccurate rendering of history, and further is essentially an anti-science argument (since one could say that about anything).

First, there is not one experiment supporting the EPR conclusion that a more complete specification of the system is possible. There are thousands supporting Bell's assertion that LR and QM are incompatible, and those also show that QM is supported.

Further, most people read EPR as only proving that if QM is complete, there cannot be local realism. This conclusion is still accepted today. Even at the time, it was not generally agreed that QM was or was not complete. So to imply there was something once "proven" which was later overturned, well, that is highly misleading.

I have urged you to attempt to construct a model which is realistic so you could see that is not possible. I think if you would focus on that, which is pretty easy (and I would be glad to show you), you would gain some understanding of Bell. Or you can reject Bell without gaining that understanding, your call.

 

[JesseM]

Yes, I agree with you. And I think that constructing correlations that you would expect from "classical" photons is half of the answer about what's going on in these entanglement experiments.

So are you agreeing with jed that it would be impossible to construct a local hidden variables theory where photons exhibited perfectly correlated behavior when measured with polarizers at the same angles (ignoring what the statistics are when different angles are selected)? Again keep in mind that the hidden variables can work in any way that doesn't violate local realism, there's no reason they need to behave like measurable polarization vectors.

 

[cosmik debris]

And just a reminder to everyone reading this thread that might have some doubts about entanglement as a non-classical state:

a) You can entangle photons that have NEVER existed in the same light cone (so there is no joint point of origin) and therefore there is no classical mechanism to build from;

Can you expand on this a little? How can two photons that are spacelike separated be entangled if they never exist in the same light cone?

Cheers

 

[DrChinese]

Can you expand on this a little? How can two photons that are spacelike separated be entangled if they never exist in the same light cone?

Cheers

Why, I am glad you asked this!

2 Separate sources emit entangled pairs of photons. Through a lot of work, one photon from one pair is brought together with a photon from the other pair. This is done in such a way that entanglement swapping occurs (sometimes, not all the time, but there are markers to let you know). The other of each pair is now entangled! But they did not ever interact as a separate independent photon.

It's complicated to follow, but here is the reference:

http://arxiv.org/abs/0809.3991

Abstract:
"Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics. "

Keep in mind, in a local realistic universe this is completely unthinkable. But it is a straightforward application of QM concepts post Bell/Aspect.

 

[JesseM]

There are plenty of examples in the history of science when the powerful logic eventually failed. The closest example is EPR argument which undeniable logic dominated discussion in QM for decades.

No, there are no cases where a purely theoretical argument based on mathematics "failed"--such a mathematical argument will always make clear what its starting assumptions are, and the argument will only say that conclusion Y follows from assumptions X, the argument is still completely valid even if assumptions X turn out to be invalid as statements about physics in the real world. So the EPR argument is still correct about what follows from the assumptions they made, it's just that physicists don't think all those assumptions can be true in the real world any more. What Bell proved is that the assumption of local realism is incompatible with the assumption that the laws of QM are totally accurate, the proof doesn't depend on whether either of the assumptions hold in the real world, although the evidence for the correctness of QM (particularly those aspects of QM that are incompatible with local realism) is pretty good at this point.

Regarding the overwhelming experimental evidences in favor of “non-locality”

Be careful, it's not really accurate to say there is evidence in favor of "non-locality", only that the evidence for the correctness of QM is evidence against local realism. Advocates of the many-worlds interpretation, for example, argue that theirs is a local interpretation of QM, it just doesn't qualify as "local realism" as in Bell's proof because it violates the assumption that each measurement by the experimenters should yield a unique definite outcome.

- only a theory “knows” what these experiments really mean. QM is notoriously famous with mutually exclusive interpretations and therefore it should not be a surprise that a search for an ultimate meaning of these experiments is continuing.

But the fact that we don't know the correct interpretation of what's "really going on" (if indeed there is any objective truth of the matter) doesn't mean you can throw up your hands and say "since we don't know, anything is possible"--some possibilities can logically be ruled out as incompatible with QM's predictions, and that's exactly what Bell did with local realism.

 

[jed clampett]

Yes, I agree with you. And I think that constructing correlations that you would expect from "classical" photons is half of the answer about what's going on in these entanglement experiments.

I know. There are people who like to say that classical e-m is so thoroughly discredited that it's a waste of time to even think about how an experiment would be explained classically. But I think those people are wrong.

Look if you take Type I PDC source with one crystal you get say H-H pairs of photons and you observe such correlations:
$$P(\alpha,\beta) = cos^{2}\alpha\, cos^{2}\beta$$

Then you take Type I PDC source with two crossed crystal and you get H-H and V-V pairs of photons mixed together.
And you observe correlations like that:
$$P(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta + cos^{2}\alpha\, cos^{2}\beta$$

Now to produce polarization entangled photons you put walkoff compensators in both photon beams and you get correlations like that:
$$P(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta + cos^{2}\alpha\, cos^{2}\beta + \frac{1}{2}sin 2\alpha\, sin 2\beta = cos^{2}(\alpha-\beta)$$
This third term that appeared is called interference term and it depends from indistinguishability of H-H and V-V pairs in detectors.

So the question is about physical nature of this interference between H and V modes.

I'm ready to believe that you are right but I don't know what Type I and Type II sources are.

It is unclear to me what do you mean with singlet state entangled photons and triplet state entangled photons.

I'm really arguing here from analogy to electrons. There is the singlet state |up*dn> - |dn*up> and there is the triplet state with a plus sign instead of a minus sign. I'm guessing that the weird correlations for electrons occur only with the singlet state, and that there is something analogous with photons.

 

[JesseM]

I know. There are people who like to say that classical e-m is so thoroughly discredited that it's a waste of time to even think about how an experiment would be explained classically. But I think those people are wrong.

Classical EM is a local realistic theory, so Bell's theorem proves that it cannot reproduce the predictions of QM in Bell type experiments.

I'm ready to believe that you are right but I don't know what Type I and Type II sources are.

Ready to believe zonde is right about what? If you interpreted the post as saying the quantum correlations can be explained classically you misread it.

 

[jed clampett]

(Originally Posted by zonde:)
Let's say it's photon that has property "polarization" at all times not only when it's measured.

Isn't that already a restricted class of realist/classical possibilities? For example, one can imagine that "polarization" is the result of the measurement of a hidden variable, right?

Yes. If Zonde and I are on the same page, we are more concerned with the fact that there is already a problem for local realism based on old-fashioned, electromagnetic light waves. Speaking for myself, I am not all that interested in the philosophical question of whether local realism could perhaps be salvaged by some very unusual or bizarre modification to the ordinary properties of light. Which is what to me appears to be the genius of Bell: that he appears to rule out even such extreme means of salvaging local realism.

So in short, I would say I am only interested in trying to salvage local realism by means that I personally find physically realistic. That's why the Bell-type arguments based on colored balls have limited interest for me.

 

[JesseM]

Yes. If Zonde and I are on the same page, we are more concerned with the fact that there is already a problem for local realism based on old-fashioned, electromagnetic light waves.

How do you figure? The electromagnetic field is defined locally at each point, and in classical EM an event at one point in spacetime can't have an influence on anything outside the future light cone of that point, do you disagree?

Speaking for myself, I am not all that interested in the philosophical question of whether local realism could perhaps be salvaged by some very unusual or bizarre modification to the ordinary properties of light. Which is what to me appears to be the genius of Bell: that he appears to rule out even such extreme means of salvaging local realism.

So in short, I would say I am only interested in trying to salvage local realism by means that I personally find physically realistic. That's why the Bell-type arguments based on colored balls have limited interest for me.

But those colored ball analogies are just trying to help people understand Bell's results in more accessible terms. If you understand Bell's reasoning and agree that his proof can "rule out even such extreme means of salvaging local realism", then you may not have a need of such analogies yourself, but you should be able to see why they would be useful to those who don't yet fully understand the proof as a teaching aid.

 

[cosmik debris]

Why, I am glad you asked this!

2 Separate sources emit entangled pairs of photons. Through a lot of work, one photon from one pair is brought together with a photon from the other pair. This is done in such a way that entanglement swapping occurs (sometimes, not all the time, but there are markers to let you know). The other of each pair is now entangled! But they did not ever interact as a separate independent photon.

It's complicated to follow, but here is the reference:

http://arxiv.org/abs/0809.3991

Thanks, that's very interesting. It'll take a bit of reading.

 

[miosim]

… No, there are no cases where a purely theoretical argument based on mathematics "failed"…

The Newtonian mechanics is an example of “purely" theoretical argument based on mathematics that "failed" to describe relativistic processes. This is a typical example of limitation of the “pure logic” and associated mathematics to be extrapolated outside of well defined area of knowledge.
In the same time I shouldn’t argue about EPR and “local realism” (regarding what I think) because I am not qualify to discuss these issues.
I took notes of the rest of your comments.

I have urged you to attempt to construct a model which is realistic so you could see that is not possible. I think if you would focus on that, which is pretty easy (and I would be glad to show you), you would gain some understanding of Bell. Or you can reject Bell without gaining that understanding, your call.

I am planning to discuss my “realistic” model, but l am not ready yet. First I need to understand some QM concepts and would appreciate any help. I can’t move forward until I fully understand the initial condition that lead to Bell’s theorem.

The main issue for me is that I don’t understand a mathematical difference between “classical” and QM photon that causes different interactions with a polarizer. In my understanding “classical” photon is described by the same QM functions and its mathematical behavior should be undistinguished from the QM photon; otherwise we don’t need Bell’s theorem to demonstrate a difference.
What am I missing?

 

[jed clampett]

The main issue for me is that I don’t understand a mathematical difference between “classical” and QM photon that causes different interactions with a polarizer. In my understanding “classical” photon is described by the same QM functions and its mathematical behavior should be undistinguished from the QM photon; otherwise we don’t need Bell’s theorem to demonstrate a difference.
What am I missing?

If a "classical" photon is one that does everything that classical light does, except that its detection always occurs in clicks proportional to the square of the classical wave amplitude...then I would say that it is in general very difficult to set up an experiment where this "classical" photon behaves differently from a quantum photon. One very glaring difference, and a very disturbing one, is the notion that you can set up a pair of polarizers and get a 100% correlation between simultaneous detection events, no matter what angle you turn the polarizers.

What I have been saying throughout this discussion is that this 100% correlation is hugely problematic for the "classical" photon, and it is not necessary to turn one of the polarizers by 45 or 22.5 degrees, as Bell does, in order to see the difference.

 

[JesseM]

The Newtonian mechanics is an example of “purely" theoretical argument based on mathematics that "failed" to describe relativistic processes.

Huh? Newtonian mechanics isn't a "theoretical argument", it's a physical theory based on empirical observations, no one every claimed you could derive it without some physical assumptions. When I say "theoretical argument" I mean some argument of the form "if we assume theory X, then we get conclusion Y"...the argument's validity is independent of whether or not X actually holds in the real world. There are a lot of arguments like this in textbooks on theory. In the case of Bell, the argument is of the form "if we assume the theory of local realism, we get the conclusion that certain Bell inequalities should be respected in experiments of a given type", and yet we know that QM violates those Bell inequalities in those experiments, therefore the conclusion is that local realism is incompatible with QM. This conclusion would still hold even if QM's predictions turned out to be wrong, or if (as is likely) local realism is wrong.

The main issue for me is that I don’t understand a mathematical difference between “classical” and QM photon that causes different interactions with a polarizer. In my understanding “classical” photon is described by the same QM functions and its mathematical behavior should be undistinguished from the QM photon; otherwise we don’t need Bell’s theorem to demonstrate a difference.
What am I missing?

You can't just assume that the "classical" photon can behave the same as the QM one, the whole point is to show this is logically impossible! The assumption is that the laws of physics governing the "classical" one are local realist laws, which in another thread I defined this way:

1. The complete set of physical facts about any region of spacetime can be broken down into a set of local facts about the value of variables at each point in that regions (like the value of the electric and magnetic field vectors at each point in classical electromagnetism)

2. The local facts about any given point P in spacetime are only causally influenced by facts about points in the past light cone of P, meaning if you already know the complete information about all points in some spacelike cross-section of the past light cone, additional knowledge about points at a spacelike separation from P cannot alter your prediction about what happens at P itself (your prediction may be a probabilistic one if the laws of physics are non-deterministic).

With an additional comment about 1), if it's ambiguous what it means to say "broken down into a set of local facts":

Keep in mind that 1) doesn't forbid you from talking about "facts" that involve an extended region of spacetime, it just says that these facts must be possible to deduce as a function of all the local facts in that region. For example, in classical electromagnetism we can talk about the magnetic flux through an extended 2D surface of arbitrary size, this is not itself a local quantity, but the total flux is simply a function of all the local magnetic vectors at each point on the surface, that's the sort of thing I meant when I said in 1) that all physical facts "can be broken down into a set of local facts". Similarly in certain Bell inequalities one considers the expectation values for the product of the two results (each one represented as either +1 or -1), obviously this product is not itself a local fact, but it's a trivial function of the two local facts about the result each experimenter got.

Then in a Bell-type experiment, you assume that the "classical photon" must duplicate one property of a quantum photon: namely that when both experimenters choose the same polarizer angle, they are guaranteed with probability 1 to get identical results (or opposite results depending on the experiment, it's not really important). Then from this you get the conclusion that the local variables associated with the "classical photon" (or the region of space immediately around it, it's not important) must have predetermined what its response would be to all three polarizer angles, even before the experimenter made a choice of what angle to select on a given trial. Do you understand how this conclusion of predetermined responses follows from the classical assumption of local realism? If not it's a critical step you need to understand, because this conclusion is then used to derive some conclusions about the statistics on trials where the two experimenters happen to choose different polarizer angles, and these conclusions about the statistics yield Bell inequalities which show that the "classical photon" cannot behave like the quantum photon on trials where different angles were chosen, again assuming it matches the quantum photon on trials where they both chose the same angle.

 

[jed clampett]

If you understand Bell's reasoning and agree that his proof can "rule out even such extreme means of salvaging local realism", then you may not have a need of such analogies yourself, but you should be able to see why they would be useful to those who don't yet fully understand the proof as a teaching aid.

JesseM, you've addressed me on several points now for which I apologize I haven't replied directly. In the meantime the discussion has moved forward and perhaps these points are being covered elsewhere. I'd like to hope that the shorthand term "classical photon" has some useful meaning in context, even if some of us are using it differently than others.

However, this last point that you raise is definitely a red flag for me. I probably object to these colored ball arguments more on educational grounds than anything else. In fact I entered the discussion in the first place mainly to express my wholehearted agreement with Miosim's argument on this point.

The colored ball arguments take the 100% correlation as their starting point. This avoids all the real physics. The challenge of the real physics is to explain this 100% correlation, and that is exactly what Bell's argument avoids. I first heard Bell explained quite a few years ago, and I came away with the impression that the 100% correlation was something that you would naturally expect from any two particles that were prepared in the same state. I understood that QM wanted me to understand that the state was indeterminate until the moment of detection; I believed that the case of parallel detectors, with the 100% correlation, failed to distinguish between the case of particles which were created with definite but opposite spins, versus particles created with indefinite and opposite spins. I believed that you needed the 22.5 degree experiment to distinguish between these two cases.

As I have explained in other posts, I now understand (or at least I believe I understand) that the actual expected maximum correlation for the two complimentary photons is 50%, not 100%; that the real mystery is to explain where the 100% comes from; and that Bell totally ignores this question, and thereby ignores the real physics that is going on.

 

[JesseM]

The colored ball arguments take the 100% correlation as their starting point. This avoids all the real physics.

What do you mean? The point of Bell's theorem is just to demonstrate that QM is incompatible with local realism. Do you think that this isn't "real physics"? Or do you think there's something wrong with taking 100% correlation as a starting point if we want to show QM is incompatible with local realism?

As I have explained in other posts, I now understand (or at least I believe I understand) that the actual expected maximum correlation for the two complimentary photons is 50%, not 100%

"Expected maximum correlation" under what assumption about physics? Certainly not local realism, as local realist theories can explain 100% correlation just fine.

 

[DrChinese]

... I can’t move forward until I fully understand the initial condition that lead to Bell’s theorem.

The main issue for me is that I don’t understand a mathematical difference between “classical” and QM photon that causes different interactions with a polarizer. In my understanding “classical” photon is described by the same QM functions and its mathematical behavior should be undistinguished from the QM photon; otherwise we don’t need Bell’s theorem to demonstrate a difference.

What am I missing?

To accomplish what you want, you need to fully understand and accept the Bell reasoning. Once you do this, you can move to the step where you try to poke holes.

The first element of Bell is simply the idea that there must be a result for any measurement setting independent of actually performing a measurement. That is realism. A classical photon is realistic. A quantum photon is not because it follows the Heisenberg Uncertainty Principle (HUP).

Both go through a polarizer and follow the cos^2 rule. So that seems easy enough. But according to EPR, a pair of entangled classical photons can provide more information than the HUP allows. And that conclusion assumes that these classical photons are entangled but share no ongoing physical connection. Again, easy enough.

The problem Bell discovered in all this is that the cos^2 rule does not work for a classical photon for all angles simultaneously. Imagine a thousand classical photons. If I pick any 2 angles, they will NOT follow the cos^2 rule on the average. You can see this for yourself if you attempt to construct a dataset of +/- values at different angles. There is ONE special case in which one of the angles is held constant. That is the ONLY way to get the cos^2 result on average.

So guess what? When you have 2 classical entangled ("cloned") photons, you can also ONLY get the cos^2 rule when you hold one of the angles constant (the special case I mentioned). Oops! Now you need to have Alice know what Bob's secret angle (i.e. the special case) is! That violates the basic premise that the photon angles be selected independently and still get the cos^2 result. Because you can only get that result classically in one special case.

If you don't follow any of the Bell arguments mathematically - such as why you cannot construct a dataset as I describe above - you will never make it to the next level.

 

[DrChinese]

I hope you can see from the above that there is a clear distinction between the statistics for a classical photon vs. a quantum photon:

Classical photon: has a definite polarization at all times (the special case I refer to above), could not otherwise follow the cos^2 rule AND be realistic. (By extension, this should also be true of entangled photon pairs.)

Quantum photon: follows the HUP at all times, and therefore is not realistic. Still follows the cos^2 rule when it has a definite polarization. Entangled photon pairs lack a definite polarization (which allows them to follow the HUP in an EPR setup).

Bell saw that these distinctions led to a mathematical requirement. This requirement can be expressed in different manners according to where you start in your assumptions. Ultimately, the above formulations lead to different predictions for statistics for entangled photon pairs if realism is held as a requirement for entangled photons.

 

[miosim]

DrChinese,

I really appreciate your willingness to help me.
In nutshell I know the history and issues surrounding QM and Bell’s theorem and therefore I am familiar with most of your points. This time I would like to take advantage of the opportunity to gain a dipper understanding of the physicals processes and not just generalalisations. I found that the terms “classical”, “Non-locality”, “realism” etc., often have a different meaning for different people. It is why I would like to have more specific definition of these terms or avoid them altogether. I also prefer to minimize the simplification of given explanation.
Having a general understanding of arguments EPR vs. mainstream QM views I am missing understanding of key mechanisms that put me on hold. I would like proceed by asking specific questions and you (or anybody else) just have a short answer or explain me why the question itself is incorrect.


In the Alain Aspect’s article “BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf the Fig. 3 shows "Polarisation correlation coefficient, as a function of the relative
orientation of the polarisers..." Based on what assumptions did Aspect derive DIFFERENT Polarisation correlation coefficient for QM and for the naive model?


P.S.

I apologize to be slow with my responds.

 

[zonde]

And just a reminder to everyone reading this thread that might have some doubts about entanglement as a non-classical state:

a) You can entangle photons that have NEVER existed in the same light cone (so there is no joint point of origin) and therefore there is no classical mechanism to build from;

This classical mechanism is called postselection.

Rude analogy with colored balls:
We have pair of boxes where in one box there is red ball but in other blue.
These would be A and B boxes.
Then we have similar pair of boxes C and D.

We open box A and box D at two remote locations and send boxes B and C to third location.
Then we mix together content of boxes B and C and the look at it. If we see two balls with different colors we keep them, if they are the same color we discard them.
Then if we look at the sets where we didn't discarded boxes B and C sure thing we see that A and D boxes contained balls with different colors.

b) You can freely choose to entangle photons AFTER they have both been detected, violating the classical cause-effect sequence;
c) And finally, you can do BOTH a) and b) in the same experiment, which should be enough to throw any classical explanation out the window.

No problem with postselection.
But what explanation do you propose?

 

[zonde]

I'm ready to believe that you are right but I don't know what Type I and Type II sources are.

In simple words Type I PDC source produces photon pairs with two having the same polarization but Type II PDC source produces photon pairs with two having the opposite polarization.

I'm really arguing here from analogy to electrons. There is the singlet state |up*dn> - |dn*up> and there is the triplet state with a plus sign instead of a minus sign. I'm guessing that the weird correlations for electrons occur only with the singlet state, and that there is something analogous with photons.

Plus or minus sign just means that you have symmetry between two analyzers if you rotate them in the same direction or in opposite direction (both clockwise vs one clockwise/other counterclockwise).

 

[DrChinese]

In the Alain Aspect’s article “BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf the Fig. 3 shows "Polarisation correlation coefficient, as a function of the relative
orientation of the polarisers..." Based on what assumptions did Aspect derive DIFFERENT Polarisation correlation coefficient for QM and for the naive model?

Good question!

The QM function happens to be cos^2(theta), which you will notice is the same as Malus. This is both a coincidence and not a coincidence. Although the math is a bit complicated, once you factor in rotational issues etc, it reduces to this for the QM expectation value. This is a consequence of the quantum formalism and there is no direct analog in a classical model.

(On the other hand, you are free to add in by hand in any LR model BUT you must put forth something so it can be applied in an LR manner. You cannot just say "agrees to QM" because the QM model is NOT realistic, deterministic, etc. This is where many people go wrong because they just say it agrees and go no further. This will not fly.)

The Local Realistic value is based on Aspect's "naive" model. You will find that most naive models that come anywhere near the QM values will exactly match this linear function when averaged over a random dataset. Any such model requires a couple of things to get it started: a) perfect correlations, i.e. a value of 1 when theta=0 degrees and b) -1 when theta=90 degrees. You will probably want rotational invariance which means that there is no preferred orientation around 360 degrees. With that in mind, you will be hard pressed to get anything but a linear result against a random sample.

And as a check, remind yourself that you must supply a result for ANY 2 angles I pick! I will then average those across 360 degrees since you are saying your data is realistic and there are values for everything, even if not measured. That becomes the data point for that theta on the chart. You only need to do this exercise for 3 angles to see the issue: 0, 120 and 240 degrees. All of these are 120 degrees apart. The average coincidence rate for any realistic dataset with simultaneous values for these 3 settings will never be less than 33.33% (i.e. 1/3). When you rotate around 360 degrees (i.e. 1/121/241, 2/122/242, etc.) the same result holds.

So you will plot 1/3 or higher for theta=120 degrees. The QM value is 1/4.

 

[DrChinese]

This classical mechanism is called postselection.

Rude analogy with colored balls:
We have pair of boxes where in one box there is red ball but in other blue.
These would be A and B boxes.
Then we have similar pair of boxes C and D.

We open box A and box D at two remote locations and send boxes B and C to third location.
Then we mix together content of boxes B and C and the look at it. If we see two balls with different colors we keep them, if they are the same color we discard them.
Then if we look at the sets where we didn't discarded boxes B and C sure thing we see that A and D boxes contained balls with different colors.

This is preposterous. A and D will NOT be entangled in YOUR example. For example, they will not show perfect correlations.

 

[miosim]

I have a simple question regarding attached picture. It is from

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html

I expect that the picture shows entangled pair of electrons (having opposite spins – I added blue arrows).
The picture indicates that both electrons passed their respective Stern-Gerlach filters.
In contrary I expect that only an electron on the right side will pass. Am I confused?

 

[miosim]

The QM function happens to be cos^2(theta), which you will notice is the same as Malus. This is both a coincidence and not a coincidence. Although the math is a bit complicated, once you factor in rotational issues etc, it reduces to this for the QM expectation value. This is a consequence of the quantum formalism and there is no direct analog in a classical model.

I understand this. But I have no CLEAR undersatnding what a classical model is? Can we avoid generalizations like LR, realism, determinism, etc. because this terminology (that is better suited to philosophy) doesn’t help to achieve a clarity?

At the same time, I think that I understand what is the EPR model is and if I understand it correctly, the EPR model dosn’t deny QM formalism, but provides ONLY a different interpretation to this formalism.
So how come EPR model couldn’t be “granted” with the same cos^2(theta) and with compliance with the Malus’ law.

I think that before discussing a correlated statistic I really need to understand the behavior of an INDIVIDUAL photon (not an entangled pair) interacting with an individual polarizer. What is a difference between QM and EPR model (which is also QM entity) interacting with a polarizer?

Thank you

 

[DrChinese]

I have a simple question regarding attached picture. It is from

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html

I expect that the picture shows entangled pair of electrons (having opposite spins – I added blue arrows).
The picture indicates that both electrons passed their respective Stern-Gerlach filters.
In contrary I expect that only an electron on the right side will pass. Am I confused?

In your example, only 1 passes from each pair. I believe the author says as much on the page.

 

[DrChinese]

I think that before discussing a correlated statistic I really need to understand the behavior of an INDIVIDUAL photon (not an entangled pair) interacting with an individual polarizer. What is a difference between QM and EPR model (which is also QM entity) interacting with a polarizer?

Thank you

There really isn't one. A classical realistic model can work for this fine.

For instance: I can give you a dataset that will reproduce the QM expectation value. Using my favorite polarizer angles: 0/120/240 where the photon is known to be oriented at 0 degrees. Similarly, I can provide a dataset if the photon orientation angle is unknown.

 

[DrChinese]

At the same time, I think that I understand what is the EPR model is and if I understand it correctly, the EPR model dosn’t deny QM formalism, but provides ONLY a different interpretation to this formalism.
So how come EPR model couldn’t be “granted” with the same cos^2(theta) and with compliance with the Malus’ law.

Be careful when you reference EPR. EPR concludes that if QM is complete, then there is NOT local realism. That is the opposite of the perspective you are advocating. On the other hand, what does complete really mean?

Bell goes further: if QM is correct in its predictions for a certain area, then there is NOT local realism. And this is quite specific. And testable!

Further: The meaning of a classical model is that you apply the model to Alice and Bob independently and obtain results. You don't just say: the QM and LR results are the same. Sometimes, they DO give similar predictions. But in the case of entanglement, they don't!

 

[JesseM]

I understand this. But I have no CLEAR undersatnding what a classical model is? Can we avoid generalizations like LR, realism, determinism, etc. because this terminology (that is better suited to philosophy) doesn’t help to achieve a clarity?

There is no single classical model, the proof is meant to deal with the broad class of all conceivable classical models that qualify as local realistic. As always, the crucial thing to understand is why any such model would require that the particles have predetermined results for each detector setting, even before the experimenters make the choice of which setting to use. This would need to be true in any classical model that had the property that the two experimenters are guaranteed to get the same (or opposite) result whenever they pick the same detector setting. Do you understand this part, or not?

At the same time, I think that I understand what is the EPR model is and if I understand it correctly, the EPR model dosn’t deny QM formalism, but provides ONLY a different interpretation to this formalism.

But Bell proved they must deny the QM formalism, they just didn't realize it at the time.

I think that before discussing a correlated statistic I really need to understand the behavior of an INDIVIDUAL photon (not an entangled pair) interacting with an individual polarizer. What is a difference between QM and EPR model (which is also QM entity) interacting with a polarizer?

The EPR model does assume each particle has a predetermined result for any possible measurement before the measurement is made, in order to explain how both members of the pair give perfectly correlated results when the same measurement is made on both.