Can grandpa understand the Bell's Theorem?

[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.

 

[miosim]

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?

I am taking notes from your comments. Regarding prospective I am coming from, they are different from EPR, but I share their belief that QM is fundamentally incomplete and I belief in LR, but this is just a belief I would like to validate or reject this.

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!

I don’t understand this yet, but I wonder if this either/or logic is because only two alternatives is in consideration. What if we have other alternatives? However I don’t want speculate about this; I am still lock a basic understanding and want to move slowly without jumps.

 

[miosim]

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?

I didn’t realize that in the EPR model the “particles have predetermined results for each detector setting”. I thought that the EPR model exhibits QM “determinism” that specifies polarization for both correlated particles but in terms of probabilistic wave function. Therefore, I thought, the result should not be fully deterministic.

My understanding is that the most critical characteristic of EPR model relevant to Bell’s theorem are those that are incorporated into initial condition of Bell’s theorem and becomes its starting point? So WHAT are these characteristics of EPR model that are incorporated in the Bell’s theorem? This is my ultimate question in this discussion. Bell didn’t “insert” in his theorem words like “determinism”, “LR”, “classical”, etc., but his mathematical formalism contains some very critical elements of EPR model. What these elements are? It looks to me like everybody knows, but me.

 

[JesseM]

I didn’t realize that in the EPR model the “particles have predetermined results for each detector setting”. I thought that the EPR model exhibits QM “determinism” that specifies polarization for both correlated particles but in terms of probabilistic wave function. Therefore, I thought, the result should not be fully deterministic.

But a two-particle wave function is by definition not a "local" entity. Imagine that each particle has to "make up its mind" about what to do when it encounters a detector using only the localized properties associated with that particle, or with the region of space in the immediate neighborhood of the particle and detector. Such localized properties are what is meant by "elements of reality" in the EPR paper, and they assume that the "elements of reality" in the region of one measurement can't be influenced by the what happens in the region of the other measurement, see p. 3 where they write:

On the other hand, since at the time of measurement the two systems 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. This is, of course, merely a statement of what is meant by the absence of an interaction between the two systems.

And on p. 4 they arrive at the conclusion that the two particles must have had "simultaneous elements of reality" determining both their position and momentum, based on the idea that they always give perfectly correlated results if experimenters measure the position of both or the momentum of both.

My understanding is that the most critical characteristic of EPR model relevant to Bell’s theorem are those that are incorporated into initial condition of Bell’s theorem and becomes its starting point? So WHAT are these characteristics of EPR model that are incorporated in the Bell’s theorem?

Just the idea that each particle's behavior when it encounters a detector must be determined by "elements of reality" which are not in any way causally influenced by what happens in the region of the other detector.

This is my ultimate question in this discussion. Bell didn’t “insert” in his theorem words like “determinism”, “LR”, “classical”, etc., but his mathematical formalism contains some very critical elements of EPR model.

He talked about "causality and locality" (I think equivalent to what modern physicists mean by "local realism"), and says that if this assumption holds we should be able to infer that the results of each measurement must be "predetermined" by the properties of the particle being measured--just read the first page of his original paper.

 

[zonde]

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.

Yes I think that this is impossible in a way that is consistent with known experimental observations.
But then I do not exactly agree that "the hidden variables can work in any way that doesn't violate local realism". You don't want contrived theory where all it does is gives explanation for single experiment. And it should be falsifiable. That will considerably reduce all the ways how hidden variables can work.

 

[JesseM]

Yes I think that this is impossible in a way that is consistent with known experimental observations.

That wasn't my question. I was asking whether you think it's impossible to have a local hidden variables theory that predicts 100% correlation when the experimenters choose the same angle, not a theory that is "consistent with known experimental observations" on all counts. I say this is certainly possible, but when I said that to jed clampett, your reply in post #28 was "Obviously your hypothesis breaks down even before we start to consider polarization entangled state."

But then I do not exactly agree that "the hidden variables can work in any way that doesn't violate local realism". You don't want contrived theory where all it does is gives explanation for single experiment. And it should be falsifiable. That will considerably reduce all the ways how hidden variables can work.

Whether the theory is contrived or non-contrived, whether it is falsifiable or not, is irrelevant to Bell's theorem, which is the subject under discussion. Bell's theorem deals with all conceivable local realistic theories, and shows that it's logically impossible that any of them (even ones that are contrived or non-falsifiable due to the presence of hidden variables) could agree with QM in all its predictions.

 

[zonde]

That wasn't my question. I was asking whether you think it's impossible to have a local hidden variables theory that predicts 100% correlation when the experimenters choose the same angle, not a theory that is "consistent with known experimental observations" on all counts. I say this is certainly possible, but when I said that to jed clampett, your reply in post #28 was "Obviously your hypothesis breaks down even before we start to consider polarization entangled state."

Well you can formulate some theory using some abstract entities and abstract analyzers. So what?
The moment you will try to establish correspondence between your abstract entities/analyzers and photons/polarizers I will say it's not working. Photons do not behave at polarizers like your abstract entities at your abstract analyzers.
And we would be back where we started.

Whether the theory is contrived or non-contrived, whether it is falsifiable or not, is irrelevant to Bell's theorem, which is the subject under discussion. Bell's theorem deals with all conceivable local realistic theories, and shows that it's logically impossible that any of them (even ones that are contrived or non-falsifiable due to the presence of hidden variables) could agree with QM in all its predictions.

Yes, that Bell does. And?
jed clampett said he sees the problem in QM prediction about perfect correlations.
I agree. I would be very nice if this prediction would be tested experimentally so that we can see how perfect are these correlations. Unfortunately there are no reports about such tests.

 

[zonde]

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

Hmm, I was not implying that this analogy is about entanglement. Sorry if I didn't make it clear.
I just wanted to illustrate what I mean with postselection and how it can create correlations between two entities that does not have common past.

In case of entanglement it is a bit more complicated. You have to determine similarity of polarization for two photons and sign of interference term.

From the same paper you quoted http://arxiv.org/abs/0809.3991" :
"Each source in our experiment emits pairs of polarization entangled photons along spatial directions 1 & 2 and 3 & 4, respectively (see fig. 1). We chose the singlet state \psi^{-}, which is one of the four maximally entangled Bell states:
|\psi^{\pm}\rangle=\frac{1}{\sqrt{2}}|HV\rangle\pm|VH\rangle
|\phi^{\pm}\rangle=\frac{1}{\sqrt{2}}|HH\rangle\pm|VV\rangle (1)
A successful entanglement swapping procedure will result in photons 1 and 4 being entangled, although they never interacted with each other [13? ]. This is done by performing a Bell-state measurement on particles 2 and 3, i.e. by projecting them on one of the four Bell states. Consequently, photons 1 and 4 will be projected onto the Bell state corresponding to the BSM outcome."
Respectively in this experiment only photons corresponding to one of four possibilities are detected. The rest is discarded.
But if you calculate average correlations for all four possible states it results in no correlation at all.

 

[jed clampett]

Jed Clampett wrote:

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.

To which Zonde replied:

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).

We may be miscommunicating here, but I'm pretty sure I can do the algebra at least for electrons to show that the correlations are different depending on the plus or minus sign. I think I ought to start a new thread for this, which will have to wait until later today. (Although from the very last post I now see that it is almost becoming "on topic" for this thread.)

 

[DrChinese]

Hmm, I was not implying that this analogy is about entanglement. Sorry if I didn't make it clear.

...

But if you calculate average correlations for all four possible states it results in no correlation at all.

Quite true! And that is pretty fascinating of itself. You can look at A & D all day long and you will never notice that some items are perfectly correlated. Until you check to see which ones were projected into a Bell (B & C indicate this).

 

[DrChinese]

I didn’t realize that in the EPR model the “particles have predetermined results for each detector setting”. I thought that the EPR model exhibits QM “determinism” that specifies polarization for both correlated particles but in terms of probabilistic wave function. Therefore, I thought, the result should not be fully deterministic.

My understanding is that the most critical characteristic of EPR model relevant to Bell’s theorem are those that are incorporated into initial condition of Bell’s theorem and becomes its starting point? So WHAT are these characteristics of EPR model that are incorporated in the Bell’s theorem? This is my ultimate question in this discussion. Bell didn’t “insert” in his theorem words like “determinism”, “LR”, “classical”, etc., but his mathematical formalism contains some very critical elements of EPR model. What these elements are? It looks to me like everybody knows, but me.

You are supposed to deduce certain things from both EPR and Bell. Please realize that these papers were written for a specific audience of peers, not the general public. As such, they assume you already know certain ideas. Yes, EPR is essentially saying "the result is predetermined and that creates the element of reality".

Bell starts off saying that the spin of a,b has a value of +/-1, and then later (14) extends that to say that there are 3 such values simultaneously, a/b/c. He says this mathematically (assuming we will follow this), his audience at that time being very small. He does say (2nd paragraph) the following about the EPR argument, which should help: "Since we can predict in advance the result of measuring any chosen component ... it follows that the result of any such measurement must actually be predetermined." He then says that QM would be incomplete were that true since the QM formalism lacks such determinism.

If the result is predetermined, you should be able to construct a dataset by hand which will yield certain results. You can simply make up the values yourself and try to make them work out. You will soon see that is NOT possible. Please try it, it will go a long way towards greater understanding.

 

[JesseM]

Well you can formulate some theory using some abstract entities and abstract analyzers. So what?
The moment you will try to establish correspondence between your abstract entities/analyzers and photons/polarizers I will say it's not working. Photons do not behave at polarizers like your abstract entities at your abstract analyzers.

But the reason they don't behave like the abstract entities is because you are considering results at all possible angles, not just on trials where both experimenters chose the same angle. That's what Bell shows in his proof, that you can't have a local realistic theory that matches both the prediction of 100% correlation when the experimenters choose the same angle, and the QM statistics when they choose different angles. The first alone would be compatible with local realism!

Whether the theory is contrived or non-contrived, whether it is falsifiable or not, is irrelevant to Bell's theorem, which is the subject under discussion. Bell's theorem deals with all conceivable local realistic theories, and shows that it's logically impossible that any of them (even ones that are contrived or non-falsifiable due to the presence of hidden variables) could agree with QM in all its predictions.

Yes, that Bell does. And?
jed clampett said he sees the problem in QM prediction about perfect correlations.

But he said this in the context of a discussion of local realism, so I thought he was saying that even if our only restriction on theories is that they be local realistic, there is still some problem with perfect correlations. There isn't! If you want to add additional constraints like that the local realistic theory be "non-contrived", or that it says that photons have definite polarization vectors at each moment and the probability they pass through a filter depends on the relative angle between this vector and the polarizer according to Malus' law, then in that case these additional conditions might be able to rule out two photons always having perfect correlations whenever they're measured with polarizers at the same angle. But in the context of Bell's proof such additional constraints are irrelevant, and I thought jed was saying that even with the bare assumption of local realism there'd be a problem with perfect correlations, and that you were agreeing. If you're not saying that then I don't think we really disagree on anything here.

 

[miosim]

JesseM and DrChinese
I am taking notes of your comments and it helps.

One simple question.
I would like to make sure that I understand correctly the “...100% correlation when the experimenters choose the same angle..."

Is this (100%) applys only for the detected correlated photons? Or this is true for any pair of correlated photons (traveling along the line between polorizers) regardless we detect them or not and regardless of their polarization angle in reference to polarizes (set in parallel)?

Thanks

 

[JesseM]

Is this (100%) applys only for the detected correlated photons? Or this is true for any pair of correlated photons (traveling along the line between polorizers) regardless we detect them or not and regardless of their polarization angle in reference to polarizes (set in parallel)?

Thanks

How would we know if they weren't detected? Anyway, the result assumed in Bell's theorem is specifically that when you measure two entangled photons, then whenever the two polarizers are set to the same angle, the observed results of the measurement are always identical (or opposite depending on the experiment).

 

[jed clampett]

jed clampett said he sees the problem in QM prediction about perfect correlations.
I agree. I would be very nice if this prediction would be tested experimentally so that we can see how perfect are these correlations. Unfortunately there are no reports about such tests.

I'm really glad you raised this point because I was afraid to raise it myself. In reading about the history of Bell we find of course the famous Aspect experiments, and the earlier Clauser experiments of the 70's. But all of these used the 45/22.5 degree polarizers of Bell. I haven't found any reference to the original 100% correlation experiments as seen with polarizers aligned. Surely the experiment must have been done long before Aspect or Clauser; and surely it would have drawn considerable attention in its day, at the very least because it can't be an easy experiment to do.

Where and when was the first experimental demonstration of the 100% (or greater than 50% even!) correlation of photon detections?

 

[miosim]

Quick question:

According to the traditional QM, do entangled photons have identical polarization or their polarization may slightly differ?

Thanks

 

[DrChinese]

In reading about the history of Bell we find of course the famous Aspect experiments, and the earlier Clauser experiments of the 70's. But all of these used the 45/22.5 degree polarizers of Bell. I haven't found any reference to the original 100% correlation experiments as seen with polarizers aligned. Surely the experiment must have been done...

How do you think scientists optimize their Bell test setup? There is one easy way, set your polarizers to get perfect correlations. Once you get the highest match rate possible, you can continue to test the CHSH inequality or whatever. Because you know the source is truly entangled. It is so fundamental it is not usually mentioned as it has no bearing on the experiment at hand.

 

[DrChinese]

Quick question:

According to the traditional QM, do entangled photons have identical polarization or their polarization may slightly differ?

Thanks

This question has multiple correct answers.

In the sense you are asking it, QM says that entangled photons will have identical (or crossed according to the Type) polarizations. However, the fidelity of the source is a factor so this only reaches 100% in the ideal case. Also, it is possible to intentionally (or accidentally) make pairs for which the rule is looser than perfect match. If you allow a small bit of knowledge to creep into the equation, the entanglement can be reduced accordingly. In other words, you can have 72% entanglement, 49% entanglement, etc.

 

[jed clampett]

Jed Clampett asked:

Where and when was the first experimental demonstration of the 100% (or greater than 50% even!) correlation of photon detections?

DrChinese answered:

How do you think scientists optimize their Bell test setup? There is one easy way, set your polarizers to get perfect correlations. Once you get the highest match rate possible, you can continue to test the CHSH inequality or whatever. Because you know the source is truly entangled. It is so fundamental it is not usually mentioned as it has no bearing on the experiment at hand.

I understand from DrChinese that it was a dumb question for me to ask. But I'm still interested in the answer if anyone knows it.

 

[miosim]

... localized properties are what is meant by "elements of reality" in the EPR paper, and they assume that the "elements of reality" in the region of one measurement can't be influenced by the what happens in the region of the other measurement, see p. 3 where they write:
"On the other hand, since at the time of measurement the two systems 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. This is, of course, merely a statement of what is meant by the absence of an interaction between the two systems."

I share their views.

And on p. 4 they arrive at the conclusion that the two particles must have had "simultaneous elements of reality" determining both their position and momentum ..."

I hold the same views.

... based on the idea that they always give perfectly correlated results if experimenters measure the position of both or the momentum of both.

However, in my phenomenological model the entangled photons aren't perfectly correlated when no longer interact.

I think that this is a time for me to move away form EPR model and start building my own.

In my phenomenological model any photon exhibits a random change in polarization within a limited range of values. It is why the absolute knowledge of one correlated photon doesn’t give us a knowledge of the correlated photon. However both photons should have their "simultaneous elements of reality" regardless can we observe it or not.

Another important element of my model is that the photons in my model aren’t a waves but corpuscles only. Actually, my model is a 100% corpuscular for any particle and banish wave entirely. Particles in my model are continuously jiggling in a wave-like trajectory sampling surrounding space. This wave-like motion of elementary particles determines their wave property that is matched with QM wave function. Therefore I expect that the interaction of my photons with polarizer cannot be distinguished from the traditional QM model and therefore Bell’s theorem ishould’t be valid for the photons of my local realistic model.

 

[Jonathan Scott]

Another important element of my model is that the photons in my model aren’t a waves but corpuscles only. Actually, my model is a 100% corpuscular for any particle and banish wave entirely. Particles in my model are continuously jiggling in a wave-like trajectory sampling surrounding space. This wave-like motion of elementary particles determines their wave property that is matched with QM wave function. Therefore I expect that the interaction of my photons with polarizer cannot be distinguished from the traditional QM model and therefore Bell’s theorem ishould’t be valid for the photons of my local realistic model.

You've missed the point. As we've said several times Bell's theorem does not relate to any specific classical model, although you can use particular classical models to illustrate it. Bell's theorem proves that the results of QM cannot be reproduced by ANY local realistic model.

 

[miosim]

You've missed the point. As we've said several times Bell's theorem does not relate to any specific classical model, although you can use particular classical models to illustrate it. Bell's theorem proves that the results of QM cannot be reproduced by ANY local realistic model.

It the provided links below, please pinpoint (the best would be to copy and past) the formula or logical deduction that reflects the “local realism” as a physical property/characteristic/value etc., and that enters Bell's theorem as initial condition.

“BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
by Alain Aspect
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf

 

[JesseM]

However, in my phenomenological model the entangled photons aren't perfectly correlated when no longer interact.

Then how do you explain the fact that, according to QM, if they are both measured with a polarizer at the same angle they are guaranteed to give the same results with probability 1? Do you imagine them "communicating" non-locally to coordinate their behaviors?

 

[miosim]

Then how do you explain the fact that, according to QM, if they are both measured with a polarizer at the same angle they are guaranteed to give the same results with probability 1? Do you imagine them "communicating" non-locally to coordinate their behaviors?

As I understand, with the polarizers at the same angle, there is no issue with EPR model to have the same 100% correlation as QM model, but without need of non-locality.

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell , page C2-49
http://hal.archives-ouvertes.fr/docs...198142C202.pdf

“… Thus the ad hoc model does what is required of it (i.e., reproduces
quantum mechanical results) only at (a - b) = 0, (a - b) = s/2 and
(a - b) = n, but not at intermediate angles...”

 

[JesseM]

As I understand, with the polarizers at the same angle, there is no issue with EPR model to have the same 100% correlation as QM model, but without need of non-locality.

That's true, but the whole reason there is "no issue" is that you are free to imagine that each particle just had identical predetermined results for each possible angle, so that no matter what angle was selected they would both give the same results. I'm asking how you would explain it in your model, since you said the photons "aren't perfectly correlated when no longer interact", which I took to mean they don't have a perfectly correlated set of predetermined results.

 

[Jonathan Scott]

It the provided links below, please pinpoint (the best would be to copy and past) the formula or logical deduction that reflects the “local realism” as a physical property/characteristic/value etc., and that enters Bell's theorem as initial condition.

“BELL’S THEOREM : THE NAIVE VIEW OF AN EXPERIMENTALIST”
by Alain Aspect
http://arxiv.org/ftp/quant-ph/papers/0402/0402001.pdf

BERTLMANN'S SOCKS AND THE NATURE OF REALITY by J. Bell
http://hal.archives-ouvertes.fr/docs/00/22/06/88/PDF/ajp-jphyscol198142C202.pdf

I'm not interested in rereading those papers (even though they were both very interesting first time).

"Local" is easy, in that in practice it effectively means not involving faster-than-light signals.

"Realism" is a bit more complicated, as we assume it every day and it's difficult to work out exactly what we are assuming. It's mostly to do with being able to assume that we could have done a different measurement on the same system and got some other result. One way of describing it is called "counterfactual definiteness (CFD)", which you can Google for more information.

 

[Jonathan Scott]

I should point out that if you've learned ordinary Newtonian physics and Special Relativity, then at first glance locality and realism both appear to be "obvious", and it's quite tricky to accept that QM could find a way round them.

The way to understand Bell's theorem is to learn it first in terms of that "obvious" model, then try to understand what would need to break to provide a way round it, which is far more difficult, especially when it comes to realism.

If you come up with any model involving waves, particles or whatever which are subject to the usual rules of locality and realism, Bell's theorem says it is simply impossible for it to reproduce the results of QM, regardless of the details.

Note that Bell's theorem does NOT rule out the possibility that QM has some underlying deterministic mechanism, but it does say that any such mechanism must either violate locality or realism (or possibly both).

 

[Philip000]

I also am a grandfather, and I’ve read of Bell’s theorem as follows.
A calcite crystal is set at a position similar to 12 o’clock and the spin polarity of photons directed at it gives a fixed set of readings.
The same crystal is turned to 1 o’clock and gives a different set of readings.

In a reversed world, and one that is handed, the same readings are taken of paired photons, and these agree with the set of readings taken in the non-reversed world.

Both the reversed and non reversed worlds are described as local realities or places where classical observations and measurements are made.

Bell’s theorem, as I have read of it, goes on to say that if the reading at 1 o’clock in both worlds show the same difference from readings taken at 12 o’clock in both worlds, then the differences added together represent an addition of local realities as defined by classical measurement.

It goes on to say that Bell’s inequality shows that this is not so, and that experimental results have shown that differences between the 1 o’clock measurements in both worlds are greater than that which is arrived at by adding both local measurements.

If the reversed and non reversed world’s 1 o’clock positions show 25% differences from the 12 o’clock position, then the total difference between the measurements taken in both worlds should be 25% + 25% = 50%.
However, test results show that the differences between the two 1 o’clock positions is actually 75%, hence Bell’s inequality.

Personally, I have a problem with this, because the 1 o’clock position in the reversed world represents the 11 o’clock position in the non reversed world, and if you try to compare the readings of a calcite taken at 11 o’clock with those taken at 1 o’clock in either world, you will find that there is a 75% difference.

This has nothing to do with the addition of localities, it is just a fact that as you turn a calcite crystal, so the set of results it gives change in line with the following.
If 12 0’clock is taken as the control set:
1 o’clock is 25% different from it,
2 o’clock is 75% different from it,
3 o’clock is 100% different from it.

The same would be true if any other clock position was taken as the control point, and the read out of differences to the control point is always different by the same percentages as the angles represented by moving away from it are altered, to finally arrive at a 90 degree angle from the control point, which is a totally different reading from that taken at the control point.

As I see it, if Bell’s addition of the reversed and non reversed worlds is taken as the 25% differences from a control point that is the same in both worlds, and if viewing the results of the differences between 1 o’clock positions in each world effectively becomes the difference between 11 o’clock and 1 o’clock in either of these worlds, then the sum of 25% + 25% = 50% is unrelated to the facts.

Unrelated is not unequal, it is just a totally different calculation, and if the explanation of Bell’s theorem I have been reading explains it properly, then as I see his inequality, this theorem is not based on the available classical facts, but on trying to say that 2 apples should equal a pear, when they obviously don’t.

Please understand that I am not a physicist, and that mathematical formulas leave me with a headache, however, from a simple commonsense point of view, and taken from the explanation I have read, it seems to me that the error in Bell’s theorem is not that of locality or classical measurement, but simply a problem that comes from not defining the control points of his measurements and the later experiments adequately.

Local reality, as a classical measurement, is always defined by a control point, and if you move the control point without noticing that you have done so, the result is an error of measurement and not an expression of quantum deep space or a yet to be defined non-local reality.

If my interpretation of Bells theorem is correct, then I claim grandfather rights over it, if it isn’t, then I claim a grandfather’s right to voice it based on the facts available to me.

 

[miosim]

That's true, but the whole reason there is "no issue" is that you are free to imagine that each particle just had identical predetermined results for each possible angle, so that no matter what angle was selected they would both give the same results. I'm asking how you would explain it in your model, since you said the photons "aren't perfectly correlated when no longer interact", which I took to mean they don't have a perfectly correlated set of predetermined results.

It is correct. In my model the polarization of correlated photons isn’t perfectly matched and I expect the difference is within uncertainty principle.
Therefore the correlation function of these photons is less than 100%.

I also expect that in my model correlated photons have different (within uncertainty principle) wavelength. I think that this can be tested by forcing correlated photons to interfere with each other after they passed respective polarizers.

 

[miosim]

I'm not interested in rereading those papers (even though they were both very interesting first time).

"Local" is easy, in that in practice it effectively means not involving faster-than-light signals.

"Realism" is a bit more complicated, as we assume it every day and it's difficult to work out exactly what we are assuming. It's mostly to do with being able to assume that we could have done a different measurement on the same system and got some other result. One way of describing it is called "counterfactual definiteness (CFD)", which you can Google for more information.

To understand the Bell’s theorem (as any other theorem) the initial condition need to be better understood; specifically why this theorem treats differently EPR and standard QM model. I would like to put this difference under “magnifying glass.”

It seams to me that the initial conditions for EPR model in Bell’s theorem are oversimplified to the level of Newtonian mechanics. The logic in Bell’s theorem leads to the correlation function that contradicts the classical Malus’ law. According to this law, the intensity of completely polarized light that passed polarizer is proportional to cos²θ (the same as for QM). If EPR photons aren’t in compliance with Malus’ law I need to know why. If EPR photons are in compliance with Malus’ law, it seems to me, that the Bell’s theorem should be thrown out of window.

 

[JesseM]

It is correct. In my model the polarization of correlated photons isn’t perfectly matched and I expect the difference is within uncertainty principle.
Therefore the correlation function of these photons is less than 100%.

The uncertainty principle doesn't suggest any limits to measurements of perfect correlation with the same polarizer setting, it only deals with incompatible observables like position and momentum. If you're saying the correlation function is less than 100% even under idealized experimental conditions (as opposed to it being just a practical issue), then your model disagrees with QM.