Can grandpa understand the Bell's Theorem?

[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. :rofl: 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.

 

[miosim]

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.

In my model uncertainty principle is also applicable to polarisation of photons (and probably to a range of other physical properties of subatomic particles).
However the uncertainty priniple in my model is different than Heisenberg’s unsertuntly priniple. My model accepts the existence of “hidden” variables and don’t impose the theoretical barrier studying these variables.

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.

Indeed the correlation function in my model is less that 100% under idealized experimental conditions. However I expect that my model isn’t in a conflict with mathematical formalism of QM. I am not sure if the 100% correlation is derived from QM or it is just an expectation. At the same time my model is sharply contradicts with all interpretations of QM and replaces the existing head twisting QM theories with a reasonable and realistic description of physical reality.

 

[Jonathan Scott]

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.

Bell's Theorem has nothing to do with specific models. It basically says that if you measure the number of differences between set A and set B then between set A and set C then the number of differences between set B and set C cannot exceed the sum of the differences in the two separate cases, then points out that matching certain QM predictions requires violation of this inequality.

The pairs of photons in Aspect's experiments and similar comply with Malus' law, but in a non-classical way, in that if you assume one of the photons is observed in a pure state, then the results at the other end are as predicted by Malus' law, in exactly the same way as if a single photon was emitted from one device with a known polarization and observed at the other.

In contrast, classical physics would predict that the pair of photons would start off with polarization in some definite but unknown direction, and then that each of the photons would independently reproduce Malus' law relative to that original direction. This gives a much weaker correlation, which is typically of the form (1+x)/2 where x is the QM-predicted (and experimentally observed) correlation.

If you only change one observation device, it would be theoretically possible that the experiment happens to have been producing photons which are always in a pure state relative to the other device, in which case classical and QM predictions would match. If you change both observation devices separately then it is not possible for the experiment to emit photons which are in a pure state relative to one or another device all of the time unless there is some form of communication back from the observation devices to the experiment. Experiments have been done with very fast switching at both ends (with different frequencies) between different observation devices where the switches and observation devices are far enough from the experiment that even a light-speed signal could not communicate the current state, yet even in that case the experiments continued to match QM predictions.

 

[jed clampett]

The pairs of photons in Aspect's experiments and similar comply with Malus' law, but in a non-classical way, in that if you assume one of the photons is observed in a pure state, then the results at the other end are as predicted by Malus' law, in exactly the same way as if a single photon was emitted from one device with a known polarization and observed at the other.

In contrast, classical physics would predict that the pair of photons would start off with polarization in some definite but unknown direction, and then that each of the photons would independently reproduce Malus' law relative to that original direction. This gives a much weaker correlation, which is typically of the form (1+x)/2 where x is the QM-predicted (and experimentally observed) correlation.

This is pretty much the point I was making earlier when I said you get in trouble as soon as you find correlations close to 100%. You don't need to agonize over what's going on at 45 or 22.5 degrees. Jonathan Scott has expressed this more clearly than me. (Although interestingly enough, he still finds it useful to talk about what "classical physics would predict (for a) pair of photons", as compared to my use of the phrase "classical photons".)

If you only change one observation device, it would be theoretically possible that the experiment happens to have been producing photons which are always in a pure state relative to the other device, in which case classical and QM predictions would match. If you change both observation devices separately then it is not possible for the experiment to emit photons which are in a pure state relative to one or another device all of the time...

The predictions could match only if the source happened to be producing polarized pairs with the same orientation as the arbitrarily placed detectors. There is no physical reason this should happen in practice. Again, you can rule it out by rotating the source with respect to the detectors. If the correlation is 100% at all angles, you can't explain it by saying the photons simply started out with the same polarization.

 

[DrChinese]

...Indeed the correlation function in my model is less that 100% under idealized experimental conditions. However I expect that my model isn’t in a conflict with mathematical formalism of QM. I am not sure if the 100% correlation is derived from QM or it is just an expectation. At the same time my model is sharply contradicts with all interpretations of QM and replaces the existing head twisting QM theories with a reasonable and realistic description of physical reality...

Wow, in your world what is 1+1? I mean, you say it is local realistic but don't bother to show any evidence. You are making some pretty wild claims, when you obviously lack the basic understanding of the issues involved. Does it ever occur to you that your model is completely worthless and provides absolutely no useful predictions? I think you have a serious misunderstanding of theoretical and experimental science, and how they relate to each other.

You have strayed far from the point where you are asking questions. Now you are making more and more statements as if they are factual. Sorry, sir, they are not! Personal theories are not welcome here when presented in this manner. Cite evidence to support your ideas. Or ask a question that can be answered by someone with suitable knowledge. But the "head twisting" QM you mention has been around longer than you have and generations of physicists have used it with good effect. (Unless you were born before 1927.)

You might try doing your research BEFORE making the claim. It shocks me to see people wanting the credit before they doing the requisite work. Well, that might work around your friends but it doesn't work that way in science. (Oh, and please present that research elsewhere as it violates forum rules.)

P.S. The 100% correlation IS derived from theoretical predictions of QM and they have been experimentally verified to over a hundred standard deviations. Do you know what a standard deviation is? Or is that just another "head twisting" concept?

 

[DrChinese]

I really think this thread was misnamed. It should be named: "Posts from a grandpa who doesn't really want to learn anything about Bell, and would rather tell us his 'common sense' views on the subject."

To all the Grandpas (and grandmas and dads and moms and sons and daughters) out there: Try taking a little time to understand the argument BEFORE you reject it! If you don't understand the mathematical basis, that's fine, hey I don't understand a lot about biochemistry myself. But I think I know not to embarrass myself by pulling opinions out of the blue and posting them publicly.

Meanwhile, the Bell argument is pretty simple to follow if you will just sit down and work through it. The math is NOT hard at all! And the Bell logic works with pretty much any assumptions of local realism you would care to define. But you will need to put forth such a definition (or accept the standard ones, such as Einstein's).

a) QM: generally accepted and supported by tens of thousands of experiments with no significant modification to theory in the past 80 years.
b) QM+LR: generally rejected, per Bell, approaching 50 years.
c) If you want to keep LR, you will need to change QM somehow, in which case it will no longer match experiments! So it will be useless!
d) Or you can change LR so it is no longer LR per Bell. In which case no one really cares.