The match rates in Bell Tests -- Lower than 50%?

[Cerenkov]

Hello.

A friend and I are having a good-natured argument about tests of Bell's Theorem and he has directed me to this link.

http://electron6.phys.utk.edu/phys250/modules/module 3/entangled_electrons.htm

Our understanding of quantum physics should be considered as Basic.

What we would like to understand is a little more about the match rates mentioned in the concluding section of the above article.

• For a large number of trials, ~50% of the time the lights on both filters will flash the same color. Experiments similar to the one described here have now been carried out many times and have always yielded this predicted result.​

What is so special about that?

Quantum mechanics predicts incompatible observables for a system. An observer cannot know the values of two incompatible observables of a system at the same time. Does this mean that the system really does not have well defined values for these observables before a measurement, or is it possible that the system has well defined values, but these values are hidden from the observer, and the observer just cannot obtain the complete information?
In 1964 J.S. Bell showed that the assumption of hidden variables is inconsistent with the outcome of the above described experiment. If there were hidden variables, we would have to observe the light flashing the same color more than 50% of the time. We will examine at a simple version of Bell's thought experiment in an in-class activity.

We read this to mean that Bell tests in favour of hidden variables would have values above 50%.

But a little searching through this forum has revealed this, from 2011.

https://www.physicsforums.com/threads/violation-of-bells-theorem.496839/post-3290045 [Moderator's note: Fixed link to point to the specific post being referenced.]

If, on the other hand, you care to put forth a Local Realistic dataset (i.e. like your Example 1) for the angle settings 0, 120 and 240 degrees, you will discover something very quickly. Your match rate will be greater than 33 percent. Now YOUR prediction will not match experiment (which is 25%). Try it, really (psssst you already have proven my point with your example 1)! Suddenly, the assumptions you made about this not being a meaningful test completely falls apart because YOUR predictions will be flat wrong.

This appears to say that Bell Theorem experiments have a match rate well below 50%

So, question 1.
Are we mistaken in our understanding of the match rates from these two sources? If so, could we please be corrected in a way that someone at a Basic level can grasp?

Question 2.
Where can we find source material that gives the discovered match rates for various Bell tests?
(This Wiki page cites a list of Notable Experiments. https://en.wikipedia.org/wiki/Bell_test )
Should we start there and investigate each citation sequentially or is there a 'condensed' source which summarises what we'd like to find out?

Thanks in advance for any help given and apologies in advance for any rookie-level blunders made in this posting.

We would gladly accept gentle correction and instruction, if its needed.

Thank you.

Cerenkov.

 

[PeterDonis]

What we would like to understand is a little more about the match rates

The first thing to understand is that the meaning of the match rate depends on the details of the experiment. There is no single rule that match rates must always be above or below some threshold to either satisfy the Bell inequalities or to satisfy the QM predictions. You have to look at the details of the experiment to figure out what the appropriate Bell inequalities will be (they are different for different experiments) and what the appropriate QM predictions are.

 

[DrChinese]

But a little searching through this forum has revealed this, from 2011.

https://www.physicsforums.com/threads/violation-of-bells-theorem.496839/post-3290045 [Moderator's note: Fixed link to point to the specific post being referenced.]

If, on the other hand, you care to put forth a Local Realistic dataset (i.e. like your Example 1) for the angle settings 0, 120 and 240 degrees, you will discover something very quickly. Your match rate will be greater than 33 percent. Now YOUR prediction will not match experiment (which is 25%). Try it, really (psssst you already have proven my point with your example 1)! Suddenly, the assumptions you made about this not being a meaningful test completely falls apart because YOUR predictions will be flat wrong.

This appears to say that Bell Theorem experiments have a match rate well below 50%

So, question 1.
Are we mistaken in our understanding of the match rates from these two sources? If so, could we please be corrected in a way that someone at a Basic level can grasp?

As PeterDonis has correctly commented, it is dependent on the specifics of the described experiment. In theory, you could adjust the setup so that any number would be the boundary point between a hidden variables prediction and the quantum prediction (and you could make either one be higher or lower). So that difference does not in and of itself indicate any fundamental difference.

I have a page fairly similar to the one you referenced on electrons: http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

The stats are somewhat similar, even though I use entangled photons rather than electrons, because the angles happen to give the similar effects for both particle types. Regardless of what examples you look at, the important thing thing is to understand how a hidden variables type description must include assumptions that are not present in pure quantum descriptions. Those assumptions - as Bell showed us - are what lead to contradiction with experiment.

 

[Cerenkov]

The first thing to understand is that the meaning of the match rate depends on the details of the experiment. There is no single rule that match rates must always be above or below some threshold to either satisfy the Bell inequalities or to satisfy the QM predictions. You have to look at the details of the experiment to figure out what the appropriate Bell inequalities will be (they are different for different experiments) and what the appropriate QM predictions are.

We didn't fully appreciate this Peter, so thank you for that help.

It was our naïve (mis)understanding that the 50% set by the Bell test itself was a threshold that any experiment had to exceed to confirm the assumption of local reality. Clearly we were wrong.

When it comes to the details of each experiment, we, at our Basic level, have little hope of understanding the mathematics needed for such exacting work. We also understand that the use of different types of particle sources in different types of experiment will necessarily require a lot of technical knowledge that we simply don't possess. Lastly, neither of us has the necessary training to understand the subtleties and nuances of thinking that QM might require.

We freely acknowledge these shortcomings. However, our interest remains undimmed and we still would like to advance a little further in these matters. We had hoped that, instead of looking in great detail at the particulars of a single experiment, it might help if we could gain a kind of general overview of the history of how the Bell tests have proceeded, from the 1970's up to today.

Hence the tentative request for some material that might summarise the outcomes of each test in chronological order, or something like that? We're asking for your guidance here because even though we can find various articles about the Bell tests across the web, we've found that they're either pitched at a 'popular' level for the general public or are too advanced for us to make any headway.

Can you please guide us to something like a general overview of the history of the Bell tests?

Thank you.

Cerenkov (& friend).

 

[Cerenkov]

As PeterDonis has correctly commented, it is dependent on the specifics of the described experiment. In theory, you could adjust the setup so that any number would be the boundary point between a hidden variables prediction and the quantum prediction (and you could make either one be higher or lower). So that difference does not in and of itself indicate any fundamental difference.

I have a page fairly similar to the one you referenced on electrons: http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

The stats are somewhat similar, even though I use entangled photons rather than electrons, because the angles happen to give the similar effects for both particle types. Regardless of what examples you look at, the important thing thing is to understand how a hidden variables type description must include assumptions that are not present in pure quantum descriptions. Those assumptions - as Bell showed us - are what lead to contradiction with experiment.

Thank you very much Dr. Chinese.

We will we be following your link and reading it in the coming week.

Cerenkov (& friend).

 

[PeterDonis]

it might help if we could gain a kind of general overview of the history of how the Bell tests have proceeded, from the 1970's up to today

The general overview is that more and more experimental tests of the Bell inequalities have been done, using more and more sophisticated procedures to close various loopholes that skeptics have come up with, and the overall trend of the results is confirmation with higher and higher confidence that the Bell inequalities are violated in actual experiments and that the predictions of QM (which of course violate the Bell inequalities) are correct. There are still a few skeptics--most of whom are actually philosophers, not physicists--but the alternative models they propose to account for the experimental results are increasingly contrived and implausible as more and more experiments are done that close various loopholes.

I'm not aware of any single review article that gives a more detailed history of this field; perhaps one of the other experts on the forum is. The overview I have just given is based on what I have seen in a large number of papers and in other threads here on PF over many years.

 

[DrChinese]

Can you please guide us to something like a general overview of the history of the Bell tests?

Hahaha, you asked...

Marco Genovese (2007), 100+ pages and 500+ papers referenced:
https://arxiv.org/abs/quant-ph/0701071

And for good measure once you whip through that:
From 2008: https://arxiv.org/abs/0806.0270
From 2013: https://arxiv.org/abs/1303.2849

Now it is true these references are a bit dated, but that doesn't much matter. Since then, there have been probably 5-10,000 additional DIFFERENT Bell tests performed and documented in papers. This is because they have explored as many different forms of entanglement as possible. I see over 100 papers a month on the subject (I don't read but a very small subset). After a while, you will get the idea.

FOR YOUR PURPOSES: There is a specific measure that is most commonly used for the more straight-forward Bell tests of photons. It is called the Clauser Horne Shimony Holt inequality, abbreviated CHSH. In these tests, local realistic (hidden variable) theories always have a max of exactly 2. In a perfect case, the quantum prediction has a max about 2.82 (Tsirilson's Bound). Actual experimental tests usually yield results around 2.3 to 2.4 but any value above 2 is a rejection of classical (a la EPR) assumptions of reality. Below is a great paper that incorporates these ideas, and you probably won't find a better/more readable paper that includes both some theory and some actual experimental results.

https://arxiv.org/abs/quant-ph/0205171

Abstract:

We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds S=2.307±0.035, in clear contradiciton of hidden variable theories. The experiments described can be performed in an afternoon.

 

[Cerenkov]

The general overview is that more and more experimental tests of the Bell inequalities have been done, using more and more sophisticated procedures to close various loopholes that skeptics have come up with, and the overall trend of the results is confirmation with higher and higher confidence that the Bell inequalities are violated in actual experiments and that the predictions of QM (which of course violate the Bell inequalities) are correct. There are still a few skeptics--most of whom are actually philosophers, not physicists--but the alternative models they propose to account for the experimental results are increasingly contrived and implausible as more and more experiments are done that close various loopholes.

I'm not aware of any single review article that gives a more detailed history of this field; perhaps one of the other experts on the forum is. The overview I have just given is based on what I have seen in a large number of papers and in other threads here on PF over many years.

Hello again Peter.

Once again, thank you for your help.

It looks like Dr. Chinese has come through with a lot of helpful information for us to look at.

Thanks again.

Cerenkov (& friend).

 

[Cerenkov]

Hahaha, you asked...

Marco Genovese (2007), 100+ pages and 500+ papers referenced:
https://arxiv.org/abs/quant-ph/0701071

And for good measure once you whip through that:
From 2008: https://arxiv.org/abs/0806.0270
From 2013: https://arxiv.org/abs/1303.2849

Now it is true these references are a bit dated, but that doesn't much matter. Since then, there have been probably 5-10,000 additional DIFFERENT Bell tests performed and documented in papers. This is because they have explored as many different forms of entanglement as possible. I see over 100 papers a month on the subject (I don't read but a very small subset). After a while, you will get the idea.

FOR YOUR PURPOSES: There is a specific measure that is most commonly used for the more straight-forward Bell tests of photons. It is called the Clauser Horne Shimony Holt inequality, abbreviated CHSH. In these tests, local realistic (hidden variable) theories always have a max of exactly 2. In a perfect case, the quantum prediction has a max about 2.82 (Tsirilson's Bound). Actual experimental tests usually yield results around 2.3 to 2.4 but any value above 2 is a rejection of classical (a la EPR) assumptions of reality. Below is a great paper that incorporates these ideas, and you probably won't find a better/more readable paper that includes both some theory and some actual experimental results.

https://arxiv.org/abs/quant-ph/0205171

Abstract:

Wow! What can we say, Dr. Chinese? So much information! Thank you.

Ummm... is it too much to ask for further help in parsing and understanding certain aspects of this plethora?

As I mentioned to PeterDonis, we don't hold out much hope of understanding the math or the intricacies of the Bell test, but we would like to further our comprehension of what it means about QM in a more general way. For example, a scatter plot or a pie chart can compress a lot of data points into one, easily-understood graphic. (Providing one understands the context of the data.)

Whereas, if a mass of complex data is presented in rows and columns of numbers, a lot more is required of the person reading that data to properly comprehend (for instance) a subtle trend or pattern in those numbers. I suspect that the same is true for higher math. Those trained and familiar with the higher forms of math can see at a glance what this or that function or equation means and also grasp the significance of what, to an untrained person, appears to be just an esoteric symbol.

Please don't take what I'm writing here as any kind of complaint about what you've provided for us, Dr. Chinese. Far from it! We are delighted with your help. It's just that we may well need further assistance in a form that is more appropriate to our Basic level of comprehension.

I hope this doesn't come across as us being ungrateful or picky.

Once again, thank you.

Cerenkov (&friend).

Edit:
Ooops! I forgot to mention that one of your supplied links appears to be broken.

http://drchinese.com/David/Bell_Theorem.htm

Thank you.

 

[Nugatory]

we don't hold out much hope of understanding the math or the intricacies of the Bell test, but we would like to further our comprehension of what it means about QM in a more general way.

For that, you will find this Scientific American article helpful. (ignore the subtitle about human consciousness - that's just something the editor did to jazz up the page).

And although a history rather than an explanation, Louisa Gilder's "The age of entanglement" is a good perspective on the twisty road that got us to where we are.

 

[DrChinese]

Wow! What can we say, Dr. Chinese? So much information! Thank you.

Ummm... is it too much to ask for further help in parsing and understanding certain aspects of this plethora?

As I mentioned to PeterDonis, we don't hold out much hope of understanding the math or the intricacies of the Bell test, but we would like to further our comprehension of what it means about QM in a more general way. For example, a scatter plot or a pie chart can compress a lot of data points into one, easily-understood graphic. (Providing one understands the context of the data.)Edit:
Ooops! I forgot to mention that one of your supplied links appears to be broken.

http://drchinese.com/David/Bell_Theorem.htm

Thank you.

Thanks for informing me about the broken link. Looks like I have several on that page...

Yes, I knew that was a bit much. Each different experiment has its own scatter plot of data, which is often different from experiment to experiment. It will help me if I have a better idea of what you understand, and where you still have questions or want to know more.

1. Do you see how local realistic assumptions (such as those in the EPR paper) lead to mathematical requirements? This usually is built around looking at values for 3 settings, 2 of which can actually be measured at one shot.

2. Do you see how Bell uses specific angles (such as 0/120/240) with those assumptions to contradictions? We are seeking settings at which the inequality becomes large enough to be experimentally seen.

3. Do you understand how actual photon experiments show that the predictions of QM are supported, but the local realistic ones are not? Or do you have questions around whether the experiments are valid?

Or if you can frame a few questions, I (or others here) can probably drill into those.

 

[Cerenkov]

For that, you will find this Scientific American article helpful. (ignore the subtitle about human consciousness - that's just something the editor did to jazz up the page).

And although a history rather than an explanation, Louisa Gilder's "The age of entanglement" is a good perspective on the twisty road that got us to where we are.

 

[Cerenkov]

Many thanks Nugatory.

We appreciate it.

Cerenkov (&friend)

 

[Cerenkov]

This is very kind of you Dr Chinese. To give us your time, like this.

I hope you won't be too daunted to read that we understand these things on a Basic level. Which means that Nugatory's Scientific American article is pitched about right for us. So, we understand the historical context of the EPR and how it was formulated originally as a thought experiment. We also realize that Bell's theorem is a proof by contradiction.

But your three questions are way over our heads because, as I explained to PeterDonis, we're aware of our limitations and for now we are content to just to gain a better general understanding.

So, what we'd like to do is to take you up on your kind offer and put some questions your way, please.

Thank you.

Cerenkov (&friend)

 

[PeterDonis]

we understand these things on a Basic level

Unfortunately, there isn't a lot that can be said about this topic on that level. See below.

your three questions are way over our heads because, as I explained to PeterDonis, we're aware of our limitations and for now we are content to just to gain a better general understanding.

I'm not sure how much more basic you can get than the questions @DrChinese asked you. If those are over your head, pretty much anything beyond the general overview I gave in post #6 is probably going to be over your head. We'll be glad to try to answer questions as best we can, but I want to make sure your expectations are set appropriately; we might not be able to give answers in much detail at the "B" level.

 

[Cerenkov]

Unfortunately, there isn't a lot that can be said about this topic on that level. See below.
I'm not sure how much more basic you can get than the questions @DrChinese asked you. If those are over your head, pretty much anything beyond the general overview I gave in post #6 is probably going to be over your head. We'll be glad to try to answer questions as best we can, but I want to make sure your expectations are set appropriately; we might not be able to give answers in much detail at the "B" level.

We understand what you are saying, Peter.

So perhaps its best if we back up a bit and not discuss the specific details of the Bell tests themselves, but look at how and why we (my friend and I) came to think that the match rates of every test would be couched in terms of values above or below the 50% threshold.

This was the article that lead us to the belief.

http://electron6.phys.utk.edu/phys250/modules/module 3/entangled_electrons.htm

For a large number of trials, ~50% of the time the lights on both filters will flash the same color. Experiments similar to the one described here have now been carried out many times and have always yielded this predicted result.

We suspect that we erroneously took the words, 'similar to the one described here' to mean ALL Bell tests. Whereas, from the advice we've received in this thread, it seems that there are Bell tests that are not similar to the one described here. Is this so?

Furthermore, we think that our reading of this Wiki page was not as careful as it should have been.

https://en.wikipedia.org/wiki/Bell_test

Upon closer reading and in the light of the input we've received, we think that we should have realized the full import of this sentence. (Emboldening is mine.)

'Many types of Bell tests have been performed in physics laboratories, often with the goal of ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests.'

If there are many different types of Bell test, it would seem to follow that they need not all follow the 50% threshold requirement specified in the original article. Are we correct in this conclusion?

So, talking only in the context of the original article that lead us here, is it correct to say that experiments of this type have always fallen short of that 50% threshold?

Lastly, we now have a large body of information to go through and, in the light, of our misunderstandings we would like to be able to discern between the various TYPES of Bell tests that are being described. People like yourselves will have no problem finding your way around these papers, but for us they are effectively minefields.

So, as a cautious first step, we would like to understand what the various types of Bell test experiments are and which type was being described in our original article. Thank you.

Once again, we would like to express our thanks to Peter, Dr. Chinese and Nugatory for their help and assistance.

Cerenkov (& friend).

 

[PeterDonis]

We suspect that we erroneously took the words, 'similar to the one described here' to mean ALL Bell tests. Whereas, from the advice we've received in this thread, it seems that there are Bell tests that are not similar to the one described here. Is this so?

Yes.

If there are many different types of Bell test, it would seem to follow that they need not all follow the 50% threshold requirement specified in the original article. Are we correct in this conclusion?

Yes.

is it correct to say that experiments of this type have always fallen short of that 50% threshold?

The 50% is not a "threshold". It is an exact prediction of QM. Experiments to date have always confirmed the predictions of QM; for this particular type of experiment, that means exactly 50%, within the experimental margin of error.

That page is unfortunately very vague about what the corresponding Bell inequalities are for the given experiment; it just says "more than 50% of the time". That doesn't really tell you whether a violation of the Bell inequalities would be detectable in this experiment, given that the actual results are exactly 50% within experimental error.

 

[DrChinese]

This was the article that lead us to the belief.

http://electron6.phys.utk.edu/phys250/modules/module 3/entangled_electrons.htm

For a large number of trials, ~50% of the time the lights on both filters will flash the same color. Experiments similar to the one described here have now been carried out many times and have always yielded this predicted result.

1. We suspect that we erroneously took the words, 'similar to the one described here' to mean ALL Bell tests. Whereas, from the advice we've received in this thread, it seems that there are Bell tests that are not similar to the one described here. Is this so?'Many types of Bell tests have been performed in physics laboratories, often with the goal of ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests.'

2. If there are many different types of Bell test, it would seem to follow that they need not all follow the 50% threshold requirement specified in the original article. Are we correct in this conclusion?3. So, as a cautious first step, we would like to understand what the various types of Bell test experiments are and which type was being described in our original article. Thank you.

1. Correct. In fact this particular one (with the 50% threshold) may not have ever been performed. I've never seen it. On the other hand, my analogous page features an experiment that has also probably never been performed. These are just learning aids.

2. Correct. Almost none do. More common are the CHSH inequality discussed in post #7. But original experiments (which is what are presented in most papers) may feature an inequality specific for that particular experiment and which is not presented in any other original experiment. For learning purposes, most examples use spin (electrons) or polarization (photons) entanglement. In reality, there are actually thousands of types of entanglement. Almost anything that exhibits quantum behavior, especially if the Heisenberg Uncertainty Principle is involved, is subject to being presented in an entangled form.

3. Most entangled examples use photons. Most photon entanglement is created using standard lasers using nonlinear crystals designed to create entangled photon pairs. These use a process called spontaneous parametric down conversion. The only thing you need to know about this is that the abbreviation is SPDC or PDC. There are 2 basic subtypes of these, cleverly called Type I and Type II.

Type I: the photon pairs have the same polarization.
Type II: the photon pairs have the opposite polarization.

Electrons are used in the original page you referenced. In these types, the electrons always have opposite spins.

When 2 angles are measured (one by Alice, the other by Bob), the match stats are calculated as follows:

theta=[Alice's angle]-[Bob's angle]

a. Type I photons:
Match=cos^2(theta)
b. Type II photons:
Match=sin^2(theta)
c. Electrons:
Match=sin^2(theta/2)

As it happens, when theta=+/-120 degrees, a Bell Inequality can be constructed for a, b and c. On the other hand, the EPR Paradox is demonstrated when theta=0 or 180 degrees (photons also +/- 90 degrees).

Hopefully this helps a little. There are a lot more examples and papers around photon entanglement than electron entanglement, because high quality and quantity production of photon pairs is easier to create, control and detect.

 

[Cerenkov]

Gentlemen,

Thank you for these replies, which confirm what we suspected. We are grateful.

After some discussion we'd like to 'pull back' a little in this thread because we've realized that going further and deeper isn't something we're equal to. At least, not yet. But I'd just like to reaffirm that our interest in QM remains undimmed and its probably just a matter of time before we ask something else about this fascinating field.

As demonstrated by our misunderstandings and misreading's it's clearly essential to be as precise and exact as possible. With that lesson in mind, could we please tap into your expertise and ask you to help us refine our understanding of two things that we believe to be relevant to this thread?

1. In non-mathematical, non-technical language, what is a good working description of the concept of Local Realism? (Assuming that such a description can be exact enough to be of benefit.)

2. In non-technical, non-mathematical language, could you please explain how the various types of Bell test have demonstrated that Local Realism cannot apply? (Same proviso as before.)

Let me reiterate our appreciation for the help you've given us recently. We feel that its just as much a good thing to discover where one is going wrong as where you are doing something right. So, even if we have back up and retrace our steps, we're pleased to do so.

Thank you.

Cerenkov (& friend)

 

[PeterDonis]

In non-mathematical, non-technical language, what is a good working description of the concept of Local Realism?

There isn't a completely non-mathematical description because the concept is inherently mathematical; it is a mathematical condition on the function that gives the joint probability of the results of measurements on two entangled particles. Roughly, "local realism" means that the joint probability function can be factorized; that is, the joint probability function, which in the general case is of the form $P(a, b | A, B)$, i.e., the probability of measuring result $a$ on one particle and result $b$ on the other, given measurement settings $A$ for the first particle and $B$ for the second, can be factorized into two functions multiplied together: $P(a, b | A, B) = P_A(a | A) P_B(b | B)$, i.e., one function is only a function of the result and measurement setting on the first particle, and the other is only a function of the result and measurement setting on the second particle.

The QM prediction violates this condition: the QM joint probability function is a function of the angle between the two measurement settings, which obviously requires both settings; there is no way to express it as a product of two functions, each of which is only a function of one measurement setting.

In non-technical, non-mathematical language, could you please explain how the various types of Bell test have demonstrated that Local Realism cannot apply?

The mathematical condition of Local Realism, as above, is a condition on the joint probability function, and you can prove mathematically that this condition places limits on the correlations you can observe between the measurement results. These limits are the Bell inequalities, which, as noted, the QM predictions violate. But by how much the QM predictions violate the Bell inequalities can vary for different types of experimental setups. So experimentalists look for setups where the QM predictions violate the applicable Bell inequalities by as much as possible. And many such experiments have been run, which have confirmed the QM predictions and have shown violations of the Bell inequalities by enough of a margin that, except for a few extreme skeptics, as I mentioned in my earlier post, everybody accepts that the Bell inequalities really are violated.

 

[Nugatory]

In non-mathematical, non-technical language, what is a good working description of the concept of Local Realism?

”Local realism”: The result of Alices’s measurement can be calculated from what we know of Alice, her detector, and the particle that reaches her; nothing that happens with Bob’s particle after they’ve separated will affect this calculation.

2. In non-technical, non-mathematical language, could you please explain how the various types of Bell test how the various types of Bell test have demonstrated that Local Realism cannot apply?

If local realism is correct, then there is an upper limit on how correlated Bob’s measurements and Alice’s measurements can be; the two particles can’t be any more connected than they were when they separated. Bell’s inequality and its corollaries state this limit for various experimental setups. We do these experiments and we find that the limit is exceeded, which cannot happen if local realism is correct.

Most people get hung up on the second part. It really is somewhat amazingly counterintuitive that local realism (as defined above) would imply such an upper limit - but it does. To see how this can be, I suggest that you work through the “Simplest Proof” section of @DrChinese’s website, or follow d’Espagnat’s Venn diagrams from that Scientific American article I linked.

Once you see the logic, you’ll find it compelling. It’s like saying that the number of married men in a room will always be less than or equal to the number of men who smoke cigarettes plus the number of married non-smokers.

 

[DrChinese]

1. In non-mathematical, non-technical language, what is a good working description of the concept of Local Realism? (Assuming that such a description can be exact enough to be of benefit.)

2. In non-technical, non-mathematical language, could you please explain how the various types of Bell test have demonstrated that Local Realism cannot apply? (Same proviso as before.)

My take, for what it's worth, no math involved!

1. Realism (in the context of the Einstein's view of the quantum world, and not as a general philosophical topic) means as follows:

Realism: If you can predict the outcome of a quantum measurement of spin, momentum, etc. with certainty, then that outcome must be "real" (already determined) in this sense. Since any standard quantum observable can be so predicted using entangled particle pairs (Alice measures to predict what Bob will see), then collectively those attributes are "real" even if they are not all simultaneously measured. This is the EPR* perspective, and it is completely reasonable.

Local realism is the same thing, but simply with the added criteria that there are no faster than light influences involved. You'd expect that from Einstein**, correct?2. While the EPR conclusion is reasonable, Bell discovered it was wrong. He discovered that while it works for identical measurements on entangled particles, it does NOT work for most other non-identical measurements. In terms of your original reference on electron pairs, that would be those measurements where one is at 0 degrees and the other is at 120 degrees; or at 120 and 240 degrees; etc. Note that in these situations, the outcomes are NOT being predicted with certainty; instead, the outcomes have statistical predictions per quantum theory. So the predictions become measurable correlations.

The important point: the correlations cannot work if you consider all possible measurements as being "real" (already determined) per answer #1. You cannot even hand pick values to make the statistics work out. We conclude:

Either nature is not local; or nature is not "real" in the EPR quantum sense; or both. Regardless: local realism is falsified by experiment and the predictions of quantum mechanics are confirmed.

-DrC*Einstein is the "E" in "EPR". The 1935 EPR paper was the primary starting point for all of this, and what Bell was responding to with his discovery.
** Since Einstein says c is a upper limit on action.

 

[Cerenkov]

PeterDonis, Nugatory and Dr.Chinese,

Thank you for these interesting replies. You've given us something to think about.

https://www.drchinese.com/

There's plenty here to keep us occupied. Love the cartoons, btw.

We feel that this thread may well be drawing towards a natural ending, but before that happens we have just one more question.

It concerns the best choice of words, when it comes to describing the relationship between Alice and Bob's particles after they become separated.

Nugatory used the word, 'connection'. Should we adopt this wording in future posts or do other options, like relationship, correlation or correspondence serve just as well?

In the light of what we've discovered and what we've been advised in this thread we'd like to improve the quality of not just what we say in this forum, but how we say it.

Thank you.

Cerenkov (& friend)

 

[DrChinese]

It concerns the best choice of words, when it comes to describing the relationship between Alice and Bob's particles after they become separated.

Nugatory used the word, 'connection'. Should we adopt this wording in future posts or do other options, like relationship, correlation or correspondence serve just as well?

In the light of what we've discovered and what we've been advised in this thread we'd like to improve the quality of not just what we say in this forum, but how we say it.

Thank you.

Cerenkov (& friend)

Haha, "connection"! This is the subject of much debate here (there is a subforum devoted mostly to that - quantum foundations/interpretations). There is no single suitable and agreed upon language (outside of mathematical) to describe entangled particles. There is nothing at all wrong with "connection", probably being as good (or better) as any. Except that you will have plenty of folks denying that strongly, and with some good reasons as well.

Just keep in mind that the word you select to use doesn't change anything, it simply reveals something about your viewpoint. Many prefer to use "correlation" instead of "connection", for example. I tend to talk about "quantum nonlocality", this is also common. Sometimes this is shortened to "nonlocal", although that is not strictly correct either. Entangled systems cannot be considered as systems of 2 independent particles (they wouldn't be entangled if that was the case). So some people leave it at that.

 

[Nugatory]

Nugatory used the word, 'connection'. Should we adopt this wording in future posts or do other options, like relationship, correlation or correspondence serve just as well?

Natural language is sufficiently imprecise that it’s seldom worth debating which imprecise formulation to use - they’re all wrong, or incomplete, or invite the listener to read more into the statement than the speaker intended.

 

[Cerenkov]

Thank you again gentlemen for your input and I think this is where we had best bring the curtain down on the thread.

C & friend.

 

[vanhees71]

Haha, "connection"! This is the subject of much debate here (there is a subforum devoted mostly to that - quantum foundations/interpretations). There is no single suitable and agreed upon language (outside of mathematical) to describe entangled particles. There is nothing at all wrong with "connection", probably being as good (or better) as any. Except that you will have plenty of folks denying that strongly, and with some good reasons as well.

Just keep in mind that the word you select to use doesn't change anything, it simply reveals something about your viewpoint. Many prefer to use "correlation" instead of "connection", for example. I tend to talk about "quantum nonlocality", this is also common. Sometimes this is shortened to "nonlocal", although that is not strictly correct either. Entangled systems cannot be considered as systems of 2 independent particles (they wouldn't be entangled if that was the case). So some people leave it at that.

I'd prefer to call it "inseparability" like Einstein did in his clarifying paper about what he really wanted to say instead of the confusing EPR paper (with the even more confusing answer by Bohr). It precisely describes that parts of an entangled quantum system, where the parts can be as far distant from each other as you like (e.g., the location of the detectors measuring two entangled photons from parametric down conversion), cannot be taken as separate objects but only as one system as a whole. These stronger-than-classial correlations between far distantly observed parts of such an "inseparable system" are due to the preparation in the entangled state and cannot be caused by the measurements on the parts, at least not when the measurement events ("clicks in the detectors") are space-like separated, which is guaranteed by the locality (!) (i.e., the validity of the microcausality principle) of the interactions in relativistic QED.

Unfortunately I don't know, whether Einstein's paper of 1948 has been translated into English (I guess it has, because it's for sure among the best about Einstein's opinion on the meaning of QT):

A. Einstein, Quantenmechanik und Wirklichkeit, Dialectica 2, 320 (1948),
https://doi.org/10.1111/j.1746-8361.1948.tb00704.x

 

[DrChinese]

Unfortunately I don't know, whether Einstein's paper of 1948 has been translated into English (I guess it has, because it's for sure among the best about Einstein's opinion on the meaning of QT):

A. Einstein, Quantenmechanik und Wirklichkeit, Dialectica 2, 320 (1948),
https://doi.org/10.1111/j.1746-8361.1948.tb00704.x

Einstein, Quantum Mechanics and Reality (English translation):
https://informationphilosopher.com/solutions/scientists/einstein/dialectica.html

 

[Stephen Tashi]

An explanation of the math as it happens when there are hidden variables: https://theworld.com/~reinhold/bellsinequalities.html