## Bell's Theorem

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In trying to understand Bell’s theorem and lacking the math and science to read it directly, I have had to try to reduce it to a story in words that makes sense. I think I’ve got it and offer it here fwiw and for constructive criticism. Most of what follows is synthesized from an old Scientific American article, here,

https://static.scientificamerican.com/sciam/assets/media/pdf/197911_0158.pdf

And other articles, papers, and videos. There’s nothing especially difficult here, but altogether it’s not-so-easy. Probably not worth the read unless you’re interested in Bell’s theorem.

It takes several steps: what it’s about, what is tested and how, a preliminary observation about a limit, Bell’s inequality and how that’s constructed, what happens - with a tiny bit of trigonometry - and a quick sketch of what it means.

John S. Bell published his paper in 1963 as a thought experiment. Since then it has been verified with increased refinement in successive experiments. The idea is that the number of events that occur one way cannot exceed the number of similar events that occur another way – the inequality. But they can and do and that is what all the fuss is about!

A device is set up to emit in opposite directions entangled sub-atomic particle-pairs that are then detected by devices set equidistant from the source, with their spin measured and recorded. Each detector can be set independently to any of 360 degrees. (What, exactly, spin and entanglement are is a separate subject.)

When a detector detects a particle, it signals “up” or “down,” sometimes rendered as “+” and “-”. We shall suppose that the devices always work perfectly, and that certain random sequences always break even, like tossing a coin 100 times and always getting 50 heads and 50 tails. The results do not in any way depend on these assumptions; they’re merely for convenience.

A particle-pair is emitted and the detectors together record either ++, +-, -+, or --. We test the detectors separately by running 1000 particles at each of the possible 360-degree settings. At each setting we get 500+ and 500- (our assumption). And we’re satisfied that each + and – occurs randomly and unpredictably.

The settings of the detectors are going to matter, so we’ll call them a, b, and c. Each detector will be set at either a or b or c (degrees), and the result of each detection will be, e.g., a+ or a- or b+ or b- or c+ or c-. It should be noted that each particle can be effectively measured once and once only.

Both detectors are turned on, and both set to the same setting, e.g., zero degrees. And when the setting is the same for both, each combined result is always either +- or -+. Never ++ or --. We represent the count of the pairs as (in this case) n(a+, a-). If we run 1000 tests then we get 500(a+, a-) and 500(a-, a+). That is, there were 500 pairs with an a+ at the left detector and an a- at the right detector, and there were 500 pairs with just the opposite results of 500 a- at the left detector and 500 a+ at the right detector.

Call it perfect correlation or anticorrelation, either way the magnitude of correlation is always perfectly one, the reason being that spin is a measure of angular momentum and that the particle-pair comes from an original single particle with spin zero. The sum of the angular momentum of the two must then always be zero.

The detectors are reset with an offset of 180 degrees, e.g., 0 degrees and 180 degrees. We can again call these settings a and b. 1000 particle-pairs results in 500(a+, b+) and 500(a-, b-). Never +- or -+. Again, a perfect correlation.

A third experiment, this time the offset 90 degrees. Again a and b, offset by 90 degrees. And now we get 250(a+, b+), 250(a+, b-), 250(a-, b+) and 250(a-, b-). Zero correlation.

To recap, when the detectors are set to the same setting, the results are always different. When offset 180 degrees, the results are always the same. And at 90 degrees, always random. But at the same time, always 500+ and 500- at each detector. The question arises, what happens at other settings?

Now to make clear what Bell’s inequality is and how it comes about. It’s easy to be persuaded that what the detectors measure is some quality or attribute of the particle itself. And whatever the setting of the detector, the result is always either + or -. It is a simple step to assume that before the measurement, the particle really has a determinate spin value that the detector measures. And we keep in mind that the spin can be measured at any setting.

This leads to the very plausible and reasonable conclusion that every such particle, for given test settings of a or b or c, is in one of eight states with respect to a and b and c. That is, any of a+b+c+ or a+b+c- or a+b-c+ or a+b-c- or a-b+c+ and so forth.

Following the Sci. Am. article referenced above, we’re going to assume we have a device – which does not exist and maybe never will exist – that can measure one particle at two settings. Suppose we measure at the left detector a particle at settings a and b and get (a+, b-). Based on the above, we can infer that the particle on the right would have measured (a-, b+). And it must be that the number of single particles N(a+, b-) is equal to N(a+, b-, c+) plus N(a+, b-, c-). That is, the whole is equal to the sum of its parts. Writing it a little more efficiently and keeping in mind that the “N” refers to the number of single particles:

1) N(a+, b-) = N(a+, b-, c+) + N(a+, b-, c-).

Clearly N(a+, b-) is larger than or equal to either of N(a+, b-, c+) or N(a+, b-, c-) taken separately.

Similarly consider

N(b-, c+) = N(a+, b-, c+) + N(a-, b-, c+),

And

N(a+, c-) = N(a+, b+, c-) + N(a+, b-, c-).

We can see that N(b-, c+) is strictly larger than or equal to N(a+, b-, c+) in 1). And we can see that N(a+, c-) is strictly larger than or equal to N(a+, b-, c-) also in 1). We can make substitutions with this result:

N(a+, b-) ≤ N(b-, c+) + N(a+, c-)

All this is tangled and confusing, but it is stone simple once you work through it and see it.

Now we want to look at particle pairs, which, as above, are indicated, e.g., n(a+, b-). That is, with a small “n.” And that might be read as follows, “the number of particle-pairs that measure a+ on the left and b- on the right.”

The following relations hold:

n(a+, b+) / N(a+, b-) + N(a-, b+) = n(b+, c+) / N(b+, c-) + N(b-, c+) = n(a+, c+) / N(a+, c-) + N(a-,c+)

Which yields,

n(a+, b+) ≤ n(b+, c+) + n(a+, c+), which is just Bell’s inequality.

It’s worth noting that a, b, c, + and – are all arbitrarily selected. That is, the inequality holds for any combination of these.

Whew! And so what?

Toss a fair coin 1000 times and you know that the sum of the resulting heads and tails will be 1000. You don’t have to count both to know both. If you tally 383 heads, you know there were 617 tails. Simple, and linear. But not so simple with the entangled particle pairs – and it is the pairs being considered here, not the separate particles. To be sure, in 1000 tests there will be 500+ and 500- at both the left and right detectors, but how they align with each other is the question. We see above that the alignment depends on the settings of the detectors. If the particle on the left is +, the particle on the right seems to “know” that if the settings are the same, then it’s a -, if 180 degrees offset, then the same, and at 90 degrees, randomly one or the other.

As it happens, the results of experiments accord with the sin^2 of one-half the angle between the detectors.

If the angle between the detectors is zero degrees, then the probability of ++ or a – match between the detectors is equal to sin^2 0/2 degrees = 0, and that is what happens. At zero degrees it’s always +- or -+. If the angle is 180 degrees, then the sin^2 180/2 degrees = 1, and the probability of a match is 1, that is, either ++ or --. At 90 degrees, then sin^2 of 90/2 = .5 and it will match half the time and be different half the time.

Here is a listing of sin^2 at various angles between zero and 90 degrees.

Sin^2 (rounded):

0 = 0

7.5 = .017

15 = .067

22.5 = .1465

30 = .25

37.5 = .37

45 = .5

52.5 =.63

60 = .75

67.5 = .8535

75 = .933

82.5 = .983

90 = 1

We can read this as saying that the probability of a match is sin^2 of the detector setting difference divided by two. Or the same thing, the number of matches in 1000 tests. At 37.5, 45, and 52.5 degrees we can expect 370, 500, and 630 matches respectively, and each of these is less than the sum of the other two. And that works above 45 degrees, but it doesn’t work below 45 degrees! At 7.5, 22.5, and 30 we get 17, 146, and 250 matches. And 250 is greater than 17 + 146. The series can be inspected for a whole range of violations of Bell’s inequality! QED!

The assumptions behind Bell’s inequality, according to one discussion, are simple reality, locality, and logic. Reality meaning that the particle and its spin exist, and persists in its existence; that communication speed is bounded by the speed of light; and the logic in which and by which these matters are expressed is reliable; I.e., 2+2=4 all seven days of the week. The speed of light as speed limit is what is sacrificed, but with an interesting qualification: that the particles “communicate” instantaneously, but that no message can be sent using entanglement.
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Hey Tim. It's good to hear from you. I've tried to figure out Bell's Theorem before with little success. I read your post and was still lost. I downloaded the Scientific American article to read.

The one thing that is really shocking is remembering that SA used to be a serious science magazine before it tried to make itself into another Discover or Popular Science. Not that that there's anything wrong with them, but SA used to be hard to read.
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I think this is well-articulated even though I'm still not sure that I understand Bell's Inequality. So the sin^2 rule does not adhere under 45 degrees. Why is this a problem?
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It's a plod, but like a lot of things, the more you get (at) it the simpler it is. And I am sure you have had the same experience I've had, that sometimes - often - the popular explanations of things just seem always to leave out some critical step or detail. Among my problems in understanding is getting the right perspective and understanding just what the important points are. With Bell's theorem I was blocked because I kept looking for the why and how, and there ain't none. So it reduces to a limit on what the outcomes of the experiments can be, comparing that with observed experimental outcomes, and noticing that a range of observed outcomes violates the limit. Not how Bell did it, of course. And so far (afaik) the accepted explanation is that "spooky action at distance" is how the universe works, but that you and I cannot send messages that way. I reckon you're long since engineer enough to make sense of the sin^2, the sin^2 plus the cos^2 as representing the chances of the possibilities summing to one.

So you have a mathematical expression of a limit, and a mathematical description that accurately predicts the actual outcomes, and they're inconsistent with each other. And alas, there's no more than that to it.
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(Ty!) Not so much a problem as a fact. In QM terms, it seems, 2+2 sometimes equals 5. The problem, such as it is, is accounting for the fact, and so far spooky action at distance seems to get the vote. Understanding the inequality itself is just a matter of plodding through it, a somewhat tedious exercise, but simple once grasped.
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and that the particle-pair comes from an original single particle with spin zero
This part is incorrect. The original particle does not have a known spin, zero or otherwise. It is simply a thing not measured.
The sum of the angular momentum of the two must then always be zero.
The particle does not have angular momentum. Spin in quantum theory is not a measurement of its rotation, a classical concept meaningful only to something with extension. It just means that they send the particle through a pair of charged plates and it is deflected one way or the other, never not at all, and always the same magnitude of deflection. This has been dubbed 'spin', but the word has nothing to do with the classical meaning of the word.

It is a simple step to assume that before the measurement, the particle really has a determinate spin value that the detector measures.
That assumption should not be made. I'm pretty sure it can be falsified. It's a counterfactual assumption, and I'm not sure how counterfactual interpretations describe the state before measurement.

The rest of the post seems to run with this assumption, and thus diverges from what Bell shows. I'm no huge expert, and could not exactly explain what Bell shows other than the fact that it cannot be explained with any classic model. I mean, otherwise you can treat entangled pairs as a pair of coins facing in unknown but exactly opposite directions, and the 'spin measure' is just a camera oriented a certain direction relative to the coin which must, if the cameras are aligned the same way, read heads on one and tails on the other (and nothing else, not 'edge', not 'barely heads, damn it's almost edge and hard to read'). But that model fails with entangled particle behavior.
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Breathe, noAxioms, breathe. We read, have read, different things. On spin, here:
https://www.scientificamerican.com/article/what-exactly-is-the-spin/#:~:text=%22Spin%20is%20the%20total%20angular,of%20all%20its%20elementary%20particles.

And certainly not like the spin of a billiard ball or a basketball. My own opinion is that both spin and entanglement are defined as a kind of behavior of particles. I.e., if they behave that way, then they have spin and are entangled, and if they have spin and are entangled then they behave that way. I am unaware of anything more substantive than that, though I'm sure more is said.

As to assumptions that should or should not be made, this from the Sci. Am. article referenced, a part of a longer section - I refer you to it to read it.
"Considering a fresh batch of proton pairs in the singlet state on which no spin measurement has yet been made (and perhaps on which no such measurement will ever be made), he can infer that in every pair one proton has the property A + and the other has the property A -. Similarly, he can conclude that in every pair one proton has the property B+ and one B- and one has the property C+ and one C-."

But I am not looking to argue details. I have come to think that all there is to Bell's theorem is the establishment of his inequality, based on so-called classical grounds, and it's inconsistency with observed facts, which Bell must have deduced from the math, because when he wrote there were no results which he could have observed, those coming years after he published. The gee-whiz factor comes from seeing that the violation of the inequality, in terms of how it is arrived at, is kind of a big deal.
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Hi Tim - here's a rather good video presentation on the topic by Jim Baggott, whom I think is a respectable physics author and commentator. This was the presentation he gave at the launch of his latest book, and has a graphic overview of the inequality experiments. (I've attempted to queue the video to the start of the preceeding section which explains the context).

Helped me understand it!
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Better than most of such things - thank you for it! And it's interesting to reflect on both what he says and does not say. The treasure, such as it may be, isn't found until and unless a person has some sense at least of what the treasure is. In this, it's the unresolved tension the violation causes, call it realist or non-realist. And likely for the best he doesn't wade too deep into just what the real is, and isn't - that for the experts at TPF!

The inequality itself, once how it's made is understood, can be successively reduced to x ≤ (y+z) and finally to x≤y for appropriate substitutions for x and y. Graphically this is just a 45 degree line from SW to NE starting at (0,0), x being the line (equality) and everything below the line, and y everything above. But this is a straight line, and the sin*2 is not a straight line but instead a curve that crosses the straight line back and forth, thus graphically representing where the violations occur. Which I find interesting, and being able to reproduce it persuades me I got it. The important lesson of the video being that at least for now, that's all there is to get. (Btw, setting Youtube videos to run fast sometimes makes them easier to listen to, certainly faster.)

And his presentation of the non-realist, realist debate seems too shallow. Something happens over there followed by something happening over here, with apparently something happening in-between. That in-between something must be a something, whether or not the best we can do is merely describe it. But this another topic.
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If you really want to understand Bell's theorem, you should visit a science forum Tim Wood. The terminology like "spin" is often misconstrued as an English equivalent. Often times words that sound like English are used as placeholders for deep mathematical and scientific concepts. At this level, everything is math with an often poor attempt to convert it into language. Only someone with a very clear scientific background would be qualified to speak with on this. Layman's understanding of quantum theories are often woefully inadequate and misunderstood.
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with an often poor attempt to convert it into language.
Indeed! But I will quibble with you. In what sense do you suppose I do not understand the theorem, against what I do claim to understand about it? I recognize spin and entanglement in this context as terms of art and do not pretend to understand them - nor do I think anyone does understand them. And Bell was able to express and make clear just how mysterious some of the results of experiments are by showing that two mathematical descriptions, one seeming incontrovertible and the other making accurate predictions, were inconsistent. I get it, the referral to a specialist forum, but too often the content, as with a forum we're both familiar with, is not worth the candle. But if you can enlighten my darkness here, please go ahead!
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Indeed! But I will quibble with you. In what sense do you suppose I do not understand the theorem, against what I do claim to understand about it?

Oh, my point was not that you do or do not understand the theory. You may very well have full mastery of it. I don't pretend to. I'm just noting that if you want to be assured of such I'm sure a scientist is going to be able to give you affirmation and/or enhance your understanding more than us philosophers. :)
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So you have a mathematical expression of a limit, and a mathematical description that accurately predicts the actual outcomes, and they're inconsistent with each other. And alas, there's no more than that to it.

Sorry it took me so long to get back to you. I read the SA article and a book called "What is Real" by Adam Becker recommended to me by @Count Timothy von Icarus. I think you've laid it out correctly in your OP. After struggling with reading the argument, one section of text allowed me to simplify things without necessarily understanding the details:

The Bell inequality constitutes an explicit prediction of the outcome of an experiment. The rules of quantum mechanics can be employed to predict the results of the same experiment. I shall not give the details of how the prediction is derived from the mathematical formalism of the quantum theory; it can be stated, however, that the procedure is completely explicit and is objective in the sense that anyone applying the rules correctly will get the same result. Surprisingly, the predictions of quantum mechanics differ from those of the local realistic theories. In particular, quantum mechanics predicts that for some choices of the axes A, B and C the Bell inequality is violated, so that there are more A+ B+ pairs of protons than there are A+C+ and B+ C+ pairs combined. Thus local realistic theories and quantum mechanics are in direct conflict.

Here's my simplified understanding:
• The Bell inequalities are calculated based on standard classical probability theory
• Their applicability is based on three assumptions - 1) the phenomena in question actually exist 2) induction works and 3) locality - i.e. things can only effect other things at the speed of light.
• You can use quantum mechanics to calculate the probabilities and you get different answers than classical probability theory.
• Experiments show that the quantum probabilities are correct.
• Therefore, looks like locality loses.

And certainly not like the spin of a billiard ball or a basketball. My own opinion is that both spin and entanglement are defined as a kind of behavior of particles. I.e., if they behave that way, then they have spin and are entangled, and if they have spin and are entangled then they behave that way. I am unaware of anything more substantive than that, though I'm sure more is said.

I think there's more to it than that. In my, limited, understanding, when they're figuring out the total angular momentum of a hydrogen atom, they add the spin angular momentum of the electron with it's orbital angular momentum. So saying that spin is "not really" angular momentum misses something.

the popular explanations of things just seem always to leave out some critical step or detail.

Yes, popular explanations seem to get lost in the ooh, ahh of the phenomena. I have often found that going back to original sources can give insights, even if you can't follow the whole argument. I'm going to take a look at Bell's original paper and see what I find. That may take a while.

The speed of light as speed limit is what is sacrificed, but with an interesting qualification: that the particles “communicate” instantaneously, but that no message can be sent using entanglement.

This confuses me. What does it mean that communication takes place instantaneously but no information can be transmitted? I would have thought that "communication" means the transfer of information. I have to do more reading.
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This confuses me. What does it mean that communication takes place instantaneously but no information can be transmitted? I would have thought that "communication" means the transfer of information. I have to do more reading

It's not you, it's a confusing solution that is invoked to save relativity's "speed limit." Non-locality suggests that causal influences can move faster than the speed of light (although there are other interpretations like retro-causality, superdeterminism, etc.). But relativity originally said that isn't possible. The theory is saved by a move whereby we say it is information that cannot move faster than light. Information of course has many definitions, but the one here is crafted with preserving the speed limit in mind.

Practically, you can't use this phenomenon to send messages faster than light.

But we already knew that relativity is not consistent with quantum mechanics, so this wasn't completely suprising. Einstein himself was deeply troubled by non-locality.

There are plenty of neat little experiments that punch tiny holes in "physical laws." You can perform a trick with cesium gas to get faster than light behavior. In some experiments conservation of mass/energy seems to be violated (open to interpretation) and in some phenomena we seem to have very short periods where conservation is out of wack (more accepted). Part of the hope for any sort of new big paradigm shift is that it will explain all the little oddities that pop up in a way that is more intuitive.

I think non-locality is just a case where it's more helpful to say "yes it's counter intuitive, cause seems to be instantaneous across distances" at least in terms of basic explanations.
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I'm going to take a look at Bell's original paper and see what I find. That may take a while.
At the moment, to borrow an inequality, I would say that my understanding is now less than or equal to yours. I looked at Bell's paper long ago, but the math was too much, and I too ignorant. He works it out in three dimensions as I recall. So, whatever comment you care to make and whenever you care to make it, I'll be more than glad to read it.

As to the "communication," I think it works like this: Alice is on earth and Bob on a spaceship near Arcturus about 37 light years' distant, monitoring his particle detector. Its bell rings and Bob sees that it registers "up." What information does that convey to him? Ans. none. The particle apparently "knows" something about its particle brother (recent tests of Bell's theorem appear to rule out the possibility that Bob's particle knew anything about Alice's; i.e., that somehow prior "knowledge" is ruled out), but that Bob himself learns nothing additional about it. To find out just what Alice's detector read, he will have to wait 37 years for a message. Or to use the jargon, the particles are entangled, but Bob and Alice are not.

Which I find interesting. Because (from reading) I think we all have a quantum character. But any incidence of quantum weirdness on the macro-scale of a person or the battleship New Jersey, while finite, is just really, really unlikely. And I don't have any idea what it would take to entangle Bob and Alice.
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I think it works like this: Alice is on earth and Bob on a spaceship near Arcturus about 37 light years' distant, monitoring his particle detector. Its bell rings and Bob sees that it registers "up." What information does that convey to him? Ans. none.

Let's take a classical situation. Alice takes a black and a white bead and puts each in a separate opaque box without looking at them. She sends one box in a rocket 37 light years away and keeps the other in a desk drawer. Bob gets the box 50 or so years later, opens it, sees a white bead, and knows that Alice has a black bead. How is that different from the situation you describe?
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Greetings! Different because the respective spins are not limited to opposites. Imagine yourself Bob a little more. You've got the beads covered. Now the detector says "Up." What now do you know about the other particle, and how?

That is, if you knew ahead of time Alice's setting, then depending on the setting you might immediately know the spin of her particle. But how would you know that? It might be by prearrangement, but then you have prior knowledge, as with beads. The particle situation, in terms of beads, would be not that they were either bw or wb, but instead any of bb ,bw wb ,ww. Thus whatever you find, you cannot tell what the other is. Yes? No?
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We have definitely gotten to the end of my competence and then gone on few extra lengths. I have some more reading and thinking to do. This was a useful conversation for me.
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Different because the respective spins are not limited to opposites.

"Spin" is a highly deficient concept. It is an attempt to represent non-dimensional, non-spatial activity which is understood to occur within the internal of a non-dimensional point (a somewhat incoherent idea), with a three-dimensional representation. So the property which is represented by "spin" is not adequately represented in this way, and restricting the possibilities to two opposites will ensure that the law of excluded middle is always violated.
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May I know what you were drinking before you wrote your post? I should like to try some for those occasions when I too would like to loosen my grip on reality. As to "spin," that seems to be a term of art. I find these on line:
"spin, in physics, the amount of angular momentum associated with a subatomic particle or nucleus and measured in multiples of a unit called the Dirac h, or h-bar (ℏ), equal to the Planck constant divided by 2π,"
and,
"When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets. In the classical world, a charged, spinning object has magnetic properties that are very much like those exhibited by these elementary particles. Physicists love analogies, so they described the elementary particles too in terms of their 'spin.'

"Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate' in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."

Alas, MU, they did not check with you before they adopted the term.
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I've found this article to be the most straight forwardly comprehensible explanation of bells theorem

https://www.lesswrong.com/posts/AnHJX42C6r6deohTG/bell-s-theorem-no-epr-reality#:~:text=%22If%2C%20without%20in%20any%20way,corresponding%20to%20this%20physical%20quantity.%22

It took me a few reads and quite a lot of solitary thought to fully grok what this explanation is saying, but I can say with relative confidence that I understand Bells Theorem to some reasonable degree. I understand both what it is saying and why it is saying it.

So you have a mathematical expression of a limit, and a mathematical description that accurately predicts the actual outcomes, and they're inconsistent with each other. And alas, there's no more than that to it.

I will say I think you've done bells theorem a little bit of a disservice here. The fundamental proof can maybe loosely be summed up like what you've said here, but exactly what it proves is far more interesting than this gives it credit, in my view. You've said the dry bit but left out why anybody cares - and the real reason is truly fascinating.
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if you've tried and struggled to understand it, I definitely recommend at least one go of the above article. It took some effort but it really clarified everything for me.
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if you've tried and struggled to understand it, I definitely recommend at least one go of the above article. It took some effort but it really clarified everything for me.

Thanks. I took a look.

I'm not really confused about the mechanics of tests of the Bell inequality. If you do this and this, then this happens. Relatively straightforward. The implications of those results are a bit harder to get a grip on - What do they say about realism and locality? Where this all started for me was with the question whether or not the results of Bell inequality experiments have any implications for determining which interpretation of quantum mechanics is the correct one. As far as I can see, the results have nothing definitive to say about QM interpretations.

That leaves me where I started - if the different interpretations give the same results, they are equivalent. Any differences between them are metaphysics, not science. That will remain the case until someone can figure out how to test for differences between the interpretations. I predict, on the basis of my limited understanding, that it will not be possible.
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The implications of those results are a bit harder to get a grip on - What do they say about realism and locality?

Sure, I thought the article maybe did a good job at explaining that but perhaps it's not as explicit as it could be. I'm only a layman, but I do have what I consider to be a relatively compelling analogy, if you're interested.
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Sure, I thought the article maybe did a good job at explaining that but perhaps it's not as explicit as it could be. I'm only a layman, but I do have what I consider to be a relatively compelling analogy, if you're interested.

The article was fine. It did explain the Bell inequalities well. I also am very much a layman. Very, very much. That's why I have been struggling with the implications of QM once you get beyond the basic questions. Different expert sources give very different answers to the questions I am looking for answers to. Locality matters. It doesn't. Realism matters. It doesn't. All interpretations of QM are equivalent. They're not. Just because locality is violated, that doesn't mean that QM can be used to send information faster than the speed of light. It does.
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well, if you're not interested in my long explanation of the implications of the results then, in short, what bells theorem proves is that we do in fact live in a quantum universe and not a classical one. Quantum measurements are indeterminate prior to measurement, genuinely and actually indeterminate rather than just a question that we don't yet have the answer to. Ontologically indeterminate, if you will. Bells theorem settles that question pretty cleanly, which is why it's so valuable in the history of quantum mechanics.

I can go into why at length but it doesn't look like you're asking for that.

Almost all experts are going to agree that you can't use qm to send information faster than light. Some people don't care about interpretations at all, they just care about qm as a tool to get predictions out of. Other people take the question of interpretations very seriously.
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Quantum measurements are indeterminate prior to measurement, genuinely and actually indeterminate rather than just a question that we don't yet have the answer to. Ontologically indeterminate, if you will. Bells theorem settles that question pretty cleanly, which is why it's so valuable in the history of quantum mechanics.

Except you'll find people who disagree with that. The whole many earth's interpretation was developed to address that issue. Reality is a metaphysical characteristic, not a scientific one.
• 8.5k
I've found this article to be the most straight forwardly comprehensible explanation of bells theorem.... I will say I think you've done bells theorem a little bit of a disservice here.
Hi and thank you! I've read it, without yet doing the hard work of it, and I don't yet understand the second part of it. I think I have a general understanding of Bell's attack, in that he worked out the math of the probabilities, which I could not follow, having to be satisfied with the dumbed down version, and the inequality itself. So think I pretty get both sides. What comes after that is interpretation/speculation, and these are beyond Bell's theorem.

Here is Bell's paper:
https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf
Not-so-easy for the rest of us.

And I agree with brother Clark, here:
...the results have nothing definitive to say about QM interpretations.... Except you'll find people who disagree with that. The whole many earth's interpretation was developed to address that issue. Reality is a metaphysical characteristic, not a scientific one.

As to our living in a quantum universe, I buy that. But I accept that most of the effects are too small or too unlikely to matter much. Not impossible, just unlikely.

If you care to lay out your own interpretation, "compelling analogy," I'm a reader!
• 11.7k
"When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets. In the classical world, a charged, spinning object has magnetic properties that are very much like those exhibited by these elementary particles. Physicists love analogies, so they described the elementary particles too in terms of their 'spin.'

"Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid 'objects' that can 'rotate' in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term 'spin,' however, still remains."

Just as I said, the so-called "spin" is not a property of a particle at all. The 3-d geometrical representation which is called "spin" cannot be the property of a non-dimensional point.

May I know what you were drinking before you wrote your post? I should like to try some for those occasions when I too would like to loosen my grip on reality.

As you've already indicated, we ought not focus on realism, so reality might be completely irrelevant to this subject. I believe that now might be the optimum time for you to go a ahead and loosen that grip on your assumed "reality". So, if you're interested in purchasing some of my special intelligence boosting juice, you'll need to send the money first, then I'll decide whether you're likely to benefit from it.
• 8.5k
Just as I said, the so-called "spin" is not a property of a particle at all. The 3-d geometrical representation which is called "spin" cannot be the property of a non-dimensional point.

Maybe I'm misreading you, MU. It seems to me you're objecting to the use of the English word "spin" to refer to something meaningful to a technical user as a term of art. If that's the case, why?
• 328
Do you mean many worlds? Many worlds doesn't disagree with it at all. Many worlds actually very naturally fits in with my description (I should also clarify that a world, in Many Worlds, doesn't mean a planet like earth. )
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