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.

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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and that the particle-pair comes from an original single particle with spin zero — tim wood

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. — tim wood

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. — tim wood

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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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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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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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? — tim wood

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. :)

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. — tim wood

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. — Scientific American

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. — tim wood

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. — tim wood

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. — tim wood

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.

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 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. — tim wood

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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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.

Different because the respective spins are not limited to opposites. — tim wood

"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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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. — tim wood

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.

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.

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. — flannel jesus

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.

The implications of those results are a bit harder to get a grip on - What do they say about realism and locality? — T Clark

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.

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. — flannel jesus

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.

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.

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. — flannel jesus

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.

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"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." — tim wood

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. — tim wood

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.

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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. )