sure, despite the misunderstanding I appreciate your participation and hope I run into you again in the future. Wish I could have expressed myself more clearly. Have a good one

quantum mechanics certainly RESULTS in human decisions, I'm not disputing that. I'm saying it isn't ABOUT human decisions. Quantum mechanics is mathematical equations, and there's no operator in those equations for a "human decision".

So human decisions result from quantum events, yes, but quantum events aren't generally about human decisions. Some quantum events, according to MWI, CAN occasional spawn branches of the universal wave function where one human decision happened in this branch and another human decision happened in that branch - that can happen, but it is not required to happen for every imaginable decision you think you might be able to take, in my opinion.

I don't speak for everyone who prefers MWI, though.

There's interpretations within interpretations. Agggh

my previous reply was possibly too short. I meant it as a serious reply but I'm concerned the brevity of it might come across as snark rather than serious, so let me go into detail.

Many scientific papers are published for purposes. I believe this particular paper (on the EPR paradox by John bell) was, like many, published in order to persuade people about an idea that author had. That's certainly the effect it had - it has persuaded many people of an idea.

Do you think it was published to persuade? If so, what do you think it was trying to persuade people of?

you're still talking about "decisions", which sounds to me like human decisions. I've indicated that in my view, quantum mechanics is not about human decisions. I don't believe that every imaginable human decision is realized in some world.

you're of course free to think many worlds is wrong headed, I'm not here to defend many worlds, I'm not qualified to defend many worlds. I was just trying to answer your questions in good faith, to humour your curiosity. Reject it as you like.

Scientific papers are absolutely published for purposes.

and why did he ask for the specific number of votes he'd need to win Georgia?

Well, I applaud your consistency.

That’s the biggest farce because in a republic one is allowed to believe an election was stolen and take steps to challenge it, — NOS4A2

Are you allowed to call governors and ask them to find you some votes? Would you defend Bidens right to do that?

It seems to on any macro-scale. — tim wood

Yes, and the standard idea there is that macro level classical behaviours are emergent from micro level quantum behaviours

I would appreciate an excellent sentence or two on just what many-worlds is and entails. I understand it as a theory that says when you have to decide between apple and blueberry pie, the universe instantly divides into four separate and distinct universes where in each respectively you have either one or the other or both or neither. And this bifurcation occurring for every thing at every moment. But this is nonsense. How does it really work? — tim wood

First of all let me say that I don't want to derail this thread about Bells Theorem to be about many worlds. I'll try to briefly answer your questions, but it's not my intention to convince you of many worlds or defend it in any way. That being said...

At the center of many worlds is not humans, so centering the discussion on human decisions is not really advisable. Imo the idea that many worlds means anything you can imagine doing, there's some world where you do it is a misunderstanding. There may be some actual proponents of many worlds who agree, but I do not.

Many worlds is about the behaviour of fundamental particles. The wave functions in QM give a probability distribution of what properties those particles have and where they might be. The "world splitting" happens in the context of that probability distribution. If a particle has 50% of being here and 50% of being there, well there are worlds where it's here and worlds where it's there.

If you imagine some scenario about pie, there's not necessarily any sequence of quantum probabilities where you choose pumpkin pie, regardless of your ability to imagine yourself doing that.

If you ask other people who prefer many worlds, they may disagree with me on that point. I'm just speaking for myself here.

May we also agree that the reason is in some sense real? Not the description of it, although that real in an irrelevant sense. Perhaps usually the reason is some force? But whatever, real? My point here, that you may have already adverted to, being that everything that is, is real and distinct at some level in some way. (And thus that a god might know it if s/he cared to look, a perfect God always already knowing it.) — tim wood

The wording here is too vague for my liking. God might know what if God cared to look?

The wave functions themselves a function of inadequate knowledge — tim wood

Not in my opinion, no. Happy to explain why if you care.

What leads me to this is the notion of the electron as a cloud. I buy that as a description, but if it really is a cloud, then, to my knowledge, no one has yet given an account for how the cloud works. — tim wood

People have given an account of that. It's called the Schrödinger equation and it's a fundamentally important equation to quantum physics. It governs how that cloud evolves over time.

Interestingly, even though the common interpretation of quantum mechanics (not many worlds) is indeterministic, this particular equation is itself deterministic. Which means that, in the common understanding, you have a deterministic function determining the probabilities, which are then selected from indeterministically.

so every universe that isn't deterministic is a universe of free will? It doesn't even need life or consciousness in it? It's free will even if there's no beings in the universe who have a will?

I'm gonna go out on a limb here and say that I don't actually care about the "rape" angle at all. I would prefer people to not rape, and I would prefer rapists to not be successful politicians, but it's not even really on my radar as one of the top reasons to not want trump as president.

Top reason is, I'm not ready for Americas first dictator, and him trying to wrest the election out of the hands of the voters clearly indicates that that's exactly what he wants to be. He's an existential threat to American democracy. I don't think about his rape allegations at all, it doesn't even register to me as something to consider when much more important things are on the line.

(I also don't trust him to do what's right for Ukraine. He's a lackey for Putin, it seems.)

Many philosophers agree with you. Some say a statement like that isn't actually meaningful, it doesn't have any meaningful content, it doesn't refer to anything.

It's certainly a valid take on the subject, don't consider your intuition here naive. You're very possibly right to find it incomprehensible.

I'm going to take a minute to just ramble and muse, if that's okay. I've given an explanation of what I think Bells Theorem is about, and in a nutshell it's simply that the universe doesn't work on classical causality.

I want to clarify something - that doesn't mean it doesn't operate on causality. I believe the universe DOES in fact operate on causality, just not classical causality.

I believe that bells theorem proves that you can't say "the particle was at this specific location at time t=50", and other such classical statements about the particle at moments when it's not being measured, BUT that doesn't mean I don't think you can say anything about the particle at t=50. I think you CAN say things, objectively true things, about the particle at t=50, just not most classical things.

I said above in my response to t.clark that my wording of the implication of bells theorem is actually less extreme than bells, because bell says QM is incompatible with local casualty - I'm only saying it's incompatible with Classical local causality.

None of what I'm saying should be taken to mean things cannot be casual, or things happen for no reason. They simply mean things aren't Classically casual, and they don't happen for Classical reasons.

I have been steering clear of a specific QM interpretation, because I didn't think it would help clarify anything, but I'm starting to think that both you and t.clark might benefit from me telling you unambiguously what I think in that regard, so here it is:

I believe Many Worlds is in fact the most likely reality. Many worlds is casual (locally, I think, though some people argue it's not local) - but it is not CLASSICALLY casual. In many worlds, things happen for "reasons", deterministically, just not CLASSICAL reasons. In many worlds, you can say things about a particle at t=50, you just can't say CLASSICAL things about that particle.

The sorts of things you can say about a particle at t=50 aren't "it was at this specific location going at this velocity", instead you can say things somewhat like "the wave function of the particles position at t=50 looks a bit like this, a cloud with dense regions here and here and less dense regions here, here, here and here." These are the sorts of objective statements you can make in a quantum world about unmeasured objects. This is what I meant when I said you have to bend your mind to accept different answers to the ones you're used to expecting. Most people expect the particle to have a specific location, and not to have an amplitude distribution.

I think many worlds is the most likely reality, but I'm not super confident of it. If it's not many worlds, the most likely alternative I think is that qm operates on some level of genuine randomness with non local causality, but I think that's pretty unlikely.

I hope that sheds some light on what you're trying to touch on with your "no reason" questions, Tim - I don't believe quantum things happen for "no reason", and I don't believe the things I've said necessarily imply that.

But at the end of the day, my goal here was not to talk much about what I believe about qm, but just about what Bells Theorem is fundamentally about. I think it's just about proving that QMs predictions are incompatible with classical physics. I believe the experiments that won the Nobel prize in 2022 demonstrate sufficiently that the physics of our universe at the scale of protons and photons etc are not classical.

I actually have the words from Bell himself, this is the opening paragraph of his very own paper on his very own theorem (I'm having trouble getting a link on mobile, but it's easy enough to Google, just search BELLS THEOREM PAPER)

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics
could not be a complete theory but should be supplemented by additional variables. These additional vari-
ables were to restore to the theory causality and locality [2]. In this note that idea will be formulated
mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. It is
the requirement of locality, or more precisely that the result of a measurement on one system be unaffected
by operations on a distant system with which it has interacted in the past, that creates the essential dif-
ficulty .

I believe the picture painted here by Bell himself is remarkably similar to the picture I painted of bells theorem. I painted a picture of bells theorem being about settling the difference between QM and the EPR paper, and that first statement by Bell is that this paper is going to be about that disagreement. I keep saying that it's about certain predictions of QM being incompatible with classical mechanics, and though he doesn't use the word "classical mechanics" here, he uses instead the phrase "causality and locality" - and I think it ought to be clear the relationship between that phrase and "classical mechanics" - and then says in the next sentence that that's incompatible with the predictions of quantum mechanics.

I do think that my interpretation of bells theorem is very much something Bell himself would agree with. I think I'm only barely using slightly different wording. I think I've pretty much got it. (In fact, I would argue my wording is less extreme than Bells)

The scientific side of all the Bell stuff comes in 2 parts. Part 1 is bells paper, where he argues that QM and "locality and causality" (which I'm calling classical mechanics) give irreconcilably different predictions, and then part 2 is the actual physical experiments done to confirm which of the two predictions bears out in reality, for which the nobel prize in physics in 2022 was awarded, which confirmed that we see the predictions of QM bear out.

I started my participation in this thread because I thought I could shed some light on a topic you said you didn't understand but wanted to. If you still want to, I think I've got plenty of good evidence that the understanding I have on offer is at least in the right direction. I won't quote you again though if you're done now, I just felt the need to defend my understanding given what you said about it.

After I gave my understanding of bells theorem, your initial response was this:

In my understanding, this is not true. It is your interpretation, not mine and probably not Bell's. The inequalities are not "there to help us," they describe phenomena at very small scales.

And ever since that post, it's been me trying to defend what I've said about bells theorem. If that response you gave isn't you saying I've misinterpreted bells theorem, what is it? What else could it possibly be?

It's okay for you to think I've misinterpreted it. I'm here to talk about ideas, I'm not afraid of disagreement. I'm clearly willing to put in some energy and work to try to understand things properly, and defend my understanding when I think I've got it right.

I really just don't understand why your interactions with me are going in this direction. You said early in the thread that you've tried to understand what bells theorem is about. I made a post explaining what bells theorem is about. Then, somehow you went from not knowing what bells theorem is about to being incredibly confident that it's not about what I said, and you're confident bell himself would probably disagree.

But that's okay, you can disagree with me, I'm not throwing a temper tantrum about it, I'm communicating why I think what I think and defending my understanding. I'm not being aggressive towards you. I'm just trying to talk. If you don't want to talk about it you don't have to, but your role in this conversation has been quite strange and confusing from my perspective. I can't get a read on you at all. There's an air of hostility and I have no idea where it came from. And I can't understand why you're now saying you never said I misunderstood bells theorem. I'm so confused

I'm just trying to chat about this topic that I've spent a lot of energy over the past years understanding, because you said you didn't understand.

It was never my intention to deliberately misunderstand anything you wrote. The only misunderstanding you've explicitly pointed out so far is that bit about Many Worlds. If you don't want to explicitly lay out the things you think I'm misunderstanding, then of course I cannot correct my misunderstanding.

I don't even know what you mean about how what you're saying doesn't contradict bells theorem. As far as I can tell, this whole conversation lately has just been you telling me I'm misinterpreting bells theorem. I've never said your ideas contradict bells theorem, because I don't even know what your ideas are.

But if you're done, then see ya I guess.

What's the big deal? Well, some dudes won the Nobel prize in 2022 in large part because of their experiments confirming violation of bells inequality, so the scientific establishment at large seems to understand that it's a big deal. I think it's pretty clear that the big deal is, violations of bells inequalities are unreproducible using classical means, and I believe that's what the Stanford quote is saying. I think it's a pretty big deal. You are of course under no obligation to think it's a big deal. You're under no obligation to be interested in QM at all. I, personally, think it's fascinating, mind blowing even.

Here's some other people across the internet who are apparently understanding it in similar ways to me:

https://physics.stackexchange.com/questions/732672/any-bell-experiments-showing-inequality-violations-in-purely-classical-systems-a

https://www.quora.com/In-simple-layman-s-terms-what-does-it-mean-to-violate-Bells-inequality-In-experiments-that-are-actually-done-how-is-the-violation-detected#:~:text=Short%20answer%3A,repetitions%20of%20a%20simple%20experiment.

(On the above link, see the second answer by amit)

https://physics.stackexchange.com/questions/370386/is-bells-inequality-always-violated

https://physics.stackexchange.com/questions/139880/can-bells-inequality-violation-be-explained-by-the-will-of-the-scientist-someho

https://physics.stackexchange.com/questions/675344/what-is-it-about-quantum-entanglement-that-cannot-be-explained-classically?noredirect=1&lq=1

Of course, all of these links do not prove I am correct. I'm not trying to prove I'm correct. I am trying to give you some signals that this isn't just some silly misunderstanding of bells theorem that I've invented. You may disagree that it is the correct way to understand bells Theorem, but I'm not pulling this understanding out of no where. I'm not just some silly goober inventing new nonsensical ways of understanding experiments. I believe my understanding is in fact the intended understanding.

I don't see how the two phrases are interchangeable at all. — T Clark

Does the second quote from stanford lend any clarity in that direction for you at all?

Bell’s theorem reveals that the entanglement-based correlations predicted by quantum mechanics are strikingly different from the sort of locally explicable correlations familiar in a classical context.

Sorry to bombard, but here's another quote from the same Stanford article:

7. Significance for Quantum Information Theory
The set-up envisaged in the proof of Bell’s theorem highlights a striking prediction of quantum theory, namely, long-distance entanglement, and experimental tests of the Bell inequalities provide convincing evidence that it is a feature of reality. Moreover, Bell’s theorem reveals that the entanglement-based correlations predicted by quantum mechanics are strikingly different from the sort of locally explicable correlations familiar in a classical context.

"Bell’s theorem reveals that the entanglement-based correlations predicted by quantum mechanics are strikingly different from the sort of locally explicable correlations familiar in a classical context." This sounds a lot like what I've been saying.

in addition to the above quote from Wikipedia, please see this quote from the Stanford article on bells theorem

https://plato.stanford.edu/entries/bell-theorem/

Finally, in 2015, experiments were performed that demonstrated violation of Bell inequalities with these loopholes blocked. This has consequences for our physical worldview; the conditions that entail Bell inequalities are, arguably, an integral part of the physical worldview that was accepted prior to the advent of quantum mechanics. If one accepts the lessons of the experimental results, then some one or other of these conditions must be rejected.

If one accepts the experimental results, then some of the conditions that were integral to the physical world view accepted prior to quantum mechanics must be rejected. The physical world view prior to quantum mechanics was what I've been referring to as "classical". I do believe Stanford is saying, in different wording, the same thing I'm saying : the experimental results we get from the tests of bells theorem tell us that we, in fact, do not live in a classical world.

I'm not pulling this interpretation of bells theorem out of my ass. It is possible, however, that I'm terrible at explaining myself or defending myself

The inequalities in Bells Theorem are there to help us test if our universe is one where it's in fact true that we might live in a classical universe where those questions have singular, definite answers.
— flannel jesus

In my understanding, this is not true. It is your interpretation, not mine and probably not Bell's. The inequalities are not "there to help us," they describe phenomena at very small scales. — T Clark

The Wikipedia page on bells theorem states explicitly - Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories. The quote of mine is just rewording that, where I replace "local hidden variable theories" with the phrase "classical universe where those questions have singular, definite answers." Those phrases may not be perfectly interchangeable, but they are close to interchangeable. Despite your misgivings, I have read enough about bells theorem to be relatively confident that what I said is at least loosely close to the way it was intended by bell and understood by modern physicists.

my mistake. Your post said some disagree, and then you brought up many worlds in a way that sounded like you think many worlds is an example of disagreement.

no, not about you, I was referring to something that happened on another forum possibly around a year ago.

I don't know why you keep saying this "no reason" stuff. I've never indicated that things happen for no reason

No, this whole line of questioning doesn't even make sense to me. I don't understand why you're even asking it. Quantum indeterminacy doesn't mean everything happens for no reason, and I've never claimed it does. Your questions along this line seem nonsensical to me.

I'm also still concerned that you're treating the words indeterminate and indeterministic as interchangable.

QM will always be indeterminate in the sense I've said above - that even God himself doesn't have a singular answer to a question like "where was this particle at t=50" - that's the nature of qm. That doesn't mean there aren't objectively true facts, however, even at t=50. It just means those objectively true facts aren't the type of facts we're used to asking about, they aren't the type of answers we're used to receiving. You have to bend your mind to accept different kinds of answers than that.

by determinate do you mean deterministic? Or do you mean something else, like "what's actually happening under the hood still involves objective facts"?

Are those the two options? Well they clearly fail for a reason, I think. And the reason is, the world is not classical. That's why our experimental results show correlations that are predicted by qm, and not explainable by classical means

Are you asking me why they're not explainable by classical means?

I really don't know why you're talking about nothing happening Vs something happening. There's nothing in my understanding of any of this that leads me to think that's a debate physicists are now or have ever had.

That is, measurements on single particles allow for a classical interpretation, and on entangled particles, not. — tim wood

Sorry for multiple responses, maybe I should post these together. In any case, this bit is probably not generally agreeable either. There are other single-particle experiments which are hard to explain with classical mechanics and start making more sense when modelled with quantum mechanics. The double slit experiment is one. The Mach zender interferometer experiment is another.

So I conclude that QM, in sum, is a model that highlights deficiencies in classical physics but that does not replace classical physics, or, rather instead, becomes it. That is, that QM perfected will be seen to be a classical theory that is an advance on and refinement of current classical theory, in a way as relativity refines and advances on Newtonian physics. — tim wood

I suppose you're free to conclude that but that's certainly not my understanding, or I dare say the understanding of physicists who study qm. My entire post was getting at the point that QM is entirely at odds with some classical assumptions, and bells theorem and the experiments that test it go on to show that the classical assumptions cannot hold, they don't match experimental results.

Many Worlds takes the idea of superposition super-literally, and in many worlds any answer to a quantum question prior to measurement doesn't have a singular definite answer, it has MANY answers.
— flannel jesus
Which is not the claim that answers impossible in one world are possible in others, or is it? In some worlds do I murder my own parents before I am born? My understanding of many-worlds is that whole entire complete universes flash into and out of existence at every juncture of every instant of the existence of every thing, and that seems unlikely. — tim wood

The many worlds thing was an aside, and not at all necessary or required to understand everything I'm saying about bells theorem. The stuff I'm saying about bells theorem is entirely agnostic about which interpretation of quantum mechanics is correct.

This is the second time I've ever tried to describe at length what's so important and fascinating about Bell's Theorem, but my first time was a semi-failure (partly because I was trying to explain it to someone who rejected QM out of the gate, and didn't want to understand the maths and probabilities involved - which makes this scenario fundamentally different out of the gate, you guys seem to like QM and have some understanding of the probabilities involved), so this time I'm going to start again without using any of the material I wrote the first time. I'm going to probably be writing some shit you already know, but please bear with me. Also, sorry if this is a lot to read.

I think the best way to contextualize Bell's Theorem is to go back to the beginning, back to when QM was first being introduced to the physics community. I'm going to spin a little narrative that's perhaps not entirely true, but hopefully true enough, to set the stage for why Bell's Theorem was even thought up to begin with.

Before QM, all physical theories were what we now call "classical", including Relativity. I think of "classical" as almost being comparable to basic object-permanence. We all learn at some age that, if we put a book in our backpack and then close our backpack, we can (usually) expect to find it in our backpack later on. When we open up our backpack an hour later, we generally don't assume that the book just appeared there - we have a persistent conception of the world where, even when we weren't looking at the book, it was still in the backpack all the same. Classical Theories are object-permanence at the universal scale - every particle that exists always exists in a specific place at every moment in time, even when we're not looking at it. Our ignorance of where a particle is or how fast it's moving is just a fact about us, not a fact about the particle itself. The particle itself is always existing somewhere, and moving at some specific velocity, at every moment in time, regardless of our ignorance about it.

Then, Bohr, Planck, Heisenberg, Schrodinger and friends introduced QM to the world. They said that there are some properties of particles that, prior to measurement, we can't actually tell a Classical story about. If we shoot a particle at t=0, through a double slit for example, and measure where that particle landed at t=100, we might be tempted to ask the question "ok, so where was that particle at t=50?" If the world worked classically, then there would be an objectively true answer to that question - even if we as human beings couldn't find an answer. If we can't find an answer, that's just our own ignorance, but there still *is* an answer. QM said, actually, there *is not* an answer. Or at least, not a *singular, definite answer* -- that's the phrasing I like to use. Prior to measurement, some of these properties of things like Photons and Electrons do not in fact have singular definite answers - not even to God. If God himself were to peer into the universe and look at that particle at t=50, he wouldn't have a singular definite answer to the question "where was that particle?" (Please note that I'm using God as a narrative tool, I'm not a theist. "God" is just a stand in for the idea of some external entity who could, in principle, know the world as it really is - could answer any question about any system without disturbing that system).

Shortly after, Einstein and friends produced the EPR paper. In short, they fundamentally disagreed that the QM vision of the world was true. They said, no, if we don't know where a particle is, or its velocity, or any other measurable property of that particle, that's just a matter of personal ignorance. Quantum indeterminacy is not a real feature of reality, it's just a measure of the things we don't know. And they came up with a theoretical class of experiment to demonstrate why. They said (again, I'm using some artistic license here, this isn't exactly how it happened) -- imagine we have a pair of particles that we've arranged to have a correlated state in some measurable property. Now, we have one particle flying east and one flying west, we haven't measured this property yet so according to QM this property doesn't have a singular definite answer yet. After, say, a second we measure the particle flying west -- if their properties are correlated, as by the experimental design, then that means at the moment we measure the West particle, the East particle must also suddenly and immediately have an answer as to what it will be measured as as well, despite being 2 light-seconds away. This thought experiment, as far as I know, is the first time the idea of "entanglement", as we now call it, was discussed at length. Einstein referred to the idea that measuring one particle could affect its entangled paired particle immediately as "spooky action at a distance". The idea of instantaneous causality across space went against every intuition about physics Einstein had - it went directly against intuitive notions of Causality and his own Relativity. After all, if cause-and-effect can happen immediately across distances, that creates a real problem for the idea of Relativity of Simultaneity (please ask if you want more detail on this and why it was such a problem).

So, what we have here is 2 competing ideas: 1. the classical take of Einstein via the EPR paper, that us not knowing what a property would be measured as is just a statement about our own ignorance, not a statement about reality, and 2. the QM take, that these properties are not just something WE are ignorant about - God himself wouldn't have an answer. There objectively is not an answer to these quantum questions prior to measurement. And the tricky part here is, how could you possibly tell? How could we tell what type of universe we live in? A classical one or a QM one? What experiment could tell us the difference between "I don't know this property of this particle" and "this property of this particle genuinely does not have a singular definite value"? On the surface, those two ideas - personal ignorance vs ontoloical lack of an answer in reality - seem experimentally indistinguishable.

THIS is where Bell's Theorem steps in. Bell ingeniously figured out a way to definitely tell us if we live in a world where a lack of an answer to quantum questions was because of personal ignorance, or if in fact QM was right and ontologically the answer to this quantum questions *cannot* in fact have a singular definite answer prior to measurement. This, to me, is why Bell's Theorem is so wonderfully beautiful, and so centrally important - it took us 40-odd years to finally find a way to settle the disagreement betweein Einstein and QM. Thank you, John Bell.

When the EPR paper came out, I'm not quite sure personally how they imagined setting up an entangled pair of particles, but by the time John Bell was approaching the question, I believe physicists had a good idea about this concept of "spin" - that you could create a pair of entangled particles where, due to the perservation of the quantum equivalent of "angular momentum", you could guarantee that one particle had the opposite spin of the other particle. I actually don't believe they had experimentally confirmed this could be done at this point, I think it was still theory when Bell came up with the idea, but nonetheless this is where we can start untangling the disagreement between Einstein and QM. What Bell discovered was, Quantum Mechanics predicts certain correlations of spins at varying degrees of measurement, and the exact correlations it predicts are *incompatible* with Einstein's view of the world. If you read the wiki page on Bell's Theorem, you'll see it referred to as "local hidden variables" - local hidden variables, Bell figured out, could not (at least not without some weird loopholes) explain the statistical results that QM predicts. So let's go into why and what that means.

First, let's just talk about what you alread know: in a Bell Test, they create a pair of particles that have entangled spin. One of them goes left, one of them goes right. If you measure their spin along the same axis, if they're properly entangled then one spin will be up and one will always be down. If you measure them at a different angle, however, the statistics start to differ a little bit.

Here's where I introduce the "analogy" I've been touting prior. Local Hidden Variables and entanglement. I'm absolutely certain I'm oversimplifying this but I think the simplification I'm going to present is useful at the very least, so here it goes: Local Hidden Variables theories are basically Classical theories, which is to say they match this idea of Object Permanence I talked about - regardless of our own ignorance, every property of a particle has a singular definite value at all moments in time. Now the idea that two particles could have some correlated value isn't itself incompatible with Classical theories, so here's the first layer of the analogy: A person called FJ (me) is offering a service online. You send me 2 addresses and a dollar, and I'll send an envolope with a piece of paper in it to each address. The service is very simple: to one address I'll send an envelope with a red piece of paper inside, and to the other addrss I'll send an envelope with a green piece of paper inside. This is "classical entanglement", aka the Local Hidden Variables view of entanglement. You purchase my services and send me your address and T.Clark's address, and when you get your envelope you open it and you see a Green piece of paper. You have *immediately and instantaneously* learned information about the envelope heading to T.Clark's house. You know for a fact that the paper going to him is Red, regardless of the fact that it hasn't been measured yet. This isn't magic and it's not quantum, this is the classical view of entanglement.

So, the analogy is a "particle" is an envelope, and a "measurement" is opening the envelope here, and in a classical system, there's nothing weird or strange about the idea that the contents of one envelope could be perfectly correlated with the contents of another envelope, right? I hope that all makes sense. We consider it classical because, even if you opened the envelope, say, 24 hours after I mailed it off, you could reasonably ask the question "what color was the paper in this envlope 12 hours after it was sent?" and, common sense says, it was green when you opened it and so it was green 12 hours before you opened it as well. And 23 hours before you opened it. And 1 hour before you opened it. When you opened this envelope, you weren't generating some new fact about the color of the paper, you were discovering a fact that was true the whole time - that's what makes it classical. Complete object permanence. Objective facts regardless of your ignorance.

I send you an email a few days later letting you know I'm offering a more advanced service. I'm offering to send the 2 envelopes with a paper inside, same as before, but this time I'm going to write a number on each one. On the first paper I write a number from 0 - 359 - let's call this number X. On the second paper, I'm going to write whatever this formula outputs: (X + 180) MOD 360. So, whatever the first number is, the second number is 180 degrees rotated from the first number. If the first number is 1, the second number is 181. If the first number is 90, the second number is 270. If the first number is 320, the second number is (320 + 180) mod 360 which is 140. Now this service I'm offering is *almost* directly comparable to the experiment in a Bell test. The only thing you have left to do to make it actually comparable to a Bell test is devise a *measurement scheme* that makes it similar to a Bell test, which is actually remarkably easy.

Like before, you ask me to send one envelope to your house and one to T.Clark's house. You've agreed with T.Clark for the first round to measure every number received according to this scheme: If the number is between 0 and 180 (including 0, not including 180), you record an UP on your spreadsheet, and if it's from 180 - 360 (including 180, not including 360 aka 0) you'll record a DOWN on your spreadsheet.

So, you run the test 1000 times, say, and after you compare your spreadsheet with T.Clark's spreadsheet, you're completely unsurprised to discover that every time you've recorded UP, he's recorded DOWN, and vice versa. Again, this is just basic, classical entanglement. These envelopes are classical envelopes, filled with classical paper, written on with classical pen. You might measure a particle as UP after you receive it, but the number was already written in pen long before you received it. Nothing weird here.

But meanwhile you and T.Clark have also set up some entangled quantum photons to arrive at your houses, and you're measuring their spins, and you've noticed with the entangled particles that when you run the test above, measuring their spin at the same angle, you get the same results as the envelope experiment - every result you see as UP, T.Clark sees as DOWN, and vice versa. So in this case, our classical experiment is looking a lot like our quantum experiment.

So, you and T.Clark start changing the experiment up, and you start doing a proper Bell test. Some of the time, you measure a particle at, say, 0° and he measures it at 20°. Some of the time, you measure a particle at 20° and he measures it at 40°. And some of the time, you measure a particle at 0° and he measures it at 40°. {0° above means UP if it's [0-180) and DOWN if it's [180-360), 40° means UP if it's [40-220)}. You both record your ups and downs now, and you discover the following set of facts:

When you're measuring 0° and he's doing 20°, you BOTH record UP 5.8% of the time (as in, 5.8% of the time yours and his both register UP for the same run).

When you're measuring 20° and he's doing 40°, you BOTH record UP 5.8% of the time.

When you're measuring 0° and he's doing 40°, you BOTH record UP 20.7% of the time.

Now, you decide to run the same sort of tests using FJ's mailing service just to see what the results are, to compare your quantum measurements to a classical system. Here's what you get.

When you're measuring 0° and he's doing 20°, you BOTH record UP 5.55...% of the time.

When you're measuring 20° and he's doing 40°, you BOTH record UP 5.55...% of the time.

When you're measuring 0° and he's doing 40°, you BOTH record UP 11.111...% of the time.

You notice this, tim, and you have a little intuition: you think that in my classical mailing service, it's actually impossible for my classical mailing service to produce the 5.8, 5.8, 20.7% statistics from the quantum tests. You think that it might be the case that the 0-20 and 20-40 statistics might have to add up to the 0-40 statistics, but maybe you can't quite explain why yet. You intuitively think there's no way for me to recreate that distrubituion. So, you tell T.Clark and he disagrees (I'm sure you wouldn't actually disagree, mr Clark, it's just a story). So you make a bet - you tell T.Clark that HE can call up and tell me (FJ, the mailing man) exactly what numbers to put in the envelopes, BUT you, tim, YOU get to decide how they're going to be measured (0 and 0, 0 and 20, 20 and 40 or 0 and 40), and you decide that 12 hours after the envelope is sent off, so T.Clark and FJ have no way of knowing which angles you're going to measure them at. So the bet is this: under those conditions, can T.Clark and FJ create a scheme that will make it so that at 0 and 0, all the result are opposite, at 0 and 20 they're both up 5.8% of the time, and 20 and 40 they're both up 5.8% of the time, and at 0 and 40 they're both up 20.7% of the time?

So, at this stage, what do you think? Can FJ and T.Clark devise any system of sending these letters to you in the conditions given? Is there any strategy at all they could take to produce these distributions reliably?

Bell's Theorem says there isn't. The only out that I know of, the only loop hole, is that if T.Clark and FJ already know ahead of time how you're going to be measuring them, THEN FJ and T.Clark can conspire to rig the results (this is essentially what Superdeterminism means, it means that the mechanism creating the spin values knows ahead of time how they're going to be measured and has conspired to give the results QM predicts). But I've worded it such that that loophole is closed - "BUT you, tim, YOU get to decide how they're going to be measured, and you decide that 12 hours after the envelope is sent off" - so they can't cheat in the superdeterministic way.

If there's no way for FJ's classical mailing system to produce the statistical outputs that QM predicts - that 5.8% and 20.7% numbers - then that means we can possibly prove that we don't live in a classical world.

So what do you think? Can FJ and T.Clark devise such a system, so that the mailing system can output those numbers? Can you devise such a system?

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.
— T Clark

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! — tim wood

I will lay it out soon, because it's one of the most fascinating things I've ever tried to understand. For now let me just reiterate this:

The point of Bell's Theorem and the experiments that test it is to clarify if it's at all possible if we live in a world that's describable classically. You laid out some of the statistics that go into Bells Theorem, but in your first few posts I think you left out an explanation of why those statistics matter. That's what I'm focusing on here.

They matter because they prove with reasonable certainty that we live in a world that does not match up with classical assumptions.

T Clark said many people disagree with that and he brought up "many earths", which I assume to be many worlds - please correct me if I'm wrong. Many worlds is quantum mechanics. Many worlds is NOT classical. Many worlds also believes in indeterminate answers to measurement questions prior to measurement.

The classical idea is that any measurable property of a particle - momentum or position or spin - has a definite, objectively true answer even when you're not measuring it. If you send off a photon at t=1 and measure it at t=100, in classical mechanics that particle still has a singular, definite and true answer for any question you could ask of it at t=2 - 99. Just because you don't know the answer in classical mechanics doesn't mean there isn't one - there always is.

The inequalities in Bells Theorem are there to help us test if our universe is one where it's in fact true that we might live in a classical universe where those questions have singular, definite answers. Many Worlds does not involve singular definite answers to quantum questions, and the key to why is in the name, "many". Many Worlds takes the idea of superposition super-literally, and in many worlds any answer to a quantum question prior to measurement doesn't have a singular definite answer, it has MANY answers.

I'm going to try to take the time later to go over my analogy about why bells theorem says these questions can't have classical answers. I honestly love this topic so much. But I'll leave you with that for now.

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. )

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.

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.

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.

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.