What is the mechanism behind Quantum Entanglement?

[vanhees71]

My comment on this comment is that I see it similar to those who in misinterpreted "observers knowledge" as something having to do with human brain or consciusness.

At human level, of course Feyman is right. And its not the job of physicists to model human intelligence. It is definitely not what anyone means.

But do we have to stop there, or are rhere further insights to get? This is where we disagree.

Of course not, but you should be aware that then you leave the solid ground of the natural sciences.

1) Observers knowledge is encoded in the physical observer side of the cut. Making it a relation or contextual. This has nothing todo with brains. I guess we agree here?

Of course not. QM in its minimal interpretation describes what's objectively observed. It has nothing to do with the workings of the human brain.

But in QM the observerside is always dominant and classical. We know how to explain interactions between classical objects but the background independent description of nonclassical systema is missing.

It's not clear what you mean by "classical". Classical physics is an approximation of QT valid for coarse-grained descriptions of "macroscopic observables" with a limited range of applicability. It is a good approximation if the averages over many microscopic observables that constitute the macroscopic observables and their changes are large compared to the quantum (or thermal) fluctuations of these quantities.

Is this satisfactory? Some of us say yes, but I say no.

/Fredrik

What do you mean by "background independent description"? QT describes all there is to be described, as far as we know today.

 

[PeterDonis]

"Average-only" conservation, which is a mathematical fact about Bell states

More precisely, it's a "mathematical fact" if you ignore the interaction between the measured systems and the measuring devices. Once you include that interaction, it's obvious that conserved quantities--energy, momentum, angular momentum--can be exchanged between the measured systems and the measuring devices, so there is no reason to expect exact conservation of those quantities if you only look at the measured systems. In other words, the measured systems, by themselves, do not constitute an isolated, closed system, so you should not expect them to exactly obey conservation laws. This does not mean conservation laws only hold "on average" for quantum systems; it just means that, as always, conservation laws only hold for isolated, closed systems that don't interact with anything else.

 

[Fra]

Of course not, but you should be aware that then you leave the solid ground of the natural sciences.

I see myself in the domain of "hypothesis generation", which is the fuzzy but nevertheless a part of the scientific process, but it is not a coincidence that it's the part of the scientific process that some people (like Popper) wanted to play down.

What do you mean by "background independent description"? QT describes all there is to be described, as far as we know today.

QT rests on backgrounds in several ways ways, first in the way that is emphasised by Bohr and manifested by the Heisenberg cut. This is part of the "classical world" making up the observer, including it's encoding capacity (storing pointer variables etc) and processing power.

The other way is the one meant in GR/QG, that QFT is constructed relative to a classical spacetime. It corresponds at best to the equivalence class of the SR-observers, sitting at an asymptotic distance from the interactions they describe. This makes up for a weird relation between QFT and gravity that isn't easily dismissed. Even without a lot of engineering problems, it's a severe issue for anyone that focuses on the coherence of the explanations. It is not even clear that "gravity" should be "quantized" as per the same procedure as other fields.

So how we can use QM inference model (that presumes classical reality and classical spacetime to be defined), to infer what it assumes? What QM explains, is rather bits and pieces in the classical world, such as stability of atoms etc.

/Fredrik

 

[vanhees71]

There is no cut between a classical and a quantum world within QT, and there's no empirical evidence for one to exist in nature. This is, however, under investigation, i.e., there are experiments going on testing the (im)possibility to demonstrate "quantum behavior" of ever larger objects.

 

[Fra]

What's the obsession? The delusion of objectivity?

Can't speak for others that confess to cat 2 think, but I have no desire whatsoever to restore objectivity if that is what you mean. For me objectivity is effectively emergent among interacting systems and not fundamental, and I am fine with this.

To describe my obsession is in detail will be off topic and off limits, but I analyse the structure of physical interactions from the view of intrinsic inference (from a hypothetical inside general observer) rather than human inferences which are closely tied to the classical macroscopic world and classical apparatous. The reason for this is that I have come to my own opinion that this the core of many other open problems. Solve this, and lots of other things will be solved too. In the end of all this, there is the step of falsficiation or corroboratation. But all me "interpretations". But it's what "drives" the interpretational discussions from my side.

Without this, I would probably also prefer some sort of minimal interpretation, but the minimal interpretation gives me no sense of "direction" for modification.

/Fredrik

 

[Fra]

There is no cut between a classical and a quantum world within QT, and there's no empirical evidence for one to exist in nature.

When you make a preparation of a source and detectors etc, and data acquisiton devices, and computers that log all the data of virtual event counters, it's treated classically right? From that you compute distributions etc.

Without that SOLID support to make preparation and log massive amounts of data, how would you corroborate QM in the first place?

/Fredrik

 

[RUTA]

The statistics of measurements on Bell states consist of operations with single quantum systems (e.g., two entangled photons) event-by-event, and the conservation laws hold event by event. E.g., if you have a polarization-singlet two-photon state and you measure, e.g., the linear polarization of the two photons in the same direction you must always get opposite results, because the total angular momentum of the two-photon states is 0. Of course, to verify this, you must repeat the same experiment very often to gain sufficient statistics to meet your goal of statistical significance. That doesn't imply that the conservation laws hold only on average.

You're still missing the point entirely. Let's continue with what I said about "average-only" projection because it is exactly the same point, but with just one particle. Set your particular "constructive" account aside. [Random components of some hidden, underlying vector? And you always get +/- 1 for these random components? Weird.] You can have whatever view of the unseen underlying situation you like, it's absolutely irrelevant and won't affect what I'm saying at all because all I'm referring to are mathematical and empirical facts about spin.

Indeed. What else do you need? That's all what has been ever observed in Stern-Gerlach experiments (including those much more accurate ones like using a Penning trap to measure the electron Lande g-factor to 12 (or more?) digits of accuracy.

Again, this is your particular personal response to the situation. There are physicists who are/were not satisfied with the formalism and experiments alone, e.g., Gell-Mann, Feynman, Mermin, Bell, Einstein, etc. People with the mindset of this latter group participate in forums like this one to share ideas on how to satisfy their need for understanding.

What goes beyond the "mere formalism" and its application to real-world experiment is not subject to the objective natural sciences. An indication for that is that it seems impossible to clearly state, what "the problem" is.

Despite reading many posts and papers on the questions researchers in foundations are trying to answer, you still don't "get it." As I said before, I infer from this history that you are unlikely to ever get it. But, let's continue here and see if you can at least understand "average-only" projection whence "average-only" conservation, even if you don't appreciate why anyone would bother to characterize the mathematical and empirical facts this way.

Of course, an information theoretical approach to any kind of probabilistic description is an important aspect to understand the physics it describes. The claim that we "don't have to understand the reconstructions in detail" is another indication that here we leave the realm of exact science.

The details I'm leaving out are those not relevant to my point. Those included are "exact science."

This I don't understand. It depends on the preparation of the system before measurement, which probabilities, $p_1$ and $p_2=1-p_1$ you'll find when repeating the experiment often enough to measure these probabilities at a given level of statistical significance. That's true for both "classical" and "quantum" probabilities.

I'm just stating a fact about the classical bit to contrast its difference with the qubit, i.e., "continuity." As the reconstructions show, classical probability theory and quantum probability theory only differ in this one respect -- reversible transformations between pure states are continuous for the qubit while they are discrete for the classical bit. That's the "Continuity" part of Information Invariance & Continuity.

What do you mean by "average-only projection"? If you measure the spin component in any arbitrary direction (by the way completely determined with two angles $(\vartheta,\varphi)$ indicating the unit vector determining that direction) precisely, you always find either a value $\hbar/2$ or $-\hbar/2$ in each event, independent of the (pure or mixed) state you prepared the particle's spin in. The probabilities are given by the statistical operator describing this state prepared before measurement.

Keep reading, I explain what is meant by "average-only" projection using the mathematical and empirical facts later in the post.

Of course, quantum theory provides different (probabilistic predictions than a classical model of the electron. It was Stern's very motivation to do this experiment. It was not even clear, what the prediction of the ("old" quantum theory!) was: Should one get two or three discrete lines (Bohr vs. Sommerfeld) or a continuum (classical physics).

Yes, here's an interesting historical account.

But you can check the conservation laws only for one component, because determining one component of the spin implies that any other component is indetermined, because components in different direction are incompatible observables. Also you can measure only one spin direction, i.e., you can only choose one direction by the magnetic field. You never measure two components of the spin in different directions on a single particle. This you can achieve only on an ensemble. If you test the conservation law for angular momentum you can do that event-by-event only when measuring the spins of the two particles in a single direction. Any other measurement gives random results with probabilities given by Born's rule, given the (pure or mixed) state the particles' spin is prepared in before measurement.

In order to understand what is meant by "average-only" projection, you have to stick to the following facts, (which hold regardless of the underlying ontology you are imagining might be responsible for them):

1. When $\hat{b} = \hat{z}$, you always get +1.
2. When $\hat{b}$ makes an angle $\theta$ with respect to $\hat{z}$, you get +1 with a frequency of $\cos^2{\left(\frac{\theta}{2}\right)}$ and you get -1 with a frequency of $\sin^2{\left(\frac{\theta}{2}\right)}$. These average to $\cos{\theta}$. You never measure anything other than +1 or -1.
3. $\cos{\theta}$ is the projection of +1 along $\hat{b}$.

This collection of facts is what is meant by "average-only" projection. As you see, it is a statement of mathematical and empirical facts associated with spin. The classical constructive model (Knight figure) says we should get $\cos{\theta}$ every time, but in actuality we only get $\cos{\theta}$ on average. As you can (hopefully) see, "average-only" projection is not a matter of opinion or interpretation.

You are not in different reference frames. For that you'd have to use moving Stern-Gerlach magnets. Due to Galilei invariance the outcome of the measurements do not depend on the choice of the reference frame (defined, e.g., by the restframe of the magnets). The description of the same experiment in one frame is just a unitary transformation (given by the usual ray representation of the Gailei group for a particle with the given mass and spin). The same, of course, holds for Poincare invariance in the relativistic case (where however you have to be careful with the definition of "spin"; here you can only measure the total angular momentum of the electron, not the spin since the split into spin and orbital angular momentum is frame dependent).

That there's one and only one frame-independent value for Planck's constant, $\hbar=h/(2 \pi)$, is implemented in the realization of either non-relativistic or relativistic QT. That has nothing to do with "average-only conservation", which claim contradicts all observations made so far.

Different inertial reference frames are related by boosts (as you state), but they are also related by spatial rotations. The reference frame of the complementary spin measurements associated with $\hat{b}$ is indeed spatially rotated with respect to the reference frame of the complementary spin measurements associated with $\hat{z}$ (per Brukner and Zeilinger). Again, no interpretation here.

The relativity principle aka no preferred reference frame (NPRF) says we should measure the same value for fundamental constants of Nature like c (light postulate) and h (call this the "Planck postulate"), regardless of our inertial reference frame. Since we are in fact measuring h here (per Weinberg), then NPRF says we have to get (+\-) h for all $\hat{b}$. So, we can justify the fact that we have "average-only" projection rather than direct projection by the Planck postulate, which follows from NPRF. This justification is a "principle" account, so it is not threatened by any "constructive" account (like your "random components" model).

Here are the facts for "average-only" conservation (triplet states):
1. When $\hat{b} = \hat{a}$, Alice and Bob always get the same result, i.e., they both get +1 or they both get -1. This fact holds everywhere in the plane of symmetry. This is the rotational invariance for conservation of spin angular momentum.
2. When $\hat{b}$ makes an angle $\theta$ with respect to $\hat{a}$ (in the plane of symmetry), Bob gets +1 with a frequency of $\cos^2{\left(\frac{\theta}{2}\right)}$ and he gets -1 with a frequency of $\sin^2{\left(\frac{\theta}{2}\right)}$ corresponding to Alice's +1 outcome. These average to $\cos{\theta}$. Similarly for Alice's -1 outcome, Bob's +1 and -1 results average to $-\cos{\theta}$. Alice and Bob never measure anything other than +1 or -1.
3. $\pm\cos{\theta}$ is the projection of $\pm 1$ along $\hat{b}$ in accord with conservation of spin angular momentum in Fact 1, i.e., had Bob measured at $\hat{b} = \hat{a}$, he would have gotten the same $\pm 1$ outcome that Alice did, as demanded by conservation of spin angular momentum.
4. The situation is entirely symmetric under the interchange of Alice and Bob.

This is what is meant by "average-only" conservation. As you can (hopefully) see, it is not a matter of interpretation or opinion. It is standard textbook QM for the Bell states.

 

[RUTA]

More precisely, it's a "mathematical fact" if you ignore the interaction between the measured systems and the measuring devices. Once you include that interaction, it's obvious that conserved quantities--energy, momentum, angular momentum--can be exchanged between the measured systems and the measuring devices, so there is no reason to expect exact conservation of those quantities if you only look at the measured systems. In other words, the measured systems, by themselves, do not constitute an isolated, closed system, so you should not expect them to exactly obey conservation laws. This does not mean conservation laws only hold "on average" for quantum systems; it just means that, as always, conservation laws only hold for isolated, closed systems that don't interact with anything else.

No such qualifier is needed, see Post #129.

 

[PeterDonis]

No such qualifier is needed, see Post #129.

I see a lot of detail in post #129 about the mathematical calculations that underlie what you mean by "average only conservation" (which I didn't need, I already understand the math), but I don't see anything that addresses the physical point I made.

 

[RUTA]

I see a lot of detail in post #129 about the mathematical calculations that underlie what you mean by "average only conservation" (which I didn't need, I already understand the math), but I don't see anything that addresses the physical point I made.

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

 

[PeterDonis]

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

Even if you think I "should" understand this, i don't.

 

[RUTA]

Even if you think I "should" understand this, i don't.

Sorry, let me try again. The facts defining “average-only” conservation as listed in Post 129 do not depend on the physical facts in your post. Worse, your physical facts confuse what is meant by “average-only” conservation” as defined by my listed facts.

 

[*now*]

I am guessing Karl Popper would be proud of you both I do understand but doesn't share the stance as optimal.

About laughing, the exact same thing happened to smolin as he held a talk SETI about the evolution of law and the principle of prescedence….

There was an interesting debate held on that sort of topic recently but I think it is behind a paywall, “Is the universe fundamentally predictable or unpredictable? Does the degree to which the future remains unknown reflect our own cognitive limitations, or the fundamentally open structure of reality?… a remarkable panel comprising of Lee Smolin, Francesca Vidotto and John Vervaeke debated these questions during an IAI Live event, streamed in real time from the Institute of Art and Ideas in London. The universe, the panelists agreed, is a place of constant change and surprise, and its future remains fundamentally open.“ In the talk Fra posted Anaximander was mentioned, and this is also interesting I think-

 

[hutchphd]

If you understand what I said “average-only” conservation means in that post, then you should understand that the physical details of your post are irrelevant.

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?
Why is this to be desired? ( And why choose that name?)

.

 

[gentzen]

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?
Why is this to be desired? ( And why choose that name?)

You could ask a similar question to @vanhess71, when he keeps insisting that the word "locality" really means "microcausality principle". He complains that people keep using the word "locality" with its well established meaning instead, and even dare to doubt that QFT + the minimal statistical interpretation satisfy locality. For him, it is an established mathematical fact that QFT satisfies locality, because it satisfies the "microcausality principle" after all.

P.S.: To be honest, Demystifier's recent thread (which already got closed) trying to refute vanhees71's locality claims seemed pointless to me, because it seems pretty clear to me that in the end, it is just a disagreement about the proper use of words.

 

[RUTA]

So the result "average only conservation" is to give a new name to completely settled and understood Quantum Practice?

Yes! Did you see that immediately? Or was there something in my later posts that made that clear to you? I’m writing a book for the general reader on this so I’d like to know how best to say it.

Why is this to be desired? ( And why choose that name?)

It’s a way to distinguish quantum behavior from classical expectations. In that sense it provides the “mechanism” for the “mystery” of Bell state entanglement. For Unnikrishnan who first pointed this out for the singlet state it resolved the mystery too. Since the weirdness (violation of classical expectations) of the phenomenon resides in average-only conservation and since conservation principles are widely accepted as explanatory in physics, average-only conservation both identifies the mystery and solves it.

Most in foundations want average-only conservation explained though. NPRF + h is a principle way to do that.

 

[PeterDonis]

The facts defining “average-only” conservation as listed in Post 129 do not depend on the physical facts in your post.

I didn't say they did. Of course they don't.

Worse, your physical facts confuse what is meant by “average-only” conservation” as defined by my listed facts.

No, they don't "confuse what is meant", they just make explicit something you didn't, namely, that "average-only conservation" as you define it is perfectly consistent with exact conservation for each individual event, because each individual event involves more than just the quantum systems being measured, so those systems are not isolated. So "average-only conservation" is not any kind of alternative to exact conservation for each individual event. It's just using different words to describe a particular aspect of these types of measurements.

If you are not claiming that "average-only conservation" as you define it rules out exact conservation for each individual event, then there is no issue. But @vanhees71, at least, appears to think that you are claiming that "average-only conservation" rules out exact conservation for each individual event; that's why he keeps arguing, correctly, that exact conservation can hold for each individual event. If you are not claiming that average-only conservation rules out exact conservation for each individual event, it would probably be a good idea to clarify that point.

 

[PeterDonis]

It’s a way to distinguish quantum behavior from classical expectations.

This appears to require that average-only conservation does rule out exact conservation for each individual event. Is that your intent?

 

[hutchphd]

This appears to require that average-only conservation does rule out exact conservation for each individual event. Is that your intent?

And please carefully define what you mean by an "event". The particles that "appear" in a particular perturbation expansion are entirely chimerical until measured otherwise.

 

[PeterDonis]

And please carefully define what you mean by an "event".

I was using "event" to mean something like "a single run of an experiment that involves spin measurements on each of an entangled pair of particles".

The particles that "appear" in a particular perturbation expansion are entirely chimerical

I don't think this is relevant to the kinds of experiments being discussed in this thread; they involve quantum systems that are unproblematically "particles", in entangled pairs produced by sources that are well understood, and using spin measurements that are well understood.

 

[PeroK]

You may just have to accept the fact that you will never understand what bothered Einstein, Weinberg, Mermin, Gell-Mann, Feynman, and many others about QM. You simply cannot relate, so you have nothing to contribute to such discussions. I wish I could help you!

I think we all know what bothered Einstein about QM, but in 2022 is it really relevant? Human minds are difficult to change and perhaps if you brought the great man back to life he would still insist that QM is incomplete. Personally, I think Feynman understood perfectly what QM was saying and how it changed our whole perspective on physics and its relationship to the reality of natural phenomena (if I can phrase it like that).

You could equally well find a selection of physicists who want to find a place for God in the universe and then try to exclude atheists from such a discussion. (There was something pseudo-religious, IMO, about Einstein's objection to QM. He often brought "God" into the discussion.)

The worst thing you could do is discuss this issue only with physicists who are uncomfortable with QM and inexorably reinforce your views. We see this on social media and how it fundamentaly undermines the ability to analyse any subject.

 

[gentzen]

And please carefully define what you mean by an "event".

I was using "event" to mean something like "a single run of an experiment that involves spin measurements on each of an entangled pair of particles".

I would not call that an "event", but a "single trial" (or just a "trial", or a "single run"). But that is just me, I certainly don't want to prescribe to other people how to use language and words.

The important point for me is whether the chosen words are good enough to transmit the intended message to the target audience with sufficient detail.

The particles that "appear" in a particular perturbation expansion are entirely chimerical until measured otherwise.

For me, the word "event" implies a rather good localization in space and time. So I prefer to accept that my "events" are not classical events, and can be in superposition. This implies that they are to a certain extent chimerical and rather arbirarily defined. I prefer this over having to "wait" for a measurement, because that additional time delay (and distance) would destroy the good localization of my "events".

 

[vanhees71]

You're still missing the point entirely. Let's continue with what I said about "average-only" projection because it is exactly the same point, but with just one particle. Set your particular "constructive" account aside. [Random components of some hidden, underlying vector? And you always get +/- 1 for these random components? Weird.] You can have whatever view of the unseen underlying situation you like, it's absolutely irrelevant and won't affect what I'm saying at all because all I'm referring to are mathematical and empirical facts about spin.

I have no clue what you want to say here. Can you clearly state (a) about which spin we talk, (b) in which state the spin is prepared before measurement, and (c) which measurement is made on the so prepared spin and what you mean by "average-only" projection. Before you claimed, against all emprical facts, that conservation laws were valid only on average. If philosophy starts with denying empirical facts, I cannot understand what this should help with understanding quantum theory. To the contrary, it's just nonsense. Simple logic tells you that you get anything you like from false assumptions! Now you changed words again. Now it's "average-only" projection. Please give clear mathematical definitions what is done!

Again, this is your particular personal response to the situation. There are physicists who are/were not satisfied with the formalism and experiments alone, e.g., Gell-Mann, Feynman, Mermin, Bell, Einstein, etc. People with the mindset of this latter group participate in forums like this one to share ideas on how to satisfy their need for understanding.Despite reading many posts and papers on the questions researchers in foundations are trying to answer, you still don't "get it." As I said before, I infer from this history that you are unlikely to ever get it. But, let's continue here and see if you can at least understand "average-only" projection whence "average-only" conservation, even if you don't appreciate why anyone would bother to characterize the mathematical and empirical facts this way.The details I'm leaving out are those not relevant to my point. Those included are "exact science."

If you don't give details, of course there's no chance to understand each other.

I'm just stating a fact about the classical bit to contrast its difference with the qubit, i.e., "continuity." As the reconstructions show, classical probability theory and quantum probability theory only differ in this one respect -- reversible transformations between pure states are continuous for the qubit while they are discrete for the classical bit. That's the "Continuity" part of Information Invariance & Continuity.

I don't think that this part is in any way controversial.

Keep reading, I explain what is meant by "average-only" projection using the mathematical and empirical facts later in the post.

Please give a mathematical description without too many words. We have a concise mathematical language to avoid such mutual misunderstandings. Once more, the claim the conservation laws were valid only on average is an empirically disproven claim!

Yes, here's an interesting historical account.In order to understand what is meant by "average-only" projection, you have to stick to the following facts, (which hold regardless of the underlying ontology you are imagining might be responsible for them):

1. When $\hat{b} = \hat{z}$, you always get +1.
2. When $\hat{b}$ makes an angle $\theta$ with respect to $\hat{z}$, you get +1 with a frequency of $\cos^2{\left(\frac{\theta}{2}\right)}$ and you get -1 with a frequency of $\sin^2{\left(\frac{\theta}{2}\right)}$. These average to $\cos{\theta}$. You never measure anything other than +1 or -1.
3. $\cos{\theta}$ is the projection of +1 along $\hat{b}$.

This all are empty words, as long as you don't state, what is measured and how the measured system is prepared.

 

[vanhees71]

I think we all know what bothered Einstein about QM, but in 2022 is it really relevant? Human minds are difficult to change and perhaps if you brought the great man back to life he would still insist that QM is incomplete. Personally, I think Feynman understood perfectly what QM was saying and how it changed our whole perspective on physics and its relationship to the reality of natural phenomena (if I can phrase it like that).

The difference between Einstein and @RUTA is that he made clear statements. It's clear what bothered Einstein, and it's also clear that Einstein's local hidden-variable idea, as interpreted by Bell in a scientifically clearly decidable sense, is ruled out. In this sense, indeed Einstein's quibbles are resolved.

Of course, Feynman understood perfectly well, what QM is saying, and his treatment in the introductory chapter of the Feynman Lectures vol. III (concerning the double-slit experiment with particles) is all there is to say. That's why I don't understand when Feynman says, "nobody understands quantum mechanics"

 

[PeroK]

That's why I don't understand when Feynman says, "nobody understands quantum mechanics"

It was supposed to be a joke.

 

[vanhees71]

Surely he was joking ;-)).

 

[Fra]

I am sure there are those here that has studied the historical communication far better than me so I throw this ou. I wonder if Einstein fully accepted that Bell's theorem was a correct characterization of his own ideas?

what bothered Einstein, and it's also clear that Einstein's local hidden-variable idea, as interpreted by Bell in a scientifically clearly decidable sense, is ruled out. In this sense, indeed Einstein's quibbles are resolved.

The question is (and motivated by my own critical view on Bells ansatz): did Einstein never object to the ansatz of Bells theorem?

(note that the question has nothing todo with correctness of bells theorem, it's about wether einstein agreed with the formalisation that bell did)

/Fredrik

 

[vanhees71]

How could he? Einstein died in 1955, Bell's 1st paper was written in 1964...

 

[Fra]

How could he? Einstein died in 1955, Bell's 1st paper was written in 1964...

I knew there was someone that knew better

/Fredrik

 

[RUTA]

This appears to require that average-only conservation does rule out exact conservation for each individual event. Is that your intent?

Charge and energy are conserved exactly (for each trial) in these experiments. Does that bear at all on the mystery of entanglement per the Bell states? No, so why state it when doing so leads precisely to confusing statements like this one? I think I'll stick to my presentation of the empirical and mathematical facts that define "average-only" projection and "average-only" conservation (for spin angular momentum in this case) and not introduce extraneous facts. Indeed, I'll make my Posts 113 and 129 an Insight so I can just link to that concise explanation and list of the relevant facts in the future.