Bell's inequality refuted via elementary algebra

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Bell's inequality refuted via elementary algebra

Postby minkwe » Mon Jun 24, 2019 4:25 pm

gill1109 wrote:I think we *must* carefully separate the mathematics from the physics and from the experiment. We must separate and carefully look at all three. We next need to very carefully think about the connection between the physics and the mathematics.

Needless to say, I disagree with this approach. It is the approach that has led us to the current mess. Logic first, physics second, and math only as needed to support both at the same time with careful consideration to make sure there is direct correspondence between the physical situations and any mathematical abstractions used to describe them.

My understanding is that Bell did very carefully motivate his "local realist" picture (which is a purely mathematical model).
Einstein would definitely have agreed with Bell's motivation for the model. The motivation did come from cherished pre-existing fundamental principles of physics. So fundamental that many would consider them just "common sense" (Caroline Thompson's point of view), or perhaps "the bare minimum of assumptions that we need to make in order to make physics possible at all!" (the point of view of Alexei Nikulov, famous Russian guy, you can find him on ResearchGate).

Thus the local-realism mathematical model has fundamental physical principles or assumptions built into it.

If experiments apparently do not fit to the model, then we learn that the physical assumptions are apparently false.

As I have tried to explain many times, it is unfortunately not as easy as that. Bell proponents are too quick to eliminate their favorite assumptions which generate mystery without careful consideration of what exactly was modelled in the first place. The conclusion that certain experiments do not fit certain models and thus certain assumptions must be false, is fallacious because those experiments, properly modelled, would not be expected to fit those mathematical models anyway, even if all the assumptions are true. That is why we must go back to the drawing board and look at the mathematics together with the physics, not separately.

As I said many times before, there are now many different standpoints which can logically be taken. At least five.
...
I think that Bell's theorem should be thought of as a theorem from theoretical computer science, belonging to the field of distributed (classical) computing. Boris Tsirelson agrees. There are elegant proofs of this abstract theorem (Steve Gull's proof - an old exam question in the Cambridge master programme in theoretical physics) which do not have anything to do with statistics or with real experiments. You could say that the theorem is an easy corollary of standard results from Fourier analysis. Certain functions cannot be represented in certain ways. One does, of course, need some classical calculus (ordinary Riemann integration is enough), to formulate and prove the theorem in this way. In modern terminology, one could call it a pretty elementary theorem in functional analysis or in approximation theory. It would be very interesting to look at it from a category theory point of view.

But but but, a theorem about what exactly? Is the key question. All those proofs do the same thing. They demonstrate that given a single sample space, a certain inequality must hold. You can have 10 different ways of proving it, but if you perform an experiment in which there is not a single sample space but separate sample spaces, all bets are off. The design of the experiment requires multiple sample spaces and any apparent violation is simply telling you what you should already know from the experimental design -- that the outcomes do not originate from a single sample space. The fact that you could imagine them to have originated from a single sample space in principle is irrelevant. What matters is what is actually measured. By separating the mathematics from the physics, it becomes easy to overlook this. I think perhaps your most important paper was https://arxiv.org/abs/quant-ph/0312035 because it hinted at the solution of this mess. I understand that you disagree with my reading of that paper but I believe the roots of the solution can be found in it.

But you don't have to take my word for it. If you carefully analyze all the experiments done to date you will realize separately from any considerations of locality or realism, that there is not a single sample space for the data as required by Bell's toy model. Once you realize this, you will appreciate just how embarrassingly meaningless Bell's theorem is.
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Tue Jun 25, 2019 1:09 am

minkwe wrote:
gill1109 wrote:I think we *must* carefully separate the mathematics from the physics and from the experiment. We must separate and carefully look at all three. We next need to very carefully think about the connection between the physics and the mathematics.

Needless to say, I disagree with this approach. It is the approach that has led us to the current mess. Logic first, physics second, and math only as needed to support both at the same time with careful consideration to make sure there is direct correspondence between the physical situations and any mathematical abstractions used to describe them.

But I agree with you entirely! Logic first, physics second; math is an extension of logic and/or a tool for physics.

minkwe wrote:
gill1109 wrote:My understanding is that Bell did very carefully motivate his "local realist" picture (which is a purely mathematical model). Einstein would definitely have agreed with Bell's motivation for the model. The motivation did come from cherished pre-existing fundamental principles of physics. So fundamental that many would consider them just "common sense" (Caroline Thompson's point of view), or perhaps "the bare minimum of assumptions that we need to make in order to make physics possible at all!" (the point of view of Alexei Nikulov, famous Russian guy, you can find him on ResearchGate).

Thus the local-realism mathematical model has fundamental physical principles or assumptions built into it.

If experiments apparently do not fit to the model, then we learn that the physical assumptions are apparently false.

As I have tried to explain many times, it is unfortunately not as easy as that. Bell proponents are too quick to eliminate their favorite assumptions which generate mystery without careful consideration of what exactly was modelled in the first place. The conclusion that certain experiments do not fit certain models and thus certain assumptions must be false, is fallacious because those experiments, properly modelled, would not be expected to fit those mathematical models anyway, even if all the assumptions are true. That is why we must go back to the drawing board and look at the mathematics together with the physics, not separately.

No, we must go back to the drawing board and look at the logic of the careful synthesis of separate contributions from experimental physics, mathematics, and theoretical physics.

minkwe wrote:
gill1109 wrote:As I said many times before, there are now many different standpoints which can logically be taken. At least five.

I think that Bell's theorem should be thought of as a theorem from theoretical computer science, belonging to the field of distributed (classical) computing. Boris Tsirelson agrees. There are elegant proofs of this abstract theorem (Steve Gull's proof - an old exam question in the Cambridge master programme in theoretical physics) which do not have anything to do with statistics or with real experiments. You could say that the theorem is an easy corollary of standard results from Fourier analysis. Certain functions cannot be represented in certain ways. One does, of course, need some classical calculus (ordinary Riemann integration is enough), to formulate and prove the theorem in this way. In modern terminology, one could call it a pretty elementary theorem in functional analysis or in approximation theory. It would be very interesting to look at it from a category theory point of view.

But but but, a theorem about what exactly?

A mathematical theorem is not a theorem *about* anything. If it is a well-proven theorem then it is an indisputable fact about an idealised imaginary mathematical world.


minkwe wrote:... a theorem about what exactly, Is the key question. All those proofs do the same thing. They demonstrate that given a single sample space, a certain inequality must hold.

As a mathematician, I would say that you are here talking about a simple Lemma (we are talking about the inequality, right?). You are missing the fact that the Lemma is a mathematical Lemma which leads rapidly to a mathematical Theorem. The Theorem is that "local realism" cannot reproduce the predictions of "quantum mechanics". This theorem involves Mathematical definitions of "local realism", and of "quantum mechanics". Merely as abstract entities. No "dependence" on physics. But obviously, inspired by physics.

The interesting question is whether or not this theorem could be interesting in physics. One has to ask whether or not the abstract Mathematical concept of "local realism" can be given a physical interpretation or a physical meaning; and one has to ask whether or not that meaning is interesting.

By the way there are alternative proofs of the same Theorem which do not use inequalities at all. I would say that the mathematical Theorem is a theorem belonging to Approximation Theory, to Functional Analysis. Can you well approximate members of one class of functions with members of another class? See Steve Gull's proof. One could alternatively think of the Theorem as a theorem in Theoretical Computer Science, in the subfield of Classical Distributed Computing. Can certain functions be computed by a network of computers when connections are only allowed of a certain kind? Boris Tsirelson thinks of it as a Theorem in the Theory of Cellular Automata.


minkwe wrote:You can have 10 different ways of proving it, but if you perform an experiment in which there is not a single sample space but separate sample spaces, all bets are off. The design of the experiment requires multiple sample spaces and any apparent violation is simply telling you what you should already know from the experimental design -- that the outcomes do not originate from a single sample space. The fact that you could imagine them to have originated from a single sample space in principle is irrelevant. What matters is what is actually measured. By separating the mathematics from the physics, it becomes easy to overlook this. I think perhaps your most important paper was https://arxiv.org/abs/quant-ph/0312035 [Bell's inequality and the coincidence-time loophole] because it hinted at the solution of this mess. I understand that you disagree with my reading of that paper but I believe the roots of the solution can be found in it.

I wouldn't say all bets are off. I would say - now the interesting part begins. Are there physical or metaphysical lessons to be had from the results of the experiment on the one hand, and the results of pure mathematical analysis on the other hand?

minkwe wrote:But you don't have to take my word for it. If you carefully analyze all the experiments done to date you will realize separately from any considerations of locality or realism, that there is not a single sample space for the data as required by Bell's toy model. Once you realize this, you will appreciate just how embarrassingly meaningless Bell's theorem is.

Of course the experiment does not match the situation of the little result got by Boole (a little and quite trivial exercise to the reader. Have you read Boole?). The interesting part now begins: why the hell would Bell have suggested that there is a connection? Answer: he followed ideas of Einstein expressed in the famous EPR paper. There is a famous criterion there for something to be an "element of physical reality". Bell later introduced the term "beable". Einstein hoped and believed that "below" quantum mechanics there would be some kind of individual particle mechanics, just as statistical mechanics derives macroscopic laws from classical deterministic laws about individual particles together with statistical properties of the particles' initial positions and momenta. Einstein argued that QM was *incomplete* in the sense that it was the merely statistical reflection of classical law-like behaviour at a deeper level. It couldn't be the last word!

I suggest you read what Bell wrote in terms of physical motivation for the mathematical concept of local realism (though note, these are moving targets). Note also what he wrote about what you might like to conclude from his theorem. He said that if you were Bohr, you would have said "So what. I told you so". But I think that Einstein would have been disturbed by Bell's findings.

There is nowadays a completely subjectivist interpretation of quantum mechanics called QBism, originally this was "quantum Bayesianism". Bell's theorem is uninteresting for QBists because everything is in their own mind and their own mind is all they have to go on. So they just accept the minimal mathematical rules of QM, taking the probability of Born's law to be subjective probability, i.e., as reflecting rational betting odds. The definition of rational is that you do not let yourself caught by a Dutch book. Your bets should somehow be consistent with one another.
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Re: Bell's inequality refuted via elementary algebra

Postby minkwe » Tue Jun 25, 2019 10:41 pm

gill1109 wrote:A mathematical theorem is not a theorem *about* anything. If it is a well-proven theorem then it is an indisputable fact about an idealised imaginary mathematical world.

Bingo! Then why are we discussing it in the context of a physics experiment. Why do physicists bother about Bell's theorem at all? If all Bell was doing was a mathematical theorem, there would be no issue.

As a mathematician, I would say that you are here talking about a simple Lemma (we are talking about the inequality, right?). You are missing the fact that the Lemma is a mathematical Lemma which leads rapidly to a mathematical Theorem.

The Theorem is that "local realism" cannot reproduce the predictions of "quantum mechanics". This theorem involves Mathematical definitions of "local realism", and of "quantum mechanics". Merely as abstract entities. No "dependence" on physics. But obviously, inspired by physics.

I won't use the word "inspired" because there was no inspiration in what he did. The vague statement that "local realism" cannot reproduce the predictions of "quantum mechanics" simply does not follow from proofs of the inequalities the way you think, because, for the reasons I've already explained many times, the quantum mechanical predictions in the second part of the so-called theorem, refer to a different thing than the predictions being claimed in the first part of the statement. It is a farce. Imagine a theorem which says "The geodesic distance from Richard's current location to London, is shorter than the euclidean distance from Richard's current location to London". Of course, before anyone starts claiming such a statement implies the discovery of new mystery in geometry, it may be very wise to make sure the London referred to in the first part of the statement is the same London in the second half of the statement. Because it turns out, the euclidean distance refers to London, England, while the geodesic distance refers to London, Canada.

Bell's theorem is based on such fallacies. The inequalities relate to a different abstraction than what the QM predictions relate to. I think it is unfortunate that you are too quick to point at "Local realism" as the culprit. At least, you must ask the question and seek the answer for what exactly the quantum mechanical predictions are about. Bell's proponents are often quite unwilling to seek understanding in this area. Perhaps the adage that nobody really understands quantum mechanics is very true about those chanting the Bell mantra. Bell's own thoughts on this can be quite illuminating:

John S Bell wrote:Thus the formal proof of von Neumann does not justify his informal conclusion. ....... It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made.



The interesting question is whether or not this theorem could be interesting in physics. One has to ask whether or not the abstract Mathematical concept of "local realism" can be given a physical interpretation or a physical meaning; and one has to ask whether or not that meaning is interesting.

That question has already been answered. The answer is No and No. It is irrelevant for physics.


By the way there are alternative proofs of the same Theorem which do not use inequalities at all. I would say that the mathematical Theorem is a theorem belonging to Approximation Theory, to Functional Analysis. Can you well approximate members of one class of functions with members of another class? See Steve Gull's proof. One could alternatively think of the Theorem as a theorem in Theoretical Computer Science, in the subfield of Classical Distributed Computing. Can certain functions be computed by a network of computers when connections are only allowed of a certain kind? Boris Tsirelson thinks of it as a Theorem in the Theory of Cellular Automata.

It doesn't matter. They all boil down to the same essential core principle -- incompatible sample spaces cannot be combined into a single sample space. This should have been obvious had the LHS and RHS of the "theorem" been more carefully examined.

I wouldn't say all bets are off. I would say - now the interesting part begins. Are there physical or metaphysical lessons to be had from the results of the experiment on the one hand, and the results of pure mathematical analysis on the other hand?

No. Because the two are not even comparable, they are apples and oranges. The only way to enable a proper comparison is to go back to the drawing board, and develop the mathematics by carefully considering the physical situation for which QM is making predictions, and the physical situation which corresponds to the EPR experiments. Once that is done, there is no conflict, and no mystery.

Of course the experiment does not match the situation of the little result got by Boole (a little and quite trivial exercise to the reader. Have you read Boole?). The interesting part now begins: why the hell would Bell have suggested that there is a connection? Answer: he followed ideas of Einstein expressed in the famous EPR paper. There is a famous criterion there for something to be an "element of physical reality". Bell later introduced the term "beable". Einstein hoped and believed that "below" quantum mechanics there would be some kind of individual particle mechanics, just as statistical mechanics derives macroscopic laws from classical deterministic laws about individual particles together with statistical properties of the particles' initial positions and momenta. Einstein argued that QM was *incomplete* in the sense that it was the merely statistical reflection of classical law-like behaviour at a deeper level. It couldn't be the last word!

Unfortunately, I don't believe the EPR paper proposed a rigorous mathematical definition of what conditions had to be met for "elements of reality". Boole established that very clearly in his "conditions of possible experience". Bell's result is less profound than Boole's "little result" as you call it. I think if Bell had read Boole, he would never have bothered doing what he did. Boole interpreted the relations he discovered the proper way, Bell did not. Well worth a read if you haven't read it (http://www.gutenberg.org/files/15114/15114-pdf.pdf). According to Boole's work, the apparent violation by 4 QM expectation terms simply implies that the separate terms from QM could not possibly have been experienced simultaneously. In other words, the 4 expectation terms from QM are not simultaneous possible experiences, or they do not originate from the same sample space -- which we already know because according to the design of the experiment, they are disjoint measurements. So what exactly did Bell add to this, other than confusion?

I suggest you read what Bell wrote in terms of physical motivation for the mathematical concept of local realism (though note, these are moving targets). Note also what he wrote about what you might like to conclude from his theorem. He said that if you were Bohr, you would have said "So what. I told you so". But I think that Einstein would have been disturbed by Bell's findings.

I have read it and I'm not impressed one bit. Perhaps Einstein would have been disturbed, but not for the reason you think. Perhaps for the same reason that Bell was disturbed by von Neumann's findings. There is a reason the mathematical concepts are moving targets, because they are ill-defined jello. That is a feature not a bug, the more murky the definitions, the easier it is to doge criticism.

There is nowadays a completely subjectivist interpretation of quantum mechanics called QBism, originally this was "quantum Bayesianism". Bell's theorem is uninteresting for QBists because everything is in their own mind and their own mind is all they have to go on. So they just accept the minimal mathematical rules of QM, taking the probability of Born's law to be subjective probability, i.e., as reflecting rational betting odds. The definition of rational is that you do not let yourself caught by a Dutch book. Your bets should somehow be consistent with one another.

Don't get me started on "interpretations". Why does "the best theory" need interpreting :roll:
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Re: Bell's inequality refuted via elementary algebra

Postby Joy Christian » Wed Jun 26, 2019 4:21 am

***
A clearer exposition of Boole's inequality is in his Royal Society paper of 1862: https://royalsocietypublishing.org/doi/ ... .1862.0015.

Boole's book was written some ten years before this paper, but it does provide foundations to his inequality, which was formulated some 100 years before Bell's work.

Note that Bell and (at least) his early followers never bothered to give any credit to Boole for the inequality. Ignorance is no excuse, either in a court of law or in science.

***
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Wed Jun 26, 2019 1:34 pm

minkwe wrote:I won't use the word "inspired" because there was no inspiration in what he did. The vague statement that "local realism" cannot reproduce the predictions of "quantum mechanics" simply does not follow from proofs of the inequalities the way you think ... for the reasons I've already explained many times
...
Don't get me started on "interpretations". Why does "the best theory" need interpreting?

I wrote a vague statement here for the sake of brevity but others have written precise mathematical statements, and proven precise mathematical theorems. They are precise by virtue of giving precise formal (abstract) definitions of mathematical objects (or categories) which for convenience one calls “LR” and “QM”. Do you want me to give some references?

The presently “best” theory does not need an interpretation if you follow the philosophy “shut up and calculate”. So you think that Joy Christian’s work is entirely superfluous since it does, according to him, reproduce already existing predictions of QM?

Many people believe that the problems of finding a graceful unification of QM and GR are intimately connected to the “interpretation problem” of QM. Many believe they are connected to the Schrödinger cat paradox. Of course, if you are a QBist, then there is no paradox, because everything is in the mind anyway, and all we have is Bayes theorem as the only self-consistent way to update our predictions of our future sensory perceptions. There is no “external reality” in this “interpretation” of QM.

Regarding Boole, I think you are confusing the very well known and basic Boole’s inequality with a simple exercise for the reader somewhere in his huge and not often read book. He gives no solutions to the exercises, there is no instructor’s manual. Not necessary since it is an immediate trivial corollary of the usual “Boole’s inequality”. I think it is a libellous scandal that people should demean J S Bell by supposing that he should have cited an exercise in a 1500 page book from the 19th century, not read by anyone anymore, when the inequality in question is just a trivial elementary probability exercise. Which moreover has been pointed out hundreds of times by hundreds of other scientists.

The important thing is, why would Einstein or Bell have thought it physically reasonable to suppose that those four separate real experiments could be thought of, in theory, as four margins of one bigger experiment? EPR gives a careful motivation.

But you have no interest in studying what could be the nature of more fundamental (semi-deterministic?) theories which might underlie QM. Just shut up and calculate. QM works so why bother? It’s a valid point of view... but I think a fundamentally unscientific point of view!
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Wed Jun 26, 2019 1:45 pm

Joy Christian wrote:A clearer exposition of Boole's inequality is in his Royal Society paper of 1862: https://royalsocietypublishing.org/doi/ ... .1862.0015.

Boole's book was written some ten years before this paper, but it does provide foundations to his inequality, which was formulated some 100 years before Bell's work.

Note that Bell and (at least) his early followers never bothered to give any credit to Boole for the inequality. Ignorance is no excuse, either in a court of law or in science.

The Royal Society link does not link to anything useful, as far as I can see. No pdf. No content. Just an abstract.

I think the statement about Bell and his followers is libellous. But I guess Bell’s heirs won’t be bothered, though. See my responses to Michel who seems to think the same. At least you should be grateful to Itamar Pitowsky (RIP) for this jewel. Seems he was the first quantum foundations guy in a hundred years to dig through Boole’s book. Good for him!

Similarly, Michel’s project-Gutenberg link didn’t work. I guess the Chinese are attacking Western Internet. I’ll ry again tomorrow...
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Re: Bell's inequality refuted via elementary algebra

Postby Joy Christian » Wed Jun 26, 2019 1:49 pm

***
View PDF on that link.

If anyone finds my statement about Bell and his followers libelous, then they are welcome to sue me.

***
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Re: Bell's inequality refuted via elementary algebra

Postby FrediFizzx » Wed Jun 26, 2019 2:01 pm

Joy Christian wrote:***
View PDF on that link.

If anyone finds my statement about Bell and his followers libelous, then they are welcome to sue me.

***

View PDF worked for me.
.
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Re: Bell's inequality refuted via elementary algebra

Postby minkwe » Wed Jun 26, 2019 6:24 pm

gill1109 wrote:I wrote a vague statement here for the sake of brevity but others have written precise mathematical statements, and proven precise mathematical theorems. ... Do you want me to give some references?

Please proceed, remember we are looking for precise mathematical theorems proving that Bell's apples are the same as Quantum oranges. There is a tendency to produce apples when oranges are requested, and oranges when apples are requested. I won't be fooled by that trickery.

The presently “best” theory does not need an interpretation if you follow the philosophy “shut up and calculate”.

Let me answer that question for you: Quantum mechanics is not a theory. It is a mathematical formalism. All the "interpretations" discussion are attempts to develop a theory over the formalism.

Many people believe that the problems of finding a graceful unification of QM and GR are intimately connected to the “interpretation problem” of QM.

I believe the problems have alot to do with how easy it is for well-meaning physicists to fall into mysticism. GR is a theory but QM is not, so the attempts at unification are misguided. First a proper theory, with a propery ontology has to be developed, then unifcation will be easy. Unfortunately, unification will not come from the "main-stream" of Quantum Mechanics.

Many believe they are connected to the Schrödinger cat paradox. Of course, if you are a QBist, then there is no paradox, because everything is in the mind anyway, and all we have is Bayes theorem as the only self-consistent way to update our predictions of our future sensory perceptions. There is no “external reality” in this “interpretation” of QM.

This is all mysticism, including QBism. Besides, you are being unfair to Bayes theorem by linking it so tightly to QBists.

Regarding Boole, I think you are confusing the very well known and basic Boole’s inequality with a simple exercise for the reader somewhere in his huge and not often read book. He gives no solutions to the exercises, there is no instructor’s manual. Not necessary since it is an immediate trivial corollary of the usual “Boole’s inequality”. I think it is a libellous scandal that people should demean J S Bell by supposing that he should have cited an exercise in a 1500 page book from the 19th century, not read by anyone anymore, when the inequality in question is just a trivial elementary probability exercise.

Perhaps you have not read Boole carefully. Yet you hold Pitowsky in high regard.

The important thing is, why would Einstein or Bell have thought it physically reasonable to suppose that those four separate real experiments could be thought of, in theory, as four margins of one bigger experiment? EPR gives a careful motivation.

Einstien did no such thing.

But you have no interest in studying what could be the nature of more fundamental (semi-deterministic?) theories which might underlie QM. Just shut up and calculate. QM works so why bother? It’s a valid point of view... but I think a fundamentally unscientific point of view!

As long as you purport to imply what I have interest in, I don't think you have a clue about that. It is better not to assume. In fact, I agree totally that "shut up and calculate it a fundamentally unscientific point of view"! In addition, I also think that suggestions of so-called "fundamental irreducible randomness" belong in the same category. All poppycock.
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Re: Bell's inequality refuted via elementary algebra

Postby FrediFizzx » Wed Jun 26, 2019 6:54 pm

minkwe wrote:
gill1109 wrote:The presently “best” theory does not need an interpretation if you follow the philosophy “shut up and calculate”.

Let me answer that question for you: Quantum mechanics is not a theory. It is a mathematical formalism. All the "interpretations" discussion are attempts to develop a theory over the formalism.
...


Well, I think it becomes a physical theory when you connect the math to physics. The interpretation should be simply, "Quantum mechanics is about real probability factors for real physical events". Then we don't need the "shut up" part. Just the calculate part.
.
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Wed Jun 26, 2019 8:45 pm

FrediFizzx wrote:
minkwe wrote:
gill1109 wrote:The presently “best” theory does not need an interpretation if you follow the philosophy “shut up and calculate”.

Let me answer that question for you: Quantum mechanics is not a theory. It is a mathematical formalism. All the "interpretations" discussion are attempts to develop a theory over the formalism.

Well, I think it becomes a physical theory when you connect the math to physics. The interpretation should be simply, "Quantum mechanics is about real probability factors for real physical events". Then we don't need the "shut up" part. Just the calculate part.
.

I agree, Fred! That's my point of view, too. And we can remove the paradoxes by adopting Slava Belavkin's "eventum mechanics". It seamlessly merges conventional "unitary QM" with the Born rule, making the latter a *consequence*, not an uncomfortable *add-on*.

Eventum mechanics is simply an enhancement of the usual formalism which makes sense, instead of non-sense.

It's a great slogan:
FrediFizzx wrote:"Quantum mechanics is about real probability factors for real physical events"!

Real probability factors are what I would call "irreducible randomness".
Last edited by gill1109 on Wed Jun 26, 2019 9:14 pm, edited 2 times in total.
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Wed Jun 26, 2019 9:08 pm

minkwe wrote:
gill1109 wrote:I wrote a vague statement here for the sake of brevity but others have written precise mathematical statements, and proven precise mathematical theorems. ... Do you want me to give some references?

Please proceed, remember we are looking for precise mathematical theorems proving that Bell's apples are the same as Quantum oranges. There is a tendency to produce apples when oranges are requested, and oranges when apples are requested. I won't be fooled by that trickery.

The presently “best” theory does not need an interpretation if you follow the philosophy “shut up and calculate”.

Let me answer that question for you: Quantum mechanics is not a theory. It is a mathematical formalism. All the "interpretations" discussion are attempts to develop a theory over the formalism.

Many people believe that the problems of finding a graceful unification of QM and GR are intimately connected to the “interpretation problem” of QM.

I believe the problems have a lot to do with how easy it is for well-meaning physicists to fall into mysticism. GR is a theory but QM is not, so the attempts at unification are misguided. First, a proper theory, with a proper ontology has to be developed, then unification will be easy. Unfortunately, unification will not come from the "main-stream" of Quantum Mechanics.

Many believe they are connected to the Schrödinger cat paradox. Of course, if you are a QBist, then there is no paradox, because everything is in the mind anyway, and all we have is Bayes theorem as the only self-consistent way to update our predictions of our future sensory perceptions. There is no “external reality” in this “interpretation” of QM.

This is all mysticism, including QBism. Besides, you are being unfair to Bayes theorem by linking it so tightly to QBists.

Regarding Boole, I think you are confusing the very well known and basic Boole’s inequality with a simple exercise for the reader somewhere in his huge and not often read book. He gives no solutions to the exercises, there is no instructor’s manual. Not necessary since it is an immediate trivial corollary of the usual “Boole’s inequality”. I think it is a libellous scandal that people should demean J S Bell by supposing that he should have cited an exercise in a 1500 page book from the 19th century, not read by anyone anymore when the inequality in question is just a trivial elementary probability exercise.

Perhaps you have not read Boole carefully. Yet you hold Pitowsky in high regard.

The important thing is, why would Einstein or Bell have thought it physically reasonable to suppose that those four separate real experiments could be thought of, in theory, as four margins of one bigger experiment? EPR gives a careful motivation.

Einstein did no such thing.

But you have no interest in studying what could be the nature of more fundamental (semi-deterministic?) theories which might underlie QM. Just shut up and calculate. QM works so why bother? It’s a valid point of view... but I think a fundamentally unscientific point of view!

As long as you purport to imply what I have interest in, I don't think you have a clue about that. It is better not to assume. In fact, I agree totally that "shut up and calculate it a fundamentally unscientific point of view"! In addition, I also think that suggestions of so-called "fundamental irreducible randomness" belong in the same category. All poppycock.

EPR considers four experiments concerning two separate particles: one in which Q and Q are measured. One in which Q and P are measured. One in which P and Q is measured. One in which P and P are measured. They argue from physical principles that those four experiments are strongly connected to one another at the level of individual outcomes. Add symbols a, b for Alice and Bob. Then EPR argue that the four actual possible experiments

"measure Qa, Qb"
"measure Qa, Pb"
"measure Pa, Qb"
"measure Pa, Pb"

are "reflections" of a not-directly observable reality in which

"Qa, Qb, Pa, Pb" all exist and, moreover get observed if any are measured"

Read some of the QBism work by Chris Fuchs and many others to find out why Qbism is called Qbism. They "immerse" the rules of conventional QM in the de Finetti approach to probability theory in which the laws of probability including Bayes theorem are derived from axioms of rational behaviour of an agent who has to make decisions in the face of uncertainty.

They have an interpretation of probability theory, and then consistently interpret QM from within that point of view.

I agree entirely with your statement "GR is a theory but QM is not, so the attempts at unification are misguided. First, a proper theory, with a proper ontology has to be developed, then unification will be easy. Unfortunately, unification will not come from the "main-stream" of Quantum Mechanics."

I have read the publications of Bell, Boole, Pitowsky and many others very very carefully.

I am not looking for precise mathematical theorems proving that Bell's apples are the same as Quantum oranges. Precise theorems already exist, nobody disagrees with the mathematics, and they do not do what you suggest they do; they do something a little bit more subtle. With all due respect, I humbly suggest that you might be jumping to preconceived conclusions. Are you interested in references?
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Re: Bell's inequality refuted via elementary algebra

Postby FrediFizzx » Wed Jun 26, 2019 10:01 pm

gill1109 wrote:It's a great slogan:
FrediFizzx wrote:"Quantum mechanics is about real probability factors for real physical events"!

Real probability factors are what I would call "irreducible randomness".

Hmm... randomness that we can't reduce. I don't think probability factors are always necessarily about randomness. They can simply be about the lack of knowledge about certain processes.
.
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Wed Jun 26, 2019 11:27 pm

FrediFizzx wrote:
gill1109 wrote:It's a great slogan:
FrediFizzx wrote:"Quantum mechanics is about real probability factors for real physical events"!

Real probability factors are what I would call "irreducible randomness".

Hmm... randomness that we can't reduce. I don't think probability factors are always necessarily about randomness. They can simply be about the lack of knowledge about certain processes.
.

Ah ha well that I think is the interesting question.

Lack of knowledge <-> hidden variables
Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)
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Re: Bell's inequality refuted via elementary algebra

Postby Joy Christian » Thu Jun 27, 2019 1:24 am

gill1109 wrote:
Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)

Irreducible randomness <-> unjustified mysticism that has no place in any self-respecting science. Moreover, I have demonstrated it to be entirely unnecessary in fundamental physics.

***
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Re: Bell's inequality refuted via elementary algebra

Postby Heinera » Thu Jun 27, 2019 2:05 am

Joy Christian wrote:
gill1109 wrote:
Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)

Irreducible randomness <-> unjustified mysticism that has no place in any self-respecting science. Moreover, I have demonstrated it to be entirely unnecessary in fundamental physics.

***

What is the "coin flip" in your model then?
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Re: Bell's inequality refuted via elementary algebra

Postby Joy Christian » Thu Jun 27, 2019 2:35 am

Heinera wrote:
Joy Christian wrote:
gill1109 wrote:
Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)

Irreducible randomness <-> unjustified mysticism that has no place in any self-respecting science. Moreover, I have demonstrated it to be entirely unnecessary in fundamental physics.

***

What is the "coin flip" in your model then?

It is a classic and simplest possible example of reducible randomness. It exhibits epistemic randomness, not an ontological one. It embodies the fundamental determinism of nature.

***
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Thu Jun 27, 2019 4:32 am

Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:
gill1109 wrote:Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)

Irreducible randomness <-> unjustified mysticism that has no place in any self-respecting science. Moreover, I have demonstrated it to be entirely unnecessary in fundamental physics.

What is the "coin flip" in your model then?

It is a classic and simplest possible example of reducible randomness. It exhibits epistemic randomness, not an ontological one. It embodies the fundamental determinism of nature.

In Joy's model, all the randomness is determined by which side a fair coin has fallen, which was tossed in advance of doing any measurements at all. The randomness of the measurement outcomes is totally determined by that single hidden outcome, which we don't know in advance: whether the coin fell head or tails. Trouble is, that in that case, if we repeatedly do one measurement on a new pair of "spin half" particles, with Stern-Gerlach devices aligned to a suitable pair of angles, then the experimenters actually observe four different outcomes: (up, up), (up, down), (down, up) and (down, down) and moreover the four probabilities are generally not equal to 0, 1/2 or 1. So no way that each pair of particles had its own fair coin toss determine which of the four possibilities actually determine what happened, by the same deterministic rule.
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Re: Bell's inequality refuted via elementary algebra

Postby minkwe » Thu Jun 27, 2019 6:53 am

gill1109 wrote:The important thing is, why would Einstein or Bell have thought it physically reasonable to suppose that those four separate real experiments could be thought of, in theory, as four margins of one bigger experiment? EPR gives a careful motivation.

gill1109 wrote:EPR considers four experiments concerning two separate particles: one in which Q and Q are measured. One in which Q and P are measured. One in which P and Q is measured. One in which P and P are measured. They argue from physical principles that those four experiments are strongly connected to one another at the level of individual outcomes. Add symbols a, b for Alice and Bob. Then EPR argue that the four actual possible experiments

"measure Qa, Qb"
"measure Qa, Pb"
"measure Pa, Qb"
"measure Pa, Pb"

are "reflections" of a not-directly observable reality in which

"Qa, Qb, Pa, Pb" all exist and, moreover get observed if any are measured"

You are starting to play word games again. Provide a reference where Einstein considered that "four separate real experiments could be thought of, [b]in theory, as four margins of one bigger experiment". Be careful now, it is not enough to show that Einstein considered four separate experiments!
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Re: Bell's inequality refuted via elementary algebra

Postby gill1109 » Thu Jun 27, 2019 7:56 am

minkwe wrote:
gill1109 wrote:The important thing is, why would Einstein or Bell have thought it physically reasonable to suppose that those four separate real experiments could be thought of, in theory, as four margins of one bigger experiment? EPR gives a careful motivation.

gill1109 wrote:EPR considers four experiments concerning two separate particles: one in which Q and Q are measured. One in which Q and P are measured. One in which P and Q is measured. One in which P and P are measured. They argue from physical principles that those four experiments are strongly connected to one another at the level of individual outcomes. Add symbols a, b for Alice and Bob. Then EPR argue that the four actual possible experiments

"measure Qa, Qb"
"measure Qa, Pb"
"measure Pa, Qb"
"measure Pa, Pb"

are "reflections" of a not-directly observable reality in which

"Qa, Qb, Pa, Pb" all exist and, moreover get observed if any are measured"

You are starting to play word games again. Provide a reference where Einstein considered that "four separate real experiments could be thought of, [b]in theory, as four margins of one bigger experiment". Be careful now, it is not enough to show that Einstein considered four separate experiments!


Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
A. Einstein, B. Podolsky, and N. Rosen
Phys. Rev. 47, 777 – Published 15 May 1935

https://journals.aps.org/pr/abstract/10 ... Rev.47.777

Thus, by measuring either A [momentum of the first particle] or B [position of the first particle] we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the quantity P [momentum of the second particle] (that is p_k) or the value of the quantity Q [position of the second particle] (that is q_r). In accordance with our criterion of reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality.


In my notation, EPR establish the simultaneous existence of values of four variables Qa, Qb, Pa, Pb and show that measuring Q or P on either particle would simply reveal the values which already exist "within the whole system". They don't do this explicitly, only implicitly, by considering the simultaneous measurement of Qa and Qb, and alternatively of the simultaneous measurement of Pa and Pb. But my "extension" of what they did say is direct and trivial and well known (and uncontroversial). No further thinking is required.
Last edited by gill1109 on Thu Jun 27, 2019 8:16 am, edited 2 times in total.
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