Sign mistake in the GHZ variant of Bell's theorem

[Joy Christian]

.
A popular variant of Bell’s theorem by Greenberger, Horne, and Zeilinger (GHZ, 1990) claimed that the premisses of the argument by Einstein, Podolsky, and Rosen (EPR, 1935) are inconsistent for systems of more than two particles in entangled quantum states. In the following new comment paper,

https://doi.org/10.48550/arXiv.2408.10256 ,

I point out a sign mistake in the argument by GHZ, invalidating their claim of inconsistency in the EPR program for completing quantum mechanics.

Incidentally, Zeilinger was one of the recipients of the 2022 Nobel Prize in physics. No one is infallible in physics.
.

[FrediFizzx]

.
A popular variant of Bell’s theorem by Greenberger, Horne, and Zeilinger (GHZ, 1990) claimed that the premisses of the argument by Einstein, Podolsky, and Rosen (EPR, 1935) are inconsistent for systems of more than two particles in entangled quantum states. In the following new comment paper,

https://doi.org/10.48550/arXiv.2408.10256 ,

I point out a sign mistake in the argument by GHZ, invalidating their claim of inconsistency in the EPR program for completing quantum mechanics.

Incidentally, Zeilinger was one of the recipients of the 2022 Nobel Prize in physics. No one is infallible in physics.

Yeah, those guys probably screwed up but it doesn't matter anyways. The notion that quantum mechanics is incomplete and that hidden variables complete it is total nonsense. The incorporation of topology into the relevant calculations proves that it is nonsense.
.

[FrediFizzx]

.
A popular variant of Bell’s theorem by Greenberger, Horne, and Zeilinger (GHZ, 1990) claimed that the premisses of the argument by Einstein, Podolsky, and Rosen (EPR, 1935) are inconsistent for systems of more than two particles in entangled quantum states. In the following new comment paper,

https://doi.org/10.48550/arXiv.2408.10256 ,

I point out a sign mistake in the argument by GHZ, invalidating their claim of inconsistency in the EPR program for completing quantum mechanics.

Incidentally, Zeilinger was one of the recipients of the 2022 Nobel Prize in physics. No one is infallible in physics.

Yeah, those guys probably screwed up but it doesn't matter anyways. The notion that quantum mechanics is incomplete and that hidden variables complete it is total nonsense. The incorporation of topology into the relevant calculations proves that it is nonsense.

What this means is that Bell's junk theory and this junk GHZ theory are completely irrelevant since they include hidden variables. It doesn't take hidden variables to prove Nature is local.
.

[FrediFizzx]

It is pretty unbelievable that a genius like Einstein got sucked into the hidden variable nonsense but then along comes another genius, Bell, and makes it worse by also getting sucked into it.
.

[Joy Christian]

It is pretty unbelievable that a genius like Einstein got sucked into the hidden variable nonsense but then along comes another genius, Bell, and makes it worse by also getting sucked into it.
.

Einstein never mentioned "hidden variables" anywhere in his writings. He didn't like Bohm's hidden variable theory and called it "cheap." The phrase "hidden variable" became popular later, especially after the pioneering work by von Neumann in 1932, but his treatment concerns dispersion-free states that do not necessarily involve hidden variables. In any case, I am perfectly happy with hidden variables since the 3-sphere model is a hidden variable model. The first successful "hidden variable theory" was statistical mechanics that explained thermodynamical behavior (such as Brownian motion) in terms of microstates.

That quantum mechanics is an incomplete theory of objective reality was first demonstrated by Einstein, Podolsky, and Rosen in 1935 without mentioning hidden variables or dispersion-free states. It is a logically impeccable argument. There is no way out of the fact that quantum mechanics is "incomplete."
.

[FrediFizzx]

It is pretty unbelievable that a genius like Einstein got sucked into the hidden variable nonsense but then along comes another genius, Bell, and makes it worse by also getting sucked into it.
.

Einstein never mentioned "hidden variables" anywhere in his writings. He didn't like Bohm's hidden variable theory and called it "cheap." The phrase "hidden variable" became popular later, especially after the pioneering work by von Neumann in 1932, but his treatment concerns dispersion-free states that do not necessarily involve hidden variables. In any case, I am perfectly happy with hidden variables since the 3-sphere model is a hidden variable model. The first successful "hidden variable theory" was statistical mechanics that explained thermodynamical behavior (such as Brownian motion) in terms of microstates.

That quantum mechanics is an incomplete theory of objective reality was first demonstrated by Einstein, Podolsky, and Rosen in 1935 without mentioning hidden variables or dispersion-free states. It is a logically impeccable argument. There is no way out of the fact that quantum mechanics is "incomplete."

"Einstein famously referred to the phenomenon of quantum entanglement as “spooky action at a distance,” suggesting that hidden variables must be at work to explain how information about one particle could instantaneously affect another particle, even if they were light-years apart."

https://scienceworld.wolfram.com/physic ... ables.html

It doesn't matter if QM is complete or not, Classical mechanics is probably incomplete also. Together they give a good description of Nature.

What is a hidden variable in the 3-sphere model?
.

[Joy Christian]

It is pretty unbelievable that a genius like Einstein got sucked into the hidden variable nonsense but then along comes another genius, Bell, and makes it worse by also getting sucked into it.
.

Einstein never mentioned "hidden variables" anywhere in his writings. He didn't like Bohm's hidden variable theory and called it "cheap." The phrase "hidden variable" became popular later, especially after the pioneering work by von Neumann in 1932, but his treatment concerns dispersion-free states that do not necessarily involve hidden variables. In any case, I am perfectly happy with hidden variables since the 3-sphere model is a hidden variable model. The first successful "hidden variable theory" was statistical mechanics that explained thermodynamical behavior (such as Brownian motion) in terms of microstates.

That quantum mechanics is an incomplete theory of objective reality was first demonstrated by Einstein, Podolsky, and Rosen in 1935 without mentioning hidden variables or dispersion-free states. It is a logically impeccable argument. There is no way out of the fact that quantum mechanics is "incomplete."

"Einstein famously referred to the phenomenon of quantum entanglement as “spooky action at a distance,” suggesting that hidden variables must be at work to explain how information about one particle could instantaneously affect another particle, even if they were light-years apart."

https://scienceworld.wolfram.com/physic ... ables.html

It doesn't matter if QM is complete or not, Classical mechanics is probably incomplete also. Together they give a good description of Nature.

What is a hidden variable in the 3-sphere model?
.

Wolfram does not know what he is talking about. Einstein never used the words "hidden variables", ever, in his writings. This is quite well known.

I am not answering your question about the hidden variable in the 3-sphere model again. We have discussed it at length before and we disagree.
.

[FrediFizzx]

Einstein never mentioned "hidden variables" anywhere in his writings. He didn't like Bohm's hidden variable theory and called it "cheap." The phrase "hidden variable" became popular later, especially after the pioneering work by von Neumann in 1932, but his treatment concerns dispersion-free states that do not necessarily involve hidden variables. In any case, I am perfectly happy with hidden variables since the 3-sphere model is a hidden variable model. The first successful "hidden variable theory" was statistical mechanics that explained thermodynamical behavior (such as Brownian motion) in terms of microstates.

That quantum mechanics is an incomplete theory of objective reality was first demonstrated by Einstein, Podolsky, and Rosen in 1935 without mentioning hidden variables or dispersion-free states. It is a logically impeccable argument. There is no way out of the fact that quantum mechanics is "incomplete."

"Einstein famously referred to the phenomenon of quantum entanglement as “spooky action at a distance,” suggesting that hidden variables must be at work to explain how information about one particle could instantaneously affect another particle, even if they were light-years apart."

https://scienceworld.wolfram.com/physic ... ables.html

It doesn't matter if QM is complete or not, Classical mechanics is probably incomplete also. Together they give a good description of Nature.

What is a hidden variable in the 3-sphere model?

Wolfram does not know what he is talking about. Einstein never used the words "hidden variables", ever, in his writings. This is quite well known.

I am not answering your question about the hidden variable in the 3-sphere model again. We have discussed it at length before and we disagree.

Well, it doesn't have to be in Einstein's writings. It could be in a discussion with someone else. They do give a reference on the Wolfram site so I doubt that they are wrong about it.

Ok, so the 3-sphere model is not really a hidden variable model. You are just making stuff up about that.
.

[FrediFizzx]

Here are some more references from Copilot,

Certainly! Here are some additional references about Einstein's views on hidden variables:

1. **Wikipedia**: The [Hidden-variable theory](https://en.wikipedia.org/wiki/Hidden-variable_theory) article provides a comprehensive overview of hidden variables in quantum mechanics, including Einstein's contributions and the famous EPR paper¹.

2. **Physics LibreTexts**: The section on [Hidden Variables, the Bell Theorem, and Local Reality](https://phys.libretexts.org/Bookshelves ... al_Reality) discusses the historical debate between Einstein and Niels Bohr, as well as John Bell's contributions².

3. **Wolfram ScienceWorld**: This article on [Hidden Variables](https://scienceworld.wolfram.com/physic ... ables.html) explains Einstein's concept of "spooky action at a distance" and his belief in hidden variables³.

4. **Academia.edu**: The paper on [The Discovery Of Einstein's Nonlocal Hidden Variables](https://www.academia.edu/31258693/The_D ... _Selection) explores Einstein's ideas and their implications⁴.

5. **Oxford Handbook of the History of Quantum Mechanics**: This resource provides a detailed account of Einstein's presentation of a hidden variable theory at the 1927 meeting of the Prussian Academy of Sciences⁵.

I hope you find these references helpful! If you have any more questions or need further information, feel free to ask.

Source: Conversation with Copilot, 8/25/2024
(1) Hidden-variable theory - Wikipedia. https://en.wikipedia.org/wiki/Hidden-variable_theory.
(2) 10.3: Hidden Variables, the Bell Theorem, and Local Reality. https://phys.libretexts.org/Bookshelves ... al_Reality.
(3) Hidden Variables -- from Eric Weisstein's World of Physics - Wolfram. https://scienceworld.wolfram.com/physic ... ables.html.
(4) The Discovery Of Einstein's Nonlocal Hidden Variables - Academia.edu. https://www.academia.edu/31258693/The_D ... _Selection.
(5) Hidden Variables | The Oxford Handbook of the History of Quantum .... https://academic.oup.com/edited-volume/ ... /364218615.

[Joy Christian]

.
Garbage produced by copy-a-lot. But even that genius AI bot cannot find a direct quote from Einstein using the words "hidden variables."

No AI bot can rival my 40 years of expert knowledge in the foundations of quantum mechanics. Surely, you, of all people, know that.
.

[FrediFizzx]

.
Garbage produced by copy-a-lot. But even that genius AI bot cannot find a direct quote from Einstein using the words "hidden variables."

No AI bot can rival my 40 years of expert knowledge in the foundations of quantum mechanics. Surely, you, of all people, know that.

LOL! "5. **Oxford Handbook of the History of Quantum Mechanics**: This resource provides a detailed account of Einstein's presentation of a hidden variable theory at the 1927 meeting of the Prussian Academy of Sciences⁵." Which he sub-sequentially withdrew. Probably realized it was a bunch of nonsense. You will eventually realize that also. You just have to give up some of your stubborn notions.
.

[Joy Christian]

.
Garbage produced by copy-a-lot. But even that genius AI bot cannot find a direct quote from Einstein using the words "hidden variables."

No AI bot can rival my 40 years of expert knowledge in the foundations of quantum mechanics. Surely, you, of all people, know that.

LOL! "5. **Oxford Handbook of the History of Quantum Mechanics**: This resource provides a detailed account of Einstein's presentation of a hidden variable theory at the 1927 meeting of the Prussian Academy of Sciences⁵." Which he sub-sequentially withdrew. Probably realized it was a bunch of nonsense. You will eventually realize that also. You just have to give up some of your stubborn notions.
.

Ok. So, quote Einstein's exact words from that source that include the phrase "hidden variables." I claim that he never used those words, ever.

In any case, I have no problem with hidden variables, and no intention to give them up.
.

[FrediFizzx]

.
Garbage produced by copy-a-lot. But even that genius AI bot cannot find a direct quote from Einstein using the words "hidden variables."

No AI bot can rival my 40 years of expert knowledge in the foundations of quantum mechanics. Surely, you, of all people, know that.

LOL! "5. **Oxford Handbook of the History of Quantum Mechanics**: This resource provides a detailed account of Einstein's presentation of a hidden variable theory at the 1927 meeting of the Prussian Academy of Sciences⁵." Which he sub-sequentially withdrew. Probably realized it was a bunch of nonsense. You will eventually realize that also. You just have to give up some of your stubborn notions.
.

Ok. So, quote Einstein's exact words from that source that include the phrase "hidden variables." I claim that he never used those words, ever.

In any case, I have no problem with hidden variables, and no intention to give them up.

Double LOL! You just don't "get it" at all do you? Still clinging to stubborn notions. It doesn't matter if he never used those words. He obviously knew about it if he presented a hidden variable theory! Apparently, he quickly realized it was nonsense. And..., you will eventually realize it is pure nonsense. Probably will take a while though.
.

[Joy Christian]

LOL! "5. **Oxford Handbook of the History of Quantum Mechanics**: This resource provides a detailed account of Einstein's presentation of a hidden variable theory at the 1927 meeting of the Prussian Academy of Sciences⁵." Which he sub-sequentially withdrew. Probably realized it was a bunch of nonsense. You will eventually realize that also. You just have to give up some of your stubborn notions.
.

Ok. So, quote Einstein's exact words from that source that include the phrase "hidden variables." I claim that he never used those words, ever.

In any case, I have no problem with hidden variables, and no intention to give them up.

Double LOL! You just don't "get it" at all do you? Still clinging to stubborn notions. It doesn't matter if he never used those words. He obviously knew about it if he presented a hidden variable theory! Apparently, he quickly realized it was nonsense. And..., you will eventually realize it is pure nonsense. Probably will take a while though.
.

Yes, it does not matter what Einstein did in 1927. Those were very early days so whatever he did was quite crude. We now have a much more sophisticated understanding of what "hidden variables" means after the pioneering works of von Neumann, Bell, Kochen and Specker, and many others. These works put the initial hunch of Einstein, Podolsky, and Rosen (1935) regarding the incompleteness of quantum mechanics on a much sharper footing. These works guide us in completing quantum mechanics precisely, without stumbling on many pitfalls along the way. The 3-sphere model is a major advance in this direction.
.

[FrediFizzx]

LOL! Who said that quantum mechanics had to be completed or need to be completed? In fact, the title of EPR is a ridiculous question, "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?"

The 3-sphere model does give us an understanding of how the correlations happen but it does it without any hidden variables. QM knows about all the variables. You are only fooling yourself about hidden variables.
.

[FrediFizzx]

"In quantum physics, a **hidden variable** refers to an underlying deterministic factor that is not accounted for in the standard quantum mechanics framework. The idea is that the probabilistic nature of quantum mechanics could be explained by these hidden variables, which determine the outcomes of quantum events in a predictable way."

Does anyone disagree with this definition of hidden variable?

[Joy Christian]

"In quantum physics, a **hidden variable** refers to an underlying deterministic factor that is not accounted for in the standard quantum mechanics framework. The idea is that the probabilistic nature of quantum mechanics could be explained by these hidden variables, which determine the outcomes of quantum events in a predictable way."

Does anyone disagree with this definition of hidden variable?

Correct but quite a vague definition. I have a mathematically precise definition of what is meant by "hidden variables" in Section II of this paper.
.

[FrediFizzx]

"In quantum physics, a **hidden variable** refers to an underlying deterministic factor that is not accounted for in the standard quantum mechanics framework. The idea is that the probabilistic nature of quantum mechanics could be explained by these hidden variables, which determine the outcomes of quantum events in a predictable way."

Does anyone disagree with this definition of hidden variable?

Correct but quite a vague definition. I have a mathematically precise definition of what is meant by "hidden variables" in Section II of this paper.

Oh boy, you really got sucked into the hidden variable nonsense big time! However, I didn't find any math expression for what lambda is equal to.
.

[Joy Christian]

"In quantum physics, a **hidden variable** refers to an underlying deterministic factor that is not accounted for in the standard quantum mechanics framework. The idea is that the probabilistic nature of quantum mechanics could be explained by these hidden variables, which determine the outcomes of quantum events in a predictable way."

Does anyone disagree with this definition of hidden variable?

Correct but quite a vague definition. I have a mathematically precise definition of what is meant by "hidden variables" in Section II of this paper.

Oh boy, you really got sucked into the hidden variable nonsense big time! However, I didn't find any math expression for what lambda is equal to.
.

Lambda is anything you like. It can be a single variable, a function of many variables, or a set of functions of many variables. Whatever you like.
.

[FrediFizzx]

Sorry, lambda can't be anything. It can't be a "factor that is accounted for in the standard quantum mechanics framework."

So, not really a precise mathematical definition.
.