Bell's Theorem Begs the Question

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Expand view Topic review: Bell's Theorem Begs the Question

Re: Bell's Theorem Begs the Question

by Joy Christian » Mon Jan 29, 2024 6:46 pm

FrediFizzx wrote: Mon Jan 29, 2024 12:34 pm
Joy Christian wrote: Sat Jan 27, 2024 7:49 am
FrediFizzx wrote: Sat Jan 27, 2024 7:28 am
Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.
Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.
Sure, that is obvious so really no need for the sub 1 and 2. So, we have a Pauli vector interacting with a direction vector. Seems screwy as we don't get a cross product (a x sigma).

Why is lambda all of a sudden appearing in eq. (16)?
The eigenvalues omega are determined by lambda in Bell's proof. The discussion in Section III is a continuation of the discussion in Section II.
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Re: Bell's Theorem Begs the Question

by FrediFizzx » Mon Jan 29, 2024 12:34 pm

Joy Christian wrote: Sat Jan 27, 2024 7:49 am
FrediFizzx wrote: Sat Jan 27, 2024 7:28 am
Joy Christian wrote: Fri Jan 26, 2024 1:01 pm
sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.
Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.
Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.
Sure, that is obvious so really no need for the sub 1 and 2. So, we have a Pauli vector interacting with a direction vector. Seems screwy as we don't get a cross product (a x sigma).

Why is lambda all of a sudden appearing in eq. (16)?
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Sat Jan 27, 2024 7:49 am

FrediFizzx wrote: Sat Jan 27, 2024 7:28 am
Joy Christian wrote: Fri Jan 26, 2024 1:01 pm
FrediFizzx wrote: Fri Jan 26, 2024 12:06 pm
Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?
sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.
Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.
Because, while mathematically the same, they belong to two different spins, or particles, arriving at the spacelike separated observation stations 1 and 2.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Sat Jan 27, 2024 7:28 am

Joy Christian wrote: Fri Jan 26, 2024 1:01 pm
FrediFizzx wrote: Fri Jan 26, 2024 12:06 pm
Joy Christian wrote: Fri Jan 26, 2024 9:50 am
Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.
Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?
sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.
Why bother with the 1 and 2 designations? They are exactly the same and eq. (15) is a matrix.
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Fri Jan 26, 2024 1:01 pm

FrediFizzx wrote: Fri Jan 26, 2024 12:06 pm
Joy Christian wrote: Fri Jan 26, 2024 9:50 am
FrediFizzx wrote: Fri Jan 26, 2024 8:57 am
After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.
Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.
Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?
sigma_1 and sigma_2 represent spins at the two observation stations 1 and 2 at the two ends of the experiment.

The spins in quantum mechanics are not represented by ordinary vectors like k but by Pauli matrices, such as sigma_1 and sigma_2.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Fri Jan 26, 2024 12:06 pm

Joy Christian wrote: Fri Jan 26, 2024 9:50 am
FrediFizzx wrote: Fri Jan 26, 2024 8:57 am
Joy Christian wrote: Wed Jan 24, 2024 6:32 pm .
I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be. :D

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.
After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.
Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.
Ok, you're welcome. Now, I don't quite understand eq. (15). What do sigma_1 and sigma_2 represent?
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Fri Jan 26, 2024 9:50 am

FrediFizzx wrote: Fri Jan 26, 2024 8:57 am
Joy Christian wrote: Wed Jan 24, 2024 6:32 pm .
I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be. :D

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.
After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.
Thanks! Yes, k is a unit spin vector with arbitrary direction and a unit magnitude.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Fri Jan 26, 2024 8:57 am

Joy Christian wrote: Wed Jan 24, 2024 6:32 pm .
I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be. :D

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.
After eq. (13) you say "...where k is an arbitrary unit vector...". k is the spin vector of the particles so not exactly arbitrary. The direction of k is arbitrary. You might want to make that more clear.
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Wed Jan 24, 2024 6:32 pm

.
I have revised this paper on arXiv. In a new appendix, I show that quantum mechanics is not as mysterious as it is made out to be. :D

https://doi.org/10.48550/arXiv.2302.09519

I prove that Ehrenfest’s equation in quantum mechanics, derived from Schrödinger’s equation, is equal to an ensemble average of classical Hamiltonian equations of motion over a probability distribution of unknown or hidden variables. Heisenberg’s uncertainty relations can also be understood similarly for dispersion-free states formalized by von Neumann.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Sat Aug 26, 2023 11:42 am

The "hidden variables" saga gets even stranger... EPR was claiming that quantum mechanics is incomplete so it needs hidden variables to complete it. So, why did Bell put hidden variables on a classical mechanics scenario? He did it backwards!!!! :mrgreen:
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Re: Bell's Theorem Begs the Question

by FrediFizzx » Tue Aug 22, 2023 2:21 pm

Joy Christian wrote: Tue Aug 22, 2023 11:02 am
FrediFizzx wrote: Tue Aug 22, 2023 10:43 am
FrediFizzx wrote: Wed Aug 02, 2023 10:33 am
Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves. :D
And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.
I think by hidden variable you mean something else than what is usually meant by it. I think you mean the orientation "lambda" of the old version of the 3-sphere model. But the symbol "lambda" is not of any significance for the general meaning of the hidden variable. In the latest version of the 3-sphere model, the hidden variable is the direction s1 = s2 = s of the axis about which the spins L1 and L2 are rotating. So the model is based on a statistical distribution of the direction s1 = s2 = s of the spin initially emerging from the source. But that direction is precisely what Bell used in his local model. What we have symbolized as s1 = s2 = s is what Bell symbolized as vector lambda in the local model he presented in Section 3 of his 1964 paper. So there is indeed a hidden variable even in the latest version of the 3-sphere model. But it is symbolized as s1 = s2 = s rather than as vector lambda.

But you are right about entanglement. It is not a fundamental feature of Nature. It is just a placeholder for correlations. It is not at all mysterious.
Well, quantum mechanics knows about the singlet vector, s, and s1 and s2. So, I'm not sure how that would be classified as hidden. Let's see if we can find an agreeable definition of hidden variable... Boy! That was pretty unsatisfying! "Possibly unobservable" is maybe the best. Other descriptions don't have the variable all that hidden. Anyways, s, s1 and s2 can be used in both classical and quantum mechanics solutions for the correlations so let's not count them as hidden variables. So, I stand by the fact that hidden variables as far as the EPR scenario goes is a bunch of junk physics.

But we still have the strong correlations predicted by both classical and quantum mechanics and no need for hidden variables. Now..., how about superposition?
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Tue Aug 22, 2023 11:02 am

FrediFizzx wrote: Tue Aug 22, 2023 10:43 am
FrediFizzx wrote: Wed Aug 02, 2023 10:33 am
Joy Christian wrote: Tue Aug 01, 2023 7:02 pm .
I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:
Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves. :D
And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.
.
I think by hidden variable you mean something else than what is usually meant by it. I think you mean the orientation "lambda" of the old version of the 3-sphere model. But the symbol "lambda" is not of any significance for the general meaning of the hidden variable. In the latest version of the 3-sphere model, the hidden variable is the direction s1 = s2 = s of the axis about which the spins L1 and L2 are rotating. So the model is based on a statistical distribution of the direction s1 = s2 = s of the spin initially emerging from the source. But that direction is precisely what Bell used in his local model. What we have symbolized as s1 = s2 = s is what Bell symbolized as vector lambda in the local model he presented in Section 3 of his 1964 paper. So there is indeed a hidden variable even in the latest version of the 3-sphere model. But it is symbolized as s1 = s2 = s rather than as vector lambda.

But you are right about entanglement. It is not a fundamental feature of Nature. It is just a placeholder for correlations. It is not at all mysterious.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Tue Aug 22, 2023 10:43 am

FrediFizzx wrote: Wed Aug 02, 2023 10:33 am
Joy Christian wrote: Tue Aug 01, 2023 7:02 pm .
I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.
Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves. :D
And..., we sort of got tricked ourselves by "hidden variables". So, what exactly does this mean for the foundation of quantum mechanics? It looks like to me that "entanglement" is explained by both classical and quantum mechanics so it is not a property of quantum mechanics. It simply reduces down to opposite angular momentum.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Wed Aug 02, 2023 10:33 am

Joy Christian wrote: Tue Aug 01, 2023 7:02 pm .
I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.
Well, the whole problem is "hidden variables" to begin with. Classical mechanics can predict the same as quantum mechanics by using 3 or 7-sphere topology for the EPR scenario. No hidden variables are needed. Bell got tricked by von Neumann. And a whole bunch of idiots got tricked by Bell and themselves. :D
.

Re: Bell's Theorem Begs the Question

by Joy Christian » Tue Aug 01, 2023 7:02 pm

.
I have updated this paper again, with a significantly improved presentation: https://doi.org/10.48550/arXiv.2302.09519

The abstract now reads:
I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with.
.

Re: Bell's Theorem Begs the Question

by FrediFizzx » Thu Jul 20, 2023 10:58 am

"Hidden variables" are a red herring. Bell screwed up.

Re: Bell's Theorem Begs the Question

by Joy Christian » Thu Jul 20, 2023 2:32 am

Dirkman2 wrote: Wed Jul 19, 2023 8:56 pm Sabine Hossenfelder, in her 9th of July youtube video about Bell, said that the conclusion is we can either have a) or b), and the nobel was actually awarded for proving that we have either a) or b)

a)measurement independence=>violation of local causality
b)local causality=>violation of measurement independence
Sabine is a friend of mine, but I do not agree with her on this point. She, like 't Hooft, is a proponent of what is usually referred to as "superdeterminism", which amounts to assuming a "violation of statistical independence." Sabine has now invented a new name for "statistical independence" and calls it "measurement independence." That is a rhetorical trick. But "What's in a name? That which we call a rose by any other name would smell as sweet." :)

Whatever we call it, mathematically "measurement independence" means the following condition on the probability distribution:

p(h | a, b) = p(h),

where "h" stands for "hidden variables" (which I prefer to call "the initial state of the system"), "a" and "b" are the experimental settings, and p(h) is the probability distribution of the hidden variables (or the initial states) "h".

Unless Sabine allows violation of the above condition assumed by Bell, she cannot do her superdeterminism stuff. Indeed, Bell inequalities are derived assuming p(h | a, b) = p(h) explicitly. So Sabine wants to abandon this condition. And voila, Bell inequalities can no longer be derived!

That sounds pretty innocent but it is not. Because a violation of the above condition introduces a subtle form of non-locality. This is very well known. So, by violating "measurement independence" Sabine violates local causality after all. She has not got rid of the problem --- just renamed it. Sorry, Sabine. :)
.

Re: Bell's Theorem Begs the Question

by Dirkman2 » Wed Jul 19, 2023 8:56 pm

Sabine Hossenfelder, in her 9th of July youtube video about Bell, said that the conclusion is we can either have a) or b), and the nobel was actually awarded for proving that we have either a) or b)

a)measurement independence=>violation of local causality
b)local causality=>violation of measurement independence

Re: Bell's Theorem Begs the Question

by Joy Christian » Sun Jun 11, 2023 11:58 pm

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Here is a slightly revised version of my paper: https://doi.org/10.48550/arXiv.2302.09519

Image
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Re: Bell's Theorem Begs the Question

by Joy Christian » Fri Jan 13, 2023 12:09 am

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The bottom line is, Bell's theorem is based on a hefty dose of cheating and dishonesty. Not to mention aggressive defense and gaslighting by its advocates.
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