Sci.Physics.Foundations

FrediFizzx wrote: ↑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!!!!

I guess I hijacked Joy's thread enough so starting a new thread here about hidden variables. Seems to me the whole point of hidden variables was to show that quantum mechanics is local for the EPR-Bohm scenario. Well, I did that without using any hidden variables.

viewtopic.php?t=40

All that is required is 3-sphere topology.
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FrediFizzx wrote: ↑Sun Aug 27, 2023 11:05 am

FrediFizzx wrote: ↑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!!!!

I guess I hijacked Joy's thread enough so starting a new thread here about hidden variables. Seems to me the whole point of hidden variables was to show that quantum mechanics is local for the EPR-Bohm scenario. Well, I did that without using any hidden variables.

viewtopic.php?t=40

All that is required is 3-sphere topology.
.

Fred, you have s = a random point on a 2-sphere. So "s" is a hidden variable in your simulation. You can't generate statistics without a hidden variable.
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Joy Christian wrote: ↑Mon Aug 28, 2023 3:30 am

FrediFizzx wrote: ↑Sun Aug 27, 2023 11:05 am

FrediFizzx wrote: ↑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!!!!

I guess I hijacked Joy's thread enough so starting a new thread here about hidden variables. Seems to me the whole point of hidden variables was to show that quantum mechanics is local for the EPR-Bohm scenario. Well, I did that without using any hidden variables.

viewtopic.php?t=40

All that is required is 3-sphere topology.
.

Fred, you have s = a random point on a 2-sphere. So "s" is a hidden variable in your simulation. You can't generate statistics without a hidden variable.

Sigma(a), sigma(b), sigma(s1) and sigma(s2) are all observables so s1 and s2 can't be hidden. The cross products (a x s1) and (b x s2) are not observables but are necessary for the topology.
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FrediFizzx wrote: ↑Mon Aug 28, 2023 10:16 am

Joy Christian wrote: ↑Mon Aug 28, 2023 3:30 am

FrediFizzx wrote: ↑Sun Aug 27, 2023 11:05 am
I guess I hijacked Joy's thread enough so starting a new thread here about hidden variables. Seems to me the whole point of hidden variables was to show that quantum mechanics is local for the EPR-Bohm scenario. Well, I did that without using any hidden variables.

viewtopic.php?t=40

All that is required is 3-sphere topology.
.

Fred, you have s = a random point on a 2-sphere. So "s" is a hidden variable in your simulation. You can't generate statistics without a hidden variable.

Sigma(a), sigma(b), sigma(s1) and sigma(s2) are all observables so s1 and s2 can't be hidden. The cross products (a x s1) and (b x s2) are not observables but are necessary for the topology.
.

The word "hidden" is stuck with us because of historical reasons. Sometimes they are called "supplementary variables" instead of "hidden variables" to prevent misunderstanding. Nothing requires such variables to be hidden. That is why I prefer to call them "initial states." Essentially, whatever generates statistics are the "hidden variables" in the model. So we are just arguing about terminology.
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Joy Christian wrote: ↑Mon Aug 28, 2023 10:32 am

FrediFizzx wrote: ↑Mon Aug 28, 2023 10:16 am

Joy Christian wrote: ↑Mon Aug 28, 2023 3:30 am
Fred, you have s = a random point on a 2-sphere. So "s" is a hidden variable in your simulation. You can't generate statistics without a hidden variable.

Sigma(a), sigma(b), sigma(s1) and sigma(s2) are all observables so s1 and s2 can't be hidden. The cross products (a x s1) and (b x s2) are not observables but are necessary for the topology.
.

The word "hidden" is stuck with us because of historical reasons. Sometimes they are called "supplementary variables" instead of "hidden variables" to prevent misunderstanding. Nothing requires such variables to be hidden. That is why I prefer to call them "initial states." Essentially, whatever generates statistics are the "hidden variables" in the model. So we are just arguing about terminology.

Ok, thanks. Do you have an online reference for that? I looked around and couldn't find anything about that. From what you are saying, then the polarizer angles "a" and "b" could be considered hidden. I don't think so. From Wiktionary,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics; local hidden variables have been proved to be inconsistent with quantum mechanics."
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FrediFizzx wrote: ↑Mon Aug 28, 2023 12:58 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 10:32 am

FrediFizzx wrote: ↑Mon Aug 28, 2023 10:16 am
Sigma(a), sigma(b), sigma(s1) and sigma(s2) are all observables so s1 and s2 can't be hidden. The cross products (a x s1) and (b x s2) are not observables but are necessary for the topology.
.

The word "hidden" is stuck with us because of historical reasons. Sometimes they are called "supplementary variables" instead of "hidden variables" to prevent misunderstanding. Nothing requires such variables to be hidden. That is why I prefer to call them "initial states." Essentially, whatever generates statistics are the "hidden variables" in the model. So we are just arguing about terminology.

Ok, thanks. Do you have an online reference for that? I looked around and couldn't find anything about that. From what you are saying, then the polarizer angles "a" and "b" could be considered hidden. I don't think so. From Wiktionary,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics; local hidden variables have been proved to be inconsistent with quantum mechanics."
.

Wiktionary or Wikipedia cannot be trusted even if we find some information there.

Polarizer angles or settings "a" and "b" are not random variables or hidden variables. They can be held fixed throughout the experiment. In simulations we vary "a" and "b" to generate the cosine plot, but that is not physics.

The only hidden variable in your simulation is "s", which is a random point on a 2-sphere.
.

Joy Christian wrote: ↑Mon Aug 28, 2023 1:38 pm

FrediFizzx wrote: ↑Mon Aug 28, 2023 12:58 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 10:32 am
The word "hidden" is stuck with us because of historical reasons. Sometimes they are called "supplementary variables" instead of "hidden variables" to prevent misunderstanding. Nothing requires such variables to be hidden. That is why I prefer to call them "initial states." Essentially, whatever generates statistics are the "hidden variables" in the model. So we are just arguing about terminology.

Ok, thanks. Do you have an online reference for that? I looked around and couldn't find anything about that. From what you are saying, then the polarizer angles "a" and "b" could be considered hidden. I don't think so. From Wiktionary,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics; local hidden variables have been proved to be inconsistent with quantum mechanics."

Wiktionary or Wikipedia cannot be trusted even if we find some information there.

Polarizer angles or settings "a" and "b" are not random variables or hidden variables. They can be held fixed throughout the experiment. In simulations we vary "a" and "b" to generate the cosine plot, but that is not physics.

The only hidden variable in your simulation is "s", which is a random point on a 2-sphere.

Well, the first part of the Wiktionary definition seems to make good common sense and that is what I always thought the definition to be. However, the last part is probably not true but doesn't matter anyways.

"a" and "b" can be random variables so are they hidden in that case? And "s" could also be held fixed by putting it through a polarizer. I just don't really see that a, b, s, s1 or s2 could be considered hidden. Now, your original orientation variable, +/-1, was more like a hidden variable to me. But we found out much later that it wasn't necessary.
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FrediFizzx wrote: ↑Mon Aug 28, 2023 3:22 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 1:38 pm

FrediFizzx wrote: ↑Mon Aug 28, 2023 12:58 pm
Ok, thanks. Do you have an online reference for that? I looked around and couldn't find anything about that. From what you are saying, then the polarizer angles "a" and "b" could be considered hidden. I don't think so. From Wiktionary,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics; local hidden variables have been proved to be inconsistent with quantum mechanics."

Wiktionary or Wikipedia cannot be trusted even if we find some information there.

Polarizer angles or settings "a" and "b" are not random variables or hidden variables. They can be held fixed throughout the experiment. In simulations we vary "a" and "b" to generate the cosine plot, but that is not physics.

The only hidden variable in your simulation is "s", which is a random point on a 2-sphere.

Well, the first part of the Wiktionary definition seems to make good common sense and that is what I always thought the definition to be. However, the last part is probably not true but doesn't matter anyways.

"a" and "b" can be random variables so are they hidden in that case? And "s" could also be held fixed by putting it through a polarizer. I just don't really see that a, b, s, s1 or s2 could be considered hidden. Now, your original orientation variable, +/-1, was more like a hidden variable to me. But we found out much later that it wasn't necessary.
.

You have to think about what is happening physically. Only "s" originates from the source as a random variable. So only "s" is a hidden variable in your simulation. In the old model, only orientation +/-1 originated from the source. So only orientation +/-1 was a hidden variable.
.

Joy Christian wrote: ↑Mon Aug 28, 2023 10:37 pm

FrediFizzx wrote: ↑Mon Aug 28, 2023 3:22 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 1:38 pm
Wiktionary or Wikipedia cannot be trusted even if we find some information there.

Polarizer angles or settings "a" and "b" are not random variables or hidden variables. They can be held fixed throughout the experiment. In simulations we vary "a" and "b" to generate the cosine plot, but that is not physics.

The only hidden variable in your simulation is "s", which is a random point on a 2-sphere.

Well, the first part of the Wiktionary definition seems to make good common sense and that is what I always thought the definition to be. However, the last part is probably not true but doesn't matter anyways.

"a" and "b" can be random variables so are they hidden in that case? And "s" could also be held fixed by putting it through a polarizer. I just don't really see that a, b, s, s1 or s2 could be considered hidden. Now, your original orientation variable, +/-1, was more like a hidden variable to me. But we found out much later that it wasn't necessary.
.

You have to think about what is happening physically. Only "s" originates from the source as a random variable. So only "s" is a hidden variable in your simulation. In the old model, only orientation +/-1 originated from the source. So only orientation +/-1 was a hidden variable.

Ok, you can have that for your definition of a hidden variable if you wish. I suppose no one can stop you from that. I'm going to stick to,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics."

For the hidden variable definition. "s" is not a supplement to quantum mechanics as it is in the singlet wavefunction.

https://www.researchgate.net/publicatio ... glet_State
.

FrediFizzx wrote: ↑Tue Aug 29, 2023 4:40 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 10:37 pm You have to think about what is happening physically. Only "s" originates from the source as a random variable. So only "s" is a hidden variable in your simulation. In the old model, only orientation +/-1 originated from the source. So only orientation +/-1 was a hidden variable.

Ok, you can have that for your definition of a hidden variable if you wish. I suppose no one can stop you from that. I'm going to stick to,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics."

For the hidden variable definition. "s" is not a supplement to quantum mechanics as it is in the singlet wavefunction.

https://www.researchgate.net/publicatio ... glet_State

I suppose we need to know what "...to make it like classical mechanics." means? I assume that it means local and realistic. And what does "parameter" mean? Can 3-sphere topology be a "parameter"?
.

FrediFizzx wrote: ↑Fri Sep 01, 2023 10:15 am

FrediFizzx wrote: ↑Tue Aug 29, 2023 4:40 pm

Joy Christian wrote: ↑Mon Aug 28, 2023 10:37 pm You have to think about what is happening physically. Only "s" originates from the source as a random variable. So only "s" is a hidden variable in your simulation. In the old model, only orientation +/-1 originated from the source. So only orientation +/-1 was a hidden variable.

Ok, you can have that for your definition of a hidden variable if you wish. I suppose no one can stop you from that. I'm going to stick to,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics."

For the hidden variable definition. "s" is not a supplement to quantum mechanics as it is in the singlet wavefunction.

https://www.researchgate.net/publicatio ... glet_State

I suppose we need to know what "...to make it like classical mechanics." means? I assume that it means local and realistic. And what does "parameter" mean? Can 3-sphere topology be a "parameter"?
.

The sentence you have quoted from Wiktionary is a confused nonsense. "Classical mechanics" is not the same thing as local and realistic. Local realism has to do with completing quantum mechanics in the sense envisaged by Einstein. Classical mechanics cannot complete quantum mechanics because it is a fundamentally different theory. Einstein did not advocate returning to classical mechanics. He advocated a local and realistic completion of quantum mechanics by adding additional variables like "s". And "parameter" is not the same thing as "hidden variable." Usually "parameters" means "settings", like "a" and "b", chosen by Alice and Bob. Also, topology is a global concept. Like geometry, it cannot be represented by a parameter, or even a set of parameters.
.

Joy Christian wrote: ↑Fri Sep 01, 2023 1:13 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 10:15 am

FrediFizzx wrote: ↑Tue Aug 29, 2023 4:40 pm
Ok, you can have that for your definition of a hidden variable if you wish. I suppose no one can stop you from that. I'm going to stick to,

"Any parameter that would supplement quantum mechanics so as to make it like classical mechanics."

For the hidden variable definition. "s" is not a supplement to quantum mechanics as it is in the singlet wavefunction.

https://www.researchgate.net/publicatio ... glet_State

I suppose we need to know what "...to make it like classical mechanics." means? I assume that it means local and realistic. And what does "parameter" mean? Can 3-sphere topology be a "parameter"?
.

The sentence you have quoted from Wiktionary is a confused nonsense. "Classical mechanics" is not the same thing as local and realistic. Local realism has to do with completing quantum mechanics in the sense envisaged by Einstein. Classical mechanics cannot complete quantum mechanics because it is a fundamentally different theory. Einstein did not advocate returning to classical mechanics. He advocated a local and realistic completion of quantum mechanics by adding additional variables like "s". And "parameter" is not the same thing as "hidden variable." Usually "parameters" means "settings", like "a" and "b", chosen by Alice and Bob. Also, topology is a global concept. Like geometry, it cannot be represented by a parameter, or even a set of parameters.

Yeah, the definition is not very good. Let's see if we can fix it up to make better sense. "Any random variable(s) that would supplement quantum mechanics to make it local and/or realistic." Is that better?
.

FrediFizzx wrote: ↑Fri Sep 01, 2023 1:52 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 1:13 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 10:15 am
I suppose we need to know what "...to make it like classical mechanics." means? I assume that it means local and realistic. And what does "parameter" mean? Can 3-sphere topology be a "parameter"?
.

The sentence you have quoted from Wiktionary is a confused nonsense. "Classical mechanics" is not the same thing as local and realistic. Local realism has to do with completing quantum mechanics in the sense envisaged by Einstein. Classical mechanics cannot complete quantum mechanics because it is a fundamentally different theory. Einstein did not advocate returning to classical mechanics. He advocated a local and realistic completion of quantum mechanics by adding additional variables like "s". And "parameter" is not the same thing as "hidden variable." Usually "parameters" means "settings", like "a" and "b", chosen by Alice and Bob. Also, topology is a global concept. Like geometry, it cannot be represented by a parameter, or even a set of parameters.

Yeah, the definition is not very good. Let's see if we can fix it up to make better sense. "Any random variable(s) that would supplement quantum mechanics to make it local and/or realistic." Is that better?
.

That is better. But it is still vague. The meaning was made mathematically very precise by Bell by defining the functions A(a, h) = +/-1 as he did.
.

Joy Christian wrote: ↑Fri Sep 01, 2023 2:00 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 1:52 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 1:13 pm
The sentence you have quoted from Wiktionary is a confused nonsense. "Classical mechanics" is not the same thing as local and realistic. Local realism has to do with completing quantum mechanics in the sense envisaged by Einstein. Classical mechanics cannot complete quantum mechanics because it is a fundamentally different theory. Einstein did not advocate returning to classical mechanics. He advocated a local and realistic completion of quantum mechanics by adding additional variables like "s". And "parameter" is not the same thing as "hidden variable." Usually "parameters" means "settings", like "a" and "b", chosen by Alice and Bob. Also, topology is a global concept. Like geometry, it cannot be represented by a parameter, or even a set of parameters.

Yeah, the definition is not very good. Let's see if we can fix it up to make better sense. "Any random variable(s) that would supplement quantum mechanics to make it local and/or realistic." Is that better?
.

That is better. But it is still vague. The meaning was made mathematically very precise by Bell by defining the functions A(a, h) = +/-1 as he did.

That can't be very precise because we don't agree on the definition of "h". That is what this whole thread is about. So, what or how would you change the above definition to make it less vague?
.

FrediFizzx wrote: ↑Fri Sep 01, 2023 2:19 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 2:00 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 1:52 pm
Yeah, the definition is not very good. Let's see if we can fix it up to make better sense. "Any random variable(s) that would supplement quantum mechanics to make it local and/or realistic." Is that better?
.

That is better. But it is still vague. The meaning was made mathematically very precise by Bell by defining the functions A(a, h) = +/-1 as he did.

That can't be very precise because we don't agree on the definition of "h". That is what this whole thread is about. So, what or how would you change the above definition to make it less vague?
.

The standard definition of the hidden variable "h" is that it is a random variable that originates at the source. Therefore, it can be thought of as an initial condition for the measurement functions A(a, h) = +/-1, which is supposed to be a solution of a hypothetical differential equation that governs the dynamical equation of motion within a hypothetical hidden variable theory. The setting "a" then acts as the final condition for the solution A(a, h).

You do not agree with this definition, which is the standard definition, because what you are doing is something completely different.
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Joy Christian wrote: ↑Fri Sep 01, 2023 3:06 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 2:19 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 2:00 pm
That is better. But it is still vague. The meaning was made mathematically very precise by Bell by defining the functions A(a, h) = +/-1 as he did.

That can't be very precise because we don't agree on the definition of "h". That is what this whole thread is about. So, what or how would you change the above definition to make it less vague?
.

The standard definition of the hidden variable "h" is that it is a random variable that originates at the source. Therefore, it can be thought of as an initial condition for the measurement functions A(a, h) = +/-1, which is supposed to be a solution of a hypothetical differential equation that governs the dynamical equation of motion within a hypothetical hidden variable theory. The setting "a" then acts as the final condition for the solution A(a, h).

You do not agree with this definition, which is the standard definition, because what you are doing is something completely different.

If it is the "standard" definition, then why can't I find it online? And why haven't you given me an online reference for it? Or... how would you make the above definition less vague? I will scan through Bell's book to see what I can find while waiting for your reference.
.

FrediFizzx wrote: ↑Fri Sep 01, 2023 3:22 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 3:06 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 2:19 pm
That can't be very precise because we don't agree on the definition of "h". That is what this whole thread is about. So, what or how would you change the above definition to make it less vague?
.

The standard definition of the hidden variable "h" is that it is a random variable that originates at the source. Therefore, it can be thought of as an initial condition for the measurement functions A(a, h) = +/-1, which is supposed to be a solution of a hypothetical differential equation that governs the dynamical equation of motion within a hypothetical hidden variable theory. The setting "a" then acts as the final condition for the solution A(a, h).

You do not agree with this definition, which is the standard definition, because what you are doing is something completely different.

If it is the "standard" definition, then why can't I find it online? And why haven't you given me an online reference for it? Or... how would you make the above definition less vague? I will scan through Bell's book to see what I can find while waiting for your reference.
.

Bell's 1964 paper is online, so there is your online reference. He explains very clearly what is meant by a hidden variable.

My recent paper is also online, so that is another online reference: https://arxiv.org/abs/2302.09519 (see section II and III).

This is what Bell wrote in his paper:

In a complete physical theory of the type envisaged by Einstein, the hidden variables would have dynamical significance and laws of motion;
our lambda can then be thought of as initial values of these variables at some suitable instant.

By "initial values of these variables at some suitable instant" he means at the source.
.

Joy Christian wrote: ↑Fri Sep 01, 2023 5:35 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 3:22 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 3:06 pm
The standard definition of the hidden variable "h" is that it is a random variable that originates at the source. Therefore, it can be thought of as an initial condition for the measurement functions A(a, h) = +/-1, which is supposed to be a solution of a hypothetical differential equation that governs the dynamical equation of motion within a hypothetical hidden variable theory. The setting "a" then acts as the final condition for the solution A(a, h).

You do not agree with this definition, which is the standard definition, because what you are doing is something completely different.

If it is the "standard" definition, then why can't I find it online? And why haven't you given me an online reference for it? Or... how would you make the above definition less vague? I will scan through Bell's book to see what I can find while waiting for your reference.
.

Bell's 1964 paper is online, so there is your online reference. He explains very clearly what is meant by a hidden variable.

My recent paper is also online, so that is another online reference: https://arxiv.org/abs/2302.09519 (see section II and III).

This is what Bell wrote in his paper:

In a complete physical theory of the type envisaged by Einstein, the hidden variables would have dynamical significance and laws of motion;
our lambda can then be thought of as initial values of these variables at some suitable instant.

By "initial values of these variables at some suitable instant" he means at the source.

LOL! You can't give your paper as a reference; the definition of "hidden variable" needs to be independent. And... I'm actually rejecting Bell's whole hidden variable program. It is junk physics. Quantum mechanics does not need any hidden variables.

"A random variable that originates at the source." That is your definition. It is not acceptable. You need to state in the definition the relation to quantum mechanics. So, your definition is way too broad. And... I don't see that definition in your paper nor Bell's.
.

FrediFizzx wrote: ↑Fri Sep 01, 2023 6:24 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 5:35 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 3:22 pm
If it is the "standard" definition, then why can't I find it online? And why haven't you given me an online reference for it? Or... how would you make the above definition less vague? I will scan through Bell's book to see what I can find while waiting for your reference.
.

Bell's 1964 paper is online, so there is your online reference. He explains very clearly what is meant by a hidden variable.

My recent paper is also online, so that is another online reference: https://arxiv.org/abs/2302.09519 (see section II and III).

This is what Bell wrote in his paper:

In a complete physical theory of the type envisaged by Einstein, the hidden variables would have dynamical significance and laws of motion;
our lambda can then be thought of as initial values of these variables at some suitable instant.

By "initial values of these variables at some suitable instant" he means at the source.

LOL! You can't give your paper as a reference; the definition of "hidden variable" needs to be independent. And... I'm actually rejecting Bell's whole hidden variable program. It is junk physics. Quantum mechanics does not need any hidden variables.

"A random variable that originates at the source." That is your definition. It is not acceptable. You need to state in the definition the relation to quantum mechanics. So, your definition is way too broad. And... I don't see that definition in your paper nor Bell's.
.

In deterministic hidden variable theories, hidden variables emerge from the source, as in Bell's local model from Section 3 of his 1964 paper.

But you are of course free to reject this definition and everything else from the standard hidden variable program, which goes back to Einstein.
.

Joy Christian wrote: ↑Fri Sep 01, 2023 11:53 pm

FrediFizzx wrote: ↑Fri Sep 01, 2023 6:24 pm

Joy Christian wrote: ↑Fri Sep 01, 2023 5:35 pm
Bell's 1964 paper is online, so there is your online reference. He explains very clearly what is meant by a hidden variable.

My recent paper is also online, so that is another online reference: https://arxiv.org/abs/2302.09519 (see section II and III).

This is what Bell wrote in his paper:

By "initial values of these variables at some suitable instant" he means at the source.

LOL! You can't give your paper as a reference; the definition of "hidden variable" needs to be independent. And... I'm actually rejecting Bell's whole hidden variable program. It is junk physics. Quantum mechanics does not need any hidden variables.

"A random variable that originates at the source." That is your definition. It is not acceptable. You need to state in the definition the relation to quantum mechanics. So, your definition is way too broad. And... I don't see that definition in your paper nor Bell's.
.

In deterministic hidden variable theories, hidden variables emerge from the source, as in Bell's local model from Section 3 of his 1964 paper.

But you are of course free to reject this definition and everything else from the standard hidden variable program, which goes back to Einstein.

I didn't say that I "reject" it. I actually agree with that part. Here it what a hidden variable has to be,

1. A random variable

2. A variable generated by the source

3. A variable that is in addition to or supplements quantum mechanics.

You seem to not agree with number 3. But that is absurd since that is the actual "hidden" part.
.