Hidden Variables

[Joy Christian]

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.
.

I agree with all three. Bell also agrees with all three. In fact, everyone agrees with all three.

See Section II of my paper for a discussion about how all three are implemented in a hidden variable theory: https://arxiv.org/abs/2302.09519
.

[FrediFizzx]

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.
.

I agree with all three. Bell also agrees with all three. In fact, everyone agrees with all three.

Good. Then why are you claiming "s" is a hidden variable? It does not meet criteria number 3. "s" is in the quantum mechanical wavefunction. It is a quantum mechanical variable.
.

[Joy Christian]

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.
.

I agree with all three. Bell also agrees with all three. In fact, everyone agrees with all three.

Good. Then why are you claiming "s" is a hidden variable? It does not meet criteria number 3. "s" is in the quantum mechanical wavefunction. It is a quantum mechanical variable.
.

Because it is. It is a random point on a 2-sphere. It is a hidden variable that originates from the source. It is not a quantum mechanical variable.

The easiest way to see this is to look at your definition of the function A(a, s). It depends on the setting "a" and the hidden variable "s".
.

[FrediFizzx]

I agree with all three. Bell also agrees with all three. In fact, everyone agrees with all three.

Good. Then why are you claiming "s" is a hidden variable? It does not meet criteria number 3. "s" is in the quantum mechanical wavefunction. It is a quantum mechanical variable.
.

Because it is. It is a random point on a 2-sphere. It is a hidden variable that originates from the source. It is not a quantum mechanical variable.

The easiest way to see this is to look at your definition of the function A(a, s). It depends on the setting "a" and the hidden variable "s".

What do you suppose "n" is in the singlet wavefunction above? It's "s", a quantum mechanical variable.
.

[Joy Christian]

Good. Then why are you claiming "s" is a hidden variable? It does not meet criteria number 3. "s" is in the quantum mechanical wavefunction. It is a quantum mechanical variable.
.

Because it is. It is a random point on a 2-sphere. It is a hidden variable that originates from the source. It is not a quantum mechanical variable.

The easiest way to see this is to look at your definition of the function A(a, s). It depends on the setting "a" and the hidden variable "s".

What do you suppose "n" is in the singlet wavefunction above? It's "s", a quantum mechanical variable.
.

"n" is an ordinary vector in R^3. It is not a variable in a complex-valued Hilbert space like psi is.

If you want "s" not to be a hidden variable, then you must not have it in your function A(a, s). You should write that function as A(a), showing its dependence only on the setting "a".
.

[FrediFizzx]

Because it is. It is a random point on a 2-sphere. It is a hidden variable that originates from the source. It is not a quantum mechanical variable.

The easiest way to see this is to look at your definition of the function A(a, s). It depends on the setting "a" and the hidden variable "s".

What do you suppose "n" is in the singlet wavefunction above? It's "s", a quantum mechanical variable.
.

"n" is an ordinary vector in R^3. It is not a variable in a complex-valued Hilbert space like psi is.

If you want "s" not to be a hidden variable, then you must not have it in your function A(a, s). You should write that function as A(a), showing its dependence only on the setting "a".

"n" is the singlet spin vector "s". What else would/could it be? The rest of what you have written is pure nonsense since A depends on both "a" and "s".
.

[Joy Christian]

What do you suppose "n" is in the singlet wavefunction above? It's "s", a quantum mechanical variable.
.

"n" is an ordinary vector in R^3. It is not a variable in a complex-valued Hilbert space like psi is.

If you want "s" not to be a hidden variable, then you must not have it in your function A(a, s). You should write that function as A(a), showing its dependence only on the setting "a".

"n" is the singlet spin vector "s". What else would/could it be? The rest of what you have written is pure nonsense since A depends on both "a" and "s".
.

"n" is not a random variable. It is a fixed vector. "s", on the other hand, is a random hidden variable in your model. This is confirmed because, as you say, A(a, s) depends on the setting "a" and a random variable "s", which can only be a hidden variable since it is not a setting.
.

[FrediFizzx]

"n" is an ordinary vector in R^3. It is not a variable in a complex-valued Hilbert space like psi is.

If you want "s" not to be a hidden variable, then you must not have it in your function A(a, s). You should write that function as A(a), showing its dependence only on the setting "a".

"n" is the singlet spin vector "s". What else would/could it be? The rest of what you have written is pure nonsense since A depends on both "a" and "s".
.

"n" is not a random variable. It is a fixed vector. "s", on the other hand, is a random hidden variable in your model. This is confirmed because, as you say, A(a, s) depends on the setting "a" and a random variable "s", which can only be a hidden variable since it is not a setting.

LOL! I guess Bell has you brainwashed also to the point of talking nonsense. "n" is a variable that is randomly different for each singlet iteration and is the singlet spin vector "s". That is just plain common sense. And just because "s" is not a setting doesn't mean it is "hidden". More plain common sense.
.

[Joy Christian]

"n" is the singlet spin vector "s". What else would/could it be? The rest of what you have written is pure nonsense since A depends on both "a" and "s".
.

"n" is not a random variable. It is a fixed vector. "s", on the other hand, is a random hidden variable in your model. This is confirmed because, as you say, A(a, s) depends on the setting "a" and a random variable "s", which can only be a hidden variable since it is not a setting.

LOL! I guess Bell has you brainwashed also to the point of talking nonsense. "n" is a variable that is randomly different for each singlet iteration and is the singlet spin vector "s". That is just plain common sense. And just because "s" is not a setting doesn't mean it is "hidden". More plain common sense.
.

You are wrong. "s" is a random hidden variable in your model. Since you don't believe me, ask someone else (like Michel) for a second opinion.
.

[FrediFizzx]

"n" is not a random variable. It is a fixed vector. "s", on the other hand, is a random hidden variable in your model. This is confirmed because, as you say, A(a, s) depends on the setting "a" and a random variable "s", which can only be a hidden variable since it is not a setting.

LOL! I guess Bell has you brainwashed also to the point of talking nonsense. "n" is a variable that is randomly different for each singlet iteration and is the singlet spin vector "s". That is just plain common sense. And just because "s" is not a setting doesn't mean it is "hidden". More plain common sense.
.

You are wrong. "s" is a random hidden variable in your model. Since you don't believe me, ask someone else (like Michel) for a second opinion.

I don't need a second opinion. It is very plain to see and just common sense that "s" is not hidden at all. Ok, you can stop talking nonsense now.
.

[FrediFizzx]

Anyways, we have a huge implication since there are two different local EPR-Bohm models with no hidden variables! It means that Bell's theorem may be correct but it doesn't matter because it is nonsense anyways due to specifying hidden variables that aren't even needed.
.

[FrediFizzx]

Anyways, we have a huge implication since there are two different local EPR-Bohm models with no hidden variables! It means that Bell's theorem may be correct but it doesn't matter because it is nonsense anyways due to specifying hidden variables that aren't even needed.

So, Bell made a huge mistake. He assumed that hidden variables might be the solution to the problem. And then he thought he had proven that hidden variables were impossible to be a solution. So, what was the problem?
.

[FrediFizzx]

Anyways, we have a huge implication since there are two different local EPR-Bohm models with no hidden variables! It means that Bell's theorem may be correct but it doesn't matter because it is nonsense anyways due to specifying hidden variables that aren't even needed.

So, Bell made a huge mistake. He assumed that hidden variables might be the solution to the problem. And then he thought he had proven that hidden variables were impossible to be a solution. So, what was the problem?

Yep, you guessed it! The supposed problem that Bell was trying to solve was locality and realism. It was thought by many at the time that quantum mechanics did away with locality and realism in Nature. What nonsense!
.

[minkwe]

The Original EPR paper proved that the Quantum Mechanical Wavefunction was not a complete description of physical reality:

Previously we proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that two physical quantities, with non-commuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2). We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete
...
While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however that such a theory is possible.

This has been interpreted by many as the origin of the "hidden variables" concept. Note that two related things are being discussed here:

1. The quantum mechanical state is completely characterized by ψ, which is a function of variables chosen to describe the system. EPR proved that ψ is incomplete, which means there must be additional variables beyond those of which ψ is a function. These variables may be called "hidden" because they are not part of ψ, but it doesn't mean they must be hidden in every aspect. They are hidden to QM only.
2. A more complete theory of physical reality. EPR states that they believe one is possible. Note that this is not necessarily the same thing as adding variables to the quantum-mechanical description. It could be a completely different theory which provides a more complete description.

Here's how Bell described the EPR argument and his response to it:

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics.
...
Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.
Let this more complete specification be effected by means of parameters λ.

Therefore, when Bell writes A(a, λ), λ here does not just represent "hidden variables" or " additional variables". It represents all relevant variables that constitute a more complete specification. That is, either:

• The quantum-mechanical description + additional variables required to complete it, OR
• A description from a new theory which provides a more complete description.

I hope this helps in resolving this dispute.

[FrediFizzx]

The Original EPR paper proved that the Quantum Mechanical Wavefunction was not a complete description of physical reality:

Previously we proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that two physical quantities, with non-commuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2). We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete
...
While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however that such a theory is possible.

This has been interpreted by many as the origin of the "hidden variables" concept. Note that two related things are being discussed here:

1. The quantum mechanical state is completely characterized by ψ, which is a function of variables chosen to describe the system. EPR proved that ψ is incomplete, which means there must be additional variables beyond those of which ψ is a function. These variables may be called "hidden" because they are not part of ψ, but it doesn't mean they must be hidden in every aspect. They are hidden to QM only.
2. A more complete theory of physical reality. EPR states that they believe one is possible. Note that this is not necessarily the same thing as adding variables to the quantum-mechanical description. It could be a completely different theory which provides a more complete description.

Here's how Bell described the EPR argument and his response to it:

THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality [2]. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics.
...
Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.
Let this more complete specification be effected by means of parameters λ.

Therefore, when Bell writes A(a, λ), λ here does not just represent "hidden variables" or " additional variables". It represents all relevant variables that constitute a more complete specification. That is, either:

• The quantum-mechanical description + additional variables required to complete it, OR
• A description from a new theory which provides a more complete description.

I hope this helps in resolving this dispute.

Well, thanks but it doesn't resolve the dispute. Joy claims the singlet spin vector, "s", above is a hidden variable. I say it is not a hidden variable since quantum mechanics knows about it via the singlet wavefunction. What say you?

What we have here is two different local EPR-Bohm models that give the prediction of quantum mechanics with NO hidden variables. One is a classical type of model the other is a quantum mechanical model.
.

[minkwe]

Well, thanks but it doesn't resolve the dispute. Joy claims the singlet spin vector, "s", above is a hidden variable. I say it is not a hidden variable since quantum mechanics knows about it via the singlet wavefunction. What say you?

What we have here is two different local EPR-Bohm models that give the prediction of quantum mechanics with NO hidden variables. One is a classical type of model the other is a quantum mechanical model.
.

I say as far as Bell's theorem is concerned, "hidden variables" used to mean "additional variables added to the quantum-mechanical description" are irrelevant. As I explained above, the variables in Bell's theorem are not "hidden variables", although they may include hidden variables. If someone is able to demonstrate that A(a, s) reproduces the correlations and deterministically produces individual outcomes, whatever you call "s", then "s" must be a more complete description of reality. If "s" is ONLY the quantum-mechanical description without any additional variables, then EPR and Bell both don't think that is possible. As bell further explains:

With the example advocated by Bohm and Aharonov [6], the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the Spins and . If measurement Of the component , where a is some unit vector, yields the value + 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.
Now we make the hypothesis [2], and it seems at least worth considering that if the two measurements are made at places remote from one another, the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of by previously measuring the same component of, it follows that the result of any such measurement must actually be predetermined. Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.

Note that here, simply reproducing the QM correlations is not enough to fulfill the requirements laid out by Bell. The model must be able to produce the results of individual measurements deterministically.

Secondly, the idea that you have a different EPR-Bohm model that gives the prediction of QM with "NO hidden variables" is also meaningless. Once you start dealing with a completely different theory than quantum mechanics, then the concept of "hidden variables," understood to mean "variables added to QM to complete it", is meaningless since they refer only to the variables required to "expand" the quantum-mechanical description.

On the other hand, if you have adopted the recent trend where λ in Bell's A(a λ) is casually referred to as "hidden variables," then nitpicking about whether "s" is a hidden variable or not is a waste of time because it obviously is (according to this view) if your functions are A(a, s). Also, according to this view, the idea that anything can reproduce the correlations without any hidden variables is also meaningless unless your functions are A(a). In this case, all particles are identical (obviously false), and the outcomes are always identical for the same angle for every experiment (obviously false).

[FrediFizzx]

Well, thanks but it doesn't resolve the dispute. Joy claims the singlet spin vector, "s", above is a hidden variable. I say it is not a hidden variable since quantum mechanics knows about it via the singlet wavefunction. What say you?

What we have here is two different local EPR-Bohm models that give the prediction of quantum mechanics with NO hidden variables. One is a classical type of model the other is a quantum mechanical model.
.

I say as far as Bell's theorem is concerned, "hidden variables" used to mean "additional variables added to the quantum-mechanical description" are irrelevant. As I explained above, the variables in Bell's theorem are not "hidden variables", although they may include hidden variables. If someone is able to demonstrate that A(a, s) reproduces the correlations and deterministically produces individual outcomes, whatever you call "s", then "s" must be a more complete description of reality. If "s" is ONLY the quantum-mechanical description without any additional variables, then EPR and Bell both don't think that is possible. As bell further explains:

With the example advocated by Bohm and Aharonov [6], the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the Spins and . If measurement Of the component , where a is some unit vector, yields the value + 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.
Now we make the hypothesis [2], and it seems at least worth considering that if the two measurements are made at places remote from one another, the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of by previously measuring the same component of, it follows that the result of any such measurement must actually be predetermined. Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.

Note that here, simply reproducing the QM correlations is not enough to fulfill the requirements laid out by Bell. The model must be able to produce the results of individual measurements deterministically.

Secondly, the idea that you have a different EPR-Bohm model that gives the prediction of QM with "NO hidden variables" is also meaningless. Once you start dealing with a completely different theory than quantum mechanics, then the concept of "hidden variables," understood to mean "variables added to QM to complete it", is meaningless since they refer only to the variables required to "expand" the quantum-mechanical description.

On the other hand, if you have adopted the recent trend where λ in Bell's A(a λ) is casually referred to as "hidden variables," then nitpicking about whether "s" is a hidden variable or not is a waste of time because it obviously is (according to this view) if your functions are A(a, s). Also, according to this view, the idea that anything can reproduce the correlations without any hidden variables is also meaningless unless your functions are A(a). In this case, all particles are identical (obviously false), and the outcomes are always identical for the same angle for every experiment (obviously false).

Well Ok, thanks for trying but you seem to think a concise definition for "hidden variable" is not required any more. It can just be a free for all and defined however one wants to define it. To me, that is a bunch of nonsense. But here is what Joy and I agreed to for the definition,

1. A random variable

2. A variable generated by the source

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

Can you agree with that?
.

[minkwe]

Well Ok, thanks for trying but you seem to think a concise definition for "hidden variable" is not required any more. It can just be a free for all and defined however one wants to define it. To me, that is a bunch of nonsense. But here is what Joy and I agreed to for the definition,

1. A random variable

2. A variable generated by the source

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

Can you agree with that?
.

Fred, note that I gave a very concise and precise definition and quoted the original sources (EPR and Bell) to back it up. Hidden variables are variables added to the quantum mechanical description to achieve a more complete state specification.

I, however, recognize that there is inconsistency in its use in the community, and that's what I also tried to take into consideration. I do not agree with points 2 and 3 above for the following reasons:

1. A hidden variable does not necessarily have to be random or stochastic. In a deterministic model, randomness or stochastic properties are synonymous with "incomplete specification"; therefore, a more complete specification of a state will not have random or stochastic elements in the model. Although.
2. A hidden variable does not necessarily have to be generated by the source because "a more complete specification" could include everything from the source to the point where the measurement device interacts with the system.
3. Yes, I agree with this point and only this point.

In Bell's formulation, λ includes everything that could possibly contribute to the particle state independently of the setting "a." In which case, you must agree that λ does not represent hidden variables but represents the full state (according to Bell). Your point (3) implies that you agree that hidden variables are not the complete state. They are just supplementary to quantum mechanics.

But Joy and you are talking about a different model than QM; that's why arguing about hidden variables is a waste of time. You aren't trying to supplement QM; you are trying to replace it, at least as far as the model is concerned.

[FrediFizzx]

Well Ok, thanks for trying but you seem to think a concise definition for "hidden variable" is not required any more. It can just be a free for all and defined however one wants to define it. To me, that is a bunch of nonsense. But here is what Joy and I agreed to for the definition,

1. A random variable

2. A variable generated by the source

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

Can you agree with that?
.

Fred, note that I gave a very concise and precise definition and quoted the original sources (EPR and Bell) to back it up. Hidden variables are variables added to the quantum mechanical description to achieve a more complete state specification.

I, however, recognize that there is inconsistency in its use in the community, and that's what I also tried to take into consideration. I do not agree with points 2 and 3 above for the following reasons:

1. A hidden variable does not necessarily have to be random or stochastic. In a deterministic model, randomness or stochastic properties are synonymous with "incomplete specification"; therefore, a more complete specification of a state will not have random or stochastic elements in the model. Although.
2. A hidden variable does not necessarily have to be generated by the source because "a more complete specification" could include everything from the source to the point where the measurement device interacts with the system.
3. Yes, I agree with this point and only this point.

In Bell's formulation, λ includes everything that could possibly contribute to the particle state independently of the setting "a." In which case, you must agree that λ does not represent hidden variables but represents the full state (according to Bell). Your point (3) implies that you agree that hidden variables are not the complete state. They are just supplementary to quantum mechanics.

But Joy and you are talking about a different model than QM; that's why arguing about hidden variables is a waste of time. You aren't trying to supplement QM; you are trying to replace it, at least as far as the model is concerned.

Michel, I agree with your first sentence above which rules out the singlet spin vector "s" as being a hidden variable. But I am NOT trying to replace quantum mechanics. I think QM is just fine as is. Is it a complete description of Nature? Probably not but it doesn't need to be. And..., for sure, arguing about hidden variables is a waste of time since hidden variables are not needed to solve Bell's problem.
.

[FrediFizzx]

Well Ok, thanks for trying but you seem to think a concise definition for "hidden variable" is not required any more. It can just be a free for all and defined however one wants to define it. To me, that is a bunch of nonsense. But here is what Joy and I agreed to for the definition,

1. A random variable

2. A variable generated by the source

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

Can you agree with that?
.

Fred, note that I gave a very concise and precise definition and quoted the original sources (EPR and Bell) to back it up. Hidden variables are variables added to the quantum mechanical description to achieve a more complete state specification.

I, however, recognize that there is inconsistency in its use in the community, and that's what I also tried to take into consideration. I do not agree with points 2 and 3 above for the following reasons:

1. A hidden variable does not necessarily have to be random or stochastic. In a deterministic model, randomness or stochastic properties are synonymous with "incomplete specification"; therefore, a more complete specification of a state will not have random or stochastic elements in the model. Although.
2. A hidden variable does not necessarily have to be generated by the source because "a more complete specification" could include everything from the source to the point where the measurement device interacts with the system.
3. Yes, I agree with this point and only this point.

In Bell's formulation, λ includes everything that could possibly contribute to the particle state independently of the setting "a." In which case, you must agree that λ does not represent hidden variables but represents the full state (according to Bell). Your point (3) implies that you agree that hidden variables are not the complete state. They are just supplementary to quantum mechanics.

But Joy and you are talking about a different model than QM; that's why arguing about hidden variables is a waste of time. You aren't trying to supplement QM; you are trying to replace it, at least as far as the model is concerned.

Michel, I agree with your first sentence above which rules out the singlet spin vector "s" as being a hidden variable. But I am NOT trying to replace quantum mechanics. I think QM is just fine as is. Is it a complete description of Nature? Probably not but it doesn't need to be. And..., for sure, arguing about hidden variables is a waste of time since hidden variables are not needed to solve Bell's problem.

In fact, Joy solved Bell's problem in 2007 using 3-sphere topology. Hidden variables were not needed then and they certainly are not needed now.
.