Is non-locality a necessary consequence of the Bell theorem?

[Igael]

What is the difference between quantum mechanics and realism ? quantum mechanics states on statistics while the hardy assumption of EPR is that hidden variables may describe exactly the outcomes of each individual test. Bell refutes the last idea. But, he didn't need to refute the case where realistic outcomes are random because accepting this possibility would imply directly that the EPR assumption was wrong.

Now, take the Bell demonstration. He integrated one application ( function defined for any input value with an unique outcome for each ). If the lambda function that results from the hidden variable is not a mathematical function ( hence having different outcomes for different tests ), the integral being not applicable, the demonstration would become invalid. Not saying invalid for the main purpose of the EPR-Bell discussion but not available to claim that the outcomes cannot be a result of randomness. Maybe it's true but the demonstration doesn't handle the case. ( And it's normal, this case is useless for the main discussion )

Is this reasoning exact ?

Non-locality doesn't make any assumption on the existence or not of hidden variables. In general, it is the reverse. We say, since hidden variables are impossible to predict the individual outcomes, hence 1) we need a phenomenon to explain the correlations, 2) this phenomenon seems to be the non-locality.

But never one demonstrated mathematically that a part of hidden variables and a part of randomness may not be statistically predictive.
It's not the EPR assumption, nor its exact opposite.
But to infer on a new kind of 'relation' between states of distant objects, the non-locality theorists needs also to exclude it. Else, a 'natural' explanation, even not realistic, would make the concept of non-locality useless.

Am I wrong when saying that this demonstration doesn't exist ? if yes, please let me know its references.

end of the post

pure opinion now : It's not a pure original thought. I'm trying this explanation searching for an interpretation of the efficiency of some random algorithms ( that may be improved with math and/or machine powers ) giving so similar results, continuously from -PI/2 to PI/2.

 

[atyy]

Now, take the Bell demonstration. He integrated one application ( function defined for any input value with an unique outcome for each ). If the lambda function that results from the hidden variable is not a mathematical function ( hence having different outcomes for different tests ), the integral being not applicable, the demonstration would become invalid. Not saying invalid for the main purpose of the EPR-Bell discussion but not available to claim that the outcomes cannot be a result of randomness. Maybe it's true but the demonstration doesn't handle the case. ( And it's normal, this case is useless for the main discussion )

Yes, the Bell theorem fails if the functions cannot be integrated.

strangerep once posted some interesting attempts to construct local models that use this loophole (I have no idea if the constructions were right).

 

[zonde]

quantum mechanics states on statistics while the hardy assumption of EPR is that hidden variables may describe exactly the outcomes of each individual test. Bell refutes the last idea. But, he didn't need to refute the case where realistic outcomes are random because accepting this possibility would imply directly that the EPR assumption was wrong.

You have something wrong here. EPR assumes locality and that QM holds. And from these two assumption EPR concludes that outcomes of certain individual tests are not random. Hidden variables is just a way how Bell models this certainty.

You can look at Maudlin's paper http://arxiv.org/abs/1408.1826

 

[Igael]

@zonde : I tried to be precise and emphasized as possible. My question is related to mainstream theories and their understanding.

The purpose is not a HVs discussion but the the non-locality conclusion after a very strict conclusion of the Bell demonstration.

I mean that if any theory, even random, may explain the outcomes, non-locality becomes not necessary . The randomness above is the MQ randomness, the one EPR say that its outcomes are not random but ruled by unknown laws and/or unknow variables. We know that this EPR assumption is false.

I read "Computation and Consciousness" and "Quantum Non Locality and Relativity" by Maudlin.
He doesn't evoke the mixed case as I do. On another hand, Maudlin has many ( respectable ) opinions when I wait formal demonstrations.

If the context fullfills the conditions of applicability of the Bell theorem, it's just maths and hence it is always right.
Then, the applicability is my question :
does the Bell theorem refute "mixed functions built on hidden variables + randomness" ?

For me, obviously no because the integrability general conditions. Does your answer mean yes ? Could you elaborate please ?

I don't say that there is not another demonstration for this precise case. I'ld be very interested , if it exists.

 

[DrChinese]

@zondeI mean that if any theory, even random, may explain the outcomes, non-locality becomes not necessary . The randomness above is the MQ randomness, the one EPR say that its outcomes are not random but ruled by unknown laws and/or unknow variables. We know that this EPR assumption is false.

Randomness does not save you from quantum non-locality in any way, shape or form. EPR nowhere says that outcomes are not random. It says that if the outcome of a measurement can be predicted with certainty, there is an element of reality to that which is measured.

That such outcome is truly random is not in and of itself relevant. In other words: EPR did not prove that something that observed to be "real" must also have a determinate "cause" that explains the outcome of the observation.

 

[Igael]

The hidden reference is a good mainstream course on the Bell inequalities.

@DrChinese :

That such outcome is truly random is not in and of itself relevant.

It is based on a peculiar demonstration that makes the assumption that the outcome for a specific ( set of hidden ) variable is constant ... It's a question on the demonstration and its applicability in the experiments contexts ; interpretations don't matter at this step.

In other words : Are the Riemann integrability conditions fulfilled ? I know the answer. It's just maths too ...

 

[zonde]

I mean that if any theory, even random, may explain the outcomes, non-locality becomes not necessary . The randomness above is the MQ randomness, the one EPR say that its outcomes are not random but ruled by unknown laws and/or unknow variables. We know that this EPR assumption is false.

QM says that certain outcomes are not random. It has nothing to do with EPR.

Then, the applicability is my question :
does the Bell theorem refute "mixed functions built on hidden variables + randomness" ?

For me, obviously no because the integrability general conditions. Does your answer mean yes ? Could you elaborate please ?

"mixed functions built on [local] hidden variables + [local] randomness" can not reproduce predictions of QM and experimental results.
How they are relevant to discussion?

 

[DrChinese]

It is based on a peculiar demonstration that makes the assumption that the outcome for a specific ( set of hidden ) variable is constant ...

The interaction between the EPR particles may produce a random result that related for the two (a "constant" in your terms). But again, the randomness (either way) is not relevant to the EPR result.

 

[Igael]

"mixed functions built on [local] hidden variables + [local] randomness" can not reproduce predictions of QM and experimental results.

I'm just asking where is the demonstration.

How they are relevant to discussion?

I tried to explain it in the first post.

 

[Igael]

The interaction between the EPR particles may produce a random result that related for the two (a "constant" in your terms). But again, the randomness (either way) is not relevant to the EPR result.

I never wrote that. See the definition of a mathematical application. For each input, you must get only one image. Assume that f(1) = 18. You cannot have next f(1)=20. Each time you input 1 , you must get 18 . But in quantum physics, individual outcomes may vary ...

Coming back to the questions :
I see only that a demonstration uses a tool and that this tool needs somes conditions to be used. It's just basic questions to ask
1) do you see like me that these conditions aren't fulfilled in the case of randomness in the results ?
2) where it the complementary demonstration ?
3) If there is not such demonstration, then non-locality is not necessary the consequence of the Bell theorem. We would need more assumptions to get non-locality

It is just basic maths in a well known physical context. Perhaps, it is a question to reword and to move to the undergraduate maths section with the tag Riemann integrability.

Nothing here states against the Bell theorem or the experiments. It's about physical non-locality.

 

[jk22]

Indeed Bell made the assumption A (a,x) where x is the hidden variable is a function.

We could imagine an algorithm that gives several result being called several times with the same a x.

In other words before the integration is done in Chsh it is noted that AB-AB'+A'B+A'B'=+\-2

If we take such another algorithm the possible values are 4,-4,0 too.

So the proof does not work for such algorithm.

However it can be seen numerically that statistical significant deviation from 2 do not occur.

In fact i thought about it and the algorithm could be replaced by its average then Bell's proof works again.

 

[Igael]

In fact i thought about it and the algorithm could be replaced by its average then Bell's proof works again.

Does averaging have a meaning here ? Each answer must be -1 or +1 to be compared with the other side. How to compare 0.75 and 0.25 ?

Averaging is a good idea ! perhaps there is a trick for the comparison ...

 

[DrChinese]

I never wrote that. See the definition of a mathematical application. For each input, you must get only one image. Assume that f(1) = 18. You cannot have next f(1)=20. Each time you input 1 , you must get 18 . But in quantum physics, individual outcomes may vary ...

Coming back to the questions :
I see only that a demonstration uses a tool and that this tool needs somes conditions to be used. It's just basic questions to ask
1) do you see like me that these conditions aren't fulfilled in the case of randomness in the results ?
2) where it the complementary demonstration ?
3) If there is not such demonstration, then non-locality is not necessary the consequence of the Bell theorem. We would need more assumptions to get non-locality

It is just basic maths in a well known physical context. Perhaps, it is a question to reword and to move to the undergraduate maths section with the tag Riemann integrability.

Nothing here states against the Bell theorem or the experiments. It's about physical non-locality.

I do not see how there is any particular connection between randomness, non-locality and/EPR.

As to Bell: "non-locality is not necessary the consequence" of Bell's Theorem + Bell test results. That it rules out local realism is the generally accepted conclusion.

 

[Jilang]

Doesn't a lack of realism imply randomness?

 

[zonde]

"mixed functions built on [local] hidden variables + [local] randomness" can not reproduce predictions of QM and experimental results.

I'm just asking where is the demonstration.

What kind of demonstration do you want to see?
Maybe for a start it would be a good idea to establish some basic things and see if we can agree on them.
Do you agree that there are predictions of QM where outcome is completely certain at one location given result at other location (measurement of entangled particles with the same measurement settings)?

 

[jk22]

Do you agree that there are predictions of QM where outcome is completely certain at one location given result at other location (measurement of entangled particles with the same measurement settings)?

This is an idealization in a real experiment particles that are not entangled could be detected hence it were not certain. The thing is do experiments tend towards the theoretical ideal or is there an irreducible lack of correlation. In the latter case theory should explain why the correlation were not 1 at same angles.

 

[Igael]

What kind of demonstration do you want to see?
Maybe for a start it would be a good idea to establish some basic things and see if we can agree on them.
Do you agree that there are predictions of QM where outcome is completely certain at one location given result at other location (measurement of entangled particles with the same measurement settings)?

if the details above don't talk to you, I'm sorry.

 

[Igael]

This is an idealization in a real experiment particles that are not entangled could be detected hence it were not certain. The thing is do experiments tend towards the theoretical ideal or is there an irreducible lack of correlation. In the latter case theory should explain why the correlation were not 1 at same angles.

I'm not in charge of a counterexample, nor have any solution today. Perhaps tomorrow ...

With the maths, there is no ideology , guru, or priest legitimacies.
I'm just trying to understand why the Bell theorem demonstration leads to the non-locality conclusion, with the help of the professional mathematicians and physicists of the forum.