The mathematics why a hidden information channel can violate the BI

[Schmelzer]

FrediFizzx seem to have a problem which I don't understand.

My claim is that if there exists some hidden faster than light information channel between the particle flying to Alice and the particle flying to Bob than the Bell inequalities can be easily violated.

How does this work in QT? The particles fly away. If one particle is measured by Alice in direction a, and it has not received a message from Bob's particle, it makes some choice for and sends an immediate message to the other particle which contains the information about the direction of the measurement a and the measurement result . This immediate information transfer is the reduction of the wave function of the other particle to the eigenstate . But, of course, we don't need here quantum mystery. All we need is the possibility to send to Bob's particle the information immediately, faster than light.

Then Bob measures in direction b. And Bob's particle, having received the information , can give now as B any answer defined by whatever function one likes to violate the Bell inequalities.

The straightforward choice would be the quantum choice, where we already know that it violates the BI. But you can have even stronger violations, so that you lose the game described in https://ilja-schmelzer.de/realism/game.php always.

My question to FrediFizzx is where do you need more mathematical details? Or maybe you were thinking about something else, different from my claim that with some hidden FTL information transfer one can violate the Bell inequalities also in a quite classical way?

Man, I am really really tired of your freakin' nonsense!!!
Perhaps you can show a valid situation where the bounds of the inequality are exceeded?
Let's see your math right here and now. You can't do it because it is impossible.
So, you Bell fanatics need to quit lying about it.
No Bell inequality has EVER been "violated" or had its bounds exceeded. It is just freakin' mathematically impossible. And it boggles my mind big time that smart intelligent people don't realize that.

I'm impressed by the high standards of politeness here. I especially like the red color and the large size. Impressive.

[FrediFizzx]

FrediFizzx seem to have a problem which I don't understand.

My claim is that if there exists some hidden faster than light information channel between the particle flying to Alice and the particle flying to Bob than the Bell inequalities can be easily violated.

What a bunch of freakin' nonsense of which I snipped most of it out. It was just a bunch of word salad. Let's see some freakin' math. This is a "Bell was/is wrong forum" so we are not going to be polite to Bell fanatics in the least bit and not going to be sorry about it at all. YOU were not very polite at all by throwing a bunch of word salad at us instead of the math I requested.

Use the math for CHSH. Let's see how your faster than light scheme mathematically exceeds the bound of 2 for CHSH.
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[minkwe]

So why would such "hidden faster than light information channel" operate only at certain setting angles, and for a particular combination of "cyclicly dependent" setting pairs?

But the main point is that nothing can violate a mathematical inequality. Any apparent violation points to a mathematical error in it's application.

[FrediFizzx]

So why would such "hidden faster than light information channel" operate only at certain setting angles, and for a particular combination of "cyclicly dependent" setting pairs?

But the main point is that nothing can violate a mathematical inequality. Any apparent violation points to a mathematical error in it's application.

Yeah, and Gill claims he is going to show us tomorrow how to exceed the bounds of an inequality while still using that inequality. This I gotta see.
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[Schmelzer]

So why would such "hidden faster than light information channel" operate only at certain setting angles, and for a particular combination of "cyclicly dependent" setting pairs?

But the main point is that nothing can violate a mathematical inequality. Any apparent violation points to a mathematical error in it's application.

Of course, nobody violates some "mathematical inequality". If you have three predefined values, at least two of them have to be equal, thus, choosing two values gives an equal result in at least 1/3 of the cases. No doubt.

But here we have six values, and if there is an immediate communication channel, there is no way to find out that some of them are predefined. And if they are not even predefined, you have no base to apply that "mathematical inequality".

[Schmelzer]

Just to explain the argumentation behind it.

Alice can measure in any direct a, and the result A predicts what Bob measures if he chooses direction a too, namely he will measure -A.

Now we apply the EPR criterion of reality:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity"

If we have Einstein causality, and the two measurements are spacelike separated, then the measurement of Alice cannot disturb the particle near Bob in any way. Thus, we can conclude that what Bob will measure in direction a is an element of reality, that means, it is well-defined even before Bob decides what to measure.

But if the measurement of Alice immediately disturbs the state of the particle near Bob, we cannot apply this principle. And so we cannot know if the value -A of the measurement in direction a already existed before, or if it is simply the effect Alice' measurement influencing Bob's particle.

[gill1109]

So why would such "hidden faster than light information channel" operate only at certain setting angles, and for a particular combination of "cyclicly dependent" setting pairs?

But the main point is that nothing can violate a mathematical inequality. Any apparent violation points to a mathematical error in its application.

Yeah, and Gill claims he is going to show us tomorrow how to exceed the bounds of inequality while still using that inequality. This I gotta see.

Michel and Fred have seen my proof of what I see as the mathematical core of Bell's theorem before, and did not shoot it down. I have the impression that neither of you know quite enough about probability theory to be able to follow the proof. I also have the impression that Fred uses words like "inequality", "bound", "violation" to mean something a bit different from what mathematicians mean. And I really don't understand what Fred means by "using an inequality".

Of course, a correct mathematical theorem in which some inequality is proven is a tautology. Talking about violating it makes no sense. But you can violate the conclusion of a theorem by violating the assumptions. If a true (correctly proven) theorem says "if A, then B", you can still come up with situations where "not B" is true. Such situations are only possible if "not A" is also true.

In ordinary logic "A implies B" is actually equivalent to "not B implies not A".

For the time being, here is a reference to a short *mathematical* proof of a Bell-CHSH inequality.
https://arxiv.org/abs/quant-ph/0208187
No time loophole in Bell's theorem; the Hess-Philipp model is non-local
R.D. Gill, G. Weihs, A. Zeilinger, M. Zukowski
PNAS 2002, 99: 14632-14635
DOI: 10.1073/pnas.182536499

By the way, Fred keeps claiming that his simulation disproves Bell's theorem. But this is not true. His simulation model does not satisfy the assumptions of Bell's theorem. Hence he can escape the conclusions.

I'm not saying the simulation is wrong or uninteresting. It is interesting. I am saying that it is not what it seems to be.

[gill1109]

I wrote out the theorem I meant here:
viewtopic.php?p=72#p72

[FrediFizzx]

... By the way, Fred keeps claiming that his simulation disproves Bell's theorem. But this is not true. His simulation model does not satisfy the assumptions of Bell's theorem. ...

(Much nonsense snipped out.) You DON'T even know what Bell's junk theory is!!! Maybe some day you will learn what it really is!! The simulation not only shoots down Bell's junk physics theory, it also shoots down Gill's junk math theory!!

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