Question about Dr. Chinese's example of Bell's Theorem

[prajor]

Hello, this could be a basic question. I saw the link http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm" on one of the threads.

Following the table there the probability of complete match between two detectors happens twice out of 8 times. i.e. 1/4.

How how can we say that it happens at least 1/3 times, where the table clearly shows 1/4.

 

[LukeD]

We can't. Bell's Inequality is violated.

 

[prajor]

Luke, But the local interpretation (EPR) (the Table with 8 possibilities) also gives 1/4 only !

 

[LukeD]

Luke, But the local interpretation (EPR) (the Table with 8 possibilities) also gives 1/4 only !

Yes, this was the source of Einstein's objection. EPR had essentially believed in local hidden variables and complained that Quantum Mechanics doesn't make any sense unless their hidden variables were non-local. Bell responded by saying "yes, that's quite right".

There are ways out of this however. The usual way of doing this is to say that hidden variables do not exist and not assume the existence of anything that cannot be constructed from the rules of Quantum Mechanics.
Many Bohmians would rather allow their descriptions even though they are non-local.

I, myself, having learned Consistent Histories from Robert Griffiths (not to be confused with any other Welshman with the name Griffiths), am of the view that a classical definition of objective reality is simply too limited to talk about Quantum Mechanics. Griffiths, by the way, constructed his ideas firmly in the mathematics of Quantum theory. However, and I'm trying to work this out myself, Consistent Histories seems to be able to use very similar tools and the same formulas as the Bohmian approach.

 

[DrChinese]

Hello, this could be a basic question. I saw the link http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm" on one of the threads.

Following the table there the probability of complete match between two detectors happens twice out of 8 times. i.e. 1/4.

How how can we say that it happens at least 1/3 times, where the table clearly shows 1/4.

Welcome to PhysicsForums, prajor!

I think if you look again, the thing you say happens 1/4 of the time actually happens 1/2 of the time. When you consider the lowest possible scenario, from the table, you can get as low as 1/3 but no lower. That is for the classical analysis.

On the other hand: the Quantum prediction is not presented in the table. It is per the cos^2 theta formula, and is .25 or 1/4.

Does this help?

 

[prajor]

Thanks DrC for the welcome and clarification.

1. Should the QM probability be cos²(\theta/2) or is it true only if we take Stern-Gerlach devices instead of photons with polarizers ?

2. Obviously 3 polarisers at 120 degrees is a special case. Isn't it right to have a generic case for QM probability ?
\int cos²\theta integrated over 0 and 2\pi

 

[prajor]

ok. I will try and explain why I have the below questions. May be someone can throw some light on this.

I am following the argument of Bell's theorem with Stern Gerlach Analyzers (SGA) and silver atoms (Daniel Styer). In this first probablilty that is calculated is for a simple setup where we know the direction of SGA, so a given single atom coming through has a 1/2 probability of going to output +m_b (and same probability for -m_b).

Now we introduce a SGA mounted on a pivot with three specific orientations and then do the same experiment. We get probability 1/2 again for the output to be +m_b.

The questions:
1. Why complicate the setup by introducing SGA which can take one of the 3 fixed positions ? What is the rationale behind this ?
2. If we extend the above to infinite number of positions around the circle also, the probability of output being +m_b should be 1/2 ?
3. How is the probability in above (#2) calclulated ? Is it not by integrating cos²(\theta/2) around the circle ?

 

[prajor]

Folks, any thoughts on my questions below ?

 

[prajor]

Guess these are not right questions..