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

In summary, the SGA setup introduces an additional degree of freedom which affects the outcome of the experiment, while the silver atom experiment still uses only the input and output degrees of freedom.
  • #1
prajor
18
0
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.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2


We can't. Bell's Inequality is violated.
 
  • #3


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


prajor said:
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.
 
Last edited:
  • #5
prajor said:
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?
 
Last edited by a moderator:
  • #6
Thanks DrC for the welcome and clarification.

1. Should the QM probability be cos2([tex]\theta[/tex]/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 ?
[tex]\int[/tex] cos2[tex]\theta[/tex] integrated over 0 and 2[tex]\pi[/tex]
 
  • #7
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 +mb (and same probability for -mb).

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 +mb.

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 +mb should be 1/2 ?
3. How is the probability in above (#2) calclulated ? Is it not by integrating cos2([tex]\theta[/tex]/2) around the circle ?
 
  • #8
Folks, any thoughts on my questions below ?
 
  • #9
Guess these are not right questions..
 

1. What is Bell's Theorem and why is it important in science?

Bell's Theorem is a concept in quantum mechanics that states that certain predictions made by quantum mechanics cannot be reproduced by a classical theory. It is important because it challenges our understanding of reality and has implications for our understanding of the universe.

2. Who is Dr. Chinese and what is their example of Bell's Theorem?

Dr. Chinese is a hypothetical scientist who presents an example of Bell's Theorem in which two particles are entangled and their properties are measured at different locations. This example demonstrates the violation of a principle called local realism, which states that distant objects cannot instantaneously affect each other.

3. What are the implications of Bell's Theorem for our understanding of reality?

Bell's Theorem suggests that reality may be non-local, meaning that objects can affect each other instantaneously regardless of distance. This challenges our traditional understanding of cause and effect and raises questions about the true nature of the universe.

4. How does Bell's Theorem relate to quantum entanglement?

Bell's Theorem is closely related to quantum entanglement, as it is often used to explain the phenomenon. Entanglement occurs when two particles become connected in such a way that the state of one particle affects the state of the other, regardless of the distance between them. Bell's Theorem demonstrates that this phenomenon cannot be explained by classical theories.

5. How has Bell's Theorem been tested and what were the results?

Bell's Theorem has been tested in various experiments, including the Aspect experiment in 1982. The results showed that the predictions made by quantum mechanics were correct, and local realism was violated. This provided strong evidence for the validity of Bell's Theorem and the implications it has for our understanding of reality.

Similar threads

I Looking For Help Understanding Bell's Theorem, Hidden Variables & QM
    • Quantum Physics
3
Replies
80
Views
3K
I Bell's Theorem - why product of (2)spins can be +1 (Griffith's text)
    • Quantum Physics
Replies
1
Views
721
B The match rates in Bell Tests -- Lower than 50%?
    • Quantum Physics
Replies
28
Views
1K
B Bell's theorem, QFT, and the Relativity of Simultaneity
    • Quantum Physics
2
Replies
64
Views
4K
I Bell vs Kolmogorov: Unravelling Probability Theory Limits
    • Quantum Physics
3
Replies
93
Views
4K
I Hidden phase in polarization tests of Bell's inequality?
    • Quantum Physics
2
Replies
49
Views
2K
B Some questions about "superdeterminism" and Bell's Theorem
    • Quantum Physics
3
Replies
75
Views
8K
A How does Bell's 1964 theorem address detector independence and local realism?
    • Quantum Physics
Replies
18
Views
1K
B Simple proof of Bell's theorem
    • Quantum Physics
3
Replies
95
Views
8K
I Model used to refute Bell's theorem
    • Quantum Interpretations and Foundations
Replies
19
Views
1K

Hot Threads

Recent Insights

Back
Top