Understanding the Bell Inequality and its Impact on Quantum Mechanics

In summary, there is a loophole in the quantum nonlocality test that allows for the detection of particles.
  • #1
jerromyjon
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I went through a paper last week about the Bell inequality and how it is incompatible with QM. Something along the lines of probability in classical regards being 1/3 but in quantum mechanics it is 1/4. It went into some basic principles of how this is determined through quantum entanglement to be 2 separate variables measured on 2 entangled particles. OK then. I file it away in the pile labeled "not fully understood". But then something doesn't sit right... wouldn't 2 variables with 2 possible values be 1/4 chance of any of the 4 possible "states" occurring? That's just classical probability.
 
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  • #2
You'll have to ask a specific question if you want a specific answer.

Why would 2 variables with two possible values have a 1/4 probability of each combination of values? Is the probability that a randomly selected person is male and not retired equal to 1/4 ?
 
  • #3
I was trying to explain it in a simple boolean manner, 0 or 1, true or false, heads or tails fits best... 2 coins with 2 possible states. 25% both heads 25% heads/tails 25% tails/heads 25% both tails.
 
  • #4
jerromyjon said:
I was trying to explain it in a simple boolean manner, 0 or 1, true or false, heads or tails fits best... 2 coins with 2 possible states. 25% both heads 25% heads/tails 25% tails/heads 25% both tails.

That's clear. Now what is the question? Are you asking why ordinary probability theory gives an answer of 1/3 in the quantum entanglement problem? To answer that I, myself, would need to hear a statement of the entanglement problem you read about. Perhaps someone else knows the problem just from the mention of the word "entaglement".
 
  • #5
I think I need to be a bit more organised... I read it from a link in a post here several days ago and now I can't find it. :-(
Aha! Browser history...
http://drchinese.com/David/Bell_Theorem_Easy_Math.htm
I'm going to read through it again hoping to catch what I missed or realize where I misunderstood.
 
  • #6
I just absorbed another version found in another thread here: http://www.felderbooks.com/papers/bell.html
It makes the same case of what should be 5/9 chance turns out 50/50.

But just before reading that version I had the "aha!" moment and realized this is because entanglement gives 100% (or close to, ideally) chance of pairs being opposite spin in any 1 of the 3 axes. We can only measure 1. So then we double up pairs, and we measure 2 axes on 1 of each pair. Then when we think we can predict what the measurements of the other pair will be it turns out random?
 
  • #7
I'm still not sure if I explained that well enough or correctly, or if the original paper by Bell? would provide any additional insight. All I am trying to do is relate what is expected locally (meaning classically as in all 3 axes in 1 particle should always be the opposite spin in all 3 axes of entangled pairs) to what truly occurs non-locally (the measurements in the other 2 axes is affected in the pair by measuring the first axis on the first particle). This is truly the gist of the inequality, is it not?
 
  • #8
Another very good resource for your level of understanding is this article.
 
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  • #9
I haven't finished reading it yet, but can I assume there is verification that we know for sure a singlet state that we've partnered that we can measure vectors A,B and verify we know what C is or is that inferred from Bell's Theorem exclusively?
 
  • #10
I don't think anyone understands your question or what article you are referring to, since there are now 3 references in the thread.
 
  • #11
Forget it I'm good thanks for the links everyone.
 
  • #12
Detection-Loophole-Free Test of Quantum Nonlocality, and Applications, arXiv:1306.5772)

Here's a recent proof...
 

What is the Bell Inequality?

The Bell Inequality is a mathematical inequality proposed by physicist John Stewart Bell in 1964. It is used to test the validity of local hidden variable theories in quantum mechanics. In simpler terms, it provides a way to distinguish between classical and quantum systems.

How does the Bell Inequality impact quantum mechanics?

The Bell Inequality has had a significant impact on quantum mechanics because it helped to disprove the idea of local hidden variables. This means that quantum mechanics cannot be explained by any underlying classical theory, and the behavior of particles at the quantum level is inherently random and non-local.

What is the significance of violating the Bell Inequality?

Violating the Bell Inequality means that the results of an experiment cannot be explained by a classical theory. This is significant because it provides evidence for the non-local and random behavior of particles at the quantum level, which challenges our understanding of the nature of reality.

How is the Bell Inequality tested?

The Bell Inequality is typically tested through experiments involving entangled particles, which are particles that are connected in such a way that the state of one particle can affect the state of the other, even at great distances. By measuring the correlations between the particles, scientists can determine whether the Bell Inequality is violated.

What are the implications of understanding the Bell Inequality?

Understanding the Bell Inequality has important implications for the field of quantum mechanics and our understanding of the nature of reality. It has led to the development of new technologies, such as quantum cryptography and quantum computing, and has opened up new avenues for research in areas such as quantum entanglement and non-locality.

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