# Understanding Bell's Inequality & Theorem

• pibomb
In summary, Bell's theorem is a mathematical statement about the behavior of pairs of particles that have been separated by a distance.
pibomb
Hello,

I don't understand Bell's Inequality and Bell's theorem in general. Someone want to help me?

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I have tried to write a Homer Simpson's guide to Bell's Inequality at:
http://www.ronsit.co.uk/weird_at_Heart.asp

D'oh...

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pibomb said:
Hello,

I don't understand Bell's Inequality and Bell's theorem in general. Someone want to help me?

If you really want to know, try to get your hands on the little book "speakable and unspeakable in quantum mechanics" by Bell himself.

Recommend you do not use Bart or Homer Simpson explanation :

“QM goes against Einstein's ideas of determinism

Locality -Says that what happens in one place is affected from a distant place. As an example, the spin of a paired particle at a distant location will 'affect' the spin of the other paired particle.”

Quotes from guide at site:
wawens said:
I have tried to write a Homer Simpson's guide to Bell's Inequality ...

D'oh...
D'oh is right
Einstein did not promote “determinism”.

He was unconcerned with how the multiple values of multiple particles might randomly interact to create a pair of photons out of one photon for example. What he was concerned about was when the pair are created it happens in a “local space” with “local and realistic” values of various attributes or variables assignable to each of the two newly created photons. He wished to find “determent” variables attached to each photon, remaining fixed with each photon until detected later. As they separated from each other Quantum issues "at a distance" like the Bell-EPR paradox (which he never got to personally review) would still be resolvable. Even if the variable he needed was to remain hidden as an unobservable Locally created “Hidden Variable”. With local information retained independently by each photon they would not need any kind of communication or “entanglement” between them to resolve the issue no matter how far apart they separate.

Thus:
This 'Homer' description of “Locality” is upside down! It better describes what Non-Local Theories and EPR-Bell proofs require in a non-local or at least unrealistic reality.
I stopped reading after finding these two:

pibomb said:
Hello,

I don't understand Bell's Inequality and Bell's theorem in general. Someone want to help me?

I would humbly point you to one of my own pages: Bell's Theorem: An Overview with Lotsa Links

I give a short background and history, and there are links (flip down to the bottom of the page) to all kinds of more detailed sites - from beginner to expert. From these sites, you can learn the state of the art in Bell's Theorem, entanglement, and experimental tests of all variety of setups. There are at least 30 links, which will in turn take you everywhere you would care to go.

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## What is Bell's Inequality?

Bell's Inequality is a mathematical theorem that describes the limitations on local hidden variable theories in explaining the correlations between quantum particles.

## What is the significance of Bell's Inequality?

The significance of Bell's Inequality is that it provides a way to test whether quantum mechanics is a complete theory or if there are hidden variables at play.

## How does Bell's Theorem relate to Bell's Inequality?

Bell's Theorem is a proof that shows that no local hidden variable theory can reproduce the predictions of quantum mechanics, thus supporting Bell's Inequality.

## What does it mean when Bell's Inequality is violated?

When Bell's Inequality is violated, it means that the correlations between quantum particles cannot be explained by local hidden variable theories and that there must be some non-local influences at play.

## How is Bell's Inequality tested in experiments?

Bell's Inequality is tested by measuring the correlations between entangled particles in different directions and comparing them to the predictions of local hidden variable theories. If the results violate Bell's Inequality, then quantum mechanics is favored as the more complete theory.

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