Bell's Theorem - can anyone explain it?

[the tree]

"indeterminacy isn't the result of unmeasurable properties" is exactly what Bell's Theorem is all about. Bell's inequality has been proven, which implies that there are no hidden variables.

So I read this "explination" which uses two analogies, one where there definately are hidden variables and one where I don't see why there shouldn't be.

 

And so, I don't understand what Bell's theoem is getting at.

 

So in short, how can the absense of hidden variables be proven?

[5614]

You might want to read this:

http://atschool.eduweb.co.uk/rmext04/92andwed/pf_quant.html#Q30

 

The short story is that Einstein said that QM was wrong. He said there must be "hidden variables" which goes against QM. His argument is called the EPR paradox.

 

The solution to the paradox is Bell's Theorem or Bell's Inequality.

 

Bell thought this up as a thought experiment, he never thought it would be experimentally proven.

 

Bell set up an inequality (ie. some calcuation is bigger than some value) and said that if his inequality was correct then there were hidden variables.

 

Bells Inequality has been tested experimentally many times and every (reliable) time it has been violated. That is Bell's Inequality is wrong, meaning there are not hidden variables.

 

This, thus, disproves Einstein's claim that hidden variables must exist. Einstein was dead long before all these solutions were discovered.

 

"[bell's inequality says:] No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics" -- wikipedia

That means that no theory which involves hidden variables will give the same predictions as QM. Since the predictions of QM are correct (and hidden variable theory cannot agree with QM) the predictions of hidden variable theory must be incorrect, as is the theory.

 

I don't think most of that post is what you're looking for, but that link (top of my post) should help you.

[timo]

Bell set up an inequality (ie. some calcuation is bigger than some value) and said that if his inequality was correct then there were hidden variables.

Small remark: I haven´t read it up, but I am almost sure it should read: If there were hidden variables, then the inequalities would hold. Not the other way round as you wrote it (note the difference!).

[5614]

The two sentences seem, to me, to have the same meaning. So are you commenting on a grammatical error?

 

If so I think you're correct, it should be your way around. Although the meaning is still fundementally the same.

 

[edit] tree: on that link I gave:

http://atschool.eduweb.co.uk/rmext04/92andwed/pf_quant.html#Q30

you only want to read the section titled: The EPR Paradox and Bell's Inequality Principle. I mean you can read the rest of it, but it's not relevant.

[Severian]

No, Athiest is correct.

 

You said: inequality holds => hidden variables

Athiest said: hidden variables => inequality holds

 

Since the inequality doesn't hold, your statement would give no information (since there is no implication 'inequality false => no hidden variables').

 

Atheist's statement can be written in the negated sense to read 'inequality false => no hidden variables' (a negation changes the statements to their negatives, and changes the direction of the implication), so finding Bell's inequlity to be violated does imply no hidden variables.

[Locrian]

Everyone keeps saying "no hidden variables." But I think many (though not I) would disagree and say we should be writing "no local hidden variables."

 

yes no?

[bascule]

Well, this certainly threw me for a loop, and the more I thought about it, the more I began to wonder about questions like "Isn't quantum indeterminacy necessary to expain the non-uniformity of the Big Bang?" and so forth. From a strong deterministic view, you are left to wonder "What is the cause of the initial non-uniformity?" I always loved cellular automata as an explanation for this, particularly the non-repeating Rule 110 and have always wondered if they could serve as an explanation for quantum indeterminacy (being a cellular automaton)

 

 

 

Everyone keeps saying "no hidden variables." But I think many (though not I) would disagree and say we should be writing "no local hidden variables."

 

yes no?

 

Wikipedia had this to day:

 

http://en.wikipedia.org/wiki/Bell's_Theorem

 

Some advocates of the hidden variables idea prefer to accept the opinion that experiments have ruled out local hidden variables. They are ready to give up locality (and probably also causality)' date=' explaining the violation of Bell's inequality by means of a "non-local" hidden variable theory, in which the particles exchange information about their states. This is the basis of the Bohm interpretation of quantum mechanics. It is, however, considered by most to be unconvincing, requiring, for example, that all particles in the universe be able to instantaneously exchange information with all others.

[bascule]

Here's a more thorough description:

 

http://en.wikipedia.org/wiki/Hidden_variables

[bascule]

And here are some people talking about the universe as a cellular automaton idea:

 

http://www.lepp.cornell.edu/spr/2002-12/msg0046458.html

[Severian]

"Isn't quantum indeterminacy necessary to expain the non-uniformity of the Big Bang?"

 

To be honest I am not sure. Generally, if one had deterministic laws and physics which was rotationally and translationally invariant, then you would always have a completely symmetric universe (ie. no non-uniformity). To get non-uniformity you need to break the symmetry somehow.

 

In Quantum Mechanics this is quite easy to do, because you can do it dynamically but it is mor difficult in classical systems.

 

Imagine a ball sitting at the top of a perfectly symmetric hill. There is a stationary point at the top of the hill, so in principle the ball can sit there quite happily. With a classical system and no other effects it would sit there forever because the law of gravity is symmetric (it prefers no direction for the ball to roll down).

 

Now you could imagine that there is a gust of wind. It will blow the ball ever so slightly off-centre and then gravity will take over and the ball will roll down the hill in one particular direction. The symmetry has been broken. But this was really a cheat because in a purely classical (deterministic) world I should be able to predict the direction of the wind, so the laws of physics could not be symmetric around the hill after all. I had to choose the wind direction myself or include a non-rotationally invariant mechanism to generate it.

 

In a quantum mechanical system, the ball makes its own movements, without needing the wind. It wiggles about in random directions due to quantum uncertainty and this wiggle will move it away from the top of the hill (just like the wind did) and it will roll down. The difference here is that the direction is completely random since it is set by the random wiggles, not an outside effect.

 

So my gut feeling is that you are correct and we need non-determinism to get any structure whatsoever in the universe (assuming a symmetric starting point). On the other hand, just because I can't think of a mechanism doesn't mean one doesn't exist.