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Author Topic: What is Bell's Theorem?  (Read 1621 times)

Offline cheryl j

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What is Bell's Theorem?
« on: 22/05/2013 16:48:12 »
and why is it important? Is it still important? (If you wouldn't mind, please explain it in the simplest terms possible. I probably won't get the math.) I heard one physicist (Neil Turok) say that it "proved that the universe was not a machine."
« Last Edit: 24/05/2013 22:07:27 by chris »


 

Offline dlorde

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Re: What is Bell's Theorum
« Reply #1 on: 22/05/2013 19:04:44 »
It's to do with an apparent contradiction between Einstein's relativity theory and new-fangled quantum mechanics. Relativity requires a principle called 'locality', which says that an event here can't instantaneously affect an event somewhere else; all influences must travel slower than the speed of light.

Einstein and a couple of associates showed that quantum mechanics predicts that this isn't always the case; that sometimes doing something to a particle here has an instantaneous effect on a particle there. This caused a lot of head scratching.

John Bell devised a theorem that showed that no theory that preserved locality could explain this quantum mechanical prediction. This meant that relativity would not be explain the effect.

For example, if two particles are produced from the same source at the same time and fly off in different directions ('entangled' particles in quantum mechanics), if you measure the spin direction of one particle, that instantaneously determines the spin direction of the other particle to be opposite. Some people suggested that the spin directions were set that way when the particles were created, so you'd expect that by measuring one you'd know the other. This was a called 'hidden variable' explanation because it suggested the particles carried their spin information with them from the start, and we just didn't know it until it was measured.

Bell's theorem showed that in experiments measuring many pairs of such particles, you would get slightly different results if quantum mechanics (non-local) was correct than if relativity (local) was correct. For relativity to be correct, certain inequalities in the measured results should be observed. These are known as Bell Inequalities.

Numerous experiments have shown that Bell Inequalities are violated in the real world, which means that quantum mechanics really does allow a measurement on one particle to instantaneously affect another, distant, particle. Relativity can't explain it with hidden variables, or anything else. Locality is toast.

There are some caveats; this effect only happens in very particular circumstances, and it doesn't allow information to be transmitted faster than light. Although measuring one particle determines what a measurement of the other particle will show, there's no way to setup in advance which particle will spin which way.

Here's the simplest proper explanation I could find: Spooky action at a Distance.
 

Offline cheryl j

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Re: What is Bell's Theorum
« Reply #2 on: 23/05/2013 02:45:29 »
So does any of this matter in something like the design of quantum computers? Is there an actual discrepancy or uncertainty there?
 

Offline dlorde

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Re: What is Bell's Theorum
« Reply #3 on: 23/05/2013 09:06:37 »
So does any of this matter in something like the design of quantum computers? Is there an actual discrepancy or uncertainty there?
I'm no expert in quantum computing, but I don't think it particularly matters in quantum computers. They rely on features of quantum mechanics that are not accounted for by relativity in any case.

What it seems to tell us is that relativity isn't a complete description of the universe; it's generally fine for large-scale stuff where quantum effects generally get averaged out or lost in the noise, but if you want a really precise description, especially at the micro-scale, quantum mechanics is the way to go. Unfortunately, QM is difficult to calculate with above the smallest scales, so we'll be using relativity for the big stuff for a while yet. Lots of work is being done on trying to resolve the differences & find a theory that has the best of both QM and relativity.
 

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Re: What is Bell's Theorum
« Reply #3 on: 23/05/2013 09:06:37 »

 

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