Bell's inequality

John K Clark (
Sat, 1 Feb 1997 21:01:27 -0800 (PST)


>>Steve Witham :
>>Isn't Bell's inequality derived correctly from QM as we know it?

>Omega :
>Yes, a totally correct result of orthodox theory.

If Bell's inequality was derived from Quantum Mechanics then modern Physics
would be in big trouble because Bell's Inequality is wrong.

Many people including Einstein and Bell himself were unhappy that Quantum
Mechanics could not make exact predictions, only statistical ones. They were
even more unhappy about what Einstein contemptuously called "spooky action at
a distance". They thought that these deficiencies were just caucused by our
lack of information, hidden variables, and of course they though these
variables were local.

So what's the difference between local and non local?
1) A local force changes with distance and usually diminishes, a non local
force has the same strength at one nanometer as it has at 10 billion light
2) A local force acts by the exchange of particles, so if A changes B locally
then A must touch B or touch something that does touch B; a non local
force jumps directly from A to B without doing anything in-between and so
you can't stop it or change it in any way by doing things in the
intervening space.
3) Most important of all, a local force originating at point A can not change
anything at point B in less time than it takes for light to travel from
A to B, a non local force acts instantly.

Bell's genius was in asking exactly the right question, "Assuming that there
is such a thing as objective reality, is there anything every conceivable
local hidden value theory would have in common?". The answer is yes, Bell
found that even if we are ignorant of important variables, as long as the
world was local, an inequality he found about the correlation of polarized
photons was always true. Bell also found that Quantum Mechanics predicted
that his equality was always false.

If took over 20 years for somebody to convincingly perform the very difficult
experiment that Bell suggested, but when they did, Bell's inequality was
violated. This does not prove that Quantum Mechanics is the last word on the
subject, but it does prove that all local hidden variable theories are wrong.

>>Aren't there some experiments (one by Aspick? (sp?)) that pretty
>>convincingly demonstrate the inequality?

>The name is "Aspect", and I believe some others have worked on this
>too, although I don't have any other names. My impression is that
>his work is fairly well accepted.

The first one to test Bell's inequality was John Clauser in 1972. Clauser was
convinced that the world was local and thought his experiment would prove it;
he was disappointed when it pointed in the opposite direction. Clauser's
experimental method did contain some very small logical loopholes, and those
who were desperate to have a local universe clung to them. Years later when
Aspect did the experiment he was much more rigorous and the loopholes were
closed. If there is an objective reality then a local Universe is dead.

John K Clark

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