[SEQ RERUN] Bell's Theorem: No EPR "Reality"

A terminological correction:

Bell's Theorem itself is agreed-upon academically as an experimental truth.

A theorem is a deductive truth. Only formally-proved mathematical results get to be called "theorems". As such, a "theorem" can never be falsified by experiment.

The confusion is revealed a bit earlier in the post:

"Bell's inequality" is that any theory of hidden local variables implies (1) + (2) >= (3). The experimentally verified fact that (1) + (2) < (3) is a "violation of Bell's inequality". So there are no hidden local variables. QED.

And that's Bell's Theorem.

Eliezer evidently thinks that "Bell's inequality" and "Bell's theorem" are two different things. They're not. The theorem -- the only thing that can be called such -- is the mathematical statement that "any theory of hidden local variables implies (1) + (2) >= (3)". The statement that "there are no hidden local variables [in the world as it actually exists]" is not purely mathematical -- an empirical premise ("the experimentally verified fact that (1) + (2) < (3)") was used to deduce it. -- and therefore cannot be labeled a "theorem".

Actually, I lied slightly: there is a subtle difference between "Bell's inequality" and "Bell's theorem". "Bell's inequality" is just the bare formula "A+ B >= C" (where A,B, and C are whatever they are in the context), without the accompanying assertion that the inequality actually holds. "Bell's theorem", by contrast, is the statement that if A,B, and C are numbers satisfying [whatever conditions they are asserted to satisfy], then Bell's inequality is true. As such, while it makes sense to speak of Bell's inequality being "violated" (as it is for some triples of numbers), it does not make any logical sense to speak of "violations" of Bell's theorem.

A theorem can never be violated. When people say, for example, "the Pythagorean theorem is violated in spherical geometry", they are merely abusing language out of laziness. What they mean to say is that the conclusion of the Pythagorean theorem is violated. Strictly speaking, the Pythagorean theorem is not the statement that "the square of the hypotenuse is equal to the sum of the squares of the other two sides"; it is, rather, the statement "if a triangle is Euclidean and right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides." The hypotheses of the theorem are not satisfied in spherical geometry in the first place, so spherical geometry does not "falsify" it or present "exceptions" to it. (Indeed, it exemplifies it as much as Euclidean geometry does, via the contrapositive: because the square of the hypotenuse of a spherical triangle does not equal the sum of the squares of the other two sides, we know, by the Pythagorean theorem, that spherical triangles are not Euclidean and right-angled!)

Is there any place we can see actual data on one of the photon polarization experiments? Not statistics, but actual data? And a probabilistic analysis, a la Jaynes, of the data?

In theory, I'm fine with non local interactions, but I'm not yet convinced they are necessary. I don't see anything about detector efficiency here, which I believe is key to the reality of what happens. It seems completely natural to me that if a photon had some directional local variable, that it would effect the likelihood of detection in a polarizer dependent on the direction of the polarizer.

Jaynes has reservations about Bell's Theorem, and they made a fair amount of sense to me. And in general I find it good policy to trust him on how to properly interpret probabilistic reasoning.

Jaynes paper on EPR and Bell's Theorem: http://bayes.wustl.edu/etj/articles/cmystery.pdf

Jaynes speculations on quantum theory: http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf

It's really simple. The hidden variables are not local. General Relativity does not apply in the case of the particles below a certain size. Can you create a logically consistent belief set such that the FTL particles are not FTL and really just existing in multiple states at once? Yes.

You can also say that on 4/25/12, up is down and down is up so I fell up and couldn't get back down again.

IE there are infinite labeling systems for every set of observations. The minimal set has the least computational cost to consider, and thus is easier for people to process. Some people however, tribals to be specific, are more interested in protecting legacies than they are with using the computationally cheaper belief set. The cost is reduced frequency of new inspirations of understanding.