Bell's theorem proof. Does it really proofs anything?

0xDEAD BEEF

Hmm. Ok, so i have "tuned" my program a bit and now i get more interesting results. Thought - i doubt that i have properly implemented photon physics in my program.

So - as i now understand it -
If those two photons would not be entangled twin-photons, then (for example), when Anna has her detector at 0 angle and Bob has his at 90, then photon flying in at 45 angle could cause Anna's detector to fire 0 and Bobs detector to fire 0, since now this photon has cos^2(45) probability hitting Anna's + sames as Bob's -, so some times this 45 degree photon should cause 0 for Anna and 0 for Bob, when they have 0 vs 90 degree setup, but since experiment shows, that Anna and Bob are always correlated at 0 angle delta and always 100% uncorrelated at 90 angle delta -> this proves that something strange is going on???

EDIT:
if that non-sense text was not clear, then here is another try to explain what i meant.
So, Anna has 0 setup, Bob has 90 setup. There is photon coming in at 45 degrees angle.
Sometimes we should se:
++
--
+- (more often)
-+ (more often)

But we see only:
+-
-+

So this is strange and proves non-locality. Right?

EDIT2:
Further more. (if mine understanding above was correct) -
Now one could start patching "theory" and try to come up with new formula, so, that photon has 100% probability going one way, if delta < 45. However soon one would discover, that no mater how hard he tries, but having photon always go up, when angle < 45, means, that it always goes down, when angle > 45, so cos^2(delta) formula can only be replaced with |delta| < 45. But if one does so and creates simulation, he sees, that correlations (mismatches) should form linear graph. But we see cos, so how is that possible???

Am i right?
Beef

zonde

Minor point. You don't see +- and -+ more often with photon polarization at 45°. According to your description you have sometimes photons with 45° polarization sometimes with 0° or 90° and sometimes another angle. So photons with 45° polarization will not contribute to correlation but photons with 0° or 90° will always contribute to correlation. When you sum up all angles it turns out that correlation is half of the maximum.

Yes, this is reasoning behind Bell theorem.

As a die hard local realist I would like to point out that other side of the story is experimental tests of theory that poses quite different questions.

0xDEAD BEEF

What are key points how local-realism explains these experiments?

No! My configuration was different. It was - Bob 0, Alisa 90. Photons flying in sometimes have angle 45, so they sometimes must hit ++, --, +-, -+, BUT, we only get +- and -+.

BTW - thank you guys a lot! With every reply I grow smarter and smarter! :)

Beef

DevilsAvocado

QM !!!!!!!!!!!!!!!

DrChinese

You can put pepperoni on mine. And crank up some Steely Dan.

DevilsAvocado

HAHAHA

YES! Pepperoni + Steely Dan = makes my life worth living!!

(sorry for the "sentence violation", going to jail now... )

zonde

Photon experiments that test Bell (or CHSH) inequalities relay on so called fair sampling assumption.
The thing is that you don't detect all photons that leave beam splitter but only portion. Typically you have around 10% coincidence rate i.e. you discard 9/10 of detections because you don't have matching detection at the other side.
Idea of fair sampling assumption is that if you would detect them it would not change observed correlations.
So if you assume that detected sample of photons is biased then you have to conclude that photon tests don't prove non-locality.
And I would like to add that this is the only way out of the paradox consistent with local realism.

Btw there was another idea (so called "locality loophole") but it was disproved by experiment with fast switching polarizers.

And you can try to look here as well:
Loopholes in Bell test experiments

I guess you misunderstood me. My point was that photons flying in sometimes have 45° angle and sometimes different angle.

DevilsAvocado

Da Capo: Mamma Mia

DrChinese

1. If you know that the photons coming in are polarized at 45 degrees, then they cannot be polarization entangled. And you will get: ++, --, +-, -+.

2. zonde has given a pretty good answer already. This is a very complex question and the answers tend to arouse controversy. But the short answer is that NO local realistic explanation also matches QM. In the view of zonde, local realism + fair sampling can match QM experimentally. This is far from certain (but *may* be possible). What is certain is that such local realism means that a complete sample will not agree with QM. Which follows Bell's Theorem, which essentially states:

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.