I keep looking at these experiments that demonstrate violation of Bell's inequality and I really can't figure out why anyone cares. The scenario always seems wrong in some way.(adsbygoogle = window.adsbygoogle || []).push({});

For example the EPR paradox. The argument goes like this, if you start out with a source of entangled "photons", you know that they have 100% correlated polarization. So you set up some polarizers at +120, 0, and -120 degrees. Alice and Bob can pick randomly which one they use. They do it a bunch of times and they find that they measured the polarization of the light to be in the direction of their polarizer 50% of the time independently, but recorded the same as one another only 25% of those times. This defies the idea that there are hidden variables flying around on little local point-like "particles" that are discovered upon measurementorit could alternatively allow for that idea to be trueifthey are also able to signal each-other superluminally.

Wait a minute, why does it defy that idea? Because if the "particles" had little hidden variables such as "I will go through polarizer 0, and -120, but not +120" then we could make a table like this

-120...0..120..........A:0,B:+120.....A:0, B:-120...A:+120, B:-120....%Same

Y........Y....Y..............Same..............Same...............Same...................1

Y........N...Y................Diff................Same................Diff...................1/3

Y........Y....N..............Same................Diff.................Diff...................1/3

Y........N....N...............Diff..................Diff...............Same..................1/3

etc...

and then no matter what combination of polarizer was picked, we would never get less than 33% of the same measurements, unlike the 25% we got by experiment. Ok.. Why is this bogus? There's gotta be a reason. Ok I got one.

Consider each of Alice's settings separately, draw a different table

A:-120

-120..0...120............B:+120..............B:0...............%Same

Y.......Y....Y...............Same..............Same....................1

Y.......N....Y...............Same...............Diff....................1/2

Y.......Y.....N...............Diff................Same..................1/2

Y.......N....N................Diff.................Diff.....................0

A:0

-120..0...120...........B:+120.............B:0................%Same

Y.......Y.....Y.............Same...............Same...................1

N.......Y.....Y.............Same................Diff...................1/2

Y........Y....N...............Diff................Same.................1/2

N.......Y.....N...............Diff.................Diff......................0

A:+120

-120..0...120.........A:0,B:+120......A:0, B:-120.......%Same

Y.......Y.....Y................Same.............Same...................1

Y.......N.....Y.................Diff...............Same.................1/2

N.......Y.....Y...............Same................Diff...................1/2

N.......N.....Y.................Diff.................Diff....................0

And average the same % with a weight depending on how likely it is to happen... To do that look at the intensity of light that passes through two consecutive polarizers at 120°, Cos(120°)^{2}= 0.25.

So a "photon" that goes through a 0 has a 25% chance of also going through a +120, and a 6.25% chance of going through all three in a row. On average for every 16 "photons" I shoot, 1 of them will go through all 3 polarizers, 3 of them will go through 2 only, and the rest of them will only go through the first one.

I define 4 states, {111, 101, 110, 100} and assign them probabilities based on observation. The 1s mean it would go through a polarizer if it encountered it.

Theres a 1/16 chance to be in state 111 in which case the "photon" will go through all 3 polarizers.

Theres a 4/16 chance that the "photon" will go through 2 filters including the 1 from 111, therefore, state 110 and 101 have a 3/16 chance.

Theres a 12/16 chance to go through 1 filter but not the second, but 3 of those could be 101 or 110 depending on which order your filters are in, so that leaves 9 for state 100.

-120..0...120...........B:+120..............B:0.......%Same.......weight.......proportion

Y.......Y.....Y..............Same..............Same............1..........0.0625............1

Y.......N....Y...............Same...............Diff............1/2........0.1875.............3

Y.......Y....N................Diff.................Same.........1/2.........0.1875............3

Y.......N....N................Diff..................Diff............0...........0.5625............9

Average:..........................................................0.25

This exactly reproduces the quantum mechanical prediction. Can anyone tell me if any assumptions made depend on non-locality, non-realism, superluminal communication, counter-factual definiteness, conspiracy, magic, or an all-powerful deity?

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# Bell, EPR, paradox or not

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