- #1
Greg-ulate
- 72
- 0
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.
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 measurement or it could alternatively allow for that idea to be true if they 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 got to 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?
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 measurement or it could alternatively allow for that idea to be true if they 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 got to 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?