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 November 21st, 2016, 07:15 PM #1 Newbie   Joined: Mar 2016 From: Saskatoon, Saskatchewan, Canada Posts: 29 Thanks: 1 Math Focus: Logic Bell's Theorem error.... I'm reading Brian Greene's "The Fabric of the Cosmos" and wonder if anyone has read his explanation (chapter 4) on how Bell's Theorem was used to prove the non-locality of entangled particles exists using this. I've found a serious error and have discussed this before with a similar kind of error in the Monty Hall problem (elsewhere). Is anyone here familiar with this and would like to discuss? I find that there seems to be an error in thinking relating to quantities of 1/2s and 1/3s that is interesting in these kind of problems. I can also show HOW there is an error in using Bell's Theorem in the setup similar to Aspect's in the 1980s. But Brian's book gives a good explanation I can help relate this too if others are familiar with it.
November 21st, 2016, 09:20 PM   #2
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 Originally Posted by Scott Mayers I'm reading Brian Greene's "The Fabric of the Cosmos" and wonder if anyone has read his explanation (chapter 4) on how Bell's Theorem was used to prove the non-locality of entangled particles exists using this. I've found a serious error and have discussed this before with a similar kind of error in the Monty Hall problem (elsewhere). Is anyone here familiar with this and would like to discuss? I find that there seems to be an error in thinking relating to quantities of 1/2s and 1/3s that is interesting in these kind of problems. I can also show HOW there is an error in using Bell's Theorem in the setup similar to Aspect's in the 1980s. But Brian's book gives a good explanation I can help relate this too if others are familiar with it.
Hi, I agree with you, Same as I cross check this theorem which states No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.. Well, I am not an expert, so if you would like to share any solutions regarding this than it would be grateful. Thank you.

 November 21st, 2016, 09:42 PM #4 Newbie   Joined: Mar 2016 From: Saskatoon, Saskatchewan, Canada Posts: 29 Thanks: 1 Math Focus: Logic First, imagine have a pair of gloves in which you wrap in two separate boxes, mix them up randomly, and then send one a great distance away. If you open one box to discover you have a left glove, you know the other has a right one and vice verse. This is basically what might happen if have some "entangled" particle that originates in some specific location and gets sent away in two different directions. What quantum mechanics is claiming is that the boxes themselves contain BOTH a left and right version 'entangled' UNTIL you open one of the boxes. Before opening any box, they each are both 1/2 a left and right glove. But as soon as you open it, the probability "collapses" and becomes only one of them. Then the other one, no matter how far away in space it is, "knows" which one is being observed and 'becomes' the opposite. Brian opted to treat each box's content as just having either both a spherical light that flashes the SAME color of two kinds, red and blue. He had Mulder, from the "X-files" send a whole bunch of these boxes to his most skeptic partner, Scully, with a note to have her call him when she receives them. Scully gets these boxes of which each are numbered with matching versions that Mulder keeps. So one pair of boxes might be labeled #1, with one that Scully has and one that Mulder keeps. He tells her that he wants to prove that entangles boxes with these spheres break the speed limit of light and informs whatever one discovers in one to be equal in kind to the other. But he tells her that the spherical light inside randomly flashes red or blue. Scully objects that this could prove anything because each pair can be originally 'programmed' to flash in sync from the time when Mulder sent the boxes. As such, each pair would have a 'HIDDEN FACTOR' that pre-assigns what the other box will be by default and not because they actually communicate instantaneously to the other. So Mulder offers an altered experiment. He sends the set of boxes with each box having 3 doors on it that both can open to reveal the flashed sphere. (note that the sphere only flashes once per random selected opening not to be repeated again. So imagine that each 'top' has a door, one on a 'side', and another on the 'front' [don't worry about how this is arranged]. We label one door with "T", and the others, "S" and "F" respectively. The given colors flashed are Red and Blue as possibilities (and probabilities that each have of 1/2 for any one of them). For each box, the experiment is to make a list of the colors one observes flashed upon RANDOMLY selecting ANY door EACH of Mulder or Scully selects 'silently' (without each other knowing which door they choose). Beginning with the first box, say, Mulder might randomly decide to open "T", sees a blue flash, then records 'blue' at the beginning of the list; Scully opens her first box by randomly picking "F" and sees a red flash and does the same. As a DEFAULT, if they choose the same identical door, they already know that the colors flashed would be identical. This is no surprise because Scully already suspects this is the WAY these flashes were programmed. But then there is a set of probabilities that we can expect in this experiment. Let us first notice that the KINDS of pattern are going to either be ALL one color or TWO of one color, and ONE of the remaining. You could NOT have THREE different colors because they are only RED or BLUE. So taking one random possible arrangement that might occur to each door of one box, let this be T = Blue, S = Blue, F = Red This means that if this box was 'programmed', if Scully opens door S, she will see Blue as will Mulder if he too should open the box. If actually 'programmed', then each box would have something predictably fixed this way as one probability, not all of them simultaneously, right? So if that was one box arrangement, if Scully randomly picked T while Mulder picked S, they'd both have the SAME COLOR. So the question begins with setting up all possible arrangements for doors. The paired possibilities for what Mulder and Scully respectively could choose would be as follows: (T,T), (T,S), (T, F), (S,T), (S,S), (S,F), (F,T), (F,S), (F,F) [9 of them] Given the box possibility above like, T = Blue, S = Blue, and F = Red, we then have the set of possible colors mapped to the above: (T,T), (T,S), (T, F), (S,T), (S,S), (S,F), (F,T), (F,S), (F,F) (B,B), (B,B), (B,R), (B,B), (B,B), (B,R), (R,B), (R,B), (R,R) Counting the 'sames' only, we have 5/9 of that possible set in which each are certain to have discover the "SAME" color. This means that for every combination KIND that involves two doors with the same color, there is 5/9 of them as the same. There is also the kind where all are the same color which would assure that all 9/9 would turn out to be the same. So listing the KINDS of boxes by their door types, there are eight: T S F B B B <- 9/9 B B R <- 5/9 B R B <- 5/9 B R R <- 5/9 R B B <- 5/9 R B R <- 5/9 R R B <- 5/9 R R R <- 9/9 Collectively, IF the distribution is 'FAIR' as probable, then the totals of all 'sames' are 48/72 = 2/3 That is, if there IS NO HIDDEN factor, 2/3 of them on average should turn out to be the SAME when counting their lists later. The way this was assured in the experiment by Bell's theorem, is to state that at least all the sums of all SAMES ≥ 50% [Obviously they should be more like 2/3 = 67% average] When this was done is real life experiments, the averages were no greater than 50%. This 'proved' that there IS spooky action at a distance because when either Mulder or Scully picked DIFFERENT doors, it had to 'relay' the information to make their partner's boxes similar doors the same to meet only 50% as the same. So does this make sense so far? This is what Bell's Theorem asserts by the example of Brian Greene. Can you see the error? ...or is there one?
 November 21st, 2016, 10:58 PM #5 Newbie   Joined: Mar 2016 From: Saskatoon, Saskatchewan, Canada Posts: 29 Thanks: 1 Math Focus: Logic The error lies in the nature of treating the cases where all doors are equal as simply 1/3 of all options and for the other 1/3 where they are the same as equivalent in weight. The probabilities should break down as: 1/3 (all 3 doors equal color and both select the same door) <--> 100% same 1/3 (of non-similar selected doors for 2/3 same color) <--> 50% same 1/3 (of non-similar selected doors for 2/3 different color) <--> 50% different The bolded are what make up the cases as 2/3 when that first 1/3 must be split or the other two divided. For any one door selected by both Scully, say, Mulder can pick the same door and automatically is assured of a match. But this 'appears' as it should be treated as ONE probability: If Scully picks door T and it is blue, and Mulder picks door T, it can ONLY BE 1 x blue. But if Mulder picked any of the other doors instead, he has 1/2 x blue or 1/2 x red. So this would be more appropriately be: 1/3 x 1 = probability for identical door selection when all 3 the same = 1/3 1/3 x 1/2 = probability for non-similar door selection for the same = 1/6 1/3 x 1/2 = probability for non-similar door selection for differences = 1/6 Thus, when corrected, should 50% in experiment demonstrate they are the same, you have to treat this as constituting the 1/3 + 1/6 weighted parts (= 1/2) in actuality! This definitively disproves Bell's theorem to be useful to prove anything!! Last edited by Scott Mayers; November 21st, 2016 at 11:07 PM. Reason: mistake in number
 November 21st, 2016, 11:28 PM #6 Newbie   Joined: Mar 2016 From: Saskatoon, Saskatchewan, Canada Posts: 29 Thanks: 1 Math Focus: Logic P.S. This is a theorem, by the way, and disproves Bell's own theorem as able to be sufficient to prove the EPR false!
 November 23rd, 2016, 02:37 AM #7 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,099 Thanks: 703 Math Focus: Physics, mathematical modelling, numerical and computational solutions You might find this thread and the links within it interesting: Bell's theorem: simulating spooky action at distance of Quantum Mechanics
November 24th, 2016, 09:28 PM   #8
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 Originally Posted by Benit13 You might find this thread and the links within it interesting: Bell's theorem: simulating spooky action at distance of Quantum Mechanics
Thank you. But in context here if anyone follows, I prove that Bell's Inequality cannot possibly work because when the math is done properly, it leads precisely to what is expected by Aspect.

I was at least hoping for some critical look at this but am guessing my writing is too long or awkward. I might have to clarify this better. (?)

November 25th, 2016, 01:23 AM   #9
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 Originally Posted by Scott Mayers Thank you. But in context here if anyone follows, I prove that Bell's Inequality cannot possibly work because when the math is done properly, it leads precisely to what is expected by Aspect. I was at least hoping for some critical look at this but am guessing my writing is too long or awkward. I might have to clarify this better. (?)
In the thread I linked there is a paper that describes how to perform the violation of Bell's inequality experiment in an undergraduate laboratory, including an explanation of the relevant theory. I think the mathematics laid out there should be the mathematics that you should endeavor to break if you wish to demonstrate an error.

 November 25th, 2016, 01:41 AM #10 Newbie   Joined: Mar 2016 From: Saskatoon, Saskatchewan, Canada Posts: 29 Thanks: 1 Math Focus: Logic I'd prefer a link first to Bell's actual theorem then, not the literal experiments. What I DO understand is the LOGIC, which my proof above satisfies. You start simple BEFORE you introduce the other issues. And if it can't pass the simple logic, then the rest is just a smokescreen to make it seem more legitimate than it actually is. I don't get why some think it satisfactory to demand one go more complex before starting simple. If you can't pass the first stage in normal logic, the rest is just 'art' .....or politics, something I'm guessing likely has more to do with this. I mean no offense, but if you want to help, begin from where I'm seeing it to show WHAT you see is in error in the logic. Math IS logic too but you don't begin to punch numbers in to a calculator unless the actual logical motivation suffices. Thank you for the links though. I'll keep them on hand for a time when and if I can see there is something more to it than I already understand.

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