Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Scott Mayers on 22/11/2016 04:23:31
-
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.
[I'm trying to seek discussion on this in a few different forums simultaneously, btw. I just copied this from MyMathforum instead of uniquely reasking the same question in different words again. Scott.]
-
Basically, Bell's Theorem is used to prove that entangled particles at any distance 'communicates' certain information about their states that conflicts with the limits of the speed of light. It can't be used to communicate directly by adding information at one end and expecting it to transmit itself to the other. At least, this is what the theorem was meant to argue is true if one could set up an experiment which has been done.
The problem originated with the origins of Quantum Mechanics in what was called the "Copenhagen interpretation" of Heisenberg's "Uncertainty Principle". Basically, it seemed (naively) to mean simply that one cannot literally observe certain properties on the atomic scale without disturbing it. This is because to 'see' atomic properties that often deal with things smaller than light waves themselves requires shooting particles OR light itself to 'see' what is in essence changing the very thing by destroying the very thing you are trying to make sense of. For example, if you want to study light waves, how can you USE light to observe light itself? If you shoot a beam of light at a beam of light to see what it is made of, you interfere in what you are trying to make sense of. But you CAN at least do this to learn some things.
If you want to determine WHERE a particle of something is, you shoot at what you believe is its path and if it knocks it off in some way, you can infer its POSITION. But if you know its position, you destroy the capacity to know its velocity.
THIS is sensible and what many initially accepted by Heisenberg's theory. BUT, many had asserted that even in 'principle' of nature itself, like should some 'God' try to observe where a particle is, (even passively without shooting anything at it), the claim made by the theory is that not even God could determine where the particle is because they assert it is EVERYWHERE! And the only way that nature reveals some particular place (or velocity) of it is by COLLAPSING the probability when observed to one unique spot. That, to many was and still is troubling.
This made those like Einstein (et al) find distaste with those who insist this interpretation, now called, the Copenhagen Interpretation where those in strong favor of this 'met for coffee all the time'. Einstein called this "spooky action at a distance" and what the Schrodinger's Cat thought experiment was trying to insult. Einstein also famously rebuked it as though God were throwing dice.
He and others created a paper to show how it would lead to a paradox with clarity (The EPR paradox). Without concerning ourselves with it, by default, we can all seem to relate to this without the formalism. However, a mathematician named John Bell thought that one could actually PROVE this one way or the other through a clever logical argument in math.
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?
-
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!!
-
What is the question you are asking? Please follow the forum rules and phrase your thread title as a question.
Please use MODIFY on the post to alter the title to a question.
Many thanks
Chris Smith, Editor.
-
What is the question you are asking? Please follow the forum rules and phrase your thread title as a question.
Please use MODIFY on the post to alter the title to a question.
Many thanks
Chris Smith, Editor.
I'm sorry. But this definitively PROVES the EPR still true.