gill1109 wrote:Christian's experimental paper makes completely clear that every correlation is based on the whole sample. Will he revise that paper?
Joy Christian wrote:For the record, let me repeat that equation (16) of my experimental paper describes exactly how the expectation values E(a, b), E(a', b), E(a, b'), and E(a', b') are to be computed in my proposed experiment. Four separate sums are to be calculated as follows
E(a, b) = 1/N Sum_j A_j B_j ,
E(a, b') = 1/N Sum_j A_j B'_j ,
E(a', b) = 1/N Sum_j A'_j B_j ,
and
E(a', b') = 1/N Sum_j A'_j B'_j .
It is a matter of indifference whether N here is chosen to be the same or different for each of the four alternatives.
Heinera wrote:An alternative version of the bet could be that Richard only computes one correlation E(a,b) on the whole set, but he is free to pick any values of a and b he wants. He decides on values of a and b after he has received the data files from the experiment (the experiment doesn´t know a thing about detector settings anyway).
If the computed correlation differs from the QM correlation by more than +/- 0.2, we agree that QM correlations are not reproduced and Richard wins.
Even Michel seems to think that QM correlations could be achieved this way.
Joy Christian wrote:
There will be no alternative version of the bet.
Heinera wrote:Joy Christian wrote:
There will be no alternative version of the bet.
Ok. Have you reached a conclusion as to what the original version of the bet looks like? Does Richard´s last version of the R script represent that?
Joy Christian wrote:Heinera wrote:Joy Christian wrote:
There will be no alternative version of the bet.
Ok. Have you reached a conclusion as to what the original version of the bet looks like? Does Richard´s last version of the R script represent that?
I don't see sampling without replacement in the latest code by Richard. But I am not a programmer. In fact, I know nothing about programming.
Heinera wrote:How can one go through a PhD program in physics and not be exposed to some computer programming? Just curious, because from my own experience, that would be impossible for a math PhD.
Joy Christian wrote:Heinera wrote:How can one go through a PhD program in physics and not be exposed to some computer programming? Just curious, because from my own experience, that would be impossible for a math PhD.
It is not necessary to know programing to practice either physics or mathematics. Roger Penrose, Stephen Hawking, Edward Witten, Michael Atiyah, Grigori Perelman, and Andrew Wiles seem to have done just fine without knowing any programing.
Heinera wrote:Joy Christian wrote:Heinera wrote:How can one go through a PhD program in physics and not be exposed to some computer programming? Just curious, because from my own experience, that would be impossible for a math PhD.
It is not necessary to know programing to practice either physics or mathematics. Roger Penrose, Stephen Hawking, Edward Witten, Michael Atiyah, Grigori Perelman, and Andrew Wiles seem to have done just fine without knowing any programing.
Trust me: All of those six gentlemen know how to program.
Heinera wrote:Well, well. I don´t see much point in pushing that argument any further. Anyway, you have somehow agreed to enter into a bet that is of a kind where a lack of programming knowledge is a clear disadvantage to you. I venture to guess that none of the mentioned six gentlemen where ever in the same situation; i.e, they never had to make a public monetary bet to get their theory through.
Joy Christian wrote:Heinera wrote:Joy Christian wrote:
There will be no alternative version of the bet.
Ok. Have you reached a conclusion as to what the original version of the bet looks like? Does Richard´s last version of the R script represent that?
I don't see sampling without replacement in the latest code by Richard. But I am not a programmer. In fact, I know nothing about programming.
Sample <- sample(c(1, 2, 3, 4), N, replace = TRUE)
A <- sign(cos(AliceTheta[Sample == 1] - Alpha))
B <- - sign(cos(BobTheta[Sample == 1] - Beta))
Joy Christian wrote:Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of an EPR-Bohm type setup [6], with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions a and b for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the angular momentum lambda_j (or −lambda_j) for each shell, without disturbing them otherwise, at a designated distance from the center. The interfaced computers can then record this data, in the form of a 3D map of all such directions. Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station—from within their already existing 3D maps of data—and then calculate the corresponding dynamical variables sign (lambda_j · a) and sign (−lambda_j · b). This “delayed choice” of a and b will guarantee that the conditions of parameter independence and outcome independence are strictly respected within the experiment [2]. It will ensure, for example, that the local outcome sign (lambda_j · a) remains independent not only of the remote parameter b, but also of the remote outcome sign (−lambda_j · b). If in any doubt, the two computers can be located at a sufficiently large distance from each other to ensure local causality while selecting a and b. The correlation function for the bomb fragments can then be calculated using the formula
E(a, b) = 1/N sum_{j =1}^N {sign (lambda_j · a)} {sign(−lambda_j · b)}, (16)
where N is the number of trials.
Joy Christian wrote:Now consider a large ensemble of such balls, identical in every respect except for the relative locations of the two lumps (affixed randomly on the inner surface of each shell). The balls are then placed over a heater—one at a time—at the center of an EPR-Bohm type setup [6], with the common plane of their shells held perpendicular to the horizontal direction of the setup. Although initially at rest, a slight increase in temperature of each ball will eventually eject its two shells towards the observation stations, situated at a chosen distance in the mutually opposite directions. Instead of selecting the directions a and b for observing spin components, however, one or more contact-less rotational motion sensors—capable of determining the precise direction of rotation—are placed near each of the two stations, interfaced with a computer. These sensors will determine the exact direction of the angular momentum lambda_j (or −lambda_j) for each shell, without disturbing them otherwise, at a designated distance from the center. The interfaced computers can then record this data, in the form of a 3D map of all such directions. Once the actual directions of the angular momenta for a large ensemble of shells on both sides are fully recorded, the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station—from within their already existing 3D maps of data—and then calculate the corresponding dynamical variables sign (lambda_j · a) and sign (−lambda_j · b). This “delayed choice” of a and b will guarantee that the conditions of parameter independence and outcome independence are strictly respected within the experiment [2]. It will ensure, for example, that the local outcome sign (lambda_j · a) remains independent not only of the remote parameter b, but also of the remote outcome sign (−lambda_j · b). If in any doubt, the two computers can be located at a sufficiently large distance from each other to ensure local causality while selecting a and b. The correlation function for the bomb fragments can then be calculated using the formula
E(a, b) = 1/N sum_{j =1}^N {sign (lambda_j · a)} {sign(−lambda_j · b)}, (16)
where N is the number of trials.
gill1109 wrote:Apparently he actually meant, that the whole experiment has to be repeated, over and over again, for each new pair of reference directions! Moreover we are going to have to wait an awful long time till we coincidentally hit on the four pairs of reference directions which we agreed on. In the equatorial plane, 0 and 90 degrees longitude for Alice, 45 and 135 for Bob (four combinations). Seems hard to believe that this was the intention ... still if we go on long enough, eventually we will be doing the experiment with the four pairs (a, b) which are needed to resolve the bet. Seems an awful waste of resources.
Actually, reading his text closely, he says we are only allowed to compute correlations for pairs of angles "from within their already existing 3D maps of data". I always found this really weird. But I imagined that if N is large we will have observed directions for Alice close to the directions I want for Alice, and directions for Bob close to the directions I want for Bob (we have two 3D maps, right?). I imagined that since the maps *already existed* we were always talking about the same maps based on the same video footage of the same N exploding balls, for any correlations we want to calculate. Silly me.
Joy Christian wrote:Are you deliberately being dumb just to frustrate me? We are talking about actual spin directions, say u_k. And then a reference observation direction a. The component of spin is to measured about a. How does one do that? Well, Bell already told us how in his 1964 paper. See his equation (9). We have to compute A(a, u_k) = sign(a.u_k). We are doing just Bell's own local model. if you are confused about Bell's own equation (9) then you shouldn't be in this business.
(* Richard Gill's bet with Joy Christian *)
(* Translated into \
Mathematica by John Reed *)
aliceDirections =
ReadList["http://www.math.leidenuniv.nl/~gill/AliceDirections.txt", \
{Real, Real}];
aliceTheta =
Table[aliceDirections[[i, 1]], {i, Length[aliceDirections]}];
nAlice = Length[aliceTheta]
bobDirections =
ReadList["http://www.math.leidenuniv.nl/~gill/BobDirections.txt", \
{Real, Real}];
bobTheta = Table[bobDirections[[i, 1]], {i, Length[bobDirections]}];
nBob = Length[bobTheta]
nAlice
If[nAlice != nBob, Print["Error: particle numbers don't match"],
Print["Go Ahead"]]
mean[a_, b_, alpha_, beta_] :=
Mean[-Sign[Cos[a - alpha]] Sign[Cos[b - beta]]] // N
(* First pair of measurement directions *)
alpha = 0 Degree;
beta = 45 Degree;
E11 = mean[aliceTheta, bobTheta, alpha, beta];
(* Second pair of measurement directions *)
alpha = 0 Degree;
beta = 135 Degree;
E12 = mean[aliceTheta, bobTheta, alpha, beta];
(* Third pair of measurement directions *)
alpha = 90 Degree;
beta = 45 Degree;
E21 = mean[aliceTheta, bobTheta, alpha, beta];
(* Fourth pair of measurement directions *)
alpha = 90 Degree;
beta = 135 Degree;
E22 = mean[aliceTheta, bobTheta, alpha, beta];
CHSH := E12 - E11 - E21 - E22
CHSH
If[CHSH > 2.4, Print["Congratulations, Joy"],
Print["Congratulations, Richard"]]
Congratulations, Richard
(* Second experiment *)
AliceTheta = RandomReal[{0, 360 Degree // N}, 1000];
BobTheta = -AliceTheta;
correlation = ConstantArray[0, 37];
a = Sign[Cos[AliceTheta]];
Do[
delta = (i - 1) 10 Degree;
b = -Sign[Cos[BobTheta - delta]];
correlation[[i]] = Mean[a b], {i, 37}]
ListPlot[correlation, AxesLabel -> {Degrees, Correlation},
DataRange -> {0, 360}]
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