Coming Soon!

[FrediFizzx]

@gill1109 It is still a strawman; not my local model. You should have done my non-local model. It is much more simple.
.

[FrediFizzx]

. .

.

[gill1109]

:lol:

Indeed, laugh out loud, even ROTFL!

In the code Fred has:

"Matching Events Observed by Alice and Bob by Trial Numbers"

Code: Select all

listad = outA1[[All, 3]];
listbd = outB1[[All, 3]];

Note that these two variables come from Alice's and Bob's side of the experiment, respectively.
Then a bit later Fred has:

"Local Detection Analysis of the Events Observed by Alice"

Code: Select all

listA4 = Select[outA1, Intersection[{#[[3]]}, listbd] == {#[[3]]}&];

Here he is mixing up data from Alice's side ("outA1") with data from Bob's side ("listbd"). Read on in the code from here and you will see that Bob's local data can have an influence on Alice's final observed outcomes. In fact, since the data systematically violates the CHSH inequality, there are non-local things going on; Fred must be doing something non-local somewhere in the code.

The code is so complex that probably even Fred himself doesn't realise what he is doing. But maybe he is just playing games with us all. In which case: congratulations! LOL.

[FrediFizzx]

@gill1109 I know exactly what I am doing. Didn't I tell you that the 3rd element was the trial numbers? Yes, I did. The selection from outA1 goes to listA4. Completely local.

Are you trying say that I don't get to match events? Of course I get to match events. After the selection process then all the events in listA4 match all the events in listB4.
.

[jreed]

Fred: I put this version on the Wolfram cloud. Here is where it is located. You can take a look at it and execute it. Let me know if you see any differences between it and your "totally local" version.


https://www.wolframcloud.com/obj/ka5qep ... /simple.nb

[gill1109]

@gill1109 I know exactly what I am doing. Didn't I tell you that the 3rd element was the trial numbers? Yes, I did. The selection from outA1 goes to listA4. Completely local.
Are you trying say that I don't get to match events? Of course I get to match events. After the selection process then all the events in listA4 match all the events in listB4.

I'm saying that there is actually no *selection*. No events are discarded. Events are matched by their original event number.

I'm furthermore saying that "listA4" is determined by "outA1" *and* "listbd". Later, "listA4" is used to determine "outA" and that determines "A".

You called the relevant section of the code "Local Detection Analysis of the Events Observed by Alice" but that "detection analysis" is not local at all, since it also makes use of the third column of "OutB1" via "listbd". Alice's k'th outcome is co-determined by Bob's k'th setting. The model is a hidden variables model, but not a local hidden variables model. Alice's k'th outcome depends on the k'th instance of the hidden variables "s" and "lambda", and on both Alice's and Bob's k'th setting.

If you would be so kind as to rewrite your own code in Python or R so that I can rapidly run it many times myself, providing my own input settings and obtaining the complete corresponding outcomes, I will easily prove it to you, by the experiment which we discussed before.

Below I repeat my simulation, now adopting your present definition of lambda; called "R" below.

Code: Select all

M <- 100000
set.seed(1234)
aBits <- sample(c(0, 1), size = M, replace = TRUE)
bBits <- sample(c(0, 1), size = M, replace = TRUE)
aRadians <- aBits * pi / 2
bRadians <- bBits * pi / 2 + pi / 4
set.seed(5678)
R <- 0.3 * cos(runif(M, 0, 2 * pi)/3)^2  # Fodje's M hidden variables rho
S <- runif(M, 0, 2*pi)  # Angles of M spin vectors (radians)
C <- abs(cos(aRadians - S)) < R        # TRUE is "fail", FALSE is "good"
A <- ifelse(C, -sign(sin(aRadians - S)), -sign(cos(aRadians - S)))
AA <- -sign(sin(aRadians - S))
D <- abs(cos(bRadians - S)) < R        # TRUE is "fail", FALSE is "good"
B <- ifelse(D, +sign(sin(bRadians - S)), +sign(cos(bRadians - S)))
BB <- +sign(sin(bRadians - S))
A <- ifelse(D & !(A == AA), -A, A)
B <- ifelse(C & !(B == BB), -B, B)
CHSH <- - mean((A*B)[aBits == 0 & bBits == 0]) + mean((A*B)[aBits == 0 & bBits == 1]) -
          mean((A*B)[aBits == 1 & bBits == 0]) - mean((A*B)[aBits == 1 & bBits == 1])
CHSH

Result: 2.610406

Now, replace Fodje's lambda by Pearle/Gill's

Code: Select all

# R <- 0.3 * cos(runif(M, 0, 2 * pi)/3)^2  # Fodje's M hidden variables rho
R <- 2 / (sqrt(runif(M, 1, 4))) - 1 # Gill's M hidden variables according to Pearle


This leads to the amazing

Code: Select all

> CHSH
[1] 3.123296

Fred: you can get much better results by changing your definition of lambda...

[FrediFizzx]

@gill1109 Not interested in your non-local strawman code. listbd is only trial numbers which are shared HV. If you don't use the trial numbers for matching, you are non-local.
.

[gill1109]

@gill1109 Not interested in your non-local strawman code. listbd is only trial numbers which are shared HV. If you don't use the trial numbers for matching, you are non-local.
.

I suspect you are mistaken. Maybe someone who owns Mathematica would like to print out the contents of "listbd" for a small example. I think your code does not do what you think it does. And meantime you can tell us if John Reeds' program indeed generates identical data to yours.

[FrediFizzx]

@gill1109 Not interested in your non-local strawman code. listbd is only trial numbers which are shared HV. If you don't use the trial numbers for matching, you are non-local.
.

I suspect you are mistaken. Maybe someone who owns Mathematica would like to print out the contents of "listbd" for a small example. I think your code does not do what you think it does. And meantime you can tell us if John Reeds' program indeed generates identical data to yours.

I know exactly what the code does. Here is listbd for 1,000 trials.

Code: Select all

{1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, \
23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, \
40, 41, 42, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, \
60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, \
78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 95, 96, 97, \
98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, \
112, 113, 114, 115, 116, 117, 119, 121, 122, 123, 124, 125, 126, 127, \
128, 129, 132, 134, 136, 137, 138, 139, 140, 141, 143, 144, 145, 146, \
147, 148, 149, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, \
163, 164, 165, 166, 167, 169, 170, 171, 172, 173, 174, 175, 176, 177, \
178, 179, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 193, \
194, 196, 197, 198, 199, 201, 202, 203, 204, 205, 206, 207, 208, 209, \
210, 211, 212, 213, 215, 216, 218, 219, 220, 221, 222, 223, 225, 227, \
228, 230, 231, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, \
244, 245, 246, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, \
259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, \
273, 274, 275, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, \
288, 289, 290, 291, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, \
303, 304, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, \
318, 319, 320, 321, 323, 324, 325, 326, 327, 329, 330, 331, 332, 333, \
334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 345, 346, 348, 349, \
350, 351, 352, 353, 354, 355, 356, 358, 359, 360, 361, 362, 363, 364, \
365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, \
379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 390, 391, 392, 393, \
394, 395, 396, 398, 400, 401, 402, 403, 404, 406, 407, 408, 409, 410, \
411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, \
425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, \
439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 450, 451, 452, 453, \
454, 455, 456, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, \
469, 471, 472, 473, 474, 475, 476, 477, 479, 480, 481, 482, 483, 484, \
485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 497, 498, 500, \
501, 502, 503, 504, 505, 506, 508, 509, 510, 512, 513, 514, 515, 516, \
517, 518, 519, 520, 521, 523, 524, 525, 526, 527, 528, 529, 530, 531, \
532, 533, 534, 537, 538, 539, 540, 541, 542, 543, 544, 545, 547, 548, \
549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, \
563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, \
577, 578, 579, 581, 582, 584, 585, 586, 587, 588, 589, 590, 591, 592, \
594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 608, 609, \
610, 611, 612, 613, 614, 615, 617, 619, 620, 621, 622, 623, 624, 625, \
626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 637, 638, 639, 640, \
641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 653, 654, 655, \
656, 657, 658, 659, 660, 661, 663, 664, 665, 666, 669, 670, 671, 672, \
673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 687, \
688, 689, 690, 691, 692, 694, 695, 696, 697, 698, 700, 701, 702, 703, \
704, 705, 706, 707, 708, 710, 711, 712, 713, 714, 715, 716, 717, 718, \
720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, \
736, 738, 739, 740, 741, 742, 743, 745, 746, 747, 748, 749, 750, 751, \
752, 753, 754, 756, 757, 758, 760, 761, 762, 763, 764, 765, 766, 767, \
768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 779, 780, 781, 782, \
783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, \
797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 808, 809, 810, 811, \
813, 815, 816, 817, 818, 823, 824, 825, 826, 827, 828, 829, 830, 831, \
832, 833, 834, 835, 836, 837, 838, 839, 841, 842, 843, 844, 845, 847, \
848, 849, 850, 851, 852, 853, 854, 855, 857, 858, 859, 860, 861, 862, \
863, 865, 866, 867, 868, 870, 871, 872, 873, 874, 875, 876, 877, 878, \
881, 882, 883, 884, 885, 886, 887, 889, 890, 891, 892, 893, 894, 895, \
896, 897, 898, 899, 900, 901, 902, 903, 905, 906, 907, 908, 909, 911, \
913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, \
927, 928, 929, 930, 931, 932, 933, 934, 935, 937, 938, 939, 940, 941, \
942, 943, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 957, \
958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, \
972, 975, 976, 977, 978, 979, 980, 981, 982, 985, 986, 987, 988, 989, \
990, 991, 992, 994, 995, 997, 998, 1000}

It is just trial numbers from outB1. I don't care about John's strawman non-local code. Plus John never put his code up on the Wolfram Cloud and linked it here. Just like I don't care about yours. I have my own non-local code that is much better and was the inspiration for the local code.
.

[FrediFizzx]

It is really easy to publish to the Wolfram Cloud.

https://www.wolframcloud.com/obj/fredif ... r-test2.nb

Click on it and tell me what happens. I get a webpage that opens the file and displays it.
.

[jreed]

It is really easy to publish to the Wolfram Cloud.

https://www.wolframcloud.com/obj/fredif ... r-test2.nb

Click on it and tell me what happens. I get a webpage that opens the file and displays it.
.

I already did this and posted it. Here is the link to my version that substitutes do loops for your Mathematica code:

https://www.wolframcloud.com/obj/ka5qep ... /simple.nb

[jreed]

One other thing I meant to tell you. I ran your version with SeedRandom set and my version with the same SeedRandom. All inputs were the same to both programs. CHSH came out identical for both runs, up to the limit of the numbers being displayed. These two programs are doing the same thing, except your version runs much slower, due to all that unnecessary messing around with those Mathematica routines that don't accomplish anything other than switching some signs. It's much easier to do that with a do loop.

[FrediFizzx]

@jreed Sorry, but your model is still a non-local strawman where mine is local. There no way of getting around all that code if you want to keep it local by using shared trial numbers. Besides, I already have a better non-local model than yours and Gill's. And another freakin' besides; you have to match events to get results just like the experimenters. You guys are trying to tell us that we CAN'T match events. It's pure nonsense.
.

[FrediFizzx]

I guess I need to post my simple awesome non-local model again that was the inspiration for the local model.

https://www.wolframcloud.com/obj/fredif ... ops-non.nb

You can just click on the link and it will open the notebook file in a webpage. I said to myself, wow! That works really good. Now, what do I have to do to make it a local model? Well, it was quite a task but here is the result.

https://www.wolframcloud.com/obj/fredif ... r-forum.nb

Enjoy!

[gill1109]

@jreed Sorry, but your model is still a non-local strawman where mine is local. There no way of getting around all that code if you want to keep it local by using shared trial numbers. Besides, I already have a better non-local model than yours and Gill's. And another freakin' besides; you have to match events to get results just like the experimenters. You guys are trying to tell us that we CAN'T match events. It's pure nonsense.
.

I’m telling you, Fred, that experimenters do not match events: they match time-slots. Within two matched time slots, there is input data and output data, both on Alice’s side and on Bob’s side. The input data are randomly chosen, binary, settings; one on each side. They are used locally to rotate polarisers or equivalent to one of two desired angles. The output data is processed locally by a predefined algorithm to generate a binary outcome. The experimenters analyse the binary inputs and binary outputs in the usual way. You can call that “matching of events” if you like. But it is *pre-matching*.

I have a two week free trial of Mathematica just starting. That should enable me to get some interesting results. I plan to find out which loophole you are exploiting in order to violate CHSH. I don’t need to understand your code. I just need to add some judiciously chosen output statements, and to arrange that settings are chosen from a file. Another thing I can do is to rigidly enforce that only local data is processed on each side of the experiment. Trial numbers from both sides are OK. But Bob’s setting must not influence Alice’s outcome. That is easy to enforce. I’ll show you exactly what I do, so that everyone can see that it should, according to you, have no influence on the outcomes. But it will destroy the violation of CHSH…

If I am wrong, this will lead to a hat-eating event, and undying fame (maybe even the Nobel prize) for Fred. He will have demonstrated signature evidence for quantum entanglement in strictly classical physical systems (a pair of separated, classical, error-free / totally deterministic digital computers) in the strictly controlled context of a loophole-free experiment.

[gill1109]

I did the following experiment. I read 30 settings each from two files instead of generating them in the program. I fixed the random seed so that the hidden variables which are generated for, say, 30 trials will be the same, even if the settings are different. Changing Bob's settings resulted in some of Alice's outcomes being changed.

I am planning not to eat my hat for the time being. If anyone is interested I can post the program which I ran, the two sets of inputs, and the two sets of outputs. The program is simply Fred's, absolutely nothing altered, except to read settings from files and to skip the statistical calculations and graph-drawing at the end. Instead, I just printed out the settings which had been used and the outcomes which had been observed.

AliceSettings
90, 90, 0, 0, 90, 0, 0, 0, 0, 0, 90, 0, 0, 90, 0, 0, 0, 0, 90, 90, 0, 0, 90, 0, 0, 90, 90, 0, 0, 90

BobSettings
135, 135, 135, 135, 135, 135, 135, 45, 45, 135, 45, 135, 135, 45, 45, 45, 135, 45, 45, 135, 45, 135, 45, 45, 135, 135, 45, 135, 135, 135

BobAlternativeSettings
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

AliceOriginalOutcomes
A = {1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1}

AliceAlternativeOutcomes
A = {1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1}

https://www.wolframcloud.com/obj/ca4aabf8-e195-4b73-aff7-6a7cfe0ccf7b

[FrediFizzx]

@gill1109 Sorry, but your test proves nothing since it doesn't account for trial numbers being a hidden variable.
.

[gill1109]

@gill1109 Sorry, but your test proves nothing since it doesn't account for trial numbers being a hidden variable.
.

I did not touch the trial numbers. Trial numbers are not *hidden*. I changed nothing in your code. I just changed Bob’s settings (all of them, in fact). Please explain how this could affect Alice’s third outcome.

I suspect that Bill Nelson did not understand what you wanted to do, and that you do not understand his “solution”. Sorry if I’m wrong. I’m just trying to understand how you could violate Bell-CHSH. There are theorems from computer science about whether or not this can be done. It has nothing whatever to do with physics. Just about computation (with classically networked classical computers). https://community.wolfram.com/groups/-/m/t/2279360

[FrediFizzx]

@gill1109 More freakin' nonsense. Matching events for A and B is basically a non-local process. That is all your test is showing is that we are matching events between A and B.
.

[gill1109]

@gill1109 More freakin' nonsense. Matching events for A and B is basically a non-local process. That is all your test is showing is that we are matching events between A and B.

Experimenters do not “match events”. Nature does not “match events”. Experimenters pre-define matched time-slots and correlate local data generated locally in the matched time-slots. My test shows what it shows: your model is a hidden variables model, but not a local hidden variables model. A = A(a, b, lambda); B = B(a, b, lambda).

Actually I need to do a few more tests in order to show that, in the example I showed you, the outcomes of trial three only depend on the hidden variables and settings of trial three. No use of memory loophole, no retro-causality. In fact, k = k_A = k_B. The LaTeX formulas which Joy supplied are *not* the formulas actually used to compute outcomes from settings and hidden variables.