# Bell's theorem: simulating spooky action at distance of Quantum Mechanics

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Malus's law simulation and spooky action at distance

L1= (rand()%100 < ((cos(P1) * cos(P1)) * 100)) ? 1:0
L2= (rand()%100 < ((cos(P2) * cos(P2)) * 100)) ? 1:0

Using Malus's law calculate probability of photon L1 passing through polarizer P1, and L2 through P2. If random number between 0 and 100 is less than photon's probability percentage the photon goes through (= 1), otherwise it gets blocked (= 0).

if (L1 == L2) MATCH++ else MISMATCH++
RESULT= (MATCH - MISMATCH)/(N_MEASURE/100))

If both L1 and L2 passed through (1 = 1) or both got stopped (0 = 0) increase matching pairs counter, otherwise increase opposite pairs counter. That's all, just like in the experiment. Here is roughly what's happening with 100 photon pairs sequences:

P1= -25 -> Malus's law -> 82% ~ 82 out of 100
P2= 25 -> Malus's law -> 82% ~ 82 out of 100

0111110011 1111111011 1111100111 1111111111 1111111110 1101111011 0111101110 1111111111 1111111111 1111101111
1111111111 1110111011 1111001111 1111111101 0111111101 0011011111 1011111011 1111110001 1110001111 1101110111

match= 71
mismatch= 29
num_data= 100
Result: (71-29)/(100/100) = 42%

QM prediction: cos^2(50) * 100 = 41.32%

Ooops, this was supposed to be impossible. So Quantum Mechanics is just misunderstood classical physics. Awwww.

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This is a forum for game developers. There are better places on the net to bother physicists with your theories.

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This is a forum for game developers. There are better places on the net to bother physicists with your theories.

I tried physics forums, they don't understand it, plus they do not want to believe it. They do not see Malus's law in those first two lines of code, they think I "programmed" the result. Then I tell them it works for any setup with whatever polarizers, light beams, photons and photon pairs, and that they only need to try it out and see for themselves. Then they get mad and I get banned.

In any case, can you suggest some of those better places, hopefuly where people would understand the code at least that much so they don't accuse me of "cheating"?

Edited by humbleteleskop

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Ignoring how you've come to set up your code above, the "game" that the code represents is:

Pick a number from 0 to 99. Is the number less than 82?

Repeat.

How often does the answer to that question match the previous answer?

Exactly. There is no setup, you just plug in P1 and P2 angles for the two polarizer and let it ride. The more loops there are, the more result converges to "correct" answer, just like in the actual experiments.

So given 100 samples, a result of 70 or 71 matches and 29 or 30 mismatches is completely expected... The code produces the numbers that you've told it to produce... Which doesn't prove anything...

So far, this seems the same as saying: If you flip a coin, you will get heads 50% of the time... therefore aliens!

Exactly. The problems is the scientific world looks at that data and concludes... therefore photons must be magically correlated and communicating faster than light, which they call "spooky action at distance". It's nice to see how people not indoctrinated with the QM theory can see right through this superstitios quantum nonsense.

What is your simulation supposed to prove? You should probably try explaining it with math instead.

Is it that you've arrived at the same answer using two techniques, one of which is QM and the other is Malus' law?

It's a long story to explain. Try this, post #18:

In short, yes. According to Bell's theorem it is impossible for deterministic or classical methods to ever predict that result. It is the proof of what they call "non-locality" of Quantum Mechanics. It's a pretty big deal for QM, it has to do with entagled particles and quantum computing, uncertainity principle, double-slit experiment, and all that stuff.

There's 100 numbers, 18 result in yes, 82 result in no.

Two 'no's in a row is 0.822, or 67.24%.

Two 'yes's in a row is 0.182, or 3.24%

A 'no' and a 'yes' is 0.18*0.82 + 0.82*0.18, or 29.52%

Two 'yes's or two 'no's is 67.24% + 3.24%, which is 70.48%

That's beyond me. Could you express that as some probability function I could use in Wolfram Alpha online?

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#include <math.h>
#include <time.h>
#include <stdio.h>

void main()
{
int         N_REPEAT= 10000;
float       P1=                  30;        // <--- polarizer-1
float       P2=                  30;        // <--- polarizer-2

//    printf("Number of measuremnts: "); scanf("%d", &N_REPEAT);
printf("\nAngle polarizer P1: "); scanf("%f", &P1);
printf("Angle polarizer P2: "); scanf("%f", &P2);

Init_Setup:;
system("cls");
srand(time(NULL));
int         N_MEASURE= 0;
int         MATCH= 0;
int         MISMATCH= 0;

// relative angle & radian conversion
float       REL_P1= 0.0174533* (P1-P2)/2;
float       REL_P2= 0.0174533* (P2-P1)/2;

BEGIN:;
int L1= (rand()%100 < ((cos(REL_P1)*cos(REL_P1))*100)) ? 1:0;
int L2= (rand()%100 < ((cos(REL_P2)*cos(REL_P2))*100)) ? 1:0;

printf("\n %d%d", L1, L2);
if (L1 == L2) MATCH++; else MISMATCH++;
if (++N_MEASURE < N_REPEAT) goto BEGIN;

printf("\n\nMATCH: %d\nMISMATCH: %d", MATCH, MISMATCH);
printf("\nMalus(%d): %.0f%%", abs((int)((P1-P2)/2)), ((cos(REL_P1)*cos(REL_P1))*100));
printf("\n\n>>> RESULT: %.2f%%", (float)(MATCH-MISMATCH)/(N_MEASURE/100));

printf("\n\nPress a key to repeat.");
getch(); goto Init_Setup;
}



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There's 100 numbers, 18 result in yes, 82 result in no.
Two 'no's in a row is 0.822, or 67.24%.
Two 'yes's in a row is 0.182, or 3.24%

A 'no' and a 'yes' is 0.18*0.82 + 0.82*0.18, or 29.52%
Two 'yes's or two 'no's is 67.24% + 3.24%, which is 70.48%

That's beyond me. Could you express that as some probability function I could use in Wolfram Alpha online?

It's just basic probability... here's the working:

Looking at one interaction:
* Chance of Y = 0.18
* Chance of N = 0.82
Total of above = 0.18 + 0.82 = 1.0 (making sure we've covered all possibilities)

Looking at two interaction, there's 4 possibilities: N and N, N and Y, Y and N, Y and Y.
* Chance of NN = N*N = 0.82 * 0.82 = 0.822 = 0.6724
* Chance of NY = N*Y = 0.82 * 0.18 = 0.1476
* Chance of YN = Y*N = 0.18 * 0.82 = 0.1476
* Chance of YY = Y*Y = 0.18 * 0.18 = 0.182 = 0.0324
Total of above = 0.6724 + 0.1476 + 0.1476 + 0.0324 = 1.0 (still making sure we've covered all possibilities)

If we then classify Match is NN or YY, and Nonmatch is NY or YN, we get
* Chance of Match = NN+YY = 0.822 + 0.182 = 0.6724 + 0.0324 = 0.7048 = 70.48%
* Chance of Nonmatch = NY+YN = 0.82*0.18 + 0.18*0.82 =  0.1476 + 0.1476 = 0.2952 = 29.52%
Total of still above = 0.7048 + 0.2952 = 1.0 (still making sure we've covered all possibilities)

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You're obviously misinterpreting Bell's theorem, because it's obvious you can write a program that approximates any probability distribution (and I don't know anything about quantum mechanics, but even that is clear to me). You do sound like a crank, though, especially reading through that physicsforums thread, so I'll pass.

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There's 100 numbers, 18 result in yes, 82 result in no.
Two 'no's in a row is 0.822, or 67.24%.
Two 'yes's in a row is 0.182, or 3.24%

A 'no' and a 'yes' is 0.18*0.82 + 0.82*0.18, or 29.52%
Two 'yes's or two 'no's is 67.24% + 3.24%, which is 70.48%

That's beyond me. Could you express that as some probability function I could use in Wolfram Alpha online?

It's just basic probability... here's the working:

Looking at one interaction:
* Chance of Y = 0.18
* Chance of N = 0.82
Total of above = 0.18 + 0.82 = 1.0 (making sure we've covered all possibilities)

Looking at two interaction, there's 4 possibilities: N and N, N and Y, Y and N, Y and Y.
* Chance of NN = N*N = 0.82 * 0.82 = 0.822 = 0.6724
* Chance of NY = N*Y = 0.82 * 0.18 = 0.1476
* Chance of YN = Y*N = 0.18 * 0.82 = 0.1476
* Chance of YY = Y*Y = 0.18 * 0.18 = 0.182 = 0.0324
Total of above = 0.6724 + 0.1476 + 0.1476 + 0.0324 = 1.0 (still making sure we've covered all possibilities)

If we then classify Match is NN or YY, and Nonmatch is NY or YN, we get
* Chance of Match = NN+YY = 0.822 + 0.182 = 0.6724 + 0.0324 = 0.7048 = 70.48%
* Chance of Nonmatch = NY+YN = 0.82*0.18 + 0.18*0.82 =  0.1476 + 0.1476 = 0.2952 = 29.52%
Total of still above = 0.7048 + 0.2952 = 1.0 (still making sure we've covered all possibilities)

I see, but how to get 42% out of that, the "correct" answer?

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I see, but how to get 42% out of that, the "correct" answer?

You tell me, what's the logic behind this step below?
What does result = matches - mismatches mean?

match= 71
mismatch= 29
num_data= 100
Result: (71-29)/(100/100) = 42%

Inserting the numbers from the probability above, that gives result = 40.96%... but what is result?

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You're obviously misinterpreting Bell's theorem, because it's obvious you can write a program that approximates any probability distribution (and I don't know anything about quantum mechanics, but even that is clear to me). You do sound like a crank, though, especially reading through that physicsforums thread, so I'll pass.

You are forgetting that if they thought it's just some "normal" probability function, they wouldn't be saying photon pairs are entangled with some mysterios bond and are communicating faster than ligh. They would not call it "spooky", they would not be proving their theories and "non-locality" with it.

http://en.wikipedia.org/wiki/Quantum_nonlocality

http://en.wikipedia.org/wiki/Local_hidden_variable_theory

Rigorously, quantum nonlocality refers to QM predictions of many-system measurement correlations that cannot be simulated by any classical physics.

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I see, but how to get 42% out of that, the "correct" answer?

You tell me, what's the logic behind this step below?
What does result = matches - mismatches mean?

match= 71
mismatch= 29
num_data= 100
Result: (71-29)/(100/100) = 42%

Inserting the numbers from the probability above, that gives result = 40.96%... but what is result?

Uh, I missed that, somehow. So, if that is so simple, what about it could possibly posses QM white-coats to interpret those results as a proof of non-locality and spooky action at distance?

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What does result = matches - mismatches mean anyway?

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What does result = matches - mismatches mean anyway?

We are asking the same question. They call it "correlation", but it can be inverted so that 30% correlation is the same thing as what they sometimes call 70% discordance.  Apperantly it is discribing some instantenous magical entanglement between pothon pairs regardless of distnace. You do something to one photon in Amsterdam, and its twin brother photon in Tokyo instantly does soemthing in response. How is that number supposed to contain or represent such information is beyond me. I wish we could unswer that question here.

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What does result = matches - mismatches mean anyway?

http://en.wikipedia.org/wiki/Quantum_nonlocality

http://en.wikipedia.org/wiki/Local_hidden_variable_theory

- "Imagine two experimentalists, Alice and Bob, situated in separate laboratories. They conduct a simple experiment in which Alice chooses and pushes one of two buttons, A0 and A1, on her apparatus, and Bob observes on his apparatus one of two indicating lamps, b0 and b1, lighting. In this case there are four possible events that could occur in the experiment: (A0,b0), (A0,b1), (A1,b0) and (A1,b1). Suppose that after many runs of the experiment, only the events (A0,b0) and (A1,b1) occur; this is good evidence that A has an influence on b."

Here is how the experiment goes:

N= number of discordance (mismatches)

N(+30°, -30°) ? N(+30°, 0°) + N(0°, -30°) <- "Bell's inequality"

25%+25% = 50% ??

But, according to QM and physical experiments we will now get 75% discordance!

25%+25% = 75% !!

QM prediction: sin^2(60º) = 75%

------------------ END -------------------

Apperantly only that last "discordance" of 75% is "paranormal", for some reason.

The mistake they are making must be this assumption: 25%+25% = 50%

Those percentages simply don't add up like that.

Edited by humbleteleskop

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i think simulating a photon would be much more reailable than this pseudo code of yours/

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i think simulating a photon would be much more reailable than this pseudo code of yours/

All the known variables are taken into equation exactly replicating experimental setup as well as the results. What is more reliable and correct than already correct and reliable result? How do you "simulate" a photon, what is it you are actually suggesting?

edit: my spell-checker doesn't work on this form.

Edited by humbleteleskop

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If we then classify Match is NN or YY, and Nonmatch is NY or YN, we get
* Chance of Match = NN+YY = 0.822 + 0.182 = 0.6724 + 0.0324 = 0.7048 = 70.48%
* Chance of Nonmatch = NY+YN = 0.82*0.18 + 0.18*0.82 =  0.1476 + 0.1476 = 0.2952 = 29.52%
Total of still above = 0.7048 + 0.2952 = 1.0 (still making sure we've covered all possibilities)

// Hodgman's exact probabilty equation
float T= cos(REL_P1)*cos(REL_P1);
float F= 1.0 - T;

float MCH= (T*T)+(F*F);
float MSM= (T*F)+(F*T);
printf("\n\n>>> EXACT RESULT: %.2f%%", (MCH-MSM)*100);


Hope you don't mind, we'll share Nobel Price money for debunking QM's paranormal mysteries. Thanks!

Marge:
- Homer, is this the way you pictured married life?

Homer:
- Yeah, pretty much. Except we drove around in a van solving mysteries.

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Is it apparent the OP here has absolutely no idea of quantum mechanics what-so-ever. I'm very much unsurprised that people on physics forums ignored your arguments Humbleteleskop!

I suggest you read up on quantum field theory until you realize how wrong you were, and only then start thinking of ideas of how to disprove quantum entanglement (which will be tough, as it's theoretically and experimentally well established). A good start might be to follow these lectures on QM: https://www.youtube.com/watch?v=2h1E3YJMKfA

Edited by Mats1

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Is it apparent the OP here has absolutely no idea of quantum mechanics what-so-ever. I'm very much unsurprised that people on physics forums ignored your arguments Humbleteleskop!

One one hand you have spoky magic of QM for which there is no explanation or understanding, and on the other you have clasical mechanics which you can simulate and see with your own eyes it's all simply a matter of how the odds go, naturally. Believe what you will.

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Is it apparent the OP here has absolutely no idea of quantum mechanics what-so-ever. I'm very much unsurprised that people on physics forums ignored your arguments Humbleteleskop!

One one hand you have spoky magic of QM for which there is no explanation or understanding, and on the other you have clasical mechanics which you can simulate and see with your own eyes it's all simply a matter of how the odds go, naturally. Believe what you will.

You do know that a lot of our modern technology depends on quantum mechanics in one way or the other, right? Nanotechnology such as modern processors could not work without an understanding of quantum tunnelling, so the computer you are typing this post on is a (successful) product of the (successful) research that's gone into quantum mechanics. Precise timekeeping depends on quantum mechanics and the theory of relativity. Some medical scan technologies rely on an understanding of quantum mechanics to give accurate results, for instance. You and I live in a quantum-mechanical world - literally.

So allow me to flip your argument around: quantum mechanics has been very successful in predicting small-scale phenomena and giving scientists an understanding of how particles behave at this scale. It allowed teams of engineers to build devices which could not have even been conceived a few decades earlier. Every time I look at a computer or pull out my phone or use a GPS, that's a very real and tangible outcome of quantum mechanics. Seems to work fine, wouldn't you agree? Now what does your "experiment" tell us, that scientists were in fact completely wrong, and that the whole theory can be disproved by a layman experiment and is therefore bogus? (and as I understand it Bell's theorem is kind of the heart of quantum mechanics - if it is shown to be incorrect, the entire theory falls apart).

On one hand we have your "theory", which just claims all our modern technology works on fairy dust with no explanation or understanding behind them, and also offers no alternative whatsoever, on the other hand we have quantum mechanics, developed over decades of work by many of the brightest scientists of all time, and incredibly sophisticated technology that exists and works today, in the real world. What do you honestly expect people to think? If you truly had something worth considering you would be discussing it with actual scientists and presenting conferences about your ideas, not making crackpot threads on a game development website. Please. You're not the first crank on the internet and you won't be the last, and the reason nobody listens to you is not because of a planetwide conspiracy to "cover up the truth", it's just because you are making no sense and you don't even realize it. Now, you are free to keep rambling on - it's your life to waste - but perhaps this forum is not the best place to do so, as Bell's theorem (or crackpot theories thereof) has, as far as I know, absolutely nothing to do with game programming, or even programming in general.

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You do know that a lot of our modern technology depends on quantum mechanics in one way or the other, right?

QM is statistical theory, the equations will work whether they are explained with magic unicorns or correlated photons.

So allow me to flip your argument around: quantum mechanics has been very successful in predicting small-scale phenomena and giving scientists an understanding of how particles behave at this scale.

The algorith is real and does what it does. I'm not saying the whole of QM is wrong, but I see with my own eyes they are deffinitivelly wrong about at least this type of experiment. I can only talk about this specific case, I don't have satisfactory information to talk about anything else. See if you can find any objection to what I said here, I don't claim to know anyhting else.

On one hand we have your "theory",

I don't have any theory, it's a self-evident fact. See for yourself:

#include <math.h>
#include <time.h>
#include <stdio.h>

void main()
{
int         N_REPEAT= 100000;
float       P1=                  30;        // <--- polarizer-1
float       P2=                  30;        // <--- polarizer-2

Init_Setup:;
system("cls");
printf("\Repeat #: 100,000");
printf("\nAngle polarizer P1: "); scanf("%f", &P1);
printf("Angle polarizer P2: "); scanf("%f", &P2);

srand(time(NULL));
int         N_MEASURE= 0;
int         MATCH= 0;
int         MISMATCH= 0;

// relative angle & radian conversion
float       REL_P1= 0.0174533* (P1-P2)/2;
float       REL_P2= 0.0174533* (P2-P1)/2;

BEGIN:;
int L1= ((rand()%201)/2 < ((cos(REL_P1)*cos(REL_P1))*100)) ? 1:0;
int L2= ((rand()%201)/2 < ((cos(REL_P2)*cos(REL_P2))*100)) ? 1:0;

printf("\n %d%d", L1, L2);
if (L1 == L2) MATCH++; else MISMATCH++;
if (++N_MEASURE < N_REPEAT) goto BEGIN;

printf("\n\n1.)\n--- MALUS LAW INTEGRATION (%.0f,%.0f) ---", P1, P2);
printf("\nMATCH: %d\nMISMATCH: %d", MATCH, MISMATCH);
printf("\nMalus(%d): %.0f%%", abs((int)((P1-P2)/2)), ((cos(REL_P1)*cos(REL_P1))*100));
printf("\n>>> STATISTICAL AVERAGE RESULT: %.2f%%", (float)abs(MATCH-MISMATCH)/(N_MEASURE/100));

// Exact probabilty equation
float T= cos(REL_P1)*cos(REL_P2);
float F= 1.0 - T;

float MCH= (T*T)+(F*F);
float MSM= (T*F)+(F*T);

printf("\n\n\n2.)\n--- MALUS LAW PROBABILTY (%.0f,%.0f) ---", (P1-P2)/2, (P2-P1)/2);
printf("\nMATCH: %.2f%%\nMISMATCH: %.2f%%", MCH*100, MSM*100);
printf("\n>>> EXACT PROBABILTY RESULT: %.2f%%", (MCH-MSM)*100);

printf("\n\nPress any key to repeat.");
getch(); goto Init_Setup;
}


Edited by humbleteleskop

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I didn't read all the posts and don't know about quantum mechanics, but you know that the numbers returned by rand() aren't very random, right? You'd probably want a better pseudorandom generator, or maybe a (physical) random source.

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White noise would be such thing. But how to get it into the computer without giving it a "color"?