References:
http://www.askamathematician.com/2010/06/q-how-it-is-that-bells-theorem-proves-that-there-are-no-hidden-variables-in-quantum-mechanics-how-do-we-know-that-god-really-does-play-dice-with-the-universe/
http://en.wikipedia.org/wiki/Malus%27s_law#Malus.27_law_and_other_properties

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.

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"?

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:

http://www.physicsforums.com/showthread.php?t=454275

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?

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

- "Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory."

#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;
}

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?