# humbleteleskop

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1. ## Bell's theorem: Malus's law simulation

Yes, there is srand(), here is the whole program: #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; } Yes, it gives correct results for any combination of agles of the two polarizers. The more measurements there are, the more results get stable and converge to QM prediction: cos^2(theta). There is also an exact solution, like calculating probability of matching pairs in two-coins toss sequences. //Malus's law probability for relative angle theta(P1,P2) REL_P1= (P1-P2)/2 REL_P2= (P2-P1)/2 T= cos(REL_P1)*cos(REL_P2) F= 1.0 - T MACH= (T*T)+(F*F) MISM= (T*F)+(F*T) RESULT= (MACH-MISM)*100 = CORRELATION % Take this experiment for example: 2.) "Foreground polarizer" P1= +30 "Background polarizer" P2= 0 REL_P1= (30-0)/2= +15 REL_P2= (0-30)/2= -15 T= cos(+15) * cos(-15) = 0.933 F= 1.0 - T = 0.067 MACH= (0.933 * 0.933) + (0.067 * 0.067) = 0.875 MISM= (0.933 * 0.067) + (0.067 * 0.933) = 0.125 RESULT= (0.875 - 0.125) * 100 = 75% correlation = 25% discordance 4.) "Foreground polarizer" P1= +30 "Background polarizer" P2= -30 REL_P1= (30+30)/2= +30 REL_P2= (-30-30)/2= -30 T= cos(+30) * cos(-30) = 0.75 F= 1.0 - T = 0.25 MACH= (0.75 * 0.75) + (0.25 * 0.25) = 0.625 MISM= (0.75 * 0.25) + (0.25 * 0.75) = 0.375 RESULT= (0.625 - 0.375) * 100 = 25% correlation = 75% discordance
2. ## Bell's theorem: Malus's law simulation

Malus's law simulation algorithm: 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: Example (-25,25): 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% I thought this was supposed to be impossible, classical physics simulating QM prediction?
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