Bell's theorem: actual experiment event by event

[humbleteleskop]

No, although there are obvious similarities. For example, in a Type I experiment where the MATCHES are consider, the formula happens to be the same as Malus: cos^2(theta). However, if you measured CORRELATION the formula is different: cos^2(theta)-sin^2(theta). Either way, there is a connection but it is wrong to think of it as the same case. It isn't. One involves a single photon, the other involves a pair of entangled photons.

I need the formula that relates to the experiment I am doing, I believe we call it "Type I experiment". I now need to calculate QM's predictions, so I can compare that with those results I got. What formula should I use? Is 'theta' angle difference? Do I add absolute values of angles to get 'theta'?

P1= 0
P2= 30
My result= 51%
QM prediction= ??

P1= -30
P2= 30
My result= 25%
QM prediction= ??

P1= -45
P2= 45
My result= 0%
QM prediction= ??

 

[DrChinese]

I need the formula that relates to the experiment I am doing, I believe we call it "Type I experiment". I now need to calculate QM's predictions, so I can compare that with those results I got. What formula should I use? Is 'theta' angle difference? Do I add absolute values of angles to get 'theta'?

P1= 0
P2= 30
My result= 51%
QM prediction= ??

P1= -30
P2= 30
My result= 25%
QM prediction= ??

P1= -45
P2= 45
My result= 0%
QM prediction= ??

The QM match prediction is cos^2(theta) for Type I PDC assuming perfect efficiency. So:

Theta=30, QM=.75
Theta=60, QM=.25
Theta=90, QM=0

 

[humbleteleskop]

The QM match prediction is cos^2(theta) for Type I PDC assuming perfect efficiency. So:

Theta=30, QM=.75
Theta=60, QM=.25
Theta=90, QM=0

Two out of three. And I get 75% for theta=30 if P1=-15 and P2= 15. Isn't that something?

My setup seem to be centered around zero degrees, somehow. It gives correct results but only if angles are spread from 0 to opposite signs. Should all photon pairs in Type I have only vertical polarization?

 

[DrChinese]

My setup seem to be centered around zero degrees, somehow. It gives correct results but only if angles are spread from 0 to opposite signs. Should all photon pairs in Type I have only vertical polarization?

Type I entangled photons are not vertically polarized. There is nothing special about 0 degrees or any other orientation. They do not have a specific predetermined polarization until measured. They only have a relationship with each other. This state does not really map to any classical idea.

If you do not plan to read the references, please let me know. I won't be able to continue if you are not going to do your homework.

 

[humbleteleskop]

Type I entangled photons are not vertically polarized. There is nothing special about 0 degrees or any other orientation. They do not have a specific predetermined polarization until measured. They only have a relationship with each other. This state does not really map to any classical idea.

Do you think you can explain why the algorithm produces correct results? Isn't that supposed to be impossible?

If you do not plan to read the references, please let me know. I won't be able to continue if you are not going to do your homework.

Haven't we already discussed everything? Is that paper you posted about Type I experiment? What "type" is experiment in this article: http://www.askamathematician.com/20...-god-really-does-play-dice-with-the-universe/

 

[humbleteleskop]

Here is what algorithm does, with an example...


P1= -25
P2= 25

Polarizer P1 is set to -25, and P2 to 25 degrees.


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 if both got stopped (0 = 0) add one to 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 sample 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: cos^2(50) * 100 = 41.32%Isn't that something? Spooky action at distance, pocket size. Those two are actual random sequences generated by the computer, relative to Malus probability. It is interesting to note "bunching" of those zeros between all the ones. It means that luck comes in streaks, whatever that means. But if there is anything spooky here, that would be it.

 

[humbleteleskop]

Spooky lucky streaks: what is "random" binary sequence?


a.) 1 1 1 1 1 1 1 1 1 1

b.) 0 0 0 0 0 0 0 0 0 0

c.) 1 0 1 0 1 0 1 0 1 0


Maybe total chaos is just another form of perfect order, or whatever it is, in a binary sequences at least, there are not two, but three "perfect" states. Thus random can be anything in between, but not anyone of the three.

Random will try to move away from being like a., and it will try to move away from being like b., but more it tries the closer it gets to c. Random doesn't want to be like c. either, so what does it do, where can it possibly go? A binary sequence can never be more than 50% random.

 

[DrChinese]

Do you think you can explain why the algorithm produces correct results?

Correct? You see a tree here and there and do not realize where you are in the forest.

First, the correct result is: cos^2(theta) for MATCHES. Not matches-mismatches.

Second, theta cannot depend on bunching around some specific angle such as 0, as previously mentioned. These photons are not polarized.

Third, when theta is zero, you should get 1 (also as previously mentioned). Your model produces something more like 75%.

Lastly, you need 3 angles to address Bell and your model doesn't do that. If you run it for the angles I have mentioned, it will fail. But no need to even consider this yet, you have too much prep work to complete first. READ ALL THE REFERENCES.

 

[Nugatory]

Spooky lucky streaks: what is "random" binary sequence?

Google for "random number tests".
Don't expect to gain any insight by thinking about strings of ten or twenty bits; it takes many more than that to observe randomness.

 

[humbleteleskop]

Correct? You see a tree here and there and do not realize where you are in the forest.

First, the correct result is: cos^2(theta) for MATCHES. Not matches-mismatches.

That's vague, what are you trying to say? It does not matter what do you believe how it should be calculated. The only thing that matters is whether simulation result matches actual experiment and QM prediction. And if it matches the experiments, then naturally that must be the correct way.
.

Second, theta cannot depend on bunching around some specific angle such as 0, as previously mentioned. These photons are not polarized.

I didn't say it does, just that it is interesting, kind of spooky.

Third, when theta is zero, you should get 1 (also as previously mentioned). Your model produces something more like 75%.

No, it produces 1, times 100 gives us the percentage of 100%.

P1= 0, P2= 0
Malus_Sim: 1 *100 = 100%

P1= 0, P2= 180
Malus_Sim: 1 *100 = 100%

P1= -90, P2= +90
Malus_Sim: 1 *100 = 100%

Lastly, you need 3 angles to address Bell and your model doesn't do that. If you run it for the angles I have mentioned, it will fail. But no need to even consider this yet, you have too much prep work to complete first.

It works for any angle. Try it and see for yourself. You just have to be careful to input relative, not absolute, angles in the equation.

 

[humbleteleskop]

Google for "random number tests".
Don't expect to gain any insight by thinking about strings of ten or twenty bits; it takes many more than that to observe randomness.

Does anyone mentions anything about binary sequences can never be more than 50% random? In any case each size has its own randomness factor, degrees of freedom. It's really about how do we actually define "random", when it is something that doesn't look like anything.

It's fairly easy to describe what a house is, it's not random. But defining "random" is like describing all the things that house is not. Kind of tricky.

 

[DrChinese]

No, it produces 1, times 100 gives us the percentage of 100%.

P1= 0, P2= 0
Malus_Sim: 1 *100 = 100%

P1= 0, P2= 180
Malus_Sim: 1 *100 = 100%

P1= -90, P2= +90
Malus_Sim: 1 *100 = 100%

Arggh. Yes we all see it produces the right answer at selected settings. That is impressive in the reverse because it shows you are only interested in things that confirm your wrong hypothesis.

Try P1=45, P2=45. That does not produce 100% using your last code. Also try P1=-45, P2=45 and tell me what that produces. Your code does that wrong too. Also try P1=30 and P2=30, which should be...100%.

And as to "doesn't matter how I get there if it is right..." - well, you are being a bit early in patting yourself on the back. Close (which you aren't) doesn't cut it. Do you not realize that you have walked into an advanced field of study?

As to the 3 angles: you have completed missed the entire point of this discussion. Please read Bell's Theorem and understand it. Of course you get a number for 3 angles. It just doesn't match QM predictions. P1=0, P2=120, P3=240, present a sequence after you address the above and you will see how wrong you are. Or better yet: make up the sequence as best you can by hand to get the lowest match rate possible. You cannot make one up that matches QM either! That is Bell.

 

[DrChinese]

Does anyone mentions anything about binary sequences can never be more than 50% random? In any case each size has its own randomness factor, degrees of freedom. It's really about how do we actually define "random", when it is something that doesn't look like anything.

This is outside the scope of this thread. Randomness is an entire subject of its own. And of course binary sequences can be 100% random to any degree you care to specify. I think what you mean is that 2 such sequences will average to a 50% match rate when compared. As a matter of fact any two [independent] random sequences will converge on 50% matches when compared. And they will therefore have 0 correlation.

 

[DrChinese]

humbleteleskop:

Everyone goes down the path when they first start wading into this area. Please don't get frustrated and stop posting. The best thing you can do is read, learn and ask. It takes a while to get a grasp on many key elements of QM.

-DrC

(And you might consider reviewing the first 6 letters of your moniker. )

 

[humbleteleskop]

Arggh. Yes we all see it produces the right answer at selected settings. That is impressive in the reverse because it shows you are only interested in things that confirm your wrong hypothesis.

Try P1=45, P2=45. That does not produce 100% using your last code. Also try P1=-45, P2=45 and tell me what that produces. Your code does that wrong too. Also try P1=30 and P2=30, which should be...100%.

As you can see for yourself it produces matching results. You need to be careful to enter relative angles into the equation, not absolute. RelTheta(P1)= (P1-P2)/2; RelTheta(P2)= (P2-P1)/2.P1:+45, P2:+45
-> RelTheta= (45-45)/2 = 0
-> P1:0, P2:0 -> Malus_Sym= 1 * 100 = 100%

P1=-45, P2=+45
-> RelTheta= (-45-45)/2= 45
-> P1:45, P2:45 -> Malus_Sym= 0 * 100 = 0%

P1:+30, P2:+30
-> RelTheta= (30-30)/2= 0
-> P1:0, P2:0 -> Malus_Sym= 1 * 100 = 100%

P1:-30, P2:+30
-> RelTheta= (-30-30)/2= 30
-> P1:30, P2:30 -> Malus_Sym= 0.25 * 100 = 25%

 

[DrChinese]

As you can see for yourself it produces matching results. You need to be careful to enter relative angles into the equation, not absolute.

If you put the *relative* angle in your formula, it is automatically a non-local model. QED.

On the other hand, you placed something like the following in one version of your code:

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

...Which implies separate and independent routines for each side (local). Yet that does NOT produce the results you claim. So I assume you are just skipping to the answer cos^2(theta) now and not bothering with individual event simulations.

If you don't quickly get back on track to discuss mainstream science and away from your personal pet ideas, I will alert a moderator. You are well over our forum guidelines at this point. You do not have an algorithm that accomplishes anything meaningful and the amount of science being discussed is negligible at this point.

 

[stevendaryl]

The impossibility of generating the EPR results using local models can be cast in the form of a game: There are two teams: The Red Team and the Blue Team.

The Red Team consists of three players:

1. The Generator
2. Receiver A.
3. Receiver B.

The Blue Team consists of two players:

1. Alice
2. Bob

The way the game is played is this: Each round, the following steps happen:

1. The Generator creates two messages. One message is sent to Receiver A. The other message is sent to Receiver B.
2. Alice randomly (1/3 probability each) picks one of the numbers 0, 120 or 240, and sends the result to Receiver A.
3. Receiver A replies with either "up" or "down".
4. Bob randomly generates another number, either 0, 120 or 240 and sends it to Receiver B.
5. Receiver B replies with either "up" or "down".
6. Then we record the plays made by Alice, Receiver A, Bob, Receiver B.

We require that the message passing is private--nobody is allowed to eavesdrop on a message intended for someone else.

We play this game for many, many rounds. The Red Team wins if the record of plays (Alice's play, Receiver A's play, Bob's play, Receiver B's play) produces the right statistics, which are:

1. Of those times when Alice and Bob make the same play (0,0), (120,120) or (240, 240), then Receiver A and Receiver B must give opposite responses: up, down or down, up
2. Of those times when Alice and Bob make different plays, then Receiver A and Receiver B should give the same response (both up or both down) 75% of the time, and different responses 25% of the time.
3. Of those times when Alice plays 0, the response from Receiver A should be "up" 50% of the time, and "down" 50% of the time. Similarly for 120 and 240.
4. Of those times when Bob plays 0, the response from Receiver B should be "up" 50% of the time, and "down" 50% of the time. Similarly for 120 and 240.

The claim is that there is no way for the Red Team to consistently win without cheating, and without using quantum mechanics. It can win with cheating in the following way:

• Each round, Receiver A randomly (with 50/50 chance) responds "up" or "down".
• It sends an illegal message to Receiver B saying what Alice's play was, and what its response was.
• Receiver B waits for this message. If Bob chooses the same play as Alice, Receiver B gives the opposite response.
• If Bob chooses a different play than Alice, then Receiver B either gives the same response as Receiver A (75% of the time) or the opposite response (25% of the time).

The Red Team can win by using quantum mechanics in this way:

1. Beforehand, the Red Team picks 3 directions in space so that the angle between any two directions is 120 degrees. They agree to number these directions 0, 120 and 240.
2. Each round, the Generator creates an entangled electron/positron pair.
3. It sends the electron to Receiver A, and the positron to Receiver B.
4. Receiver A waits for Alice's play, and measures the electron's spin in the direction given by Alice's play. It responds "up" or "down" depending on whether the result is spin-up or spin-down.
5. Similarly, Receiver B measures the spin of the positron along the direction given by Bob to compute his answer.

 

[humbleteleskop]

If you put the *relative* angle in your formula, it is automatically a non-local model. QED.

I have to use relative angles for the Malus's law, naturally. It's basic classical physics.

On the other hand, you placed something like the following in one version of your code:

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

...Which implies separate and independent routines for each side (local). Yet that does NOT produce the results you claim. So I assume you are just skipping to the answer cos^2(theta) now and not bothering with individual event simulations.

Of course they are separate and independent, that's how you simulate Malus's law. Give me the listing of the program that gives you wrong result so I can see what did you do there and help you figure it out.

If you don't quickly get back on track to discuss mainstream science and away from your personal pet ideas, I will alert a moderator.

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

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


Which of these four lines are you suggesting does not belong in mainstream science? That's all I'm talking about. It's not my idea, it's Malus's law.

 

[humbleteleskop]

The impossibility of generating the EPR results using local models...

Then how do you explain the algorithm replicates experimental results?

How do you explain this:

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


...impossible?

 

[DrChinese]

I have to use relative angles for the Malus's law, naturally. It's basic classical physics.

...


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

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


Which of these four lines are you suggesting does not belong in mainstream science? That's all I'm talking about. It's not my idea, it's Malus's law.

Sorry, I have explained this over and over. This is not a computer programming class, this is quantum physics. To date, you have expressed no desire to learn anything about that subject. You continue to repeat your wrong personal theories. I am out of the discussion, and will report your post to the moderators.

 

[micromass]

Thread locked pending moderation