Bell's theorem: spooky lucky streaks?!

References:
http://www.askamathematician.com/20...-god-really-does-play-dice-with-the-universe/

http://en.wikipedia.org/wiki/Malus's_law#Malus.27_law_and_other_properties



Malus's law classical (deterministic) simulation algorithm, 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 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

Code:

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%


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.

 

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

Code:

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

 

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What does "result= matches - mismatches" mean anyway?

- "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."

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


Here's how the experiment goes:

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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%

--- EXPERIMENT 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, but like this:

Code:

// relative angle conversion for Malus's law equation
    REL_P1= (P1-P2)/2
    REL_P2= (P2-P1)/2

// Malus's law for probability polarizer P1 and P2
    TRUE= cos(REL_P1)*cos(REL_P1)
    FALSE= 1.0 - cos(REL_P2)*cos(REL_P2)

// Exact probability solution
    MACH= (P1*P1)+(P2*P2)
    MISM= (P1*P2)+(P2*P1)
    RESULT= (MACH-MISM)*100 = CORRELATION %

 

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Rev.2

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No paranormal "non-locality" here. It's a classical probability just like tossing two coins, a simple matter of chances and odds, a natural probability and local causality, an inevitable statistical certainty. For example, when relative angle is 30 degrees (-15,+15), the probability for each polarizer is given by Malus's law equation -> cos(15)*cos(15) = 0.933. It means 93.3% photons will pass through, and 6.7% will get stopped at the polarizer.

Case 2 & 3:
2. Relative angle per polarizer (+30,0) = (A-B)/2, (B-A)/2 = (+15,-15)
3. Relative angle per polarizer (0,-30) = (A-B)/2, (B-A)/2 = (+15,-15)
Malus's law probability per one polarizer = cos(15)*cos(15) = 0.933
- classical probability solution ->
Coin 1 vs Coin 2 = 0.933 : 0.067 vs 0.933 : 0.067
Chance of MATCH: (H1&H2 | T1&T2) = (0.933 * 0.933) + (0.067 * 0.067) = 0.875
Chance of MSMCH: (T1&H2 | H1&T2) = (0.067 * 0.933) + (0.933 * 0.067) = 0.125
Correlation = MATCH - MSMCH = 0.875 - 0.125 = 0.755
Discordance = 1 - correlation = 0.245 = 25%

Case 4:
Relative angle per polarizer (+30,-30) = (A-B)/2, (B-A)/2 = (+30,-30)
Malus's law probability per one polarizer = cos(30)*cos(30) = 0.75
- classical probability solution ->
Coin 1 vs Coin 2 = 0.75 : 0.25 vs 0.75 : 0.25
Chance of MATCH: (H1&H2 | T1&T2) = (0.75 * 0.75) + (0.25 * 0.25) = 0.625
Chance of MSMCH: (T1&H2 | H1&T2) = (0.25 * 0.75) + (0.75 * 0.25) = 0.375
Correlation = MATCH - MSMCH = 0.625 - 0.375 = 0.25
Discordance = 1 - correlation = 0.75 = 75%


Additional example 45 deg. relative angle:
Relative angle per polarizer (+45,0) = (A-B)/2, (B-A)/2 = (+22.5,-22.5)
Malus's law probability per one polarizer = cos(22.5)*cos(22.5) = 0.8536
- classical probability solution ->
Coin 1 vs Coin 2 = 0.8536 : 0.1464 vs 0.8536 : 0.1464
Chance of MATCH: (H1&H2 | T1&T2) = (0.8536 * 0.8536) + (0.1464 * 0.1464) = 0.75
Chance of MSMCH: (T1&H2 | H1&T2) = (0.1464 * 0.8536) + (0.8536 * 0.1464) = 0.25
Correlation = MATCH - MSMCH = 0.75 - 0.25 = 0.5
Discordance = 1 - correlation = 0.5 = 50%

 

If each of 2 characters is a random event with .50 probability, then any sequence has the same probabiltiy of .5^n. You have arbitrarily selected the 3 shown only because of their simple pattern. They are rare only when compared to all possible outcomes.

 

Wouldnt this debate be compatible with this loophole free bells test or similar binary tests??

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also found this, I find the subject fascinating and want to learn more.
http://iopscience.iop.org/1367-2630/14/11/113020/article

 

I don't think it has ever been tested. The assumption is theoretical and "natural" randomness are different. Computer RNG algorithms are modeled to produce theoretically predicted results. It doesn't matter, it's unrelated to the actual topic of this thread, I really shouldn't have posted that here.

What do you think about "two-coins toss" classical probability solution for quantum entanglement phenomena?

 

It's compatible with any experiment related to quantum entanglement. I'm demonstrating there is no any "spooky action at distance" going on in these experiments. I'm saying the measured phenomena is just a normal classical local probability and not any kind of mysterious quantum effect.

 

I'm not sure what are they actually doing in their experiment, what is it they measure and how they record that data. If we can extract initial variables for that experiment I'll use the same classical probability equation and we'll see what we get.

 

We are likely not talking about the same thing. Practically, my conclusion is that there would be a tendency for "bunching" or "streaks", that distribution would be at most 50% rather than 100% "uniform", if you know what I mean. I don't think it has been tested because I don't think it's quite recognizable. To recognize it is like being able to predict a stock market at least half of the time, and I'm saying that should actually be possible. Basically I predict there are people who can play the market without overall total losses for a very long time, but on the other hand we could always say that it was just luck, so it's hard to talk about it.

The closest study I found related to what I'm talking about is this, quite interesting: - "The fascinating study looked at 565,915 sports bets made by 776 online gamblers in Europe and the United States, and found that, all things being equal, you're likely to win or lose 48 percent of the time (draws presumably account for the remaining 4 percent). After a single winning bid, the chance of winning a second goes up ever so slightly to 49 percent. But here's where things get interesting. After the second win, the chance of winning a third time increases to 57 percent. After that: 67 percent. Following a four-bet winning streak, the chances of scoring a fifth haul increase to 72 percent. The probability of a sixth win is then 75 percent, and finally, after six wins, bettors had a 76 percent chance of notching lucky No. 7."
http://www.popsci.com/article/science/are-lucky-streaks-real-science-says-yes

 

I'd call it being specific and making sure that we do start talking about the same thing in case we already haven't.

Not to me, at least not yet.

I don't know, I don't see where are you going with that. I'd rather be talking about Bell's theorem and quantum entanglement experiments.

I don't know the "standard theory" would predict that. So, no, I really don't see what would be the bias or "hidden variable".

 

We need only that one probability equation, and apparently I got it right.

Yes, if there can be "skill" to achieve such consistency it implies the source of randomness was not completely random. That's what I'm saying, but I'm also saying it is true for things that you would call "completely random", say betting red or black on a roulette. According to standard theory it shouldn't be possible to consistently achieve much more than 50% winning bets in a long run, right? Well, I predict that it should actually be possible, perhaps even up to 75%. Did anyone test that?

 

Considering the coin toss as a binary sequence, the probability is .50, constant, and therefore time independent.
Any trend or sequence then has no special meaning as to 'lucky streak', etc.
Sequences do have value for quality control purposes, in detecting departure from standards.

I have no opinion yet on the explanation of Bell's Theorem, based on polarization experiments.

Algorithms involve finite terms. There can be none capable of generating all random numbers.
I would equate randomness to unpredictability.

 

This intro to Bell's Theorem avoids the (apparently) difficult nature of probability calculations and the (apparently) confusing language of cosines and such, and lays out the conflict between quantum theory and conventional "common sense" plainly: http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html

It's worth keeping in mind, imho, that the abstraction we term "cause and effect" or "determined event" is a mental approximation or shorthand we find useful at our normal scale of action and perception. It has no more claim to being a building block of the universe independent of our mental convenience than "random chance" or "probability" do, and if repeated and duplicatable and thoroughly researched events don't square with it that's just too bad - other concepts and approaches must be employed.