Recent content by johana

The triangle inequality, a theorem about distances for anyone single triangle, where the sum of the lengths of any two sides must be greater than the length of the remaining side. On the other hand CHSH inequality is combined from four relative angles between four polarization axis...

http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation The last step of the CHSH inequality derivation is to apply the triangle inequality. I see there are relative polarization angles, but I don't see any sides have defined length to make up a triangle. Where is the triangle?

That's exactly what local hidden variable is supposed to achieve, to predict outcome based on initial conditions and classical mechanics, including classical probability, such as used for predicting six-sided dice roll or coin toss outcome. We toss a coin 10,000 times and we get this kind of...

Malus' law is a probability function with sample space S={+,-}. It means every single photon either goes "+" way or "-" way. Number of photons is arbitrary, average probability applies equally to each individually or all of them together.

http://en.wikipedia.org/wiki/Polarizer#Malus.27_law_and_other_properties \int_0^{2\pi} \frac{cos^2(x)}{2\pi} dx = 1/2 Wolfram: integrate 1/(2pi) * cos^2(x) dx, x = 0 to 2pi

It's your friendly neighborhood Malus' law. Send 10,000 0° polarized photons (as DrChinese already pointed out) through 60° polarizer A, 25% will go "+" way and 75% "-" way. Then send 10,000 0° polarized photons through 30° polarizer B, 75% will go "+" way and 25% "-" way. Ok? The point is, how...

Yes, but it depends on rotational invariance which is prerequisite for local theory prediction of 50-50%. So if rotational invariance is assumed (theory), or guaranteed (experiment), then cos^2(θ) is uniformly integrated over 360° which averages out to 50-50%, regardless of any absolute or...

For θ = 30°, cos^2(30) = 0.75: P_A(+)= 0.75, P_A(-)= 0.25 P_B(+)= 0.75, P_B(-)= 0.25 P_{AB}(+ and +) = 0.75 * 0.75 = 56.3% <- both go through P_{AB}(- and -) = 0.25 * 0.25 = 6.3% P_{AB}(+ and -) = 0.75 * 0.25 = 18.8% P_{AB}(- and +) = 0.25 * 0.75 = 18.8%

A function which outputs an average, such as Malus' law, is not deterministic but probabilistic. ...where I0 is the initial intensity, and θi is the angle between the light's initial polarization and the axis of the polarizer. It means if you send a beam of light with intensity of...

It's given here as explicit description (requirement) for EPR locality: http://en.wikipedia.org/wiki/EPR_paradox#Locality_in_the_EPR_experiment Yes, but after they are created they have yet to negotiate with their polarizers about the actual outcome. Interaction of photon A with polarizer A...

A(a,\lambda_A) = cos^2(a), S={+1,-1} It's a probability function with sample space +1 and -1. What's the problem? Is there anything else I need to do with the notation to make that more clear?

From the Wikipedia article I quoted it looks like locality in EPR experiments is defined exactly by the independence of the two data streams, which translates into prediction they should be completely random (50-50%) regardless of any absolute or relative polarizers rotation. If random...

I did say it's a probability function and that it does indeed return only \pm 1 values, as is evident from the equations. It's just like a coin has its probability function and it only returns heads or tails. You are missing the point my example is illustrating, which is that hidden variables...

I see now, this: That's absolute limit, it doesn't really say local reality prediction for E(x,y) is not zero. Kind of odd to compare a binary state in terms of numerical range, because binary state is exclusive of any other states, and +1/-1 are rather arbitrary. It could have been heads and...

Yes, unless there is no rotational invariance, in which case a and b become relative to absolute rotational variance average instead of to each other.