Loopholes in optical Bell tests

[vanesch]

On the other hand, if you apply Malus with a quantum mechanical bent (which I don't consider perverse at all), i.e. as applying on a particle by particle basis, you get exactly the values that are measured in experiment. I.e. once you know Alice's polarization, Bob's matches the application of Malus. Why wouldn't it? After all, such application also matches the results for an ensemble of particles as well.

Ah, you mean: the particles BEFORE measurement have/don't have a polarization, whatever, but ONCE Alice made her measurement, and this, by the projection postulate, MADE THE SYSTEM JUMP INTO ONE OF BOTH polarizations defined by Alice's polarization angle (parallel, or perpendicular, no other way out) and made, also through the projection postulate, JUMP BOB'S PHOTON ALSO IN THAT STATE (due to the entanglement), THEN, we apply Malus' law at Bob's side to calculate what is the probability is for him to get a click up or down according to the angle between the "polarization" (defined by Alice's measurement) and his analyser.
Yes, that's right, that gives the same result as the QM predictions of course, but I find this far-fetched to simply call this "Malus' law" because - that's what you call the quantum mechanical bent - there's the (non-local) projection postulate acting here before you apply it. My impression when people said "it's the same as Malus' law" was that it meant that using classical optics, you got the same results, which - as you point out, is totally wrong.

 

[DrChinese]

Ah, you mean: the particles BEFORE measurement have/don't have a polarization, whatever, but ONCE Alice made her measurement, and this, by the projection postulate, MADE THE SYSTEM JUMP INTO ONE OF BOTH polarizations defined by Alice's polarization angle (parallel, or perpendicular, no other way out) and made, also through the projection postulate, JUMP BOB'S PHOTON ALSO IN THAT STATE (due to the entanglement), THEN, we apply Malus' law at Bob's side to calculate what is the probability is for him to get a click up or down according to the angle between the "polarization" (defined by Alice's measurement) and his analyser.
Yes, that's right, that gives the same result as the QM predictions of course, but I find this far-fetched to simply call this "Malus' law" because - that's what you call the quantum mechanical bent - there's the (non-local) projection postulate acting here before you apply it. My impression when people said "it's the same as Malus' law" was that it meant that using classical optics, you got the same results, which - as you point out, is totally wrong.

My apologies for not making this clear. Your desciption is accurate. I was trying to show that at some level, Malus is common ground for the QM and LR positions. I absolutely believe that the projection postulate is to be applied as you describe. If it wasn't, then you could learn more about Bob that the HUP allows. That is really what EPR assumed would happen - that you could use Alice to learn about Bob. We now know that doesn't happen.

The problem from the local realist side is that for the case of unentangled photons, we still (also) have the cos^2 theta function to deal with. How does the local realist get cos^2 theta for a single unentangled photon and end up ignoring the cos^2 theta function (i.e. Malus) in the situation of entangled photons?

Of course, the local realist can say that there is no such thing as entangled photons. In that case, the probability functions are factorizable and presumably you MUST apply cos^2 theta separately. If you do that, you get the perverse 1/4 + (cos^2 theta)/2 function and this wildly deviates from experiment.

In other words, the local realist likes to think that the difference between experiment and Bell's Inequality can be accounted for by experimental error - i.e. the "loopholes". After all, there isn't a gigantic difference between the 2 even though they have easily been distinguished experimentally. But that really solves nothing for the local realist, since their alternative is even further away from experiment!

In my opinion: IF there is a consistent theory that makes a specific prediction; and that prediction is born out by experiment; THEN asserting there exist "loopholes" which cannot be measured is a specious argument. Once a scientist measures them, I will believe it. In the meantime, you MUST accept what the results of experiment tell us. Otherwise, there is no objective basis for believing anything in science.