The CHSH Inequality is valid.

The logic of the experiment is correct.

The alignment of the physical experiment is wrong.

The alignment of the 2 polarizers is from a angle of zero from vertical.  The incoming photons must be aligned with the vertically polarized photons at zero degrees and the horizontally polarized photons at 90 degrees.  That is NOT the way the experiment IS ACTUALLY DONE.

There is a ton of information about the alignment of the 2 polarizers but there are really 4 alignments.  The 2 polarizers can be rotated to set the alignment.  The BBO crystals can be rotated to set their alignment.  The Quartz Wave Plate can be rotated to set the alignment of the source beam.  The BBO crystals must be aligned with the output of the Quartz Plate so that both crystals are at 45 degrees from the output of the Quartz Plate.

The hack is that the Quartz Wave Plate is NOT ALWAYS ALIGNED so that the "vertically" polarized photons are vertical at zero degrees.

Here is evidence that the Quartz Wave Plate aligns the beam incorrectly, from the description of the CHSH experiment by Joshua Geller of the University of Rochester.

                       THE ALIGNMENT OF THE POLARIZERS

The Clauser-Horne-Shimony-Holt inequality considers a convex combination of the correlation function above, using the four angle combinations, as displayed here.

S = |E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|, where S is the quantity that is bounded for a classical system operating according to a local hidden variable theory, we must have |S| <= 2.  Note: however, that for choices of angle a = -Pi/4, b = -Pi/8, a' = 0, b' = Pi/8, the predicted value of S from the above derivation starting with the rotationally invariant entangled Bell state that descries our setup of signal/idler entangled photon pair is

S = |-1/2^.5 - 1/2^.5| + |1/2^.5 + 1/2^.5| = 2*2^.5.  So the quantum mechanical description of our system violates the inequality.

                 QUARTZ PLATE ALIGNMENT OF THE SOURCE BEAM

To achieve consistent coincidence counts of as many polarizations angles as possible of polarizers A and B, the quartz plate is rotated along its horizontal and its vertical axis, and then the coincidence counts are recorded for multiple polarizer positions. 

We used a = b = 0, a = b =45, a = b = 90 and a = b = 135 degrees.  We plot the results of these measurements against the angular positions of the quartz plate, and choose the orientation of the quartz plate at the angles where the set of four curves are nearest to equal.  We then fix this orientation for the experiment.

This shows that the Down Converted photons are NOT ALWAYS aligned vertically and horizontally.

That is how the inequality is violated.

Do you see an error in this?

2 minutes ago, Lazarus said:

Do you see an error in this?

Yes. You haven't provided a reference to the experiment you are talking about.

12 minutes ago, Strange said:

Yes. You haven't provided a reference to the experiment you are talking about.

The link to the paper is:

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/2010/OPT253_reports/Josh_Lab1.pdf

The link to the paper is:

http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/2010/OPT253_reports/Josh_Lab1.pdf