From: jos.bergervoet@xs4all.nl   
      
   On 2/4/2017 5:43 PM, ben6993@hotmail.com wrote:   
   > On Friday, February 3, 2017 at 10:24:42 PM UTC, ben...@hotmail.com wrote:   
   >> On Wednesday, December 28, 2016 at 3:43:37 PM UTC, Jos Bergervoet wrote:   
   >>>    ..   
   >>> Perhaps, but in the mean time you know exactly what the   
   >>> claim is! The photon detectors fire with:   
   >>>    1) A fraction (1+cos(2*phi))/2 of events are aligned,   
   >>>    2) A fraction (1-cos(2*phi))/2 of events anti-aligned.   
   >>> ......   
   >>   
   >> but won't that give an overall positive correlation instead of a   
   >> negative correlation when (say) phi = 45 degrees.   
      
   phi=45 gives exactly 0 for the correlation. (This was about   
   measuring photon polarizations, resulting in "H" or "V".)   
      
   > I would like to add that I am not merely pointing out the sign error here,   
   > if indeed there is one.   
      
   With the answer being 0, there cannot be a sign error.   
   For other angles, it depends on whether you start with   
   anti-aligned or aligned photon pairs. (OP of this thread   
   references a Wikipedia example with *aligned* photon pairs   
   which makes the correlation positive for phi < 45 deg.)   
      
   > My main reason for posting is that I believe I have found a similar sign   
   > error in one of Susskind's online lectures on entanglement.   
   > Susskind sets out to prove that QM can break the Bell Inequality AB' + BC'   
   >> = AC' for electrons,   
      
   Be aware that for electrons the angular variation is only   
   half of that for photons. So the correlation there is 0 for   
   phi=90 degrees. If the electrons are initially in aloigned   
   pairs (like the photons above) then we will have positive   
   correlation between detector results for < 90 deg. angle   
   between detector orientations, in particular we have full   
   correlation for phi=0.   
      
   If, however, the electrons come in anti-aligned pairs (as   
   in the 'singlet state') then it is the opposite: negative   
   correlation for less than 90 degrees orientation difference   
   between the detectors and complete anti-correlation (-1)   
   with angle phi = 0 between detectors.   
      
   I didn't look up the Susskind lecture you refer to, but   
   for electrons, this second possibility is often used:   
      sqrt(1/2) * ( |+-> - |-+> )   
      
   It is of course also possible to start with the other   
   possibility (aligned instead of anti-aligned), although   
   it may be more difficult to prepare experimentally.   
      
     ..   
   > For electrons the formula for cell (+ +) is different than for photons being   
   > 0.25*(1 - cos phi).   
      
   In any case the variation with angle phi is with half   
   the rate. And the sign may also be different if the   
   prepared electron pairs are anti-aligned and you compare   
   them with photon pairs that are created aligned.   
      
   > So did Susskind make a mistake?   
      
   I expect it is a matter of comparing different cases..   
      
   > What inequality did he break, if any?   
      
   You already wrote that it was about Bell's inequality.   
   That means he broke the inequality that describes the   
   limits of possible classical behavior. What Bell's   
   inequality does is telling you what is possible with   
   classical physics. More is possible in QM.   
      
   --   
   Jos   
      
   --- SoupGate-Win32 v1.05   
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