On Thursday, February 28, 2019 at 7:27:32 AM UTC, Tom Roberts wrote:   
   > On 2/26/19 1:30 PM, ben6993 wrote:   
   > > "However, I do not believe that electrons can be aligned exactly in   
   > > a given direction. [...]   
   >   
   > In the decay of a pi- to anti_nu_e and e-, the helicity of the electron   
   > must be exactly +1, so its spin is exactly parallel to its 3-momentum.   
   > No other value will satisfy the conservation of angular momentum.   
   >   
   > Similarly for the much more frequent decay of pi- to anti_nu_mu and mu-.   
   >   
   > Note that helicity is a scalar, so this applies in any inertial frame   
   > (not just the pi- rest frame).   
   >   
   > Tom Roberts   
      
   Thank you, Tom.   
      
   I am not clear that the electron spin axis in your post has been aligned   
   exactly with a given direction.  I agree that it is aligned in the   
   direction of its linear momentum, but that direction was not (could not   
   be?) a given or pre-selected direction.   
      
   Suppose the electron subsequently traveled on to meet Alice's detector.   
   In general, Alice's detector vector (a) could be at any angle to the   
   electron spin axis vector (p).   
      
   IMO what happens when the electron is detected by Alice is that either   
   the electron is already in its lowest energy state wrt the detector and   
   so will retain its spin vector p or else it will switch to a lower   
   energy state by emitting a photon and changing its own spin axis to one   
   along spin vector -p.  (S-G detectors can give a reading of +1 or -1   
   rather than null or +1, but I used the easier version for convenience of   
   description.)   
      
   What IMO the electron does not do is change its exact spin axis to   
   vector +a or -a.  But someone's model for a Bell test implies that I am   
   wrong.   
      
   Referring to your post, I am not sure where you write "the helicity of   
   the electron must be exactly +1," I thought that the helicity of an   
   electron cannot exceed 0.5?  Unless you mean 100% projection onto the   
   direction of linear momentum.  Or I wondered if you meant e- + anti_µ   
   had +1 helicity in total?   
      
   Commenting on the rest of your post to see if I understand ... The   
   anti_µ must have spin (both helicity and chirality) = +0.5 as it has   
   restricted handedness. That forces the electron to have chirality -0.5,   
   so that the chirality of the pair is zero which matches the original   
   chirality before decay.  So the anti_µ moves off in one direction and   
   the electron moves in the opposite direction with chirality -0.5 but   
   with helicity +0.5.   
      
   I note that as helicity is defined wrt the linear momentum vector, then   
   helicity is tied to the direction of motion of the particle.  So it is   
   not observer dependent.  However I have always thought of chirality as   
   the more ph ysically important as it gives spin direction in the   
   particle's rest frame, despite difficulties in observing chirality   
   directly.   
      
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