Probability or Impossibility in QM?

  • Thread starter dkgolfer16
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  • #26
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We see this paradox being "resolved" in Zee and P&S through a careful (if still pretty confusing) translation from a field propagator to a real, measurable "particle". For instance, Zee claims that the leaking of a field outside the lightcone does not imply a "real" particle being detected there. Also, I can't recall if some part of the apparent paradox came from adding over momenta which are far from the mass shell.
Peskin and Schroeder demonstrate that free quantum fields (anti)commute at space-like separations. However, there is no relationship between this fact and the speed of propagation of wavefunctions. In a very long thread
https://www.physicsforums.com/showthread.php?t=175155
(starting somewhere in the middle of the thread) there is a discussion of the relationship between wavefunctions and quantum fields. I still believe that these are completely unrelated things. In other words, I don't take what's written in P&S as a convincing proof.

I don't have Zee's book, but I doubt that their explanation is fundamenatally different from that in P&S.
 
  • #27
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Isn't it well proved in mathematics, that wave equations don't allow propagation with infinite speed? So just apply Klein-Gordon equation (or other variants) to the wave function, and you don't have any propagation outside light cones.
 
  • #28
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Isn't it well proved in mathematics, that wave equations don't allow propagation with infinite speed? So just apply Klein-Gordon equation (or other variants) to the wave function, and you don't have any propagation outside light cones.
In my opinion, the Klein-Gordon equation is valid for quantum fields, not for particle wavefunctions. There was a long discussion about this in

https://www.physicsforums.com/showthread.php?t=175155

Eugene.
 

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