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Internet Message Format  |  1992-12-28  |  1.6 KB
  1. Path: sparky!uunet!spool.mu.edu!uwm.edu!ogicse!psgrain!hippo!ucthpx!uctvax.uct.ac.za!naturman
  2. From: naturman@uctvax.uct.ac.za
  3. Newsgroups: sci.math
  4. Subject: Mathematical foundations of QM
  5. Keywords: QM
  6. Message-ID: <1992Dec28.154516.203431@uctvax.uct.ac.za>
  7. Date: 28 Dec 92 17:45:16 GMT
  8. Article-I.D.: uctvax.1992Dec28.154516.203431
  9. Organization: University of Cape Town
  10. Lines: 29
  11.  
  12. The following diagram shows how various mathematical formalisms for QM are
  13. related. 
  14.  
  15. Wave Mechanics            Matrix Mechanics
  16.      ^                          ^
  17.      |                          |
  18.      |                          |
  19.      ----------------------------------------------->Fringe approaches:
  20.                   |                                   Convex sets
  21.                   |                                   Transition probabilities
  22.            Hilbert space QM                           Involution algebras
  23.                   ^  ^
  24.                   |   \
  25.                   |    \
  26.                   |   Orthomodular lattice approach   
  27.                   |     ^
  28.                   |    /
  29.                   |   /
  30.         Geometry/closure space approach
  31.  
  32.  
  33. Where approaches at the bottom of an arrow can be regarded as more fundamental
  34. than approaches at the end of an arrow.
  35.  
  36. I am currently working on an approach using orthogonality relations on sets of
  37. states. So far it looks like it could turn out to be more fundamental than the
  38. closure space approach. I think that Chaos theory will be required to justify
  39. the concept of "quantum states" which is taken as a primative concept in most
  40. of the above approaches.
  41.