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Many Paths = Huygens’ Principle?

  1. Oct 26, 2011 #1
    Can someone tell me how Feynman’s many-paths differs from Huygens’ principle?

    Huygens: “All points on a wavefront can be considered as point sources for the production of spherical secondary wavelets. After a time t the new position of the wavefront will be the surface of tangency to these secondary wavelets.” [Halliday & Resnick]

    That sure sounds to me like different wording for the many-paths. All points in space-time can be regarded as point sources for further paths in space-time, with constructive or destructive interference amplitudes to any subsequent points, etc.
     
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  3. Oct 26, 2011 #2

    dextercioby

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    Huygens' principle guided Schrödinger derive his wave-equation and thus the birth of wave mechanics as a theory of quantum/quanta mechanics. Feynman built a whole theory upon an idea by Dirac who, I believe, was also inspired in a way by the Huygens' principle in classical waves theory. So yes, you can make a paralell between the seemingly related, but fundamentally different theories.
     
  4. Oct 26, 2011 #3

    Bill_K

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    Big difference. Feynman's is a formulation of quantum mechanics, meant to be a complete and accurate description, while Huygens' is only a guiding principle -- an aid to intuition and at best an approximation.

    Huygens is incomplete -- it's vague on the boundary conditions to be employed, and leaves undetermined an "inclination factor" describing the variation with direction of the amplitude of the secondary waves.
     
  5. Oct 26, 2011 #4

    It seems to me that they are basically the same. Feynman took the idea further and widened the realm of applicability.
     
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