# Many Paths = Huygens’ Principle?

• exmarine

#### exmarine

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.

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 parallel between the seemingly related, but fundamentally different theories.

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.

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.

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