Many Paths = Huygens’ Principle?

In summary: However, Feynman's theory is more complete and accurate while Huygens' is more of a guiding principle. Huygens' principle is also incomplete as it does not specify the boundary conditions and leaves out the "inclination factor" that describes the variation in amplitude with direction. In summary, Feynman's many-paths theory is a more comprehensive and precise formulation of quantum mechanics, while Huygens' principle is a basic guiding principle with some limitations.
  • #1
exmarine
241
11
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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  • #2
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.
 
  • #3
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.
 
  • #4
exmarine said:
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.
 

1. What is Huygens’ Principle?

Huygens’ Principle is a concept in physics that states that every point on a wavefront can be considered as a source of secondary wavelets, which spread out in all directions at the same speed as the original wave. This principle helps to explain the propagation of light and other types of waves.

2. How does Huygens’ Principle relate to Many Paths?

Many Paths = Huygens’ Principle is a phrase that highlights the idea that there are multiple possible paths for a wave to travel. This concept is based on Huygens’ Principle, which suggests that each point on the wavefront is a source of secondary wavelets that can take different paths to reach a given point.

3. What are some applications of Huygens’ Principle?

Huygens’ Principle has been used to explain the behavior of light, sound, and water waves. It has also been applied in the fields of optics, acoustics, and electromagnetics to understand diffraction, interference, and refraction.

4. How was Huygens’ Principle discovered?

Huygens’ Principle was first proposed by Dutch physicist Christiaan Huygens in the late 17th century. He observed that every point on a wavefront acts as a source of secondary wavelets, which together produce the next wavefront. This idea was later refined and mathematically described by French mathematician Augustin-Jean Fresnel in the early 19th century.

5. Are there any limitations to Huygens’ Principle?

While Huygens’ Principle is a useful tool in understanding wave behavior, it has some limitations. It does not fully explain wave phenomena in certain situations, such as when dealing with diffraction through narrow slits or when considering the behavior of polarized light. In these cases, other theories, such as the wave theory of diffraction and the principle of superposition, are needed to fully explain the observed phenomena.

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