Fermat's principle of least time

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Discussion Overview

The discussion revolves around Fermat's principle of least time, particularly the philosophical question of how light "knows" and "chooses" the path that requires the shortest time among all possible paths. The conversation touches on theoretical explanations and references to related literature, including quantum electrodynamics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses curiosity about the mechanism by which light selects the shortest time path, suggesting a metaphorical comparison to a supercomputer with a generic algorithm.
  • Another participant directs attention to the Wikipedia article on Fermat's principle, indicating that the principle is derived from the nature of light as electromagnetic waves.
  • References are made to Feynman's book "QED: The strange theory of light and matter" as a source for a layman-friendly explanation of the principle and its implications.
  • Additional resources, including videos related to the QED book, are shared to further explore the topic.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the philosophical implications of how light chooses its path, as participants explore different perspectives and references without resolving the underlying questions.

Contextual Notes

Participants reference various theoretical frameworks, including classical wave theory and quantum electrodynamics, but do not delve into specific mathematical derivations or assumptions underlying these theories.

LLT71
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while I was studying "fermat's principle of least time" I was (and still I am) ntrigued by the fact that "out of all possible paths that it might take to get from one point to another, light takes the path which requires the shortest time". this question may be a bit philosophical but: "how" light "knows" and "chooses" (out of all possibilities) the path which requires the shortest time? these days I am also into generic algorithms so I got this silly thought running through my head: what if light is like some kind of super computer which operates with constant CPU speed 300[km/s] and has some generic alghorithm for choosing the best path!?
thanks!
 
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LLT71 said:
"how" light "knows" and "chooses" (out of all possibilities) the path which requires the shortest time?
Take a look at the "Derivation" section of the wikipedia article on Fermat's principle: https://en.wikipedia.org/wiki/Fermat's_principle#Derivation

Fermat's principle follows directly from the fact that light is electromagnetic waves. There's also an explanation based on the theory of quantum electrodynamics; Feynman's "QED: The strange theory of light and matter" includes an excellent and layman-friendly explanation of how this works.
 
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Nugatory said:
Take a look at the "Derivation" section of the wikipedia article on Fermat's principle: https://en.wikipedia.org/wiki/Fermat's_principle#Derivation

Fermat's principle follows directly from the fact that light is electromagnetic waves. There's also an explanation based on the theory of quantum electrodynamics; Feynman's "QED: The strange theory of light and matter" includes an excellent and layman-friendly explanation of how this works.
thank you!
 
robphy said:
Following up on @Nugatory 's suggestion:
here are videos associated with QED book
oh, wow! many thanks my friend!
 

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