Is the Action Always a Minimum in the Principle of Least Action?

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Discussion Overview

The discussion revolves around the principle of least action in physics, specifically questioning why the action is typically considered a minimum rather than a maximum for a physical path. Participants explore the implications of this principle and its historical context, as well as the terminology used in describing action.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that the requirement for the action to be an extremum is expressed as ##\delta S=0##, questioning the preference for minimum over maximum.
  • Another participant suggests that the terminology is conventional and references a paper that discusses instances when the action is not minimal.
  • A different viewpoint connects the principle of least action to Fermat's principle of least time, suggesting that historical optical considerations influenced the development of mechanics.
  • One participant proposes that if the action is a minimum, then the negative of the action could be considered a maximum, arguing that "stationary" might be a more appropriate term to describe the action.

Areas of Agreement / Disagreement

Participants express differing views on the characterization of action as a minimum versus maximum, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are references to historical influences and conventional terminology, but the discussion does not resolve the underlying assumptions about the nature of action in the principle of least action.

BookWei
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Hello, When we applying the principle of least action, we require ##\delta S=0##, which corresponding to the action S being an extremum. I am just wondering why do we say that the action is a minimum instead of a maximum for a physical path? Can I use the path integral to explain this problem?
Thanks for all responses.
 
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I think that long ago, when Fermat's principle of least time came about, that people so liked the idea that they asked themselves why couldn't such a thing work for mechanics. The principle of least action was then made intentionally analogous to Fermat's principle. These optical considerations would then inspire others to develop wave mechanics.
 
If S is minimum , -S is maximum and anyway the both work. Stationary is more appropriate word to say.
 

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