Noether theorems, the Lagrangian and energy

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Discussion Overview

The discussion centers around the relationship between Noether's theorems, the Lagrangian formulation of mechanics, and the definition of energy. Participants explore the applicability of the Lagrangian to various forms of energy beyond just kinetic and potential energy, including chemical energy and energy conversion processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the Lagrangian is too limited, suggesting it primarily addresses translational kinetic energy and potential energy.
  • Another participant argues that the Lagrangian is not limited in this way and can be formulated for a variety of physical theories, including electromagnetism and gravity.
  • A participant inquires about the possibility of writing a Lagrangian for energy conversion reactions, such as those occurring during photosynthesis.
  • It is proposed that, in principle, chemical energy can be represented as electromagnetic energy, although practical applications may be rare.

Areas of Agreement / Disagreement

Participants express differing views on the limitations of the Lagrangian. While some assert its broader applicability, others remain uncertain about its relevance to all forms of energy, indicating that the discussion contains multiple competing views.

Contextual Notes

The discussion does not resolve the assumptions regarding the applicability of the Lagrangian to various energy forms, nor does it clarify the practical limitations of such applications.

Dadface
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I have read in different places that an up to date definition of energy refers to the Lagrangian and Noether. But isn't the Lagrangian too limited because it refers to an ideal situation involving translational KE and to PE only? I would have thought that a good definition of energy would be relevant to all forms of energy...electrical, chemical, radiant, heat etc.

I think I may be missing something. If so can somebody tell me what it is please?

Thank you.
 
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Dadface said:
But isn't the Lagrangian too limited because it refers to an ideal situation involving translational KE and to PE only?
The Lagrangian is not limited in this way. You can write Lagrangians for EM, gravity, and a large number of other theories.
 
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Thank you Dale. But does it apply to every form of energy, for example is it possible to write a Lagrangian which represents the energy conversion reactions occurring during photosynthesis?
 
It is possible in principle. Chemical energy is just EM energy. I don't think that is ever done in practice, but I am not a chemist.
 
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Thanks Dale.
 

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