Noether theorems, the Lagrangian and energy

[Dadface]

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.

 

[Dale]

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.

 

[Dadface]

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?

 

[Dale]

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.

 

[Dadface]

Thanks Dale.