Unraveling the Concept of Energy Position in Classical Physics

[bhobba]

But since energy is equivalent to mass and therefore generates gravity, one could in theory do an experiment that determines the direction of the gravitational field and this would tell you what quantity for the field energy is correct and therefore how it is localized.

I was referring to the above which looks like a comment on using gravity in some way to measure EM energy. That would require the so called Einstein-Maxwell action:
https://www.physicsforums.com/threads/the-einstein-maxwell-action-with-sources.764995/

But once you do that you run into exactly the same problem GR has - namely gravity is curved space-time so the symmetries required by Noethers Theorem breaks down and the modern concept of energy becomes problematical.

If it isn't can you clarify what you were getting at.

Regarding the energy of the EM field not being localised its been ages since I read the Feynman Lectures but in modern times, as per the link I gave, it follows quite naturally from the EM Lagrangian via Noethers theorem. Are you getting at the freedom we have to add a divergence-less quantity? Yes that is an ambiguity but it is usually resolved by requiring the energy momentum tensor to be symmetric.

Thanks
Bill

 

[bhobba]

IFor example, in dealing with a Newtonian mechanical system, we can define total potential energy as a calculation involving all the state information.

You lost me here.

I can't see how potential energy is a matter of definition - it follows from the Lagrangian.

I know he is a bit terse but Landau examined the whole potential energy thing in the first chapter of Mechanics. Its not a matter of definition - its a consequence of what energy is ie the conserved quantity associated with time symmetry.

I keep getting the impression I am missing something here because its not gelling with me what you guys are getting at - and I suspect conversely as well.

Thanks
Bill