[not-a-llm]

Noeter theorem and energy get complicated in General Relativity, because there is no global time translation symmetry

https://curtjaimungal.substack.com/p/what-is-energy-actually

Ignoring that, saying "energy must exist because of Noether and time-translation" doesn't really tell what energy actually is, not a very satisfactory response

[gmueckl]

On the contrary, this is best description of what conservation of energy means: all externally generated forces acting on the system do vary with time. Im other words, this is a closed system as defined in thermodynamics.

The nature of energy is really just a result of this property.

The difficulties with energy in GR are related to the fact that those equations alone allow for space-times that are truly bizarre. Some that are technically solutions to the field equations are clearly nonphysical (e.g. Goedel's solutions). There is also a priori no reason why e.g. expanding metrics should actually yield proper conservation of energy.

[Xmd5a]

> Why is this conserved? Because ∇ᵤ(Tᵘᵥξᵥ) = (∇ᵤ Tᵘᵥ)ξᵥ + Tᵘᵥ(∇ᵤ ξᵥ).

Interesting.

> This is an example of a topic that unstructured self study would likely skip.

I'm not studying physics – could you take a look at some unstructured reflexions I wrote a couple weeks ago?

https://news.ycombinator.com/item?id=48699125