In classical Newtonian mechanics, from what I understand, conservation of energy stems from the fact that all known forces are conservative forces, and vector calculus tells us that they can be represented by a potential energy function.
I understand how Energy Conservation is derived by Noether's theorem, but I'm trying to understand relativistic dynamics better in terms of four-vectors.
I know four-force can be written in special relativity as the derivative of the four-momentum with respect to proper time.
Are four-forces still conservative?
How do I write potential energy functions in SR?
If I have a constant force in classical mechanics is it still constant in SR?
(My guess abot the third question is not because four-momentum and three-momentum are quite different and four-momentum also depends on the relative velocity of the observer and the object)
My goal is to understand energy conservation is SR.
Thanx to anyone who answers!