If energy is relative, is the rest mass also relative?

[vanhees71]

I'm not sure what you mean by "for a closed system". The SET in SR always obeys the vanishing divergence condition you give, at every point of spacetime. In GR that condition becomes $\nabla_{\mu} T^{\mu \nu}=0$, and is again always true. Since it applies at each point of spacetime, there is no such thing as a "closed system" vs. "open system" if you're just looking at the SET; it's just a continuous distribution of stress-energy.

For a closed system yes. There's a lot of confusion in the literature by considering only the energy-momentum tensor of the em. field and then wondering, why there is problem with total em. energy and momentum at presence of sources $\rho$ and $\vec{j}$. You have to consider always the total EM tensor of a closed system, obeying the continuity equation, and only then the spatial integral gives an energy-momentum four-vector (for the entire system consisting of the em. field and the charges).

In relativity these conservation laws follow from the presence of Killing vector fields and are different from the divergence condition on the SET.

I didn't want to discuss the GR case here, where it is of course even more complicated. You only have local energy conservation $\nabla_{\mu} T^{\mu \nu}=0$, but you cannot so easily define total energy and momentum in a coordinate independent way. I guess you know this better than I.

 

[PeterDonis]

my own paper

Which is not a valid reference. Personal research is off limits for discussion at PF. (And no, posting it on vixra doesn't mean it isn't personal research. If you get it published in an actual peer-reviewed journal, then we might take a look.)

I'm sure other ones are possible.

I'm afraid no one else shares your belief on this point. Please do not post further about this in this thread; if you do, you will receive a warning and a thread ban.