Dale's:
So box starts out as m and an unspecified hard wall plus gravity from another source, Sun starts to attain kinetic energy losing PE, thermalizes it by hitting the wall, and creates actual rest mass via heat, fusion and pair production. What is the mass of the final thermalized Sun?
I do understand the mass conservation problem, but this does not explain what happens to m, M and the 24% solar mass equivalent energy in the final state so that it would show up as a total mass of m+M of the initial.
I explicitly avoided radiation leakeage by stopping the problem right before the merger. And ask what the weight of the box is initially versus Sun close to A*.
My gripe is with the system in the final state having a mass of m+M+ a big chunk of Kinetic energy that does something.
And I do concur...
True, sorry for the hasty reply.
I mean to say that in your reference you would measure a higher total gravity of the moving Sun but also a slower time for clocks in the moving reference frame. And for everyone to experience the same outcomes these 2 effects can cancel out, or should. IMO...
I only used Newtonian for the energy calculation, but honestly any value of KE is already problematic, so it does not matter.
I do not know what happens in SR with the mass of the Sun as it speeds up, but as I remember it is not going down to compensate for the extra KE. It usually looks like it...
Conservation of mass within the box.
As in the inital state has a mass of m+M observably, and m+M+KE in the final. I assume conservation of mass of the box, which leads to the requirement for the initial state to have an extra rest mass in the form of GPE, or the m+M to change somehow.
And if...
IMO this problem is a contradiction already. It either violates conservation of mass in the closed box or points to GPE as actual rest mass somehow.
As usual when a contradiction appears, eventually something new gets learned, even though the possibility of it not being new to anybody other than...
I would not bother that much with relativistic effects as even if the speed is small and said effects are negligeble, there should be GPE to KE mass in the system that adds to the m+M.
I went close to Sag A* in my OP only to show the magnitude of the effect in comparison to a know intuitive...
I totally agree via conservation of mass kind of reasoning. But if the Sun can attain a higher mass by transforming GPE into KE which can be transformed into rest mass, where was that mass in the initial state?