Plus, as an admittedly weird example, the computer game “portal” has conservation or momentum, but not uniform motion of the centre of mass. Which means at the very least the two can logically decouple.
That’s related to what I wrote here:
I think that second step involves spatial integration to get from a local continuity equation to a global conservation law, and so general relativity might or might not mess up that part, not sure. But anyway, we’re assuming flat space here.
The spatial integration step, to get from local properties (continuity equation for momentum density) to global properties (center of mass motion), can get screwed up by weird topology (e.g. teleportation portals), just like it can get screwed up by curved spacetime. You do have to assume that spacetime is normal flat Minkowski space.
Certainly it does for a collection of billiard balls. But, as soon as light is included things get less clear to me. It has momentum, but no inertial mass.
Maybe this link is a proof? It kinda looks right but I didn’t check it super-carefully. It uses the stress-energy tensor which applies to both matter and electromagnetic waves. Note the part where they integrate over space and set the boundary term at infinity to zero—that part doesn’t work with curved space or wormholes.
That’s related to what I wrote here:
The spatial integration step, to get from local properties (continuity equation for momentum density) to global properties (center of mass motion), can get screwed up by weird topology (e.g. teleportation portals), just like it can get screwed up by curved spacetime. You do have to assume that spacetime is normal flat Minkowski space.
Maybe this link is a proof? It kinda looks right but I didn’t check it super-carefully. It uses the stress-energy tensor which applies to both matter and electromagnetic waves. Note the part where they integrate over space and set the boundary term at infinity to zero—that part doesn’t work with curved space or wormholes.