Conservation of mass-energy in time travel

[nomadreid]

In Kip Thorne’s “Black Holes and Time Machines”, he outlines objections to using traversable wormholes, if they existed, as time machines, the main one being (roughly) that radiation could also time travel, and mount up to destroy the wormhole. But isn’t another objection the conservation of mass-energy? A photon could go back in time to meet itself from the past, suddenly giving two photons where there was only one.

 

[Orodruin]

But isn’t another objection the conservation of mass-energy?

There is no such thing as global conservation of energy in general relativity unless special requirements are put on the space-time.

 

[jfizzix]

There is no such thing as global conservation of energy in general relativity unless special requirements are put on the space-time.

Indeed!
In flat spacetime, energy is conserved as a consequence of the equations of objects' motion not depending on any absolute time, but only on relative times. This is one consequence of what's known as Noether's theorem.

If the spacetime is not flat, then there is no longer this time-translation symmetry, and energy need not be conserved.

 

[nomadreid]

Thanks for the replies, Orodruin and jfizzix. That settles that. So I shall be content with the other objections to closed time-like curves (aka time machines).