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If my understanding of wormholes is correct, anything that moves into a wormhole can be transported from one region of space-time to another. Consider a situation where an object of mass $m$ in space at $(x_1,y_1,z_1)$ and time $t_1$ travels through a wormhole and appears at $(x_2,y_2,z_2)$ in a distant future time $t_2$. In between time $t_1$ and $t_2$, it seems this object of mass $m$ doesn't exist. Hence during this span of time, the total mass-energy of the universe should be less than before. Doesn't this violate law of conservation of mass-energy?

N. Virgo
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someone_ smiley
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No. The law of the conservation of mass-energy is a purely local law (i.e. the divergence of the stress-energy tensor must be zero at any point in spacetime). You will find that, as long as your wormhole is a solution to Einstein’s equations, this law will hold anywhere in the vicinity of the wormhole or within it.

In other words, there is no point at which the mass suddenly disappears. It enters the mouth of the wormhole, pass through its throat, and emerges from its other mouth.

Belizean
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  • I don't think this is quite right. We also have global conservation of mass-energy in asymptotically flat spacetimes. There is nothing in the description that would preclude us from putting the wormholes in an asymptotically flat spacetime. –  Nov 05 '14 at 02:02
  • @BenCrowell The conservation of mass-energy in an asympotically flat spacetime is not about the sum of mass-energy inside a spacetime on sum spacelike surface, and a mass doesn't go into one wormhole and then not be anywhere there and then appear magically at another time. The asymptotic mass of an end doesn't change (in asymptotically flat region's time coordinate) as a spherically symmetric shell of matter contracts around a wormhole, in fact it doesn't change based on anything currently happening because the farther out regions are only affected by earlier things. – Timaeus Jun 15 '15 at 02:08