Re: Wormhole questions

Robin Hanson (hanson@econ.berkeley.edu)
Thu, 05 Nov 1998 09:14:51 -0800

>Everybody worries about time travel with wormholes, but I am concerned
>
>How does conservation of energy and of momentum work with a wormhole?
>What if I shoot a ball into hole A and it comes out hole B moving in a
>different direction? Momentum is not conserved.
>
>Worse, what if I position the exit of hole B above the entrance to
>hole A, and drop in a ball. The ball falls through A, comes out B
>where it then drops into A again, and continues, going faster and
>faster as it falls forever. Where does the energy come from?
>...
>I can think of two possible resolutions.
>
>First, it could be that there are some compensating forces which serve to
>balance the books. When the ball comes out of B in a different direction
>than it went in A, maybe the "substance" of the wormholes (whatever
>that is) is given a kick which balances the momentum.

Yes, that's the answer. Conservation laws can be described in terms of surface integrals around each wormhole end. When mass goes thought the hole, one end gets more massive and the other end gets less massive. When a charge goes through the hole, one end picks up a charge and the other end loses a charge. And one end gains the momentum of the mass going in, while the other end loses that momentum.

When you put one end above the other in a gravitational field and drop a ball through them, you'll need to hold them there rather than let them fall to make it work. As the top end loses mass and the bottom end gains mass, the difference in gravitional potential ends up in the kenetic energy of the ball.

Eventually the top end mass goes to zero and the hole closes, I think. After all, if you could keep pulling mass out of a zero mass end, you could create a negative mass object.

Robin Hanson

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