Wormhole questions

Hal Finney (hal@rain.org)
Wed, 4 Nov 1998 17:00:14 -0800

Everybody worries about time travel with wormholes, but I am concerned about more mundane matters.

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?

(Note that in relativity, momentum and energy are closely related,
being separate components of the four-vector which represents a particle's motion. So probably these two paradoxes are two aspects of a single phenomenon.)

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. And maybe when you try to go through a wormhole and come out higher than you were, maybe there is some kind of force opposing your motion and you have to force your way through, just enough to balance the potential energy gain.

Second, it could be that wormholes simply break the rules. Hypothetical stable wormholes require negative energy, and it could be that with negative energy you already break conservation of momentum and energy. A negative-energy mass is attracted to a positive one, but the positive one is repelled by the negative one (or is it the other way around?). So the pair goes rocketing off across the universe, accelerating steadily without any input of energy. I think Robert Forward describes this in his novel, Timemaster.

(Actually I suppose that example technically may not break the rules,
since the negative mass acquires greater negative energy and negative momentum as it accelerates, balancing the positive energy and momentum of the positive mass. So the system as a whole has constant energy and momentum.)