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.
(Note that in relativity, momentum and energy are closely related,
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.
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.)
(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.)
Hal