If one mouth of a wormhole is accelerated, one has created a time machine. Causality could be violated by definition if the mouths are closer than the distance which is travelled by light within the time which equals the relativistic time shift of the mouths (because in this case, a signal from the future could reach a mouth before a traveler could enter the wormhole).
There are several possibilities what could happen then:
1. Nothing, because the past could not be changed. This is lame.
2. The wormhole is destroyed immediately so causality could not be violated. In Orion’s Arm, this is called the Visser effect. It has its own use, too.
3. The passage through the wormhole becomes not traversable any more in the direction of the past, but could be still traversed into the future. This I call the Egan effect, because Greg Egan described it in a short story.
If we assume possibility 3, and furthermore configure the wormhole in a way that its mouths are concentric (or have instead a layer of such wormholes like bricks, if concentric wormhole mouths are not possible topologically), we would have created a barrier which could be passed in one direction, but not in the other – an impenetrable force field.
