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CTC Wormhole

wormhole metric
Image from Steve Bowers

A wormhole that forms part of a loop of wormholes enabling a closed timelike curve (CTC). Such wormholes lose stability and cease to function. For this reason wormhole networks must be designed with care.

Temporal Displacement in a Wormhole Network

When a pair of wormhole mouths are moved apart by a relativistic linelayer, the two ends often become displaced in time when compared to one another. Unless the two mouths are loaded into separate linelayers which both move so that the temporal displacement is identical, one mouth of the wormhole will be further along the timeline into the future than the other.

So long as the two mouths of the wormhole are separated by more distance than the value of this temporal displacement, there is no possibility of creating a temporal loop known as a closed Timelike Curve, which would allow information, particles or individuals to travel to the absolute past. The formation of a temporal loop is undesirable, because it allows time travel into the past and the possible creation of temporal paradoxes. But if two temporally-displaced mouths of a wormhole pair or network are moved close enough together to form a CTC, then an exponential flux of virtual particles will instantly form. This flux is known as the Visser Effect.

Note that the Visser Effect occurs even if a chain of separate wormholes are involved; whenever a closed timelike curve (or temporal loop) starts to form, the Visser Effect will propagate though the wormhole network, and all wormholes involved are disrupted to a similar extent. This will result in the collapse of the smallest wormhole pair in the affected network, thus breaking the link and destroying the temporal loop. This instability causes the emission of vast amounts of energy, equivalent to the difference between the positive mass-energy of each wormhole concerned minus the negative energy required to keep the mouth open.

Spacetime diagram of wormhole connections

Wormholes
Image from Xoanon
In this diagram, time is represented by t, and distance by x; movement at the speed of light is indicated by a diagonal line separating the grey area from the white area. H is the origin of the wormole under consideration, A and F are possible destination wormhole mouths in space-time.
In this spacetime diagram, Wormhole H-A is acceptable, because no CTC can form, but wormhole H-F is unacceptable, because it allows travel into the absolute past of the traveller, and would therefore allow space-time paradoxes to occur. Luckily the formation of a CTC would be prevented by the Visser Effect before any such paradoxes could occur.
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Appears in Topics
Metric EngineeringPhysicsSpace-Time Engineering
 
Development Notes
Text by Anders Sandberg
Additional material by Steve Bowers and Xaonon
Initially published on 07 January 2002.

 
 
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