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In "From wormhole to time machine: Comments on Hawking’s Chronology Protection Conjecture" by Matt Visser (http://arxiv.org/abs/hep-th/9202090), he summarizes how "time machines" may be created from traversable wormholes (Morris and Thorne):

"Having constructed a traversable wormhole with time–shift the final stage of time machine construction is deceptively simple: merely push the two wormhole mouths towards one another (this may be done as slowly as is desired). A time machine forms once the physical distance between the wormhole mouths ℓ is less than the time–shift T.

"Once this occurs, it is clear that closed timelike geodesics have formed — merely consider the closed geodesic connecting the two wormhole mouths and threading the wormhole throat..."

It's not clear to me though. Could someone explain why moving the mouths together creates "closed timelike geodesics (curves)"? Would pushing just one toward the other accomplish the same effect (which is what I understood from my question here Wormholes, time travel, and time dilation. Would moving them apart afterward stop the "time machine"? Perhaps the answer is in the math, which is beyond me.

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All Visser is saying is that you don't have a true time machine until the machine is able to jump into your past "light cone". Your past light cone is the region of spacetime containing all past events that could have possibly affected your present.

This diagram taken from p. 284 of a nice book on wormhole physics might clear things up for you.

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"Pushing them together" and "pushing one towards the other" have the same semantic content here; when they are close enough, the geodesic forms a closed, time-like loop. These are known solutions to the Einstein field equations, but all of the proposed physical processes are unphysical.

That is, the proposed mechanisms to build a worm hole, much less a traversible worm hole, cannot be accomplished with presently known physics.

See Why wormholes (probably) don’t exist for a nice discussion.

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