# Closed timelike curves

im trying to understand the theory of this. is a CTC supposed to actually bring an object back to the original time? or is it supposed to make it appear that way to an outside observer? im reading up on it from wikipedia: http://en.wikipedia.org/wiki/Closed_timelike_curve
but in the beginning they talk about it being a possible way of timetravel. then they say it "appears" to travel through time.

If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine

In extreme examples, in spacetimes with suitably high-curvature metrics, the light cone can be tilted beyond 45 degrees. That means there are potential "future" positions, from the object's frame of reference, that are spacelike separated to observers in an external rest frame. From this outside viewpoint, the object can move instantaneously through space. In these situations the object would have to move, since its present spacial location would not be in its own future light cone. Additionally, with enough of a tilt, there are event locations that lie in the "past" as seen from the outside. With a suitable movement of what appears to it its own space axis, the object appears to travel though time as seen externally.

but then once again, the next paragraph talks about multiple light cones curving all the way around and back to the original position and time:

A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started. An object in such an orbit would repeatedly return to the same point in spacetime if it stays in free fall. Returning to the original spacetime location would be only one possibility; the object's future light cone would include spacetime points both forwards and backwards in time, and so it should be possible for the object to engage in time travel under these conditions.

the last paragraph appears to claim that an object can physically go back in time right? so then what exactly is the other paragraph talking about saying "the object appears to travel through time as seen externally"?
somehow 1 light cone only makes it appear like time-travel but a loop of light cones makes it physically possible?

## Answers and Replies

Think of stepping into a wormhole that transports you to the past. And later, on your deathbed, you realise that you are your own great grandparent. That's what CTCs may depict: fully self-consistent histories (smacking of determinism) involving time travel (from the perspective of an outside observer, in this case meaning anybody that did not step into the wormhole; from your point of view, of course, time is always progressing forward: even as you fell down the wormhole, the hands of your fob watch kept on ticking forward at the normal rate).

o ok. that makes sense, i was just a little confused with the way they worded it.

my other question is with the last paragraph. it talks about "a series of light cones". if a light cone is all the different possible worldlines for a person/object then how can there be a series? wouldnt a person's worldline end somewhere within the first light cone?

Light cone often just refers to a range of directions in the immediate local vicinity of a single point. The full extension (or the region it encompasses) is sometimes called the null evolution (or the causal future); you're correct that the complete causal future from every point of the CTC is identical.

Can you make the article more clear to laypeople without sacrificing technical precision of language?