Time travel in the presence of closed time-like curves is like space travel. Time machines are not like, you know, a flying phone booth that you hop into and you pop into existence. You disappear and then teleport somewhere other in time. The respectable way to travel through time does not involve appearing and disappearing. It involves traveling through all the points in between,. But wrapping space in on itself in such a dramatic way that the trajectory you go on closes in on itself. However, these are still require the whole universe to conspire in some way to make a time machine.

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