Another possibility for time travel of a kind is that time is, in fact, looped. Spatial closure is often cited to explain how the universe could both be finite and unbounded, as it is curved in four-dimensional space. Temporal curvature is less understandable. However, according to Lawrence Sklar, there is nothing about temporal closure that is contrary to the principles of general relativity:
"Spatial closure is one thing, but can a spacetime have closed timelike lines? Yes, at least in the sense that the spacetime can be given a description internally consistent and consistent with the field equations of general relativity". (Sklar, Space, Time and Spacetime, 303)One does not need to abandon a causal theory of time to accept this proposition, as the loop would still be causal, and even have direction, it is just that one cause would ultimately cause its own causes. Furthermore, such a "closed" system need not be circular, such that an event must "wait" until a full cycle of all events to have its effects felt on the past. If this were the case, only our infinitely patient immortal could have any hope of affecting the past. A world could, for example, be "jug-shaped". That is, it would have a "handle" of spacetime that loops back to another point in spacetime relatively recent in the past. This possibility has been popularised in science fiction as wormholes (though the ones in science fiction tend to be spatial and not temporal).
In either of these cases, some kind of time "travel" to the past would be possible. One could accelerate to near the speed of light until enough time had passed in one's original inertial frame that one arrives before one left. As noted above, this kind of time travel and how far we consider the "distances" to be travelled is relative to our own lifespan and patience. One would not even need to use this "acceleration method" to go to the past if one were either long-lived enough to simply wait for the past to happen again, or the curvature was short enough that one could simply pass through at normal speed in a relatively short amount of time, as would be the case in a possible-world in which the universe only had a ten-year cycle or in the actual world, if there are, in fact, such "handle-shaped" anomalies yet to be discovered. Further, (and this clearly falls into the who-knows-but-we-did-after-all-manage-to-break-the-sound-barrier category of speculative science), it may even one day be possible to create such temporal anomalies, so that one could travel backwards in time, simply by "splicing" and "editing" space in such a manner that one's immediate future loops back to the desired destination in the past. In all of these "alternative geometry" cases, one would be able to travel strange paths in spacetime, such that one is able to travel to points in the past, without ever having to actually accelerate beyond the speed of light, which is rendered impossible by special relativity.
Travel to the past, even via the future, would imply what I will call the "lunch" paradox, for lack of a better term. Let us say that I discover a wormhole that can lead me back ten hours in time to before I ate lunch. At lunch that day, I had pizza, but I am a mischievous sort, and wish to change what I had for lunch to a submarine sandwich, just to see if it can be done. If I were a simple animal, who had simple desires, I would have some kind of straightforward desire like eating pizza, and would head back in time to convince myself to have that piece. Indeed, I would remember myself convincing myself to do so. However, human beings are capable of "abstract" desires, rather than specific desires. In other words, I would be capable of going back in time with the intention of changing my past, whatever it might be that I remember happening. Let us say that I remember myself convincing myself to eat pizza. In that case, I would go back and convince myself to eat a submarine sandwich. However, that would mean I would remember myself convincing myself to eat a submarine sandwich, so I would go back to convince myself to eat pizza, and so on ad infinitum. One answer is that "something" would prevent me from changing my own mind. Perhaps I would forget. Perhaps I would disobey my future self (although I would remember so disobeying if I had done so). Perhaps the wormhole would not work. However, all these answers start to look something like the Greek Fates. I cannot change the past because "something" would ultimately stop me, much as "something" caused Oedipus to marry his mother, in spite of his best intentions. There certainly does not appear to be anything in nature that would prevent me from stopping myself from eating pizza in the same way the Fates caused Oedipus to marry his mother. Lewis raises the suggestion that there is an equivocation on the meaning of "can". I "can" stop myself from eating pizza in the same way that I "can" speak Finnish, in that I have the intellectual apparatus to speak Finnish. However, this simply does not apply in my case. I have a wormhole, and I have my mischievous abstract desire. I "can" stop myself from eating pizza not in the way I "can" speak Finnish, but rather in the way I "can" speak French. In order for me to speak French, I simply need to wish to do so. I cannot be stopped from doing so by my own lack of current abilities but only if "something" stops me, and then I am back to Oedipus's Fates. It seems that certain outright contradictions would be implied if a being with such abstract desires as "I wish to change the past" would be capable of time travel.
Wells' dream of a time-ship that can simply pop in and out of time is probably absurd, as even future "time-travel" implies travelling along shorter paths in spacetime in order to create the differential in elapsed time. However, time travel would be possible in a number of ways. First, one could travel forward in time by shifting one's inertial frame to one that is nearly light speed relative to the initial frame. While travel to the past directly impossible, as that would imply superlight speeds to which it is impossible to accelerate without infinite force, one could circumvent this problem if there are in fact alternative geometries of spacetime, in which time is a closed loop, whether by simply waiting a few trillion years, by using the "acceleration method" to push oneself forward until one reaches the past, or by finding or perhaps creating singular deformations in spacetime that connect spacetime in smaller closed temporal paths that lead from the near future to the past. Such travel, though, might create incoherent paradoxes as a result of my ability to have such abstract desires as to "change the past".