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Time travel would be an amazing achievement for humanity and has been a fantasy for science fiction for a long time. Einstein's theory of relativity (1905) and experiments with atomic clocks has shown that forwards time travel is possible. The closer to the speed of light an object travels; the slower time goes for it relative to everything else. However here I will be concerned with the logical coherence of backwards time travel. Whether it is possible practically given the right technology is a separate issue in this article (It might be if we could go faster than the speed of light.) What I want to answer here is: Is backwards time travel logically coherent or incoherent? Are there any logical contradictions in its' concept? Are the paradoxes solvable? If we can answer these questions it may be possible given the right technology to actualize it.

The first paradox I want to look it is put forward by Nicholas Smith. It is an existential paradox known as "The no destination paradox":
1. Different locations of space exist.
2. But with time only the present exists.
3. The past did exist but it is gone now and cannot be accessed.
4. The future may come to exist but it does not exist now.
5. Surely one cannot go somewhere that doesn't exist.
6. Therefore one cannot time travel.

One can accept premise one that there are different spatial locations in existence. But one can argue that the past and future exist in as just a real sense as the present, and the reject premise two, three and four. Smith's concept of time is not universally accepted, and many see time as an additional dimension to space, to form four dimensions. Personally I also think this argument, as far as future time travel goes, leads to the conclusion that nobody can go forward in time at all no matter what speed, as then they would be going somewhere which doesn't exist. This seems very paradoxical in itself. It ignores the fact that time changes (in a sense flows.) The second premisis should be that only the present exists at "any given moment of time" and this would not lead to the conclusion that time travel is impossible.

Another paradox to highlight is known as the "journey time problem" and can be summarized as follows:
1. All journeys take time.
2. So time journeys take time.
3. The time journey cannot occur in the same time order as the start and end of that time journey, since there is only one time order.
4. Therefore it is impossible to time travel.

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