However, it is clearly interesting to ask why this is so. In general relativity you can have spacetimes with so called closed timelike curves, which would allow you to go back in time, and although they are a bit tricky from the point of view of quantum mechanics, one can look at them theoretically in a more or less consistent way. In practice it seems very difficult to make a closed timelike curve (i.e. a time machine), but there is no proof that it is impossible.
One argument against time travel is that we have not seen visitors from the future, but in general relativity you could only travel back to times after the first time machine was built.
We already do travel in time by moving from the present to the future, and you can change how “fast” time proceeds by sitting in a strong gravitational field or moving quickly. Travelling into the past is harder though – my understanding is that in general relativity it is possible for spacetime to be bent in such a way as to allow this, but it would need an impossibly large amount of energy to do it.
Normally I tend to think that anything that is not expressly forbidden by the laws of physics will ultimately be possible (assuming human civilisation carries on long enough), but this might be the one example where that isn’t the case.
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