Mathematicians Albert Einstein and Kurt Godel chatted, said Boston University philosophy professor Palle Yourgrau, and the “primary result was a powerful argument that if time travel is possible, time itself is not.”
Source: Walter Isaacson’s Einstein: His Life and Universe
Just my opinion - I've always thought that backward time travel is not possible. Forward time travel appears to me impossible as well, though I suppose it exists in a narrower sense of relativistic differences in experiencing time passage.
This opinion of impossibility has led me to shy away from fully enjoying science fiction that involves time travel (usually backward time travel), though some of the plots are dramatic and very enjoyable and thought-provoking in their way, I must admit.
There is another issue though, which is time-viewing, and I think this area could have some possibilities for real life and fiction. What if, for example, beings of one part of a galaxy were further advanced than beings of another part of a galaxy? And what if they somehow, from afar, arranged to record video and sound of an earlier stage civilization in development? And then the earlier stage civilization could then encounter the more technologically advanced one and there would be a logical question - "Could we have a look at your recording library?". Or I suppose maybe just a look at historical papers and studies, if recordings didn't exist. So, in this example, if Earth was the less advanced civilization we could (ideally) ask for recordings to check whether certain historical figures existed, how they died, who did and did not do what, etc. Sound doesn't cross space and I doubt recordings from another point in the galaxy would capture such detailed focus on individuals, but there are perhaps some possibilities to this. I suppose another possibility is to ask if someone could travel through curved continuum in such a way as to "catch up with and intercept" light rays conveying the information of history. Then it would not be necessary to posit another civilization with a thing for recording.
Anyway, that's all very involved, and I don't know if the science holds up, but one can see how it would lead to numerous fiction possibilities. For example, there could be a different visit to a different planet each week, showing them their history. I've proposed to others awhile back building a TV series, but I've seen no evidence of anyone acting on this, so I'm blabbing it here. Still, I suppose if they did eventually go with it, they would be able to show having heard it from me earlier than this (if others were not even earlier with it, I don't know).