"Edge of Tomorrow," the new Tom Cruise flick, has the protagonist waking up over and over to get a chance to destroy the sci-fi monsters he failed to kill the previous day. Think of it as "Ground Hog's Day" for science fiction minus the Bill Murray comedy and with a lot more explosions. This well-tread idea of going back in time to right one's wrongs harkens all the way back to Charles Dickens's novella, A Christmas Carol, of 1843.
But was the first science fiction short story that involved physical time travel? Well, as usual, we have Edgar Allan Poe to throw into the mix. In 1844 he published A Tale of the Ragged Mountains that is now contained in Edgar Allan Poe's Complete Works Annotated. In the short story the protagonist, Bedloe, claims to have been transported back to the 1780s. While we can debate whether this is really a science fiction story due to the lack of "science" in it, many believe this to be the first short story involving physical time travel.