A form of time travel may already exist, if it were possible to go into the past on one's own timeline without paradoxes then there would already have been some time travellers here from other times.
Its more likely that multiple realities which look like either our past or future exist besides ours, in which case anything you'd do there wouldn't affect the one you travelled from.
I've read a lot of stories, I read about some devices that might qualify as time travel devices, but if its real or not, I can't say.
Pretty good writeup, I voted and followed :)