Time travel is quite possible, we do it every day, and have even been able to demonstrate that we can (slightly) alter the rate of flow. Unfortunately, so far we can only "intentionally" go in a forward direction.
However, there are cases which point to accidental physical time displacements both forward and back, which would seem to indicate a mechanism that doesn't require the ridiculous amounts of energy that some physicists think would be needed. (Mental time-tripping, where one only 'sees' a future or past, is something else entirely.) There is also the theory that some UFO sightings during important historical events may be time travelers rather than extra-terrestrials.
As for alternate/parallel universes, if the differences between these universes are very slight, how would you know that you haven't been shifting between them without noticing already? Maybe you didn't actually misplace your car keys, but put them down in a different spot in the universe your conscious self recently shifted into. Or that conversation your wife claims you had and you can't remember, actually happened when either you or she was in a neighboring world. Or a stranger comes up to you and seems to know you well, but as far as you can recall you've never met before...
The shift might happen between one step and the next as you're walking along. It might happen while you're asleep. Or it might happen while driving in a fog so thick you can barely make out the taillights of a car ten feet in front of you, and you're otherwise completely disconnected from the world. All it might take is somehow losing your mental anchor to that particular universe, and suddenly you're somewhere else. You probably just don't realize it most of the time, or will chalk up any minor "slips" or differences to some more mundane explanation.
However, there are cases which point to accidental physical time displacements both forward and back, which would seem to indicate a mechanism that doesn't require the ridiculous amounts of energy that some physicists think would be needed. (Mental time-tripping, where one only 'sees' a future or past, is something else entirely.) There is also the theory that some UFO sightings during important historical events may be time travelers rather than extra-terrestrials.
As for alternate/parallel universes, if the differences between these universes are very slight, how would you know that you haven't been shifting between them without noticing already? Maybe you didn't actually misplace your car keys, but put them down in a different spot in the universe your conscious self recently shifted into. Or that conversation your wife claims you had and you can't remember, actually happened when either you or she was in a neighboring world. Or a stranger comes up to you and seems to know you well, but as far as you can recall you've never met before...
The shift might happen between one step and the next as you're walking along. It might happen while you're asleep. Or it might happen while driving in a fog so thick you can barely make out the taillights of a car ten feet in front of you, and you're otherwise completely disconnected from the world. All it might take is somehow losing your mental anchor to that particular universe, and suddenly you're somewhere else. You probably just don't realize it most of the time, or will chalk up any minor "slips" or differences to some more mundane explanation.