“Wherein the faster an object travels, the slower is perception of time becomes, in a phenomenon known as time travel.”
You are basically unaffected by time, not traveling through it, like staying in your vehicle for a day at the speed of light and for other people its a week or a month, but you cant travel back nor choose a certain time to "visit".
I was originally referring to his quote "God does not play dice with the universe." regarding Quantum Mechanics, he was dissatisfied with the theory, ironically his Nobel prize was for that very subject.
The thing is - in my opinion - imaginatively creative writers take a scientific theory, and build wild interpretations based on the most extreme forms of it, and put it in an appealing form for the audience's mind, and then it takes off.
But I'll go with the hypothetical version(s) we see in the media.
If you are able to change an event in the past, then all subsequent events to it will change as well, making the necessary alterations to one's persona/conciseness, so what we currently know/are will be altered as well, since the sequence has been changed, more like a domino effect, one action changes those related to it.
Deja Vu, is different, it is an issue in how the information is transferred in the brain, a lapse of a millisecond causes the brain to think you had the same experience before, a neuro transmission thing rather than an actual happening.
One thing, I have to admit that I am not that much into the quantum theories altogether, and I can only make assumptions based on my understanding from what I have read long ago, either in science or science fiction.