Time travel is possible.
We record and live by a system that we control, if it can be done, then it can be undone.
Although when I say time travel is possible, I don't think you can create any paradox's, like your grandfather paradox, or multiverse paradox. It's just not possible to travel backwards in "time" as our natural momentum is forward.
However, if I were to jump in a space shuttle and travel at say 10 x the speed of light in one direction for 6 months, I would have aged 6 months while on returning to earth, I find that Earth has aged 1 year, because I followed a differant system from Earth.
Or if I were to travel 20, even 30 times that speed, the gap would get bigger and my body would not age the same as my 'friend' on Earth. So in effect, I'm time travelling. Just without the paradox's.
The grandfather paradox is a funny thing. If I were to go back and kill my grandfather who was aged 20 at the time, would I still be born?
Yes.
What I'm doing is killing a differant version of him. He already existed before I built a time machine, and when I returned to the present, he would still be there, none the wiser.
Time is like rendering frames, taking living polaroid's, you would need to kill every version of your grandfather, from his first moment of his conception untill the moment you left. Even when you return, his life has not been affected because the rendering process continues with your return. You would need to skip into the future, ahead of the process, to do the dastardly deed on your grandad. Even then, you have only changed the future and not the past.
But that's not possible (imo). Time travel is.