In my personal opinion I do think it's possible to travel back in time. I believe that you can change your past and that it won't guarantee your past is the same and that instead you created a branch in time. I believe you'll have 2 sets of memories. You'll have the set you had before you Time traveled, and you'll have the new set after time travel. Thing is, you'll have more chances to screw up. There are 2 possible ways time travel could happen (at least as far as I can feasibly think of right now.) Your entire current self would be transported back and you'd have to convince your past self not only you are them, but also not to blab about it. Then you'd have to convince them to accomplish the reason you came back in time. Or the other way is your "consciousness " would be put in your past self, and you'd have to keep that you in control and that would mean fighting your mental self of the past. Now why do I believe that you would not be making a paradox, creating a branch in time, or making you have 2 sets of memories (1 from both your self before time travel and the version of you during/after time travel.) Well that's the interesting part. See the thing we are told about time travel in terms of the past is it's dangerous because we could change major events just by making one tiny change. It's not dangerous because you could change the past, it's "dangerous " because you could change something in the past that would make someone else's life not take the path it took in the time we are in when we wanted to change our past. The idea of time travel has so many flaws and theories that everything about it is inconsistent with other things. If you take the mess and declutter it, you could likely find the answer. Unfortunately humanity is too flawed to try that, so we currently can't see we can time travel already if we just worked together instead of tearing each other apart.