Put on your seatbelt: this is gonna be rough.
I've been musing on time-travel. Or more specifically, the ramifications of time-travel and possible paradoxes.
And frankly, I don't believe there are any possible paradoxes. I have two reasons, and they're polar opposites.
1. Time Travel Prevents Paradoxes - This theory works on the notion that time is directly linear. Objects are simply inserted into the stream of time, and "now" is always the sum total of that linear progression.
Huh? Basically, if you went back in time, then according to History (big H), you've already been in that moment of time, and anything you do will have already been woven into the fabric of our "now". Thus, you cannot go back and shoot your parents or kill John Connor because it never happened.
That's not to say you can't go back in time. It just means that whatever you did will not create a paradox, because now is never changed. If it were, that would mean there would have to be multiple separate "nows", each slightly different from the other, and all occurring simultaneously.
Consider: you go back in time and kill your parents. If you manage to accomplish this (and I don't think you could), you would never have been created. But if somehow you did manage to do it, it would mean that the universe fractured the moment you went back in time, creating 2 separate instances, each diverging from that moment. In one, you kill them, and never exist. In the other, you are born, grow up, and decide to go back in time.
Realizing that Occam's Razor is tough to apply to an already-metaphysical discussion, I think the multiple-universe theory gets a quick slash.
2. Time Travel is Not Actually Time Travel Because "Time" Does Not Exist - This is more of a development of what I say can't happen in 1, but it's intriguing, nonetheless.
Instead of the universe or time or whatever fracturing, what if we don't move through time in a linear progression? What if time doesn't exist? If time doesn't exist, then all moments in time are actually occurring right now. The future, the past, and the present are all right now. If that's somehow possible (say multiple planes of existence, a multiverse, or whatever else you can dream up), then travelling "back in time" is really just moving from one point to another on the fabric.
I think that's more how time worked in Dune, with the folding of space, and with warp-speed in Star Trek.
If you consider that accelerating beyond the speed of light allows you to look back in time, then finding a way to fold space (or abstracting the fabric of the multiverse to traverse it non-linearly) would accomplish the exact same thing: you'd get to a point in time before its time would normally reach you.
It makes my brain hurt to think about it, but it makes sense to me.
Personally, I'm a bigger fan of Option 1, but it too depends on something dear old Occam would frown at: time-intelligence.
For Option 1 to work, time would need to be consciously aware of its linear nature to prevent you from killing your parents. Perhaps you would be unable to gain access to them, or perhaps you would die in transit. I don't know, but if you killed them, not only would you not exist, but everything they ever did after your birth would also cease to have occurred.
A better option overall is to simply assume that time travel is incompatible with Newtonian physics and abandon it. But Newtonian physics is incompatible with quantum physics, where the rudiments of time-travel and teleportation have been proven and demonstrated.
I had more to say, but this has been a rough day, and people keep interrupting me. I'll (try to) expound later on my theory that time can be represented as an enormous sphere.