The time-travel paradox arises only if you presuppose the existence of free will: if we don't, and just consider human beings as physical objects acting deterministically, then there can be no paradox: the time traveler will simply do what was already had been done in his past.
Ah yes, can you change the past or was there a time traveler version of you running around failing to change things the whole time? See season 5 of Lost for endless discussion on this point. You also can avoid paradoxes if it turns out that time travel just puts you on an alternate timeline.
There's a different paradox with this version of time travel though. Suppose I'm a kid and future-Me comes back and tells me a story. "you will write down this story and publish it and it will be famous." I do as he asks and he's absolutely right, leading me to eventually return the favor to my past self in a time loop.
It may be that, just as it's impossible for you to be killed by yourself from the future in this type of universe, it's also impossible to create information out of nothing, so the specific scenario you described would just be impossible.
This could be a kind of conservation law - imagine that instead of a story you had a golden coin, that you receive from your future self, keep, and give back to your past self after you travel, you've added some mass to the universe, which would be impossible because of conservation of energy.
This explains absolutely nothing. “Will simply do what was already done in his past” is the non-sequitur: if they shoot themselves in the past then that was what was done in the past. Sounds paradoxical? Because it is, and determinism can’t stop a human from shooting a gun any more than free will can because this has got nothing to do with volition.
The conservation of energy only applies to a closed system. If we can "create" an apple at any given point in time, that only means that "the universe at a given point in time" isn't a closed system.
That's an interesting point. I'd even go a step further and say that which of those two definitions is true determines whether time travel is possible. Put another way, conservation across space-time (instead of a single point in time) is necessary for time travel to exist, and the existence of time travel is the only reason conservation would be across space-time.
I'm not sure that time travel is the only reason - it might turn out to explain some other peculiarities in the universe (spooky action at a distance jumps into my mind as something that could potentially have an explanation linked to this).
It also would seem to be impossible to calculate energy at a specific moment. Energy = mc^2, or expressed differently, e = m * d^2 * t^-2. If t = 0, then t^-2 is not calculable.
I know next to nothing about all this so excuse my ignorance -and limited English-, but I've always thought that if you send, say, an apple (as in GP's comment) to the past... wouldn't that apple's atoms already exist there in the past -in the same apple if it already existed (you are sending it just some minutes back) or elsewhere like in the tree, the tree's soil... animals that later died and nourished the soil/tree... in rocks... wherever- and so you are duplicating them and hence creating energy/mass and breaking the law of conservation?
Either it's impossible to travel back in time in this universe or it is not an isolated system... or the law of conservation could somehow be broken... do my thoughts make any sense?
Any variation on this: “sending this item in the past, will grab the same amount of mass from the past, taken at random in a way that preserve the energy on both ends”
What people mean by "time travel" isnt time-reversal. It's taking information from the future and injecting it into the past by moving the atoms of your now-body into the past.
This isn't "time travel" in any sense that physics uses the term. And is certainly impossible on very many grounds.
Physics has nothing to say on "time travel" in the popular imagination.
