If you stopped yourself from having the accident there would be no reason for your future self to travel back. Therefore you would still lose your leg.

I agree with the parallel universes theory. Technically, I believe the "self" that went back in time would be stuck there in one reality but the separate reality where he got his leg cut off would still be there.

This means that time travel is not technically time travel but instead universe hopping. A self from one universe travels to a second universe where an entirely different sequence of events is triggered. The original timeline continues without the time traveler and no other noticeable changes (except maybe a rip in the Time Space Continuum, who knows) while to other timeline goes on with the two selves, one old and missing a leg and one young with a leg. Where this goes from here depends on the actions of these "self"s

Thats the most logical theory I can come up with. Point out the error of my ways please

If I finished Ocarina of Time without dying once....

...am I ineligible to play the Zelda titles corresponding to the death timeline?

Seriously though, THAT is the official timeline? Methinks the creators realised how screwed up it became when they tried to put some kind of organisation to it.

The only issue is that we're looking at creation and/or destruction of matter, undermining a major law of the universe. Can matter exist in two places at the same time in a non-theoretical way (as quantum uncertainty has things existing in multiple states simultaneously, but that's only because we lack the ability to perceive energy and position at the same time).

If going backwards in time is at all possible, then i suspect it would result in a duplication of matter. There would simply be two of you, and if you were able to prevent your past self from making the decision to go back in time, then there would be two of you in the future as well, but if you do something in the past that prevents you from ever coming into existence, that doesn't impact the you that currently exists.

I dont know a ton about Time Travel but I do know a little (thank you Stein's;Gate, sadly ive forgotten most of what you've taught me). There is one theory that involve using black holes. Maybe by creating a black hole, a small amount of energy is consumed from the universe to bring the universe back into equilibrium. This could cancel out the duplication of mass but it may also leave the universe in a weird, flux-y state for a while...

Anyways, if matter/energy is constant, than why do black holes exist. Aren't they a contradiction of that universal law? Science is only based on what we know, things change with more knowledge

I'll go with Chrono Trigger theory of time travel.

So, time travels with you and the future is destroyed as you move back in time. So... you can go back from time X to time Y and prevent your past self from losing its leg and live normally from there. However, you still won't get your leg back, the timeline you belong is forever changed and your past self would disappear the moment the Y timeline reached time X so as to keep the amount of energy-matter constant; so you behave sort of as a very long-lasting virtual particle. And you then wouldn't exist in the new, rewritten timeline Y, time X until you came back to the future.

2, because I like the many-worlds interpretation of quantum mechanics.

The matter that constitutes your self right now is totally (as in entirely) different from what you were in the past. Atoms are not set in stone in your body and come and go, flow, at each passing moment. So the atoms that constitute your body right now wouldn't interfere in any way with those that constituted your past self.

Right, but those atoms probably existed somewhere. Go back five years and the carbon in your muscle from the meatball you ate is back in a cow, or perhaps further back in some feed or something. You're still bringing most of that matter (aside from radiocarbons and anything else radioactive that might have gone into you).

So you're still on simultaneous existence of matter

Or you could wait for your past self to have the accident, get the leg and go to the closest hospital to reinsert it on yourself.

*Shows sectioned and bloody leg* "Hey doc, could you put this in its place?". That would be hilarious.