For once Nat an interesting, albeit trolly and attention seeking as always, question. 

Sometime ago I read a few theories on time travel to the past, some argue that time travel is possible but the universe prevents paradoxes from occurring. For example lets say you travel back in time and try to kill yourself, ''fate'' will cause you to fail and whatever does occur will match with your own memories of the past. Then there's the idea that time travel to the past is simply impossible, again to prevent the occurrence of paradoxes. There is also this idea: 

[quote=Giygas]
How? Wouldn't you just disappear from existence?
[/quote]

That you could kill your past self but by changing the past, your future no longer exists and everything associated with it is erased from existence, include yourself at the very moment you kill yourself. Some also argue that due to this by even travelling in time you would create a new timeline and therefore eliminate yourself and your future from existence immediately which is a different version of the time travel is impossible argument. 

Furthermore it could be said that if you believe every choice or action causes a branch in time, then travelling back in time merely creates another branch in time allowing you to kill yourself and for you to remain in existence. But you wouldn't be immortal as your past self would still exist, albeit in a timeline where you didn't go back i time. 

The only way I could see this even occurring is if time travel isn't really time travel but rather going to another universe which so happens to exactly match our universe's past, in which case you could murder your ''past self'' but it wouldn't really be your past self and you wouldn't be immortal.