Note: For purposes of simplicity I am not considering the Marle Paradox in this theory.
The mechanism of TTI can be deduced through simple logic. Imagine for a moment, that you go back in time, say five minutes, with a loaded gun. You then shoot yourself in the head, killing you instantly. If you were to do this, I believe that you would not disappear. The act of killing your older self, posibally the act of time traveling period, would have no effect on the you who pulled the trigger. The act of changing the timeline can be compared to a wave. Upon the change, this wave would sweep across time, altering everything that occured after the wave began. But, and this is key, you are behind the wave. The wave, you see, only acts one way. It will destroy the you who got into the time machine, but it can't wrap around and kick the you who stepped out of the machine in the ass. You are behind it, and it can't knock you down.
By traveling through time, you have broken the normal chain of cause and effect. The version of you that stepped out of the machine was, in effect, created ex nihlo the moment you arrived in the past. If we assume that time travel breaks cause and effect, this explains at least one aspect of TTI. Another example: After killing the older version of you, you enter the time machine once again. This time you go forward in time ten minutes. You then send an automated drone into the past to kill you before you left for the future. You would not vanish. Why? Because the violation of casuality has broken the chain. The you who sent back the drone is unconnect from either of the yous who were killed in the past.
This principal would explain at least one aspect of Time Traveller's Immunity.
