This time correction theory is horribly unscientific?
Especially with the example you gave.
I mean If you become patient zero, what if you simply died, and thus can't go back in time to etc..
I think to think about time travel rationally you have to separate it from the human perspective, grandparents paradoxes etc.
If we view the universe as a giant computer, and there are 4 variables for every "fundemental" particle (X,Y,Z,T). This describes atleast WHERE everything is at any given T.
Maybe we make the (silly but handy) assumption that given the position of all fundamental particles in 3-d space, or X-d space, and a time variable, we don't have to think about forces because they are a RESULT of the coordinates, and the nature of the fundamental particles. (ie; gravity as a force can be calculated as a function of position without knowing anything about the previous states of the bodies).
When time moves forward, Each 'next' state is a function of the previous state;
Time travel basically asks can we create or witness a situation where the next state, IS the previous state, or a state that has already occurred.
ie; Time travel isn't going back in time to see your grandpa, it's every single fundamental particle in the universe being where it was at some previous time. (including your thoughts and memories).
In most mathematical systems this isn't possible, as the numbers are infinite, 3 comes after 2, 5 after 4, 1000, after 999, and there are functions that will keep counting up never to repeat.
Thus if T is continuously increasing, there is never a result of this function that will produce the same result as a previous function UNLESS that's how the whole shit was designed. (ie; some kind of SinWave-like function that periodically repeats producing the same ouput, even given a continously counting input).
So you can't turn back time. But time may turn itself back at some stage and there's nothing you can do about it, you won't even realise its happened an it COULD be happening right now.
The idea of 'personally' witnessing time travel is quite ridiculous and complex. The 'matter' that makes up your brain, and the energy that makes up your 'thoughts' could be lightyears away ins ome other galaxy at the T you elect to travel back to.
If you were to go back with your current memories, what happens to that energy that is 'holding' those memories, what happens to the distant star that's now missing some infinitesimal fraction of energy for apparently no reason as it's in your brain as a thought because you went back in time but wanted to keep your memories.
When it comes to time travel, grandpa-homicide is probably the LEAST of your concerns in terms of logical inconsistencies.
I mean think about eating food. You put food into your mouth and it becomes part of you. If you reverse time does the food go in reverse OUT of you?
Wouldn't it be the same for your memories? Flowing OUT of you?
And if you want to 'keep' your memories, you'd run into the same problem as if you kept your food. At the point you ate it, now there's a "COPY" of that food inside you and a "COPY" of your food that is reversing out of your mouth, and then what? The amount of matter in the universe and thus energy has just randomly increased out of nothing?