[time paths] need they always be linear

We just watched the 2006 Denzel Washington movie Deja Vu. If you don't know the movie, click here.

Rather than discuss the movie, I'd like to look at the issue it addresses, albeit in simplistic terms. This doesn't follow the plot but is just an idea springing from the plot.

Let's say we agree on two things:

1. Time moves forward in a linear way [1];
2. It is possible to create another path [2] by going back in the past and starting over.

So we start at a point in time before where your partner will be killed, say, in a ferry disaster. Now you are not on the ferry and you witness the disaster. Look at the diagram top left and the tick represents this path.

At that point, you are able to twist time to go back before the disaster. With the knowledge of what is about to happen, you have to stop him/her boarding that ferry and also do what you need to to prevent the disaster.

You do that but in saving the ferry, you yourself die, represented in the diagram by the cross. clearly, we don't want that to happen but you're no longer around to go back later and prevent your own death.

However, a second you now appears and joins up with your partner. This second you was the one already in this time/space position? The one dying, saving the ferry, is the "intruder" you.

Now, let's say the people controlling the machine in the future point after the original disaster move to return you to that point. Do they return the dead you or the linear, living you?

What do you think?