In the eternal moment, the past and the future are simply a matter of perspective and the past can be influenced by overlapping reinforcement or the intent of the resolving future. A time paradox is a self-informing sequence within a point.

The classic grandfather paradox assumes that time is linear, ignoring the fact that the appearance of a person from the future is an unprecedented event at that point in the past. It also ignores the consequences of his absence from the point of his departure in the future.

For the time traveler, all of the time leading up to his departure from the future, relative to his point of arrival in the past, is a precedent for his existence in the past and the method or mechanism he used to get there.

For time travel to be possible, moments in time have to be states of reality that are discrete from each other and persistent in themselves. Given that, the time traveler could go back in time.

However, the mere fact of his arrival in the past would have the potential to change the course of events, creating an alternate past or creating a feedback loop through the future.

That feedback loop could have a constructive or destructive effect, depending on how elastic the fabric of reality is. Put simply, that whole segment of reality would become Schrödinger’s Box.

The presence of the time traveler in the past would be sustained by a conservative force of causality. Insignificant changes would be relatively easy to make, while more significant ones would create bifurcations.

Multiple instances of reality would emerge, with a tendency to reconverge on the base time line or completely diverge into a maze of different paths striving to collapse into a stable path.

The model of a grandfather paradox would describe a path along the original line, through the point of departure—continuing past that point to account for a future where the time traveler simply ceased to exist.

The only way reality could accommodate this is by splitting into a loop intersecting the past and entering a tree of divergent and reconvergent branches.

At least one one branch will feature the time traveler walking away from the cooling corpse of his grandfather into an alternate future where, instead of being born, he just magically appeared out of nowhere.