The twisted paper tape of reality

It is a well-known trope in science fiction that time travel into the past leads to contradiction. Generally speaking, this is handled in two different ways: (1) By changing the past, the time-traveler wipes out his or her own existence; and (2) By changing the past, the time traveler creates a new timeline.

In the second scenario, which is consistent with the theory of multiple parallel universes, there is no such thing as a paradox, since every new causal event splits the universe into multiple alternate realities. By making some causal change in the past, the time traveler is simply shifting his or her own existence to a different parallel reality.

Yet there is a third possibility which I haven’t seen explored in the Sci-fi literature (which certainly doesn’t mean it hasn’t been explored — just that I haven’t seen it). Suppose that changing the past creates a resonant feedback loop: A change in future (A) introduced in the past creates a new future (B). In this new future (B) there was no change to the past. Consequently time moves forward toward the original future (A).

The resulting structure is a kind of temporal Möbius strip: At any moment in time it appears that there are two alternate universes. But if you follow the entire chain of causality, including the time traveler’s meddling trip backward in time, you find that it all forms a single consistent path. The twisted paper tape of reality has only one side.