The inverse bandwidth law of linear time travel

There are various kinds of time travel story. Some, like Rian Johnson’s Looper posit that time has many potential branches. When you travel back in time, you can change the course of history and thereby move your reality to another branch.

Others, like Robert Heinlein’s By his Bootstraps, posit that there is only a single time line. Anything you do by jumping back in time inevitably leads to the exact conditions that caused you to jump back in the first place.

I’m fascinated by the constraints imposed by this second kind of time travel story. Inevitably such stories convey a sense that free will is an illusion, since no matter what you do, you always end up in the same place.

But there is another interesting aspect to the linear time travel story: Higher bandwidth interventions lead to ever stranger realities. For example, if you could only send a single bit of information — true or false — from the future to, say, a year into the past, then it is reasonably plausible that whatever happens over the course of that year, the same bit value will always end up being sent back in time.

Even if a character in the story is actively trying to flip that bit, there are many reasonable storylines that could result in that character’s intent always being foiled. This is particularly true if we know that this is a linear time travel story, and that therefore paradoxes are not part of its fictional universe.

But every time we add more bits to the connection, things get a little nuttier. At the opposite extreme, a live video feed always shows reality as seen from one minute into the future. Whatever we try to do, our near future ends up being whatever is in that video. Clearly this scenario is vastly outside the bounds of any psychologically plausible narrative.

So the question I’m wondering is this: What information bandwidth that would be large enough to “break” a linear time travel story?