Imagine that humans traveling through time are like ants walking along a thread. If there’s a tangled mess of knots and chaos, the ants could walk all over the place. If the thread is not in contact at any place, the ants would be left with no choice but to keep on going in one direction.
Knots would serve as time traveling points where you can freely jump from one part of the timeline to another. Depending on how tangled the thread is, there could be multiple time jump opportunities.
I don't think it makes sense to be walking on top of a thread of time, as if we are separate from time. Our being is inseparable from the thread of time. The fibers in the fabric are our experience, we are the fibers, and we still travel through a one-directional thread, no matter how tangled.
Also, tangled knots happen in space. What kind of space can time get tangled within?
Now that's another fun question! It also makes me wonder, how would space behave in tangly time?
Would the space in which time gets tangled be primarily around extreme phenomena like black holes, or the very beginnings of the universe (or a universe, if one wants to get into multiverse angles)?
You can think of space-time as a 4D object. If it’s a flat plane (more correctly, a hyperplane), it could be infinitely big. If it’s s sphere or a torus, it would be finite. It could also be an infinitely long pipe.
Either way, the shape doesn’t have to be perfectly smooth. A plane can have wrinkles, where two points touch. Likewise, a pipe can have knots and bends. All of this would happen in 4D space, so our 3D brains can’t really visualize any of it.
Since we would be inside the frame of reference, I don’t think we would know it was happening, like imagine you’re inside a tube that is knotted. You’d go through the tube like a slide at the water park, no way to see that it’s a knot, even if we can detect the turning and tumbling, there’s little we can reference from inside to determine it’s crossing around itself.
I think that, due to the nature of chaos and the butterfly effect, any time travel at all would change the future. Unless it was just closing a time loop that was already present in the current past (which would mean any attempt to alter history would fail because that attempt is already a part of history), or if it's possible to create new branches in time.
So these rules are either unnecessary because any time travel automatically causes changes that, it's not possible to change the past from the past, or it's not possible to go back to our past, thus nothing you do will affect our present.
Spacetime (you can't talk about time only) or at least its substrate does get in knots, best we can tell. We call them fundimental particles. String theory/membrane theory are still very much theoretical physics right now, however, so it could be completely wrong.
The other alternative is a closed timelike curve. According to relativity, there are valid solutions that create such a curve. Theoretically, you could fly into one, traverse it, and exit before you entered at the start. This does require several black holes, moving at stupid speeds, orbiting each other, however. It's also theoretical. While the equations allow it, we know they are incomplete. Physics seems to have blocks on anything that can mess with causality. It's likely something, currently unknown, kicks in to stop the closed timelike curve from forming.
What size is the membrane separating one point in time from another? If the membrane is the size of the observable universe we wouldn’t see a difference. If it’s the size of your living room you’d be fucked because your living room only exists at any given point in space time for a very very short time.
Physics seems to be very protective of causality. We don't know the underlying mechanism, but it pops up in multiple areas of physics.
The speed of light being the most blatant example.
We can see events happening, apparently put of sequence. What we can't do is interfere with them.