In a universe with an at first singular but then branching timeline once time travel was invented, what would be your mechanism for visiting the other branches of the timeline?
Personally I would have it so that you need to at first go back up the timeline to before the split and then go into the future and hope you go down the branch that is an alternate one instead of the one that will just bring you back to where you came from.
I use the idea of a ‘Configuration Space’, a metaphorical space where all logical configurations of space are contained. It’s not actually a space, but it is a real structure.
It follows an eternalist or block universe way of thinking where all points in time are equally real, where other modes of thinking may say only the present, past or future are real.
This also gets rid of, as far as I know, most if not all time travel related paradoxes, as once you have a viable mechanism for backwards time travel (primarily FTL travel) that makes it a logical possibility, and therefore a reality exists(or will be made to exist) where that instance of time travel happens.
Naturally, there are logical configurations of space that have no logical place in time, or sets of configurations that loop back on themselves, and other such structures, which makes the idea of phenomena in Configuration space even more interesting. I’ve considered lifeforms ‘made’ of time, or at least how Configurations are structured.
Such a structure would also bring causality and time as an actual thing into question, as it merely becomes a way to arrange Configurations.
It will take a lot of time to explore the ideas this presents. I am still trying to get through that.
Which is also consistent with relativity/general relativity, as different observers moving at different relative velocities could see different orders of events. (see, e.g., "The Fabric of the Cosmos" by Brian Greene, chp. 5)
The way i've implemented it, is similar to yours, you need to move through your ancestors, before being able to influence or view an alternate action, where you can then move "up" through their new decedents.
All timelines already exist simultaneously, it's just a matter of finding and accessing them.
In my setting, timelines are just other universes that share a common origin with ours. They don't branch with every quantum event throughout time and space, you can't find a reality where everything is exactly the same up until a few years ago and now you and your friends have goatees and are evil.
If you don't maintain your FTL drive properly, you can end up traveling between realities / timelines or whatever you decide to call them simply by accident. They're other universes that have been causally disconnected since the big bang.
While travel between them is possible, it is mostly pointless - after almost 14 billion years of the butterfly effect, you're most likely going to pop into empty space and have to go hunting for a place to land and resupply, and if you manage that it's just as likely to be occupied as the reality you just left.
You can look at how the universe would have turned out if the dice had rolled differently for us, but that's about it.
In my setting you can only travel to parallel time lines of the past and present. They can be extremely similar and you can return to your present, but you can't go to your own past.