Time Travel and the space-time continuum

Main Question or Discussion Point

If someone were able to travel back in time and change an event in history which resulted in a divergent timeline from the one you came from would both timelines be part of the same space-time continuum?

I suspected they could be because part of their timelines are shared and connected to each other that way but I'm not sure if that's correct or not.

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What happens when an irresistible force meets an immovable object? The question has no right answer because it doesn't apply to reality. The "correct" answer will depend on whatever imaginary framework you adopt in order to make it meaningful.

What happens when an irresistible force meets an immovable object? The question has no right answer because it doesn't apply to reality. The "correct" answer will depend on whatever imaginary framework you adopt in order to make it meaningful.
okay but using your own personal definition of the space-time continuum would you consider these two timelines part of the same space-time continuum?

If someone were able to travel back in time and change an event in history which resulted in a divergent timeline from the one you came from would both timelines be part of the same space-time continuum?
I'm gonna wait until someone does it then observe the result.

okay but using your own personal definition of the space-time continuum would you consider these two timelines part of the same space-time continuum?
See this picture of a light-cone for how I would describe your scenario. There is a region of space-time in that diagram called the "future light-cone". That consists of every point in future space-time that can be reached from the point labeled "observer", by traveling at the speed of light or slower.

I'm going to suppose that the past is changed at the point labelled "observer", and the changes spread out at light-speed or less. So the only place where one timeline differs from the other is inside that future light-cone, and we can divide the overall "branching universe" into three parts: one copy of everything in that diagram outside of "future light-cone", and then the two different timelines that can fit into the "future light-cone".

Mathematically you can then describe a "branched manifold" which consists of both future cones joined to the light-cone surface. The difference between this branched manifold, and the usual single-history manifold, is like the difference between "I" and "Y". In the letter Y, the two lines at the top join at a point. In the branched space-time, instead of joining at a point, the branches join all along the cone, so it's hard to visualize if you're not used to this.

"Are the timelines part of the same space-time continuum?" "Space-time continuum" isn't a precise term in physics, it seems it was made up to convey the mixing of space and time that occurs in relativity. Mathematically we can say that the branched manifold is connected, but that along the join its topology is not locally Euclidean.

The standard laws of physics are only defined for standard space-times, so there will be major issues about how physics behaves at the join point. See all the problems you created with your time machine!

There are theories that when a future event changes past in an incompatible way, then it enters quantum superposition. Both realities coexist in the same spacetime.

Imagine a cat that goes back in time and kills his own grandpa. In the timeline where he killed his grandpa, he does not live. In the timeline where he didn't, he does live. So basically he is dead and alive at the same.

tom.stoer
There are theories that when a future event changes past in an incompatible way, then it enters quantum superposition. Both realities coexist in the same spacetime.

Imagine a cat that goes back in time and kills his own grandpa. In the timeline where he killed his grandpa, he does not live. In the timeline where he didn't, he does live. So basically he is dead and alive at the same.
Could you explain this in more detail, e.g. via a quantum mechanical wave function or a path integral in a Gödel-type universe?