marsh8472 said:
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!
