alt Hacker NewsEh, sorry chaos theory doesn't work this way.
It's just as likely you go back and perform whatever magic you need to to delete punishment for murder, then zip back to 'now' and see the world is a global panopticon making sure people don't murder each other.
Some of this may be a failure of people to realize what P !=NP is about, especially in non-linear systems.
Small perturbations in an early state of the system can lead to wildly different outcomes in the final measured state of the system. You can't determine what that will be in non-polynomial time. The only thing you can do is make probabilistic models by running a full simulation in real time (or reality with a time machine I guess).
If you look at chaos in dynamical systems, you can often find some equilibria (like attractors, spirals, saddle points etc ) at least, even if the details might vary. This is how people still manage to predict the weather somewhat, for instance. Oddly orbital mechanics is chaotic too, but it sort of rhymes over the millennia.