Messing with the space time continuum?

Sometime in the future, there probably is going to be a time machine if one hasn't been invented already. Wouldn't it make sense to prevent crime by knowing who, when, and where it's going to happen. If we travel back in time, we'd be able to greatly reduce the crime rate. I know messing with the space time continuum is dangerous. What negative effects could it possibly have f we stop crime? If there were any negative effects, couldn't we just go back in time and stop ourselves from doing that? What do you think would happen if 2 exact people were on earth at the same time, the present person, and the future person? Where can I read more about this? Sources?