I knew that jumping backwards has a high cost no matter how short the jump, but I thought that coexistance could theoretically have an arbitrarily small cost for an arbitrarily small period of time coexisting.
My thought for making a jump backwards solely for the purpose of preventing others from doing so:
- Be near a clock of whatever sort you can use to know how far back in time to go, with space in front of you where nobody is standing.
- Take out a knife, hold it level with your eye, and then stab forward while noting the time.
- If nothing happened, walk to where you just stabbed, turn around, and jump back to right before you stabbed.
- If something did happen, it should be that your future self appeared right where you were stabbing, and is now dead of traumatic brain injury. Cost to you: less than a second of coexistence.
If pausing to kill the bodyguard (and presumably the target while you're at it) is cheaper, I'd be surprised (especially because you have to pause before being noticed). It certainly has a higher chance of working, though, as the target's bodyguard might catch and stop you without needing to go back in time to before this procedure.