I have invented a machine that allows me to travel to the recent past. It can only send me back a week. So, on May 19th, I enter the machine, and re-emerge on May 12th. Knowing that my actions could affect the future, I do pretty much what i always do-eat, work, sleep. However, I decide that when May 19 arrives, I will not use the machine-I lock it away in the basement, and discard the key, Now, I cannot travel back-what happens to my “trip”? Have a created an eddy in spacetime by doing this?
Are you eating, working, sleeping alongside your other self from earlier in the week?
I would suspect that the two of you, one of you that is a week older, would continue to exist together.
So, what happens to past you?
Surely if you go back to the 12th, then the past version of you will still be there as well. Do you plan on killing him and taking over his life?
Otherwise, I’m not seeing a problem there - assuming you lay low and do your own thing for that week while past you lives his (your) life for that week, then you are a separate entity to past you.
It would be like taking a trip somewhere, turning around halfway there, going home, then resuming your journey again. It’s two separate trips - whatever happens the second time around won’t affect the first journey.
Depending on how you view the universe a couple things could happen:
When you went back you went back to a new universe where there were two of you starting on May 12th and the you native to this new universe will never travel back in time.
Or, you try to hide the machine but somehow your plans go awry and somehow your other self gets access and goes back in time. Why? Because it already happened so it has to happen again. I suppose in this scenario, you would have already met yourself on May 12th and everything that other you did you would now do because you would have gone back in time and would now be playing the part of the other you who emerged on May 12th.
What Quimby said. Or, someone from the Time Patrol comes, whups your ass good, and sets things to rights while muttering about newbie time machine inventors.