You don't get to go back and kill Hitler, or stop September 11th or anything dramatically World changing but more like Sam from quantum leap you get to go back and change small things that may or may not have big effects. Like saving one person from a Nazi WWII camp or going back to make sure that bully from high school who is now a secretary in a dentists office or a gas station cashier was never born.
Let's say time travel is possible and Paradoxes can be semi ignored or be self correcting for the sake of this little thought experiment. All depending on your point of view.
1. Save a life?
You save some guy from dying in a WWII internment camp.
His great great great granddaughter goes on to perfect a life altering drug. Extending the life of everyone who takes it. ......... Key problem is for one person to live via this anti agapic drug thousands must die to make enough for 1 person to live for several hundred years.
(Before you ask Yes I got that idea from Babylon 5)
Do you do it?
2. Is it wise to try to change yourself?
You go back in time and see YOU walking down the street right before a major turning point in your life. You chose A but you want young you to choose B or are forced to choose 3....
Say you tell young you to Not stand up to that 17 year old bully that broke your nose when you were 12 because you miss breathing through your nose at age 40?
You now go back to your own time and find you never served in the military you never took risks because you got scared by old you and now live in a small apartment as a chartered accountant(Monty Python joke) or some other sad job. And the bully that you stood up to the first life but not this one.... Is still on the state legislature. But instead of being your own man and owning your own business you are his bitch accountant or secretary or whatever? (Like back to the future if it had been George McFly instead of Marty but in reverse)
True you can breath through your nose properly at age 40 but you are a sad little wimp. Was it worth it?
3. Change yourself again.... But this time you want ReVENGE!!!!
This one gets a little trippy hope you follow it....
OK so you remember the old "real"you.... and now the new Wimp you hops into the time machine. You go back and stop old Real you and tell yourself all about the mistake. And that you have a better plan and he should return to the present you've got this.... You teach your younger self how to kill the bully and get away with it. Old Real you gets back to the present and finds he(you) now has become a serial killer. He(you) comes back and kills wimp you before you talk to young you....
(confused yet? Us Too I think this was the plot of a Lame movie but I don't remember the title)
Old Real you... killed wimpy you that he(real you) made after wimp you made young you into a NUTJOB....But before he(wimp you) could talk to young you.... This one is why I said paradoxes are semi ignored or self correcting given your personal view points. Focus on the semi ignored for this one as it is a paradox you kill you that you made before the you that you made can make you....Because it is a Boot strap paradox of sorts.
Are you Still You?
Strange little thought experiment....
If it goes well 4 thru 6 to might follow but I am trying to come up with some real corkers as I think these are a bit easy. Well at least from my perspective because I had the answer before I wrote the question.