One might consider going back in time to "right a wrong" or change some past event to the benefit of mankind, or even to one's self. Certainly, who wouldn't want to go back and prevent the assassination of Kennedy or Martin Luther King, Jr. or any number of past leaders and heroes?
Unfortunately, it cannot be done, and not because time travel is available to us as of yet (in our perception) but, rather, because the past cannot be explicitly changed for the same reason we cannot truly know the status of Schroedinger's cat without risking it's demise.
Let's say wanted to prevent Hitler from attaining his reign over Nazi Germany. You warm up the time machine, go back to when Adolf was a young, aspiring artist and you promote his efforts, buy all his paintings and inspire him to become something great instead of the miserable historic reality we all learn of in school. Now what?
He never turns into the evil, villainous leader of the third reich and, therefore, does not get listed in the historic record as such. Not being mentioned in the history books gives YOU absolutely NO incentive to go back in time to stop him!
And if you DON'T go back in time to stop him, then...well, you get the picture.
So, as cool as time travel is, the adage of "you can't change the past" seemingly still applies. Now, notice I said explicitly earlier in this article. It would seem one may inadvertently change the past much like the errant hunter in the classic story A Sound of Thunder by Ray Bradbury. He wasn't intentionally trying to change the past, however, because his alteration of the past was not motivated by that which he eliminated, the past WAS changed.
Sooo...there lays one more factor to take into consideration when planning your next time-travel novel, short story, or trip to the past to correct that little historic conundrum you deem unnecessary.