Quote Originally Posted by Bleys
Before I go into my responses, I'd like to take a moment to address a recurring answer: winning the lottery. This is a thought experiment--the laws of physics do not change, and you cannot use time travel to win the lottery any more than you can go back in time and become a wizard instead of a sales clerk. The fundamental principle of quantum physics is Heisenberg's Uncertainty Principle. It originated with the famed two-slit experiment, where wave-particle duality was discovered. When left alone and only the interference patterns were recoreded, the electron stream fired at the two slits acted like a wave, but when an attempt was made to observe its progress, it acted like a stream of particles. In short, the entire science of quantum physics is predicated on the fact that by observing something, you influence it. If you go back in time with the winning lottery numbers for the next draw memorized, initially you do nothing, but as soon as you act upon it, you alter the future, essentially re-randomizing the lottery numbers. You can go back in time to stop Señor Douchebag from winning the lottery, but you cannot control who wins.
I think this can be more easily explained by the fact that the delayed-choice variation of the double-slit experiment (where the choice to view an electron or not is not made until after it passes through the slits) shows that the past is not a set history, but only a set of probabilities until observed. Thus, the observation of an electron changes the slit it went through in the past. And therefore since the outcome of a (truly randomized) lottery was not set until it was observed, and if you go back in time before it was set, all of the particles that can affect the lottery are just another set of probabilities again -- with no guarantee as to how it will turn out this time. The new lotto, according to a strict application of current quantum theory, would just be the same one in a billion chance.

However, that only works if the system which generates the lottery is truly randomized, and not some computer program which must act a certain way and so may in fact be more inclined to repeat itself if you go back to right before the numbers are picked. The lottery is also a finite set of possible outcomes (limited by the numbers it uses), so it's not an infinite set of probabilities like quantum theory predicts of matter in general, but it seems like the above would still apply if it's randomized. And, of course, we also have no idea what effect any hypothetical time travel would have on anything, including quantum mechanics.

On topic, I would not risk going back in time further back than very recently (say days/weeks) to change anything.