I am not a physicists, I do not understand Quantum physics at all. That being said I am sure someone will say my lack of understanding is why I am saying no, if I understood Quantum physics I would understand that it is theoretically feasible.
To those people I say consider that if a person did manage to go back in time his very presence would change history. According to Newton every action has an equal and opposite reaction. Just the act of being in a time you are not meant to be in will (if Newton’s theory is correct, and so far it has been) cause problems.
Consider, you go back in time and try your very best not to do anything to change history; you simply walk around seeing how things actually looked and how people actually lived. While you are walking around someone from that time sees you and stops what he or she is doing to watch you for a moment. Watching you delays that person for less than a minute, thereby making the person late in doing whatever it was he/she was doing.
Now, consider that history records that person died on that date at one minute past the time he/she stopped to watch you. By stopping for the very brief instant the person missed a rendezvous with death. Congrats, you just saved a person’s life. You should feel very proud of yourself.
Except, that person not dieing at the time he/she was supposed to die he/she was able to continue a project that was his/her secret mission. This was a very important mission given him/her directly from Hitler and by missing death he/she was able to complete the mission giving Nazi Germany just what it needed to win the war.
Your simple act of being in the wrong place at the wrong time, even though you did nothing to directly change history, put Europe under Hitler’s control and made the U.S. a third world country.
There is another possibility that should not be overlooked. The Earth is in constant motion, both rotating on it’s axis and revolving around the sun. This means that at any given moment the Earth is in a different location than where it was a moment before. What does this have to do with time travel? In theory if you did not take into consideration the movement of the Earth while making your calculations for time travel you could conceivably end up where the planet was not where it is when you finish your journey.
Theoretically anything is possible. In reality there are a lot of variables that need to be considered. In the words of Ian Malcolm (see Jurassic Park) “Just because you can do something, doesn’t mean you should.”