I have written a reply to this question below, "Is Time Travel Possible" The answers here are all pretty good and most of them have been thought out pretty clearly. Rather then keep answering this question again and again I copied the answer I wrote from another question to this area. I sure would be interested to continuing this question with anyone who cares to answer my response.
I for one do not know the answer. Like you I have pondered this very same question is time travel possible. I initially said no way but as I kept reading a unique set of words kept popping up again and again and here is what I am reading...
A growing number of physicists are convinced that the thing we call ‘the universe’ — namely space, with all the matter and energy it contains — is not the whole of reality. According to quantum theory — the deepest theory known to physics — our universe is only a tiny facet of a larger multiverse, a highly structured continuum containing many universes.
I could easily write some deep explanation with scientific clarity but to answer your hypothesis of cause and effect and tell you that the laws that govern our universe can not be broken, but what if when you go back in time and make a change to the time line the change does not effect your future but rather a alternate future in the multiversity.
Everything in our universe — including you and me, every atom and every galaxy — has counterparts in these other universes. Some counterparts are in the same places as they are in our universe, while others are in different places. Some have different shapes, or are arranged in different ways; some are so different that they are not worth calling counterparts. There are even universes in which a given object in our universe has no counterpart
On large scales, universes obey the laws of classical physics, and so each behaves as though the others were not there. But on microscopic scales, quantum mechanics becomes dominant and the universes are far from independent. Universes that are very alike are close together in the multiversity and affect each other strongly, though only in subtle, indirect ways — a phenomenon known as quantum interference.
Without quantum interference, electrons would spiral into atomic nuclei, destroying every atom literally in a flash. Solid matter would be unstable, and the phenomena of biological evolution and human thought would be impossible. And as I shall explain, it is quantum interference that provides our evidence for the existence of the multiversity.
Through interference, its counterparts in other universes can affect each particle in our universe. What we see as a single subatomic particle is really a sprawling trans-universe structure, spanning a large region of the multiversity. Although we cannot see the parts of this structure that are outside our universe, we can infer their presence from the results of experiments.
As I said scientists are going to experiment with high speed partials at CERN so the rules have not been written yet, we have no unified theory yet. We just do not know what is possible. I for one hope for time travel, can you just imagine knocking on your families door in say 1941 would they believe you came from the future or just call the cops saying you are a madman. No one would ever believe you. I remember an old saying... we have met the aliens and they are us…. Have a great day Big Walt