Time travel is certainly possible. Go near a black hole, you'll time travel. In fact, once explained it's really not that crazy of a thing. Time being relative and all.
The issue is can we go back in time (which I think is no), and whether or not time as we perceive it even exists (also I think a no).
To touch on what was said earlier, it's very possible that we're creating the universe by our observation of it. Then again, it's possible we're creating reality by our observation of it.
*spoiler alert*
we actually might be the universe
*/spoiler alert*
I think that Schrodinger's cat is interesting, but only because of the splitting of different events and the observation of them becoming reality (double slit experiment, etc...). The juxtaposition of something being alive and dead is just a matter of which deterministic universe we're in.
Random documentary w/ Michio Kaku on time travel:
http://www.youtube.com/watch?v=au5i1Bw725o