Stephen Hawking once famously said that, if time machines are possible, why isn't there tourists from the future taking my picture right now. For a minute, that sounds all reasonable. However, he amongst many other contemporary physicists actually believe the opposite. Why we cannot see them, the answer might be simply because they are invisible to us. Physicists actually believe in that. Not only that, but they are writing papers on the possibility and design of time machines. Their current work is mainly based on Einstein theory of relativity, in which he proved that time is a river not an arrow, that has to be corrected (just like current GPS systems).

Now, what about the ultimate time travel paradox? what happens if you go back in time and kill your own parents or grand parents? Physicists have a solution for that. They argue (proved?) that no one can change his/her own future, but in fact, we may change the future of others by creating parallel universes in accordance with our actions back in time. In other words, the river of time forks into parallel paths, where new timelines are created of the same people, however in a parallel universe. This is known as the many worlds theory, which says that the world is constantly splitting into parallel universes. A time machine will allow us to go back and forth between these universes.

On the other hand, physicists proved also that the power required to harness the fabric of time is equivelant to that of a black whole. As categorized, that is only possible in a type III civilization, which is ~100,000 years in the future on a linear advancement scale. Type I being a 1000 years in the future, and can harness the power of this planet and change its weather.

The bottom line, according to our current understanding of the laws of nature, time traveling is possible.