While everything in this article is factually correct, it maybe gives a different impression than it should. Time dilation is of course a long held tenet of special and general relativity. Can we call that time travel into the future? I'm not really sure. In a way I guess it is (how is it practically different from placing yourself into a separate bubble of spacetime?). Of course, actually achieving this in a practical sense is pretty much impossible considering the energies involved.

As for time travel into the past... pretty much no. That would have a bunch of really disturbing consequences, including traveling faster than the speed of light and violating the second law of thermodynamics.

Of course, this just a former physics minor on stupid macro affects. When you get down to the quantum particle level the game probably changes considerably.