It is not a reality yet; however, indeed I believe it is possible and on a significantly small scale it has been tested. I have provided some examples...
There are various ways in which a person could "travel into the future" in a significantly limited sense: the person could set things up so that in a small amount of his own subjective time, a large amount of subjective time has passed for other people on Earth. For instance, an observer takes a trip away from the Earth and back at relativistic velocities, with the trip only lasting a few years according to the observer's own clocks, and return to find that thousands of years had passed on Earth. It should be noted, though, that according to relativity there is no objective answer to the question of how much time "really" passed during the trip; it would be equally valid to say that the trip had lasted only a few years or that the trip had lasted thousands of years, depending on the choice of reference frame. This form of "travel into the future" is theoretically allowed (and has been demonstrated at very small time scales) using the following methods:
(1) Velocity-based time dilation under the theory of special relativity, for instance:
Traveling at almost the speed of light to a distant star, then slowing down, turning around, and traveling at almost the speed of light back to Earth.
(2) Gravitational time dilation under the theory of general relativity, for instance:
Inhabiting a hollow, high-mass object;
Inhabiting the space just outside of the event horizon of a black hole or inhabiting an object whose mass or density causes the gravitational time dilation near it to be larger than the time dilation factor on Earth.