Time travel is a proven fact , Einstein predicted it and it has been proven that fast moving objects pass time slower than slow moving objects, so time travel , at least in one direction(forward) is very real .Very fast planes fitted with Atomic clocks have proven that the clock on the plane went ahead of the clock on the ground.
Also I have heard that GPS tech would be impossible without the effects of time predicted by Einstein, thus we use his theory of this everyday now .
Time travel to the future in physics
Transversal time dilation
Main article: Time dilation
Time dilation is permitted by Albert Einstein's special and general theories of relativity. These theories state that, relative to a given observer, time passes more slowly for bodies moving quickly relative to that observer, or bodies that are deeper within a gravity well. For example, a clock which is moving relative to the observer will be measured to run slow in that observer's rest frame; as a clock approaches the speed of light it will almost slow to a stop, although it can never quite reach light speed so it will never completely stop. For two clocks moving inertially (not accelerating) relative to one another, this effect is reciprocal, with each clock measuring the other to be ticking slower. However, the symmetry is broken if one clock accelerates, as in the twin paradox where one twin stays on Earth while the other travels into space, turns around (which involves acceleration), and returns—in this case both agree the traveling twin has aged less. General relativity states that time dilation effects also occur if one clock is deeper in a gravity well than the other, with the clock deeper in the well ticking more slowly; this effect must be taken into account when calibrating the clocks on the satellites of the Global Positioning System, and it could lead to significant differences in rates of aging for observers at different distances from a black hole.
It has been calculated that, under general relativity, a person could travel forward in time at a rate four times that of distant observers by residing inside a spherical shell with a diameter of 5 meters and the mass of Jupiter. For such a person, every one second of their "personal" time would correspond to four seconds for distant observers. Of course, squeezing the mass of a large planet into such a structure is not expected to be within our technological capabilities in the near future.
There is a great deal of experimental evidence supporting the validity of equations for velocity-based time dilation in special relativity and gravitational time dilation in general relativity. However, with current technologies it is only possible to cause a human traveller to age less than companions on Earth by a very small fraction of a second, the current record being about 20 milliseconds for the cosmonaut Sergei Avdeyev.
Twin paradox diagram
There are various ways in which a person could "travel into the future" in a 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 example, an observer might take 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)