Scientifically, if you board a shuttle moving at the speed of light way above the earth (gravity) and come back down after a day, you will return to a planet in the distant future.
Also, due to gravity, clocks at higher altitudes move slower than clocks at lower altitudes. I'm not sure about this though cos I'm not entirely convinced by gravity (it's a theory, not a law). One conflict in point: gravity is so strong as to hold planets in orbit, but at the same time so weak that a balloon can float high up into the sky.
Going back in time, according to current scientific understanding, requires the creation of wormholes. The energy required to warp space-time for the wormhole is beyond our means, however.
All these are from
https://www.youtube.com/watch?v=AECmzuzJoKo
Oh and by the way, the "constants" (gravity, speed of light, etc) actually changes from time to time.
On the conspiracy side, there is the Montauk Project (time tunnel experiment stemming from the Philadelphia Experiment) though on this one, I'd give it a miss (more falsifiable than verifiable). A better one to look at is CERN's Large Hardron Collider, whose purported real purpose (apart from looking for bosons) is... in opening wormholes.