If time travel were a scientific possibility, rather than a device of fiction, how could you magically find the earth when you got there? It is orbiting the sun, which is itself orbiting the galactic center, which may also be moving.
It is a reality. It's been proven with twin atomic clocks, one aboard an airplane, the other on Earth. The first such experiment was carried out back in 1975. The time was very small, but it was real. The effect is also used in GPS satellite communications. However, in both of these and other similar cases, there are TWO sources for time dilation. One is caused by the high speeds involved, the other by the gravitational field of the Earth. Clocks tick out time more slowly in a gravity field, as they do when they are in a state of rapid motion relative to a stationary observer.
“The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity.”
http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results
Of course for any significant time dilation to occur, speeds approaching that of light would be required. And that would require an almost unobtainable amount of energy, particularly for massive objects like human beings. Protons and other subatomic particles are another story.
Hawking is working on it....
Sorry, I should have clarified that I wasn't talking about relativistic time dilation, which is well established, but the "Let's go have dinner with Sun Tzu" version that reaches back before birth, and then back home by nine...