There is a great deal of experimental evidence for time dilation in special relativity and gravitational time dilation in general relativity, for example in the famous and easy-to-replicate observation of atmospheric muon decay. The theory of relativity states that the speed of light is invariant for all observers in any frame of reference; that is, it is always the same. Time dilation is a direct consequence of the invariance of the speed of light. Time dilation may be regarded in a limited sense as "time travel into the future": a person may use time dilation so that a small amount of proper time passes for them, while a large amount of proper time passes elsewhere. This can be achieved by traveling at relativistic speeds or through the effects of gravity.
For two identical clocks moving relative to each other without accelerating, each clock measures the other to be ticking slower. This is possible due to the relativity of simultaneity. However, the symmetry is broken if one clock accelerates, allowing for less proper time to pass for one clock than the other. The twin paradox describes this: one twin remains on Earth, while the other undergoes acceleration to relativistic speed as they travel into space, turn around, and travel back to Earth; the traveling twin ages less than the twin who stayed on Earth, because of the time dilation experienced during their acceleration. General relativity treats the effects of acceleration and the effects of gravity as equivalent, and shows that time dilation also occurs in gravity wells, with a clock deeper in the well ticking more slowly; this effect is 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 large gravity well such as a black hole.
A time machine that utilizes this principle might be, for instance, a spherical shell with a diameter of 5 meters and the mass of Jupiter. A person at its center will travel forward in time at a rate four times that of distant observers. Squeezing the mass of a large planet into such a small structure is not expected to be within humanity's technological capabilities in the near future. With current technologies, it is only possible to cause a human traveler 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.
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