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The faster the relative velocity, the greater the time dilation between them, with time slowing to a stop as one clock approaches the speed of light (299,792,458 m/s). In theory, time dilation would make it possible for passengers in a fast-moving vehicle to advance into the future in a short period of their own time.
In the diagram, an observer at O in the x-ct system sends a message moving faster than light to A. At A, it is received by another observer, moving so as to be in the x′-ct′ system, who sends it back, again faster than light, arriving at B. But B is in the past relative to O.
Time dilation explains a number of physical phenomena; for example, the lifetime of high speed muons created by the collision of cosmic rays with particles in the Earth's outer atmosphere and moving towards the surface is greater than the lifetime of slowly moving muons, created and decaying in a laboratory.
Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...
English: Spacetime diagram showing that moving faster than light implies time travel in the context of special relativity. A spaceship departs from Earth from A to C slower than light. At B, Earth emits a tachyon, particle that travels faster than light but forward in time in Earth's reference frame. It reaches the spaceship at C.
The proper time measured along the traveling twin's world line from O to C, plus the proper time measured from C to B, is less than the stay-at-home twin's proper time measured from O to A to B. More complex trajectories require integrating the proper time between the respective events along the curve (i.e. the path integral ) to calculate the ...
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Some processes propagate faster than c, but cannot carry information (see examples in the sections immediately following). In some materials where light travels at speed c/n (where n is the refractive index) other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation (see phase velocity below).
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