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Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
In the context of this article, "faster-than-light" means the transmission of information or matter faster than c, a constant equal to the speed of light in vacuum, which is 299,792,458 m/s (by definition of the metre) [3] or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:
the long story of spacetime and the concept of time as the fourth dimension; e.g. the ideas of Lagrange and Wells; mathematical innovations that influenced the formalism of SR, e.g. the introduction of fibre bundles; indirect evidence for SR, through the evidence for relativistic theories like general relativity or relativistic quantum mechanics;
The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic Solar System tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present.
As length contraction and time dilation are both controlled by the Lorentz transformations, the ladder paradox can be seen as a physical correlate of the twin paradox, in which instance one of a set of twins leaves earth, travels at speed for a period, and returns to earth a bit younger than the earthbound twin. As in the case of the ladder ...
The theoretical study of time travel generally follows the laws of general relativity. Quantum mechanics requires physicists to solve equations describing how probabilities behave along closed timelike curves (CTCs), which are theoretical loops in spacetime that might make it possible to travel through time.
The transverse Doppler effect and the kinematic time dilation of special relativity are closely related. All validations of TDE represent validations of kinematic time dilation, and most validations of kinematic time dilation have also represented validations of TDE. An online resource, "What is the experimental basis of Special Relativity?"
This combines the effects of time dilation due to motion (by factor α = 0.6, five years on Earth are 3 years on ship) and the effect of increasing light-time-delay (which grows from 0 to 4 years). Of course, the observed frequency of the transmission is also 1 ⁄ 3 the frequency of the transmitter (a reduction in frequency; "red-shifted").