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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.
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 ...
Rindler chart, for = in equation (), plotted on a Minkowski diagram.The dashed lines are the Rindler horizons. The worldline of a body in hyperbolic motion having constant proper acceleration in the -direction as a function of proper time and rapidity can be given by [16]
Important vector fields in relativity include the four-velocity, = ˙, which is the coordinate distance travelled per unit of proper time, the four-acceleration = ¨ and the four-current describing the charge and current densities. Other physically important tensor fields in relativity include the following:
In (1+1) dimensions, i.e. a space made of one spatial dimension and one time dimension, the metric for two bodies of equal masses can be solved analytically in terms of the Lambert W function. [11] However, the gravitational energy between the two bodies is exchanged via dilatons rather than gravitons which require three-space in which to ...
Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative ...
The second special case is that where the relative velocity is perpendicular to the x-axis, and thus θ = π/2, and cos θ = 0, which gives: ′ = This is actually completely analogous to time dilation, as frequency is the reciprocal of time.
Since the result was the same, it was shown that acceleration has no impact on time dilation. [28] In addition, Roos et al. (1980) measured the decay of Sigma baryons, which were subject to a longitudinal acceleration between 0.5 and 5.0 × 10 15 g. Again, no deviation from ordinary time dilation was measured. [30]