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Relation between the speed and the Lorentz factor γ (and hence the time dilation of moving clocks). Time dilation as predicted by special relativity is often verified by means of particle lifetime experiments. According to special relativity, the rate of a clock C traveling between two synchronized laboratory clocks A and B, as seen by a ...
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 ...
Also, the velocities in the directions perpendicular to the frame changes are affected, as shown above. This is due to time dilation, as encapsulated in the dt/dt′ transformation. The V′ y and V′ z equations were both derived by dividing the appropriate space differential (e.g. dy′ or dz′) by the time differential.
In order to find out the transformation of three-acceleration, one has to differentiate the spatial coordinates and ′ of the Lorentz transformation with respect to and ′, from which the transformation of three-velocity (also called velocity-addition formula) between and ′ follows, and eventually by another differentiation with respect to and ′ the transformation of three-acceleration ...
This is a different voyage than the one shown above, as both schemes take the same assumed total point-of-view time: T=12 (stay-at-home), resp τ=12 (ship), so the results of the calculated other-one's times must be different: τ=9.33 (ship), resp T=17.3 (stay at home). In the standard proper time formula
The Cauchy problem (sometimes called the initial value problem) is the attempt at finding a solution to a differential equation given initial conditions. In the context of general relativity , it means the problem of finding solutions to Einstein's field equations — a system of hyperbolic partial differential equations — given some initial ...
In the k-calculus methodology, distances are measured using radar.An observer sends a radar pulse towards a target and receives an echo from it. The radar pulse (which travels at , the speed of light) travels a total distance, there and back, that is twice the distance to the target, and takes time , where and are times recorded by the observer's clock at transmission and reception of the ...