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Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century. [3] [4] Joseph Larmor (1897) wrote that, at least for those orbiting a nucleus, individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio: . [5]
Fig 4–2. Relativistic time dilation, as depicted in a single Loedel spacetime diagram. Both observers consider the clock of the other as running slower. Relativistic time dilation refers to the fact that a clock (indicating its proper time in its rest frame) that moves relative to an observer is observed to run slower. The situation is ...
Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-dimensional spacetime geometry around the star onto 3-dimensional space. A curve is a geodesic if the tangent vector of the curve at any point is equal to the parallel transport of the tangent vector of the base point.
In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime ...
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").
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 ...
Larmor is credited to have been the first to understand the crucial time dilation property inherent in his equations. [ 9 ] In 1905, Poincaré was the first to recognize that the transformation has the properties of a mathematical group , and he named it after Lorentz. [ 10 ]
The geometry of general curved surfaces was developed in the early 19th century by Carl Friedrich Gauss. This geometry had in turn been generalized to higher-dimensional spaces in Riemannian geometry introduced by Bernhard Riemann in the 1850s. With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which ...
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