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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 ...
This gravitational frequency shift corresponds to a gravitational time dilation: Since the "higher" observer measures the same light wave to have a lower frequency than the "lower" observer, time must be passing faster for the higher observer. Thus, time runs more slowly for observers the lower they are in a gravitational field.
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.
More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation. [64] Gravitational redshift has been measured in the laboratory [65] and using astronomical observations. [66] Gravitational time dilation in the Earth's gravitational ...
The measured elapsed time of a light signal in a gravitational field is longer than it would be without the field, and for moderate-strength nearly static fields the difference is directly proportional to the classical gravitational potential, precisely as given by standard gravitational time dilation formulas.
[5] [8] A gravitational redshift can also equivalently be interpreted as gravitational time dilation at the source of the radiation: [8] [2] if two oscillators (attached to transmitters producing electromagnetic radiation) are operating at different gravitational potentials, the oscillator at the higher gravitational potential (farther from the ...
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.
Most modern approaches to mathematical general relativity begin with the concept of a manifold.More precisely, the basic physical construct representing gravitation — a curved spacetime — is modelled by a four-dimensional, smooth, connected, Lorentzian manifold.