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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 ...
As the relative velocity approaches the speed of light, γ → ∞. Time dilation ... In general, in special relativity, four-vectors can be transformed from one ...
General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far passed many unambiguous observational and experimental tests. However, there are strong indications that the theory is incomplete. [210] The problem of quantum gravity and the question of the reality of spacetime singularities remain open ...
These equations, together with the geodesic equation, [8] which dictates how freely falling matter moves through spacetime, form the core of the mathematical formulation of general relativity. The EFE is a tensor equation relating a set of symmetric 4 × 4 tensors. Each tensor has 10 independent components.
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 ...
From the invariance of the spacetime interval it follows = and this matrix equation contains the general conditions on the Lorentz transformation to ensure invariance of the spacetime interval. Taking the determinant of the equation using the product rule [ nb 4 ] gives immediately [ det ( Λ ) ] 2 = 1 ⇒ det ( Λ ) = ± 1 {\displaystyle \left ...
The term 'general covariance' was used in the early formulation of general relativity, but the principle is now often referred to as 'diffeomorphism covariance'. Diffeomorphism covariance is not the defining feature of general relativity, [1] and controversies remain regarding its present status in general relativity.