General relativity
= General relativity
{wiki}
<General relativity> describes <gravity> through the geometry of <spacetime>. Its <metric tensor> specifies distances, <proper time> measured by clocks, and the <causal structure> that limits communication. Matter and radiation affect this geometry through the <Einstein field equations>; freely falling <test particles> follow <geodesics> of the resulting geometry. A <planet>'s orbit and a falling apple therefore belong to the same geometric story. The <Newtonian limit> recovers familiar <Newtonian gravity> when fields are weak and speeds are small compared with the <speed of light>. See https://www.damtp.cam.ac.uk/user/tong/gr/grhtml/S0.html[David Tong's introduction to general relativity].
The most direct way to understand <spacetime> <curvature> is to compare neighboring freely falling bodies. Even when each body feels weightless, their separation can change: this is <geodesic deviation>, observed as a <tidal force>. <Curvature> concerns these relative measurements, rather than the shape of a drawing in an imagined surrounding space. A second accessible measurement is <gravitational time dilation>: identical clocks maintained at different heights accumulate different <proper times>. Together, tides and clocks turn an abstract geometry into laboratory questions.