General Relativity

General relativity reimagines gravity. Instead of a force reaching across space, mass and energy curve spacetime itself, and everything else simply follows the straightest available path through that curved geometry — what we feel as falling.^[1] It explained an old wobble in Mercury's orbit immediately, and has since passed test after test: starlight bending around the Sun, clocks ticking slower in stronger gravity, ripples in spacetime, and the existence of black holes.^[2] It's also the framework behind the expanding universe studied in cosmology.

Deep dive · The field equations

The whole theory is captured in Einstein's field equations,

G_{\mu\nu} = \frac{8\pi G}{c^4}\,T_{\mu\nu}.

Reading it left to right: $G_{\mu\nu}$ (the Einstein tensor) is built from the curvature of spacetime; $T_{\mu\nu}$ (the stress–energy tensor) tallies all the energy, momentum, and pressure present; and $8\pi G/c^4$ is the tiny constant that couples them. In one line: matter and energy tell spacetime how to curve.

The other half — how matter then moves — is the geodesic equation:

\frac{d^2 x^\mu}{d\tau^2} + \Gamma^\mu_{\alpha\beta}\,\frac{dx^\alpha}{d\tau}\,\frac{dx^\beta}{d\tau} = 0.

The $\Gamma^\mu_{\alpha\beta}$ (Christoffel symbols) measure how curved spacetime is; set them to zero — flat space — and the equation collapses to $d^2x^\mu/d\tau^2 = 0$ , a straight line at constant speed. Curvature bends that otherwise-straight path, and that bending is what we feel as gravity. In one line: curved spacetime tells matter how to move.