General Relativity: Curved Spacetime and Its Tests
General relativity describes gravity through spacetime geometry. Locally, free fall resembles inertial motion without gravity. Its tests include orbital precession, light deflection, gravitational redshift and clock-rate comparisons.
What a learner can do afterwards
- States the equivalence principle and gives an experiment it explains
- Describes gravitational time dilation and its effect on satellite navigation
- Names the classical tests of the theory and what each one measured
1 · Read
The equivalence principle applies locally: a small freely falling laboratory behaves like an inertial laboratory far from gravity when tidal effects can be neglected. Tidal effects are differences in free-fall acceleration across a region. A laboratory accelerating through empty space can reproduce the local effects of being supported in gravity. Free fall feels weightless; it does not mean spacetime curvature has disappeared.
In an upward-accelerating cabin, a horizontal light beam appears to bend downward as the cabin rises. Equivalence relates this to a supported cabin in gravity. In free fall, light is locally straight. Matter and energy, including pressure, shape spacetime. A geodesic is a locally straightest path; free matter follows one, and light follows a null geodesic. Curvature appears over larger regions. Weak fields and slow motion recover Newtonian predictions.
Classical tests measure specific predictions. Mercury's perihelion, its closest orbital point to the Sun, advances beyond the Newtonian prediction by about 43 arcseconds per century. Starlight passing near the Sun is deflected. Light received higher in a static gravitational field has a lower frequency than when emitted lower down: gravitational redshift. Compare predictions with measured values and their uncertainties.
Compare stationary clocks at different heights around the same body. A clock at lower gravitational potential accumulates less time than one higher up. This is not a rule based only on local field strength. For GPS, gravity makes satellite clocks gain about 45 microseconds per day relative to ground clocks, while their motion contributes about -7. The net gain is about 38. The navigation system accounts for both effects.
Local equivalence does not remove tidal effects. Two separated freely falling objects can approach or separate because their paths sample different parts of the gravitational field. Relative acceleration can reveal curvature. A small laboratory over a short time can neglect these effects; a larger experiment cannot always do so. Free fall follows geometry rather than a separate Newtonian gravitational force.
For light sent upward between stationary observers in a static field, the higher receiver measures a lower frequency. Light still travels locally at c. Since c = frequency times wavelength, lower frequency means longer wavelength: a redshift. Each observer measures the photon's energy locally; the differing energies do not imply that light slows down or loses energy through friction.
Equivalence is local. Curvature affects free-fall paths, and clock comparisons depend on gravitational potential and motion.
Lesson and assessment text authored for this dataset.
Rewritten readings were written for this dataset. Linked videos by Khan Academy and TED-Ed provide motion-related time-dilation and GPS context. Video reuse terms are unknown.
2 · Watch
En anglaisTake it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.