Spacetime and the cosmos
November 1915
General relativity
Albert Einstein
Why does a falling person feel weightless?
Einstein found that gravity is not a force but the curving of spacetime by mass and energy. Objects follow the straightest path they can through curved spacetime. His first test: Mercury. The new theory gave exactly the missing 43 arcseconds per century.
- Turn per orbit
- 0.00°
- Real Mercury
- 0.0000288° per orbit (43″ per century)
- Exaggeration here
- —
With Newton alone (strength 0) the ellipse closes on itself forever. Einstein’s theory adds a tiny extra pull close to the Sun, and the closest point (pink lines) creeps round, tracing a rosette. For Mercury the real effect is about 0.1 arcseconds per orbit, so here it is exaggerated many thousands of times.
How they figured it out
In 1907, sitting at his desk at the patent office, Einstein had what he later called the happiest thought of his life: a person falling freely from a roof would not feel their own weight. Gravity and acceleration are indistinguishable.
Turning that into a theory took eight years and mathematics he didn’t know; his friend Marcel Grossmann pointed him to Riemann’s geometry. In November 1915, racing the mathematician David Hilbert, he presented four papers in four weeks. When his equations gave exactly Mercury’s missing 43 arcseconds, he wrote that his heart was pounding.
The equation
The curving of spacetime (left) is set by the matter and energy in it (right).
See it in real life
A lift and a GPS
When a lift starts upwards you feel heavier; when it starts down, lighter. That is Einstein’s equivalence in your building. And the satellites guiding your map app run 38 microseconds a day fast; without relativity your blue dot would drift by about 10 km a day.
Where engineers use it
GPS
Without relativity corrections, GPS would drift by about 10 km a day.
Gravitational lensing
Astronomers use bent light to weigh galaxy clusters and find distant planets.
Worked example: GPS clocks
- Higher up (weaker gravity): +45 µs per day.
- Moving fast: −7 µs per day.
- Net +38 µs per day; times the speed of light ≈ 11 km of position error.
Where it came from
- Mercury misbehaves 1859
Led to
General relativity explained Mercury’s extra 43 arcseconds per century with no new planet.
- Curved space 1854
Built on
Einstein described gravity using Riemann’s geometry of curved spaces.
- Spacetime 1908
Built on
General relativity lets Minkowski’s flat spacetime curve.
What it led to
- The first black hole solution 1916
Led to
Schwarzschild found the first exact solution, within weeks.
- Starlight bends 29 May 1919
Led to
General relativity predicted how much the Sun bends starlight; the 1919 eclipse tested it.
- The expanding universe 1922–1929
Led to
Friedmann and Lemaître found that Einstein’s equations allow a universe that grows.
- Hearing black holes merge 14 September 2015
Led to
Einstein predicted gravitational waves in 1916; it took a century to detect them.