Shape and space
1908
Spacetime
Hermann Minkowski
What if time is a direction, like left and right?
Einstein’s former teacher showed that special relativity is geometry in four dimensions, with time as one of them. “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows,” he said.
- Time stretch γ
- 2.028
- A muon (lives 2.2 µs at rest) lives
- 4.5 µs
- At this speed, 1 year on board is
- 2.03 years for you
Each clock ticks when light bounces between two mirrors. Light moves at the same speed for everyone, so in the moving clock it has a longer, slanted path to cover, and each tick takes longer. Nothing is wrong with the moving clock: to its owner, yours is the slow one.
How they figured it out
Hermann Minkowski had taught Einstein in Zurich and reportedly called him a lazy dog who never bothered with mathematics. In 1908, in Cologne, he showed that Einstein’s theory is really four-dimensional geometry, with time as one of the directions.
Einstein first dismissed this as “superfluous learnedness”. A few years later he found he could not build general relativity without it. Minkowski did not see that: he died of appendicitis in January 1909, aged 44.
The equation
Distance in spacetime mixes time and space, with time counting negatively.
See it in real life
A train timetable graph
Plot a train’s distance against time and its journey is a line; steeper means slower. Light would be a line at a fixed slope that no train can ever beat. That graph is a little spacetime diagram.
Where engineers use it
Spacetime diagrams
Physicists and engineers use them to reason about signals and timing between moving systems.
Where it came from
- Special relativity 1905
Led to
Minkowski recast Einstein’s theory as four-dimensional geometry.
What it led to
- General relativity November 1915
Built on
General relativity lets Minkowski’s flat spacetime curve.