Frontier Science › Physics and Space · Feature · Practical STEM, Part 9
Space and time, joined: why your phone's map depends on Minkowski
Hermann Minkowski grew up in Königsberg and taught a young Albert Einstein. His idea of spacetime turned relativity into geometry — and without relativity, GPS would drift off by kilometres every day.
When your phone shows a blue dot on a map, it relies on one of the strangest facts in physics: clocks don’t all tick at the same rate.
From Königsberg to spacetime
Hermann Minkowski was born in 1864 in Aleksotas, then in the Russian Empire, and moved with his family to Königsberg as a boy. There he became close friends with David Hilbert; the two took long walks discussing mathematics. Later, at ETH Zurich, one of his students was Albert Einstein, who rarely attended lectures.
In 1905, Einstein published special relativity. Three years later, Minkowski gave it a new shape. In a famous lecture in Cologne, he said that space by itself and time by itself would fade into shadows, and only a union of the two would remain. He called that union spacetime: a four-dimensional geometry in which time is a direction, like length or height.
Einstein was sceptical at first. Later, Minkowski’s geometry became a foundation of his general theory of relativity. Minkowski died suddenly in 1909, aged just 44.
Why GPS needs it
GPS satellites carry extremely precise atomic clocks. Your receiver works out its position from the time signals they send. But relativity changes how fast those clocks tick:
- Because the satellites move fast, their clocks run slightly slow (special relativity).
- Because they orbit high up, where gravity is weaker, their clocks run slightly fast (general relativity).
The net effect is about 38 microseconds a day. That sounds tiny. But light travels about 300 metres in a microsecond, so without correction, positions would drift by roughly 10 kilometres a day. Engineers build the correction into every satellite.
The practical lesson
Minkowski’s breakthrough was to stop treating two things as separate. Space and time, he showed, are one structure seen from different angles. Many problems become simpler when you stop splitting them artificially: engineering and design, learning and working, technology and people.
Try it yourself
Light travels about 30 centimetres in a nanosecond. If a GPS clock is off by one microsecond (1,000 nanoseconds), how far off is your position? (Answer: about 300 metres.)
Sources: Minkowski, “Raum und Zeit,” Physikalische Zeitschrift 10 (1909), lecture of 21 September 1908 · Ashby, “Relativity in the Global Positioning System,” Living Reviews in Relativity 6 (2003) · Galison, Einstein’s Clocks, Poincaré’s Maps (2003).
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Gustav Hohenstein, approved by Yoshihiro Horiuchi, Editor-in-Chief.