Hermann Minkowski

Mathematician and physicist — Hermann Minkowski (Aleksotas, 1864 – Göttingen, 1909) was a German mathematician of Lithuanian origin, among the most brilliant of his generation. He was professor at Königsberg, Zurich — where the young Einstein was among his students — and finally at Göttingen. His most famous contribution to physics came in 1907-1908, when he reformulated Einstein’s special relativity by introducing the idea that space and time are not separate entities but components of a single four-dimensional structure, spacetime. This geometrisation was decisive: it provided the mathematical language that allowed Einstein, a few years later, to develop general relativity. He died suddenly at only 44 from appendicitis, at the height of his career.

Trivia

In his famous 1908 Cologne lecture he declared: “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.”

Theories and contributions

• Minkowski spacetime — Geometric unification of space and time into a four-dimensional manifold with invariant interval $ds^2 = c^2\,dt^2 - dx^2 - dy^2 - dz^2$.
• Minkowski diagrams — Graphical representation of spacetime displaying light cones, world lines and the relativity of simultaneity.

Present in chapters

20

Linked atoms

19 linked atoms.

20 Relatività ristretta

• The light clock
• Time dilation
• What is an event
• The Minkowski invariant
• Timelike, spacelike, lightlike
• The Minkowski plane and the light cone
• The physical meaning of the three classes
• Reference frames of simultaneity and of co-spatiality
• Relative simultaneity
• The reversed triangle inequality
• The twin paradox
• Length contraction
• The formula of simultaneity
• The train and tunnel paradox
• The train and the hole in the tracks paradox
• The Lorentz transformations
• Relativistic Doppler effect
• The Schwarzschild metric and black holes
• Invariance, the true heart of relativity