Gyrations: The Missing Link Between Classical Mechanics with its Underlying Euclidean Geometry and Relativistic Mechanics with its Underlying Hyperbolic Geometry

Being neither commutative nor associative, Einstein velocity addition of relativistically admissible velocities gives rise to gyrations. Gyrations, in turn, measure the extent to which Einstein addition deviates from commutativity and from associativity. Gyrations are geometric automorphisms abstracted from the relativistic mechanical effect known as Thomas precession

Minkowski’s Modern World

International audienceIn this paper I want to suggest that much of the excitement generated by Hermann Minkowski’s lecture ‘‘Raum und Zeit’’ among scientists and philosophers arose from an idea that was scandalous when announced on September 21, 1908, but which was soon assimilated, first by theorists and then by the scientific community at large: Euclidean geometry was no longer adequate to the task of describing physical reality, and had to be replaced by the geometry of a four-dimensional space Minkowski called the ‘‘world.’’ Such an affirmation engaged implicitly with the Riemann-Helmholtz-Lie-Poincaré problem of space, and flatly contradicted Poincaré’s conventionalist philosophy, whereby the geometry assigned to physical space is a matter of choice, not necessity