Spacetime rotations, understanding Lorentz transformations

Physicists studying motion use spacetime diagrams to visualize how objects move through both space and time, treating time as a fourth dimension alongside the three spatial dimensions.

Galileo and 17th-century physicists understood that motion is relative. A car moves from the perspective of someone on the sidewalk, but from the driver’s perspective, it’s the sidewalk that moves backward.

Late 19th-century physicists discovered with astonishment that light behaves unlike any other phenomenon: its speed of 299,792,458 meters per second remains exactly the same in all reference frames, regardless of the observer’s motion.

Early 20th-century physicists, building on work by Lorentz, Poincare, and Einstein, discovered that preserving light speed constancy requires shifting not only space slices but also time slices when changing reference frames.

Poincare and Minkowski invented a revolutionary way to measure distances in spacetime diagrams, revealing that Lorentz transformations are actually rotations in a hyperbolic geometry.

Physicists discovered that the angle of spacetime rotation between reference frames, called rapidity, provides a more fundamental description of motion than ordinary velocity.

Spacetime geometry reveals that electric and magnetic fields are not separate phenomena but different aspects of a unified electromagnetic field, perceived differently by observers in different reference frames.

Spacetime geometry reveals that energy and momentum are not independent properties but components of a unified four-momentum vector, mixing when reference frames change.