What transformation equations relate coordinates in different inertial frames in special relativity?

The transformation equations relating coordinates in different inertial frames in special relativity are the Lorentz transformation. They connect measurements of time and space made by observers moving at constant velocity relative to one another.

Unlike the older Galilean transformation, the Lorentz transformation preserves the speed of light for every inertial observer. Its equations produce time dilation, length contraction, and the relativity of simultaneity. The Lorentz factor, gamma, grows as relative speed approaches the speed of light.

Hendrik Lorentz and other physicists developed related equations while studying the behavior of Maxwell’s electromagnetic theory. In 1905, Albert Einstein gave them their modern physical interpretation within special relativity, without requiring a luminiferous ether. Henri Poincaré also recognized important mathematical properties of the transformations.

The Galilean transformation remains an excellent low-speed approximation. “Minkowski transformation” is not the standard name, while the broader Poincaré group includes Lorentz transformations together with spacetime translations.