# History of Topics in Special Relativity/Lorentz transformation (introduction)

The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval ${\displaystyle -x_{0}^{2}+\cdots +x_{n}^{2}}$ and the Minkowski inner product ${\displaystyle -x_{0}y_{0}+\cdots +x_{n}y_{n}}$.

In mathematics, transformations equivalent to what was later known as Lorentz transformations in various dimensions were discussed in the 19th century in relation to the theory of quadratic forms, hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group.

In physics, Lorentz transformations became known at the beginning of the 20th century, when it was discovered that they exhibit the symmetry of Maxwell's equations. Subsequently, they became fundamental to all of physics, because they formed the basis of special relativity in which they exhibit the symmetry of Minkowski spacetime, making the speed of light invariant between different inertial frames. They relate the spacetime coordinates of two arbitrary inertial frames of reference with constant relative speed v. In one frame, the position of an event is given by x,y,z and time t, while in the other frame the same event has coordinates x′,y′,z′ and t′.

Note: This and the following pages are based on a former version of the Wikipedia article History of Lorentz transformations (from 8 July 2020‎, see also full version history). In order to reduce its extreme length, the Wikipedia article is now focusing on the physical development alone, while the sections concerning the development of the Lorentz transformation in pure mathematics (written between March 2018 - July 2020) have been removed from the Wikipedia article, so that the full History of Lorentz transformations, both mathematical and physical, is now featured in this extended Wikiversity version alone, including a detailed prehistory with historical authors and their formulas in original notation. Most of the material in the former Wikipedia version (see authorship) as well as this extended Wikiversity version with its subchapters was written by User:D.H. The History of Lorentz transformation is being constantly updated on Wikiversity since September 2020, and is part of the project History of Topics in Special Relativity.