The [[Lorentz transformation]]s relate the space-time coordinates, (which specify the position ''x'', ''y'', ''z'' and time ''t'' of an event), relative to a particular inertial frame of reference (the "rest system"), and the coordinates of the same event relative to another coordinate system moving in the positive ''x''-direction at a constant speed ''v'', relative to the rest system. It was devised as a theoretical transformation which makes the velocity of light invariant between different inertial frames. The coordinates of the event in this "moving system" are denoted ''x''′, ''y''′, ''z''′ and ''t''′. The rest system was sometimes identified with the [[luminiferous aether]], the postulated medium for the propagation of light, and the moving system was commonly identified with the earth as it moved through this medium. Early approximations of the transformation were published by [[Woldemar Voigt|Voigt]] (1887) and [[Hendrik Lorentz|Lorentz]] (1895). They were completed by [[Joseph Larmor|Larmor]] (1897, 1900) and Lorentz (1899, 1904) and were brought into their modern form by [[Henri Poincaré|Poincaré]] (1905), who gave the transformation the name of Lorentz. Eventually, [[Albert Einstein|Einstein]] (1905) showed in his development of [[special relativity]] that the transformations follow from the [[principle of relativity]] and the constant light speed alone, without requiring a mechanical aether, and are changing the traditional concepts of space and time. Subsequently, [[Hermann Minkowski|Minkowski]] used them to argue that space and time are inseparably connected as [[spacetime]].
In this article the historical notations are replaced with modern notations, with the Lorentz transformation,
