TheLorentz transformations is a set of equations that describe a lineartransformation between a stationary reference frame and a reference frame inconstant velocity. The equations are given by:
, , ,
whererepresents the new x co-ordinate, represents the velocity of the other reference frame, representing time, and thespeed of light.
On aCartesian coordinate system, with the vertical axis being time (t), the horizontal axis being position in space along one axis (x), the gradients represent velocity (shallowergradient resulting in a greater velocity). If the speed of light is set as a 45° or 1:1 gradient, Lorentz transformations can rotate and squeeze other gradients while keeping certain gradients, like a 1:1 gradient constant. Points undergoing a Lorentz transformations on such a plane will be transformed along lines corresponding to where n is some number
Points undergoing a Lorentz transformation follow the green, conjugate hyperbola, where the vertical axis represents time,
