Lorentz transformation
The Lorentz transformations is a set of equations that describe a linear transformation between a stationary reference frame and a reference frame in constant velocity. The equations are given by:
<math>x'=\frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}}</math> , <math>y'=y</math> , <math>z'=z</math> , <math>t'=\frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}</math>
where <math>x'</math>represents the new x co-ordinate, <math>v</math> represents the velocity of the other reference frame, <math>t</math> representing time, and <math>c</math> the speed of light.
On a Cartesian coordinate system, with the vertical axis being time (t), the horizontal axis being position in space along one axis (x), the gradients represent velocity (shallower gradient 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 <math>t^2-x^2=n^2</math> where n is some number
