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]\displaystyle{ x'=\frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}} }[/math] , [math]\displaystyle{ y'=y }[/math] , [math]\displaystyle{ z'=z }[/math] , [math]\displaystyle{ t'=\frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}} }[/math]
where [math]\displaystyle{ x' }[/math]represents the new x co-ordinate, [math]\displaystyle{ v }[/math] represents the velocity of the other reference frame, [math]\displaystyle{ t }[/math] representing time, and [math]\displaystyle{ 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]\displaystyle{ t^2-x^2=n^2 }[/math] where n is some number
