Ian McLoughlin

Minkowski Space

$η (u_{1}, u_{2}) = u_{1} \cdot u_{2} = c^{2} t_{1} t_{2} - x_{1} x_{2} - y_{1} y_{2} - z_{1} z_{2}$

$‖ u ‖ = \sqrt{η (u, u)} = \sqrt{c^{2} t_{1} t_{2} - x_{1} x_{2} - y_{1} y_{2} - z_{1} z_{2}}$

$x^{2} + y^{2} + z^{2} + (i c t)^{2} = C$