{d\tau} = \left(\gamma \dot{\gamma} mc, \gamma \mathbf{f} \right) = \left( \frac{\mathbf{f} \cdot \mathbf{v}} {c\sqrt{1-\frac{v^2}{c^2}}} ; \frac{\mathbf{f}} {\sqrt{1-\frac{v^2}{c^2}}}\right)