## Beyond the Confines of Relativity: The Breakdown of Symmetry in Past and Future

There is a deep connection between the formula for aberration,

$$\cos\omega=\frac{\cos\omega'-\beta}{1-\beta\cos\omega'},$$

and the Mobius automorphism that swaps the relative state of motion, $\beta$, with one at rest, $0$,

$$\mathcal{M}(\cos\omega')=\frac{\cos\omega'-\beta}{\beta\cos\omega'-1},$$

except for the negative sign. If $\cos\omega'=\beta$, then $\mathcal{M}(\beta)=0$, while if $\omega'$ is a right-angle, then $\mathcal{M}(0)=\beta$. But, there is more to this than what meets the eye.