Past exam of the physics 1 paper of the University of Oxford / 2016 resit / 11 / c / Solution

Replace the frame speed by $-2v$, requiring $|2v|<c$. With $\Gamma =(1-4{\beta }^2{)}^{-1/2}$,The outbound leg is now the longer one and the inbound leg the shorter one. Doubling the speed also changes the Lorentz factor; it is not enough to swap the two original leg times. A proposed doubled speed at or above $c$ does not define an inertial observer frame.