= Solution
<Einstein's postulates> state that the laws of physics have the same form in every <inertial frame>, and that light in vacuum has the same <speed of light> $c$ in every <inertial frame>, independently of the motion of its source. For a primed frame moving with <velocity> $v\mathbf e_x$ relative to an unprimed frame, with coincident origins at $t=t'=0$, the <Lorentz transformations> are
$$
\boxed{x'=\gamma(x-vt),\quad t'=\gamma(t-vx/c^2),\quad y'=y,\quad z'=z,\qquad
\gamma=(1-v^2/c^2)^{-1/2}.}
$$
The following <worldlines> use Earth-frame time in years and distance in light years, so numerically $c=1$. The instantaneous turnaround is the idealized limit of a short acceleration stage; the elapsed <proper time> is calculated along each inertial segment.
\Image[/past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit-twin-worldlines.png]
{title=Earth-frame worldlines and clock readings for the twins' reunion}
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