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\centerline{\bf Special and General Relativity (PHZ 4601/5606) Fall 2017 
Solutions} \medskip

\centerline{\bf Set 4} 

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\item{\bf 10. Time in Minkowski space.}
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We use natural units, $c=1$.

\begin{enumerate}
\item The coordinates of B$_0$ are $(t,x)=(75,60)$. 
\item The proper time of B is then $\tau=\sqrt{t^2-x^2}=45$.
\item At position A$_2$ the time on the clock of A is 135.
\item The coordinates of position B$_1$ are $(t,x)=(25,20)$ so that
$\tau=\sqrt{t^2-x^2}=15$ holds.
\item The light signal from B reaches A at time 45 at position A$_0$,
which agrees with the time of B at B$_0$.
\item The coordinates of B$_2$ are $(t,x)=(225,180)$ and the clock
of B shows $\tau=\sqrt{t^2-x^2}=135$.
\item The times agree. That has to be the case, because the travel of 
A in the rest frame of B does just mirror (opposite velocity signs)
the travel of B in the rest frame of B.
\end{enumerate}

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