Multi-Speed Thought Experiment

We consider n \underline {\textgreater } 2 identical rockets: $R_{1}, R_{2}$\textit{, \textellipsis , R}$_{n}$. Each of them moving at constant different velocities respectively v$_{\mathrm{1}}$, v$_{\mathrm{2}}$, \textellipsis , v$_{\mathrm{n\thinspace }}$on parallel directions in the same sense. In each rocket there is a light clock, the observer on earth also has a light clock. All $n +$\textit{ 1} light clocks are identical and synchronized. The proper time $\Delta t'$ in each rocket is the same. Suppose that the $n$ speeds of the rockets verify respectively the inequalities: \textit{0 \textless v}$_{1}$\textit{ \textless v}$_{2}$\textit{ \textless \textellipsis \textless v}$_{n-1}$\textit{ \textless v}$_{n}$\textit{ \textless c.} The observer on rocket R$_{\mathrm{1}}$ measures the non-proper time interval of the event in $R_{j}$ as: $\Delta t_{1,j\thinspace }= \Delta $\textit{t'\textbullet D(v}$_{j}-v_{1}),_{\thinspace }$ therefore the time dilation factor is $D(v_{j}-v_{1}),_{\thinspace }$where j$\in $\textbraceleft 2, 3, \textellipsis , n\textbraceright . Thus the time dilation factor is respectively: $D(v_{2}-v_{1}), D(v_{3}-v_{1}$\textit{),\textellipsis , D(v}$_{n}-v_{1}), $ which is again a multiple contradiction. Because all $n$ rockets travel in the same time, we have a dilemma: which one of the above \textit{n-1} time dilation factors to consider for calculating the non-proper time as measured by the observer in rocket $R_{1}$? Similar dilemma if instead of the observer in rocket R$_{\mathrm{1}}$ we take the observer in rocket $R_{k},$ for \textit{2 }$\le k \le $\textit{ n-2.} Also a same multiple dilemma occurs if we take into consideration each rocket's length, which gets contracted in multiple different ways simultaneously!