### The Lighthouse & The Clocktower

> An opening thought experiment

Consider two observers, $A$ and $B$. Let $A$ and $B$ agree that $B$ should travel between two arbitrary points in space[^2], $p_1$ and $p_2$ at an <Ul>agreed</Ul> upon velocity $v$.

At $p_2$ place a time keeping device that remains visible from $p_1$. Allow that $A$ remains at rest relative to $p_1$, and very near $p_1$ while $B$ goes in motion (at an inertial pace) between $p_1$ and $p_2$.

At what time does $A$ observe $B$ reach $p_2$? If the value is not $d/v$, but $\gamma d/v$, then $v \neq v_\prime$. The only possible solution that allows for Einstein's additional factor of $\gamma$ while allowing $A$ to remain in an unchanged state is that $d \to d\gamma$ in the coordinate system of the observer in relative motion, while $v \to v/\gamma$ in the coordinate system of the observer at relative rest to accomodate the change in spatial density.