Far, far away?
Once we have the concept of synchronized clocks and a definition of how to relate the time coordinates of observers at different points we can define a distance. Let's choose a region of space with a family of observers moving through it, all with clocks synchronized by sending light pulses back and forth. Before when dealing with time we used the variable \(F\) for Finn's time and \(A\) for Aaron's time. Since we now have synchronized clocks, we can define a variable \(t\) as the coordinate time which is a valid, well defined coordinate everywhere in the region of interest.
Consider the scenario where Finn and Aaron are communicating with light pulses. At time \(t\)\(_1\), Finn sends a light pulse to Arron, who reflects is back, and is received by Finn at time \( t\)\(_2\). Which of these is a possible definition for the distance \(x\) between Finn and Aaron?