Its not impossible. Civil time is just this, in fact. Its true that if two observers use their own local atomic standard to precisely measure elapsed time the

Its not impossible. Civil time is just this, in fact. Its true that if two observers use their own local atomic standard to precisely measure elapsed time then they would have difficulty agreeing on when something happened. However, that's not how civil timekeeping works. One clock declares itself to be a master clock and broadcasts a time+position standard to everyone else. Other observers then construct their own PLL to compute a running estimate of the total phase shift between their local time standard and the one that is broadcast. In effect, received civil time has a velocity relative to your local atomic time. If every observer can label their observations with civil time then the paradox disappears and you are left with information flow that is bounded to the speed of light. A fast-moving observer has a local atomic standard of time that moves at one second per second, and a received civil time that appears to be running much faster. A peer-to-peer version of this is how we define international atomic time. Subtle variations in local gravity conspire to actually give the different clocks in the network a different local speed of time. They steer a global PLL to minimize the total squared phase error in the network. Each node in the network can make observations on the TAI timebase by adding its own clock offset to their local clock.