I see that in many synagogues that have a minyan for neitz (sunrise) they have exact times (to the second) that they attempt to begin Shemonah Esrei at. In the olden days before these precise clocks were invented and even before clocks were invented did they have a way of starting Shemonah Esrei at the exact time of neitz? Did they even care to be so exact?
and even before clocks were invented
Water clocks are older than Judaism.