Suppose there are two identical drones in a weak and uniform gravitational field that are initially at the same place and with synchronized clocks.
Assume drone A first rises vertically for 10 seconds of proper time and waits for 100 seconds. Drone B first waits 100 seconds and then rises for 10 seconds of proper time in exactly the same way as drone A did. Do the two drones end up at the same space-time location?
It is known that the rate with which a clock ticks increases with the altitude in such a field. As the drone rises its clock will tick faster then.
So intuitively, I would say that the two drones would not end up at the same space-time location. However, I'm not quite sure I understood mathematically how to solve this problem. Also, would they end up in the same space-time location if a drone would first wait for 10 seconds and then rise for 10 seconds (and inversely for the other drone)? What would change?