Time dilation is not a magical or conscious process but rather a fundamental consequence of the principles of special and general relativity. It is not a matter of time dilation "knowing" which direction to dilate in a specific experiment. Instead, time dilation arises due to the fundamental nature of spacetime and the relative motion of observers.
In the Hafele-Keating experiment, the time dilation observed is a result of the relative motion of the airplanes with respect to the stationary clocks on the ground. The experiment involved flying atomic clocks in airplanes in opposite directions around the Earth. The clocks on the moving airplanes were compared to stationary clocks on the ground upon their return.
The observed time dilation in this experiment arises from the fact that the airplanes were in motion relative to the stationary clocks on the ground. According to special relativity, when an object moves at a significant fraction of the speed of light relative to an observer, time dilation occurs. Clocks on the moving airplanes were subject to this time dilation effect.
The direction of motion (eastward or westward) does not determine the direction of time dilation. The important factor is the relative velocity between the moving clocks and the stationary clocks. The magnitude of the relative velocity determines the amount of time dilation experienced.
In the Hafele-Keating experiment, the eastward and westward flights were conducted to ensure that the relative velocities of the moving clocks with respect to the stationary clocks were as different as possible. This allowed for a more precise measurement of time dilation and helped confirm the predictions of special relativity.
It's crucial to note that the behavior of time dilation has been extensively verified through numerous experiments and observations, not just the Hafele-Keating experiment. The consistent experimental evidence supports the existence of time dilation as predicted by the theories of special and general relativity.