The experiment done by Hafele & Keating took clocks around the world in two directions and compared the readout to a static clock to measure time dilation effects. Everything fitted nicely with Einstein’s predictions. To avoid confusion let’s move the clocks way out in space to a real inertial frame of reference (no gravitational effects). This will eliminate the gravitational time dilation. One clock stays in a fixed place and two fly around imitating the clocks that flew around the world going east and west. We should get the same amount of time dilation as seen in the H&K experiment without the gravitational correction when the clocks are brought together at the end of the experiment. This is not a question of one clock appearing to be running at a different speed compared to a clock flying by at speed. The clocks all start at the same place and come back to the same place so that the readings can be compared at the end of the experiment. How do we decide which clocks are moving and which one is staying still?