Hafele and Keating circled the globe twice, first traveling eastward and then westward, with fours of cesium atomic clocks. They then compared the "traveling" clocks with identical clocks that remained at the U.S. Naval Observatory (USNO), as part of an experiment intended to test the theory of relativity. The aim was to demonstrate the reality of the twin paradox
– The essence of the paradox: there are two twin brothers; one of them – referred to as the "traveler" – goes on a space journey, while the other – referred to as the "stay-at-home" – remains on Earth; after the journey, the traveler returns to Earth, and it is claimed that one is older than the other, as predicted by the theory of relativity, which involves time dilation for moving objects, as well as gravitational time dilation.
Since then, after Hafele-Keating, it was believed that the theory was proven; and it is verified indeed, but not in the way Hafele and Keating thought.
The Continuation claims that the Hafele-Keating experiment unequivocally proves that density layers are real. For instance, the four atomic clocks at an altitude of 10 km become, at their hardware, different by the number of photons, from one left at the sea level, which is obvious from the indication of different times, and which is proved by the above mentioned difference in the air pressure. The same happens with GPS: there is no acceleration or deceleration of time, but there more or less photons: GPS are physically different as hardware. Indeed, photons can penetrate and stay as internal elements, which is confirmed by the presence of the fringes in the interference pattern and perihelion of Mercury.
As for the "twin paradox": there is only one clock participating for two parts of one; where twins always interact, compose a unity, see quantum entanglement experiments. The same clock cannot lag behind itself!