Suppose on the earth one put a tower of height $h$, there's two clock synchronized with respect to ground observer at $t_0$. Clock $A$ put under the tower, and clock $B$ put on top of the tower.
Since there's a velocity difference, there's time dilation.
However, according to Griffts, $A$ would see $B$ running slow, and $B$ would see $A$ running slow, and they are both right.
But this is not the case, for if $A$ send a single to $B$ or $B$ send a single to $A$(in experiments): $A$ and $B$ will always conclude that $A$ is slower than $B$.
What's went wrong here? a. Is it because the presence of centripetal acceleration changed story, and one must consider the gradient from the view of GR?(gravity filed)
Is there a way to explain it in SR for the "direction" of $A$ goes slower than B?