http://www.people.fas.harvard.edu/~djmorin/book.html
Chapter 14: "The equivalence principle has a striking consequence
concerning the behavior of clocks in a gravitational field. It implies
that higher clocks run faster than lower clocks. If you put a watch on
top of a tower, and then stand on the ground, you will see the watch
on the tower tick faster than an identical watch on your wrist. When
you take the watch down and compare it to the one on your wrist, it
will show more time elapsed."

Note that the two watches are placed at different gravitational
potentials (the alleged "gravitational time dilation" is a function of
the potential difference) but experience essentially the same
gravitational field. This means that, in Einsteiniana's wonderland,
identical clocks placed in identical physical surroundings run at
different rates, that is, there is an effect without cause.