Why does gravity slow down time?

Clocks lower in a gravitational field run slow because a settled region, one with nothing left to repair, shares one internal flow of time, and each place turns that flow into local seconds through its own temperature. In 1930 Richard Tolman and Paul Ehrenfest showed that a gas settled in a gravitational field is warmer at the bottom than at the top, by exactly the factor by which clocks at the bottom run slow. Temperature is how fast the shared flow runs against a local clock, so the warmer bottom gets fewer local seconds per step of the flow. In 1960 Robert Pound and Glen Rebka measured the difference across a 22.5-meter Harvard tower at 2.56 parts in 10¹⁵. Navigation satellites sit higher, where the settled state is colder, and their clocks gain forty-five microseconds a day.

Also in Chapter 34: Why Was Newton Right for Two Hundred Years?, Prologue: No Source Code, No Documentation.