gravitational time dilation

Clocks tick more slowly the deeper they sit in a gravitational well. A clock at sea level runs slightly slower than an identical clock on a mountaintop; a clock near a black hole crawls compared to one far away. The difference is not about the clock's mechanism — every clock, biological or atomic, is affected equally, because it is time itself that runs at different rates in different places.

You can see where this must come from using the equivalence principle. Picture a tall rocket accelerating upward, with a clock at the nose and one at the tail. Light sent from the tail toward the nose arrives shifted, because the nose has sped up during the light's travel time; working through the bookkeeping shows the tail clock ticks slow relative to the nose. Since acceleration and gravity are locally equivalent, the same must hold in a gravitational field: the clock lower down, deeper in the well, ticks slower than the one higher up.

This is not a thought experiment frozen in a textbook — it is measured every day. The GPS satellites that guide your phone carry atomic clocks that tick faster than ours by about 45 microseconds per day from being higher in Earth's gravity well (partly offset by special-relativistic slowing from their speed); without correcting for it, GPS positions would drift by kilometers within hours. Modern optical clocks are so precise that they detect the slowdown over a height difference of just a few centimeters on a lab bench.