Time on top of a mountain runs slightly faster than in the valley below

Einstein's general theory of relativity predicts that stronger gravity slows the passage of time. Because Earth's gravity is very slightly weaker at high altitude, a clock placed on a mountaintop ticks minutely faster than an identical clock down in the valley.

The difference is absurdly small — on the order of microseconds per decade for a typical altitude gap — but today's atomic clocks are precise enough to measure the difference even from a vertical shift of just a few tens of centimeters.

This isn't a theoretical footnote with no consequences: GPS satellites have to account for exactly this effect (plus the effect of orbital speed), or their clocks would drift out of sync with clocks on Earth fast enough to break GPS navigation within hours.

In other words: someone living on a high floor of a skyscraper literally ages a tiny bit faster than someone living on the ground floor of the same building — the effect is real, just completely unnoticeable in everyday life.