Gravity changes clock comparisons

General relativity relates gravity to spacetime — open definition geometry. A freely falling object with no other forces follows a natural path through that geometry. An astronaut in orbit can feel weightless while gravity remains essential to the orbital motion. Weightlessness is therefore not evidence that Earth’s gravitational influence has disappeared.

In a sufficiently small freely falling laboratory, many effects of a uniform gravitational pull can be removed from the local description. Over larger regions, neighboring free-fall paths can converge or separate: these tidal effects — open definition reveal curvature. “Locally” matters. The equivalence between free fall and an inertial laboratory does not mean every extended gravitational environment becomes indistinguishable from empty flat spacetime.

For clocks held at different positions in a static gravitational environment, the rate comparison depends on gravitational potential and the spacetime model. Near Earth, an otherwise matched stationary clock at greater height runs slightly faster than one lower down. Relative motion adds another contribution, so an orbiting clock requires both effects to be modeled.

Drawings of a heavy ball depressing a rubber sheet offer a limited analogy for curved geometry. They use an external downward force and a two-dimensional surface; neither is a literal explanation of four-dimensional spacetime. The more useful test is what the theory predicts for measurable paths, clock intervals and light propagation, and whether those predictions agree with calibrated observations.

In an illustrative weak-field, small-height approximation, the fractional rate difference is approximately gΔh/c². Take g = 9.8 m/s², a height difference of 1,000 m and rounded c = 300,000,000 m/s. The result is about 1.09 × 10⁻¹³. The higher stationary clock gains about 9.4 nanoseconds over 86,400 seconds in this simplified comparison.

The approximation assumes a nearly constant g over the stated height interval and leaves out rotation, motion and detailed geophysical corrections. It is not a GPS clock correction or a measurement of a particular mountaintop. Changing the height difference to 500 m approximately halves this small effect within the same model. A full experiment must establish the positions, motion, clock systematics and time-transfer calibration.

Near a compact object, the weak-field approximation can fail. A black hole’s event horizon — open definition marks a causal boundary: signals from inside cannot reach distant outside observers. Statements about what a distant observer sees and what a freely falling clock locally measures require distinct coordinates and signal accounts. One universal phrase such as “time stops” conceals those differences.

The International Space Station photograph offers an orbital setting for thinking about clocks at different heights and speeds, but it does not display spacetime curvature or measure a clock-rate difference. The inference comes from physical measurements. The next lesson follows light through curved spacetime, showing how changes in apparent position and shape can become evidence for the mass doing the lensing.