Why does gravity affect time too?

Two identical precise clocks are kept stationary, one low down and one on a higher shelf. Neither is running fast because of a faulty mechanism. Yet comparing their frequencies reveals a difference. Why does height matter for time?

General relativity predicts that clocks stationary at different gravitational potentials can accumulate different proper times during a shared comparison period. Near Earth’s surface, the higher clock runs slightly faster relative to the lower one. This is a measured clock-comparison effect. It does not mean someone downstairs feels “slowed down.” Bothwell and colleagues, Nature, 2022: laboratory gravitational redshift.

Beside your own clock, processes remain normal

Proper time is the duration measured by a clock along its path through spacetime. An observer beside it uses ordinary local seconds. Another sound clock nearby and local physical processes do not suddenly disagree with it.

“Faster or slower?” becomes a question when we compare different clocks. We must specify their locations, motions and comparison method. In our example, both are held at fixed heights, and we initially omit Earth’s rotation. Einstein Online: proper time and time-coordinate comparisons.

Signals let us check the difference

Suppose the lower clock sends light pulses at equal intervals of its own proper time. The upper observer receives them and compares them with an identical local clock and frequency reference. In this stationary Earth example, pulses from below arrive at slightly longer intervals than the upper reference would count for the same number of local seconds. The lower clock runs slower relative to the upper one.

For waves, this is linked to gravitational redshift: radiation travelling upward is received at a lower frequency than an identical local reference upstairs. The effect also applies to invisible radiation; the name need not mean literally seeing red. Einstein Online: gravitational frequency shift.

Signal travel time is a separate issue. A constant delivery delay shifts the entire sequence but does not by itself change the time spacing of successive pulses. Precise comparisons account for transmission, motion and instrument conditions. Ashby: relativistic clock comparison and time transfer.

Potential difference matters, not the feeling of weight

In a Newtonian approximation, gravitational potential describes potential energy per unit mass at a location. For a small upward displacement near Earth, its change is approximately gravitational acceleration multiplied by height. A higher potential corresponds to a faster stationary clock in this comparison.

General relativity describes gravity through the geometry of spacetime, which determines how much proper time accumulates along a given path. The rules for comparing time intervals at different locations change; a force is not “pressing on clockwork.” One number for the force a person feels, or a force gauge records, cannot compare arbitrary clocks. Ashby: potential, proper time and coordinate time.

Consider a very small terrestrial example. The dials deliberately look identical: representing the real difference with a visibly lagging hand would be misleading.

Two stationary clocks near Earth

Height difference: 1 m

Upper: elapsed duration

86 400 s + 9.4 ps

Lower: reference duration

86 400 s

The upper clock accumulates about 9.4 ps more

Teaching comparison in a weak field: g = 9.81 m/s², c = 299 792 458 m/s. Both clocks are held stationary; Earth rotation, motion and instrument perturbations are omitted. Values are intervals during a shared comparison period, not arbitrary dial readings. Geometry is schematic; identical hands do not portray a visible lag. 1 ps = 10⁻¹² s. Calculated example, not experimental data.

Branch · Weak-field calculationOptional · safe to skip

What does raising a clock by one metre do?

For two stationary clocks in a weak, approximately uniform terrestrial field, the fractional rate difference is approximately

\varepsilon\approx\frac{gh}{c^2}.

$h$ is the upper clock’s height above the lower one in metres, $g$ is local gravitational acceleration and $c$ the speed of light. The ratio is dimensionless: $gh$ and $c^2$ have matching units. For a small relative effect, when the lower clock accumulates $T$ , the upper gains about $\delta\tau\approx T\varepsilon$ . Bothwell and colleagues: equation 1.

Choose illustrative values $h=1\ \text{m}$ , $g=9.81\ \text{m/s}^2$ , exact $c=299\,792\,458\ \text{m/s}$ and $T=86\,400\ \text{s}$ . Then

\begin{aligned} \varepsilon&\approx1.09\times10^{-16},\\ \delta\tau&\approx9.4\times10^{-12}\ \text{s}. \end{aligned}

That is about 9.4 picoseconds: a picosecond is a trillionth of a second. At $h=0$ this gravitational contribution vanishes; doubling a small height approximately doubles it. These are calculated teaching values, not measurements of our clocks. Earth rotation and motion are omitted; this formula cannot be carried over to large field differences or a black-hole horizon.

The difference was measured without a spaceflight

A NIST experiment described in 2010 compared two optical clocks based on aluminium ions. Raising one by roughly a third of a metre revealed the predicted direction of the rate change: the higher clock ran faster. People cannot directly feel such a small difference, but that does not prevent measurement. NIST: the raised-clock experiment.

Bothwell and colleagues’ 2022 Nature study reached the millimetre scale, measuring a spatial gradient in transition frequency within a single cloud of cold strontium atoms. After accounting for shifts caused by magnetic fields and atomic interactions, the result agreed with the gravitational prediction. This involves more than a photograph of different displays: control of perturbations, statistics and uncertainty estimates are essential. Original study, figure 3 and equation 1.

A journey also requires motion and the whole path

Our higher-clock conclusion applies to a specified stationary pair. For an aircraft or satellite, the comparison includes gravitational and kinematic contributions. Motion can reduce accumulated duration relative to the chosen reference frame; final height alone cannot determine the result. If clocks return to the same place, the ascent, travel and return segments matter too. Ashby: motion and gravity in clock comparisons.

Branch · A practical consequenceOptional · safe to skip

Satellite navigation compares signal timestamps from different locations. For typical GPS orbits, the gravitational contribution speeds onboard clocks relative to the terrestrial reference, while motion contributes the opposite sign. The system needs a coordinated time coordinate and corrections, rather than assuming all readings automatically agree.

This is an application of the model, not a claim that every satellite in any orbit always has the same total offset. Ashby: Relativistic Effects on Satellite Clocks.

Predict: put the same stationary clocks at equal heights in our idealization. Does the calculated difference remain? Does a freely falling spacecraft’s zero accelerometer reading prove that all distant clocks run at the same rate?

No to both. Zero height difference removes the potential-difference contribution in our model. Feeling no weight means free fall, but does not establish a rate relationship with an arbitrary remote clock. That comparison again requires conditions and trajectories. Einstein Online: the local scope of the equivalence principle.

Gravitational time dilation is a testable difference between clearly specified clocks. Whenever you hear “time runs slower there,” first ask: relative to whom, along which path, and how was it compared? Those details distinguish a physical statement from an impressive slogan.