The best examples of atomic clock relativity experiments

When people ask for examples of atomic clock relativity experiments, physicists almost always start with the Hafele–Keating experiment. It’s the textbook case where relativity leaves the chalkboard and boards a commercial flight.

In 1971, physicists J. C. Hafele and Richard Keating took four cesium-beam atomic clocks from the U.S. Naval Observatory and flew them around the world on commercial airliners, once eastward and once westward. A reference set of atomic clocks stayed behind on the ground in Washington, D.C. After each trip, they compared the flying clocks to the stay-at-home clocks.

Relativity predicts two competing effects:

• Special relativity (SR): Moving clocks run slow. The faster the plane, the more its clocks lag.
• General relativity (GR): Clocks higher in a gravitational field run faster. At cruising altitude, the plane is farther from Earth’s center, so its clocks tick a bit faster than those on the ground.

For the eastward flight, the plane’s speed added to Earth’s rotation, so SR predicted a larger slowdown than the GR speed-up. Net effect: the flying clocks should lose time relative to the ground clocks. For the westward flight, the plane’s speed partially canceled Earth’s rotation, so SR predicted less slowdown; GR won, and the flying clocks should gain time.

That’s exactly what they measured: tens of nanoseconds of time difference, right in line with relativity’s predictions within experimental uncertainty. You can read Hafele and Keating’s original reports via the American Physical Society’s journals at aps.org (search for “Hafele Keating 1972”). This classic flying-clock test remains one of the best-known examples of atomic clock relativity experiments because it’s conceptually simple and experimentally gutsy: take your lab on a plane and see if time bends.

GPS as a living example of atomic clock relativity experiments

If you want a real example of relativity that runs in the background of your daily life, look up—literally. The Global Positioning System (GPS) is a continuous, global atomic clock experiment.

Each GPS satellite carries multiple atomic clocks (historically cesium and rubidium; newer systems are moving toward even more stable designs). These satellites orbit about 12,550 miles above Earth at roughly 8,700 mph. At that altitude and speed:

• Special relativity says the satellite clocks should tick slower than clocks on Earth’s surface.
• General relativity says the weaker gravity at that altitude makes satellite clocks tick faster than ground clocks.

The GR effect wins: overall, a GPS satellite clock would naturally run about 38 microseconds per day faster than an identical clock on Earth’s surface. If engineers ignored that offset, GPS position errors would grow by roughly 6–7 miles per day.

To prevent that, GPS designers bake relativity into the system. The satellite clocks are pre-adjusted on the ground and continuously corrected in orbit so that, as seen from Earth, they stay synchronized. The U.S. Naval Observatory and NIST explain these relativistic corrections in detail (usno.navy.mil and nist.gov).

In other words, every time your phone gives you directions, you’re relying on one of the most important examples of atomic clock relativity experiments humanity has ever built. The “experiment” here isn’t a one-off; it’s a global infrastructure that would fail without Einstein.

Gravity vs. altitude: laboratory-scale examples include tower and mountain tests

Once atomic clocks became stable enough, physicists started asking a more pointed question: how small a height difference can we detect purely from time dilation?

Early examples of atomic clock relativity experiments in this category used relatively modest height differences. In the late 1970s and early 1980s, researchers compared cesium clocks at different altitudes—on tall towers, in mines, and on mountaintops—to verify the gravitational redshift predicted by general relativity. The effect is tiny but measurable: a clock on a mountaintop ticks slightly faster than one at sea level.

These tower and mountain tests were important stepping stones. They showed that you didn’t need to fly around the world or launch satellites to see relativity; you just needed good clocks and some vertical distance. As clock technology improved, that “vertical distance” requirement shrank dramatically.

By the 2000s, NIST in Boulder, Colorado, and other national labs were routinely comparing atomic clocks at different elevations to test gravitational time dilation. Boulder itself, at about 5,400 feet above sea level, is already measurably “higher in time” than clocks at sea level. These are quieter but very real examples of atomic clock relativity experiments, carried out in controlled lab environments rather than dramatic field trips.

Optical lattice clocks: modern best examples of atomic clock relativity experiments

The real leap came with optical lattice clocks, which use atoms like strontium or ytterbium and interrogate them with optical (visible or near-visible) lasers instead of microwave radiation. Optical frequencies are about 100,000 times higher than the microwave transitions used in traditional cesium clocks, which means you can, in principle, subdivide time much more finely.

In 2010, a NIST team led by Jun Ye compared two aluminum-ion clocks at different heights within the same laboratory—one placed about one foot higher than the other. They observed a frequency difference consistent with general relativity: the higher clock ticked faster. You can find a popular summary of this work via NIST’s public pages at nist.gov.

By the early 2020s, the sensitivity had improved to the point where millimeter-scale height differences became detectable. Optical lattice clocks are now so stable that they can sense the gravitational redshift corresponding to moving one clock just a few centimeters vertically. That’s not just a nice example of relativity; it’s a new kind of measurement tool.

These modern optical clocks are among the best examples of atomic clock relativity experiments because they turn relativity from a correction into a feature. Instead of fighting gravitational time dilation as a nuisance, scientists use it as a signal.

Relativistic geodesy: using atomic clocks to map Earth’s gravity

Once you accept that clocks tick differently at different gravitational potentials, a wild idea becomes practical: use clocks to measure height and gravity instead of traditional surveying.

This field, often called relativistic geodesy, treats high-precision atomic clocks as gravity sensors. The basic idea is simple:

• Two identical clocks at different locations will tick at slightly different rates because Earth’s gravitational field and elevation differ.
• Measure the frequency difference to infer the gravitational potential difference.
• Translate that into height differences or gravity anomalies.

In the last decade, several groups in Europe, the U.S., and Japan have demonstrated real examples of this idea using optical lattice clocks connected by fiber links. They’ve compared clocks in different cities and even different countries to map subtle variations in Earth’s gravity field.

As of 2024, proposals are on the table to use networks of optical clocks to monitor groundwater changes, ice sheet mass loss, and even volcanic activity by tracking tiny shifts in gravitational potential over time. These are forward-looking examples of atomic clock relativity experiments where the goal is not just to test Einstein again, but to turn relativistic time dilation into a practical Earth-observing tool.

Space station and satellite clock comparisons: relativity in low Earth orbit

Another family of examples of atomic clock relativity experiments comes from low Earth orbit. The International Space Station (ISS), orbiting at about 250 miles altitude and roughly 17,500 mph, sits in a different relativistic regime than GPS satellites.

On the ISS, the orbital speed is higher, which increases the special relativistic time slowdown, but the altitude is lower than GPS, which reduces the general relativistic speed-up. Net result: an astronaut’s onboard clock actually runs slightly slower than clocks on Earth’s surface.

While the ISS wasn’t built as a relativity lab, its onboard clocks and time-transfer experiments provide data that must be interpreted with relativistic corrections. ESA’s ACES (Atomic Clock Ensemble in Space) mission, hosted on the ISS, is designed to compare an ultra-stable space clock with ground clocks via microwave and optical links. ACES and related projects are modern, high-tech examples of atomic clock relativity experiments, pushing time-transfer accuracy to support tests of fundamental physics and improved global timekeeping.

Beyond the ISS, navigation constellations like Europe’s Galileo and China’s BeiDou also rely on relativistic corrections for their onboard atomic clocks, providing additional real-world validation that relativity is not optional in space-based timing.

Transportable clocks: taking relativity tests on the road

Not all atomic clock relativity work happens in permanent labs or on satellites. Over the last decade, multiple groups have developed transportable optical clocks—systems precise enough for cutting-edge physics, but rugged enough to be packed into a trailer or container.

These mobile clocks have been driven to different observatories, underground labs, and national metrology institutes, then compared with local reference clocks via optical fiber links. Each comparison is another example of atomic clock relativity experiments in action, because the clocks sit at different gravitational potentials and thus tick at slightly different rates.

Transportable clocks are particularly promising for:

• Cross-checking national time standards maintained by different countries.
• Performing relativistic geodesy in regions without fiber infrastructure.
• Testing for possible tiny deviations from Einstein’s predictions over different environments.

The fact that we can now “road test” relativity with a clock in a truck is a remarkable evolution from the Hafele–Keating days of lugging cesium clocks onto commercial jets.

Future directions: next-generation examples of atomic clock relativity experiments

Looking ahead to 2024–2025 and beyond, several trends are shaping the next examples of atomic clock relativity experiments:

• Optical clock networks: National labs in the U.S., Europe, and Asia are building fiber-linked networks of optical clocks. These networks will support more precise tests of gravitational redshift over continental scales and may eventually define a new international time standard, superseding the cesium second.
• Spaceborne optical clocks: Concepts for placing optical lattice clocks on satellites or dedicated space platforms are under active study. These would combine the sensitivity of optical clocks with the dramatic gravitational and velocity differences available in space, enabling even sharper tests of relativity.
• Fundamental physics tests: Ultra-stable clocks are being used to search for possible changes in fundamental constants, violations of local position invariance, or signatures of dark matter. Each of these projects doubles as an example of atomic clock relativity experiments, because any such search must first model and subtract known relativistic effects to absurd precision.

As the technology matures, the line between “relativity experiment” and “precision tool” keeps blurring. That, in itself, is a success story for Einstein: his theory is so reliable that we now use it as infrastructure.

FAQ: common questions about examples of atomic clock relativity experiments

Are there simple, classroom-friendly examples of atomic clock relativity experiments?

Directly running your own atomic clock experiment is hard for a classroom, because the hardware is specialized and expensive. However, educators often use publicly available data from GPS satellites or published results from Hafele–Keating and NIST experiments to show how clock rates differ with speed and altitude. Some university physics departments share simplified datasets and analysis guides through their outreach pages (search physics department sites ending in .edu) so students can work with real numbers from real experiments.

Which example of an atomic clock experiment best demonstrates time dilation to non-experts?

For most people, the Hafele–Keating around-the-world flights are the most intuitive example. You can picture a clock on a plane and a clock in an observatory, then compare them afterward. For a more modern twist, GPS is arguably the best example, because it’s something people use every day. Explaining that your phone’s location accuracy collapses without relativistic corrections tends to make the abstract idea of time dilation feel very concrete.

How accurate are modern atomic clocks used in these experiments?

The latest optical lattice clocks can reach fractional uncertainties around 10⁻¹⁸ or better. In practical terms, that’s like losing or gaining one second over the age of the universe. This kind of performance is what allows experiments to detect the gravitational redshift from moving a clock just a few centimeters. NIST and other metrology institutes publish current performance figures on their public sites; see nist.gov for up-to-date numbers.

Do all atomic clock relativity experiments agree with Einstein’s predictions?

So far, yes—within the experimental uncertainties. From the earliest cesium clocks on airplanes to today’s optical lattice clocks in labs and on satellites, every credible measurement of time dilation and gravitational redshift has matched the predictions of special and general relativity. That doesn’t mean physicists stop testing; on the contrary, they keep pushing for higher precision in case tiny deviations show up at the next decimal place.

Why are examples of atomic clock relativity experiments important for everyday technology?

Because modern infrastructure quietly assumes Einstein is right. GPS and other satellite navigation systems rely on relativistic clock corrections. High-frequency financial trading, power grid synchronization, and telecommunications all depend on precise timekeeping coordinated between distant locations. The fact that these systems work as well as they do is continuous, real-world evidence that the examples of atomic clock relativity experiments are not just academic—they’re baked into the way the modern world runs.