Einstein was right. Flying clocks around the world in opposite directions proved it.

Einstein was right. Flying clocks around the world in opposite directions proved it.

If you travel relative to another observer and return to their initial location, you will age less than whatever remains stationary, according to Einstein’s relativity. Einstein also claims that the curvature of space itself impacts how fast or slow your clock works, depending on the amount of gravity at your location. We put Einstein to the test like never before by flying planes with and against Earth’s rotation and returning them all to the same starting location. Here’s what we discovered.

When Einstein proposed his special theory of relativity in 1905, our understanding of the Universe was changed forever. Prior to Einstein, scientists could describe every “point” in the Universe using only four coordinates: three spatial places for each of the three dimensions, plus a time to indicate when any particular event occurred. All of this changed when Einstein realized that, depending on their motion and location, each observer in the Universe had a unique viewpoint on where and when every event in the Universe would have occurred.

When one observer travels through the Universe in relative to another, the observer-in-motion experiences time dilation: their clocks run slower in comparison to the observer-at-rest. Based on this, Einstein proposed using two clocks to test this: one at the equator, which travels around the Earth at around 1670 km/hr (1038 mph), and one at the poles, which is at rest while the Earth rotates on its axis.

However, Einstein was wrong in this regard: both clocks operate at exactly the same rate relative to one another. It wasn’t until 1971 that a real test could be conducted , and it took much more than special relativity to make it happen.

This light-clock image demonstrates how, while at rest (left), a photon moves up and down between two mirrors at the speed of light. When you are boosted (going to the right), the photon goes at the speed of light as well, but it takes longer to oscillate between the bottom and top mirrors. As a result, relative motion objects have a longer duration than stationary ones. (Credit: John D. Norton/University of Pittsburgh)

When Einstein initially proposed his special theory of relativity, there remained one missing piece: gravitation was not included. He had no idea that being close to a massive gravitational object may also change the passage of time. Our globe bulges at the equator and compressed at the poles due to the spinning of the planet and the attractive gravitational attraction of every particle that makes up the Earth. As a result, the Earth’s gravitational pull is somewhat stronger near the poles — by roughly 0.4 percent — than at the equator.

The amount of time dilation caused by a point on the equator zipping around the Earth is precisely cancelled by the additional amount of gravitational time dilation caused by the difference in gravity at the Earth’s poles vs the equator. Being deeper in a gravitational field, as the poles are, causes your clock to tick more slowly, just as traveling faster relative to a stationary observer causes your clock to tick faster.

To account for the rate at which time appears to pass for each observer, both the relative motion effects of special relativity and the relative effects of gravity — i.e., the relative curvature of spacetime between numerous observers — must be considered.

Putting a mass down causes what would have been ‘straight’ lines to become curved by a specified amount instead of an empty, blank, three-dimensional grid. We treat space and time as continuous in General Relativity, but all types of energy, including but not limited to mass, contribute to spacetime curvature. The deeper you are in a gravitational field, the more severely your space is curved, and the more severe the phenomena of time dilation and gravitational redshift become. (Credit: Christopher Vitale of Networkologies and the Pratt Institute)

Time dilation was one of the few relativistic phenomena that was actually predicted even before Einstein put forth the ideas of special and general relativity, as the consequences of motion close to the speed of light for distances (length contraction) was worked out in the 19th century by George FitzGerald and Hendrik Lorentz. If distances changed, then in order to maintain the proper working of physics that we knew for electrons in atoms (as shown by Joseph Larmor in 1897) or for clocks in general (as shown by Emil Cohn in 1904), that the same factor — the Lorentz factor (γ) — must factor into time equations as well.

Although measuring this was first challenging, our expanding understanding of the subatomic world soon made it possible. The muon, a subatomic particle that is heavier and more unstable than the electron, was discovered in the 1930s. Muons created by cosmic ray collisions in Earth’s upper atmosphere should all decay within hundreds of meters due to their short average lifespan of 2.2 microseconds. Yet, if you reach out your palm, approximately one such muon passes through it per second, suggesting that they traveled around 100 kilometers: a feat that is physically impossible without time dilation. These muons could be observed with the naked eye as soon as we established cloud chamber technology.

Although there are four basic types of particles that may be detected in a cloud chamber, the long and straight tracks are easily identified as cosmic ray muons, especially when the cloud chamber is subjected to an external magnetic field. The findings of such experiments can be used to illustrate the validity of special relativity. (Credit: Cloudylabs/Wikimedia Commons)

Other investigations confirmed that time dilation is a real phenomena for subatomic particles.

  • The Kennedy-Thorndike experiment in 1932 demonstrated that both length contraction and time dilation are necessary to explain light mobility in various directions in space; this was an advance over the earlier Michelson-Morley experiment, which required just length contraction.
  • The Ives-Stilwell experiment evaluated the Doppler shift of light and compared it to special relativity predictions; it was the first experimental confirmation of time dilation caused by positively charged hydrogen ions and demonstrated that the Lorentz factor was the right factor for time dilation.
  • The Rossi-Hall experiment, conducted in 1940, experimentally measured the relativistic decay of muons in the atmosphere, quantitatively confirming special relativity’s predictions for time dilation.

However, Einstein’s initial objective of testing the validity of special relativity using ordinary clocks on or near the Earth’s surface remained unfulfilled. However, two advancements happened in the 1950s that eventually moved the theory into the realm of testability.

Cesium-beam atomic clocks, such as the one pictured above, were used to help synchronize and standardize time throughout the world in the 1960s. These clocks were later employed in the Hafele-Keating experiment, which demonstrated the validity of time dilation for big objects and quantified both the special and general relativistic components of the effect. (Credit: Binarysequence/Wikimedia Commons)

The first advance that would allow for such a test has been in the works for a long time: the invention of the atomic clock. Previously, the most precise timepieces were either quartz or mechanical clocks. However, when the temperature changed, they proved increasingly inaccurate, leading many to seek an alternative. The idea of utilizing an atom’s vibrational frequency to maintain time, first proposed by James Clerk Maxwell and then developed further by Lord Kelvin and then Isidor Rabi, unexpectedly leapt into the realm of practicality.

Every atom has a set of energy levels that its electrons are permitted to occupy just those levels. However, due to quantum mechanical phenomena, such as electron and nuclei quantum mechanical spins interacting with electromagnetic fields created by moving electrons, some of those energy levels divide, resulting in fine-structure and hyperfine-structure with extremely tiny energy differences. When electrons go from a little higher energy level to a slightly lower energy level, they produce a photon with a very particular frequency. By inverting the frequency, you can arrive at a value for time, and therefore, you can use properly prepared atoms to keep time. This is the idea and implementation of modern atomic clocks: currently the best device for timekeeping known to humanity.

This synthesis of three separate sets of spectral lines from a mercury vapor lamp demonstrates the effect of a magnetic field. There is no magnetic field in (A). There is a magnetic field in (B) and (C), but it is oriented differently, explaining the differential splitting of the spectral lines. Without the application of an external field, many atoms display this fine-structure or even hyperfine-structure, and such transitions are critical when it comes to constructing a functional atomic clock. (Credit: Warren Leywon/Wikimedia Commons)

However, if you intended to travel at great speeds in a single direction and return to your starting position, you’d run against another confounding factor: the Earth’s uneven terrain. You’ll very certainly have to change elevation, whether you drive, walk, sail, or fly. The issue is that when your height changes, you are now a different distance away from the center of the Earth, which alters how severely the fabric of space is curved. The impact of gravitational time dilation, which needs general relativity to account for, changes as the curvature of space changes.

That is why it is so significant that the Pound-Rebka experiment was carried out in 1959. While iron-56 is the most stable isotope of iron, with 26 protons and 30 neutrons, iron-57 may be created by adding one neutron. Iron-57 may either produce or absorb gamma rays of a specified energy: 14,400 electron-volts, depending on whether it is excited or not.

An emitting sample of iron-57 was placed at the bottom of Harvard’s Jefferson laboratory, while an absorbing sample of iron-57 was placed at the top. Because the generated gamma-rays lost energy as they traveled up out of Earth’s gravitational field, none of them were absorbed at the top of the lab. When a speaker cone was placed to the emitting sample at the bottom, the emitted photons were “kicked” with more energy. The photons were absorbed at the top of the tower when the energy matched the energy lost due to gravitational redshift, proving that the frequency shift observed lined up exactly with that predicted by Einstein’s general relativity.

Physicist Glen Rebka, at the lower end of the Jefferson Towers, Harvard University, calling Professor Pound on the phone during setup of the famed Pound-Rebka experiment. A photon emitted from the bottom of the tower would not be absorbed by the same material at the top without further modifications: evidence of gravitational redshift. When a speaker “kicked” the emitting photon with additional energy, the atoms at the top of the tower could suddenly absorb those emitted photons, strengthening the case for gravitational redshift. (Credit: Corbis Media/Harvard University)

Even if the detection of such a small, precise effect was now theoretically feasible, it required a few great minds to piece together the idea for how such an experiment would operate, as is frequently the case. Physicist Joseph Hafele realized that by bringing an atomic clock — one of the then-modern, precise cesium-133 versions available at the time — aboard a commercial airliner capable of flying completely around the world in a single flight, he could tease out both the effects of special and general relativity on time dilation.

After giving a discussion about the concept in front of an audience that included astronomer Richard Keating, Keating approached Hafele and informed him about his work with atomic clocks at the United States Naval Observatory. Soon after, funding from the Office of Naval Research arrived, as Hafele’s ideas would prove to be one of the most cost-effective tests of relativity ever conducted; 95 percent of the research funding was spent on round-the-world plane tickets, half for the scientists and half for the atomic clocks that would occupy the seats.

This map depicts the scheduled flight paths for June 2009 throughout the world. Around-the-world flights, both eastward and westward, have been technologically feasible since the mid-20th century, though most such journeys require many stops for refueling and aircraft checks.(Credit: Jpatokal/Wikimedia Commons)

The genius of this idea is that it wasn’t just, Hey, let’s fly this plane around the world and see if time dilates the way that special and general relativity predict that they ought to.” That would have been more than enough to directly test Einstein’s theories of time dilation.

Instead, Hafele and Keating went the additional mile, both metaphorically and literally. First, one clock remained on the ground in its original place, ticking away and keeping time as precisely as possible: to within a few tens of nanoseconds over weeks.

Second, two clocks were loaded on a round-the-world journey and flown around the world in the eastward direction, the same as the Earth’s rotation. Because the plane’s speed and the Earth’s rotation were both in the same direction, velocities increased, and thus its additional, faster motion through space should indicate less time passed, with time dilation forecasting a loss of time.

Finally, the clocks were loaded onto a round-the-world flight traveling west, against the Earth’s rotation. Because these planes flew slower than the rotation of the Earth, the clock on the ground moved quicker than the westward-moving plane. Because of the slower speed through space, this clock should have elapsed more time than the eastward-moving clock and the stationary one on the earth.

This photograph shows Hafele, Keating, and their two atomic clocks on an around-the-world journey when they experimented with time dilation. An unidentified flight attendant stands nearby.(Credit: Popular Mechanics, 1972)

The findings of the experiment were presented and compared to predictions at the end. The clock that was on the ground the entire time would be classified as “at rest,” and everything else would be expected and measured in relation to that reference point.

Although both clocks were designed to fly along comparable routes at equal altitudes, such designs are rarely practical. That’s why the flight crew assisted in taking measurements of the plane’s location during its twin travels, allowing for the quantification of both the projected gravitational time dilation and the predicted due-to-motion time dilation.

  • The clock would gain 144 nanoseconds due to gravitational time dilation for the eastward-moving plane, but lose 184 nanoseconds due to time dilation caused by its speed. In all, a loss of 40 nanoseconds is projected, with an uncertainty of 23 nanoseconds.
  • Gravitational time dilation was anticipated to gain 179 nanoseconds for the westward-moving plane, which flew at a greater total altitude. However, its slower speed across space resulted in a forecast of a further gain of 96 nanoseconds, for a total predicted gain of 275 nanoseconds with a 21 nanosecond uncertainty.
  • Finally, the measurements, which were first published in Science in 1972 — exactly 50 years ago — revealed a net loss of 59 nanoseconds (with an experimental uncertainty of 10 nanoseconds) for the eastward-moving plane and a net gain of 273 nanoseconds (with an experimental uncertainty of 7 nanoseconds) for the westward-moving plane.

Even a ~1 foot (33 cm) difference in height of two atomic clocks can cause a detectable change in the speed at which those clocks run. This enables us to determine not just the intensity of the gravitational field, but also its gradient as a function of altitude/elevation. Atomic clocks, which rely on electron transitions in atoms, are the most precise time-keeping devices now available to humans.(Credit: David Wineland/Perimeter Institute, 2015)

Although this first experiment only validated special and general relativity predictions to within approximately 10%, it was the first time time dilation was measured for massive, macroscopic objects using something as exact as an atomic clock. It demonstrated strongly that Einstein’s predictions for both the motion and gravitational components of relativity were both required and valid in their description of how time should pass. Today, uses range from GPS to radar tracking to determining the lifetimes of subatomic particles, among other things.

Today, we can establish the motion component of time dilations at speeds as slow as a cyclist’s and elevation variations in the gravitational field at Earth’s surface as small as 0.33 meters (about 13 inches). Because Einstein’s conception of the Universe was so drastically different from all that had come before it, there was great resistance to the ideas of special and general relativity, and it was criticized for decades. In the end, however, it is the outcomes of experiments and observations, not our prejudices, that reveal the fundamental truths of nature. The Universe truly is relativistic, and measuring the differences in atomic clocks as they flew around the world is how we truly confirmed it in our everyday lives.

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