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Physics + MathPhysics & Math

Putting Relativity to the Test

I do not consider the main significance of the general theory of relativity to be the prediction of some tiny observable effects, but rather the simplicity of its foundation and its consistency.
—Albert Einstein

When Einstein wrote these words in 1930, it had been 15 years since he'd published his revolutionary general theory of relativity. In that decade and a half, only a handful of tests had occurred that had offered some confirmation of general relativity. But Einstein, far more a theorist than an experimentalist anyway, had moved on. He had absolute confidence in his theory and believed that further experiments would fully bear that confidence out.

ByPeter TysonNova

Albert Einstein

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Albert Einstein in 1921, the year he won the Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect."
© Bettmann/Corbis

Yet objective verification is the bedrock of science. No matter how elegant a theory is, no matter the "simplicity of its foundation and its consistency," without validation by observation and by repeatable experiments it remains just a compelling idea. It doesn't have legs to stand on.

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For decades general relativity (GR) remained in scientific limbo, if only because the tools to effectively test it did not yet exist. Then, starting around 1960, those tools began to appear, both in improved technology in physics and astronomy and in theoretical advances that enabled physicists to better calculate and interpret the observable consequences of GR. Suddenly, tests of GR became all the rage.

For the next half century, right up to the present day, scientists have poked and prodded at the theory. They sought to test its veracity with ever greater precision and to seek any possible violations that might point to new physics "beyond" Einstein. So far, despite dozens of theoretical and experimental trials by physicists, radio astronomers, theoreticians, and others around the world, Einstein's biggest idea has passed every single test "with flying colors," as the astrophysicist Clifford Will puts it in his book Was Einstein Right?

Einstein cross
The "Einstein Cross" is a distant quasar seen quadruple-imaged around a closer galaxy, which is acting as a gravitational lens. Gravitational lensing is one of the predictions of general relativity.
Courtesy NASA/European Space Agency

Special vs. general relativity

Before considering the most significant of these tests, it's worth asking: What exactly is relativity?

Einstein published two theories on relativity—special relativity in 1905 and general relativity in 1915. Special relativity (SR) holds that the speed of light is constant but space and time are relative. (They also make up one four-dimensional entity, which Einstein's former teacher Hermann Minkowski dubbed "spacetime.") It may appear to us that the lengths of objects and the passing of time are fixed and unchanging—a foot-long ruler is always a foot long, and clocks always tick at the same rate. But that's not true, according to SR; that's not the way nature works. A foot-long ruler's length, and the rate at which time flows for it, depends on its speed. We only encounter rulers or anything else in our world when they're moving not much faster or slower than we are. But if that ruler were moving near the speed of light, which is roughly 670 million miles an hour, it would appear to us who are standing still much shorter than a foot, Einstein reasoned. And time for that near-light-speed ruler would be passing much more slowly than for us.

The experiment made front-page news, and overnight Einstein became world-famous.

In his 1905 paper on SR, Einstein, almost as an aside, also introduced the concept of the equivalence of mass and energy, or E = mc2. This concept led to atomic bombs and atomic energy, as well as to many of the technologies we rely on today, including cell phones and computers. SR has been experimentally verified so many times in so many ways that it is now a completely accepted part of physics and of everyday life.

With general relativity, Einstein took SR and added gravity—in essence, he took the concept of spacetime and added curvature to it. The gravity we feel on Earth, Einstein says, is nothing more than the curvature of spacetime caused by our planet's mass. That may sound straightforward, but it took Einstein eight years of intense thought to work out its particulars. Mathematically GR is frighteningly complex, which is one reason tests continue even today to verify its consequences.

So what are the tests that GR has passed "with flying colors"? Let's begin at the beginning, when GR was born.

Mercury's southern hemisphere as imaged by the Mariner 10 spacecraft in 1974 and assembled into a photomosaic
Courtesy NASA/Jet Propulsion Laboratory

Orbit of Mercury

When he published the theory in 1915, Einstein proposed three tests of GR. The first he was able to confirm himself.

For over half a century before Einstein's time, it was known that there was something odd about the orbit of Mercury. The elliptical path it carves around the sun shifts with each orbit, leaving its perihelion, or closest point to the sun, slightly forward on that orbital path with each pass. Factoring in the gravitational tug of the other planets still left a discrepancy of 43 arcseconds per century that couldn't be accounted for using Newtonian equations. This is a tiny amount—3,600 arcseconds equals 1°—but when Einstein tackled the problem with GR's equations, he came out with exactly that figure of 43 arcseconds per century.

This first validation of his theory gave him palpitations of the heart, Einstein told a colleague. "For a few days," he later recalled, "I was beside myself with joyous excitement."

solar eclipse
A total solar eclipse as seen from Australia in 2002. The image combines a photo of the eclipse, showing the sun's halo-like corona, with data taken by the Extreme Ultraviolet Imaging Telescope.
Courtesy NASA/ESA

Bending of light

The second test that Einstein suggested required taking a good look at the sun—or, rather, at starlight passing close by it. GR says that a strong gravitational field like that of the sun "warps" spacetime. Starlight that sweeps right past the sun should be slightly deflected by our star's warped spacetime, and that deflection should be measurable, Einstein figured.

In 1919, a solar eclipse was slated to occur with the sun silhouetted against the Hyades star cluster. This offered an ideal opportunity to test the deflection idea, as the eclipse would conveniently block much of the sun's light and the positions of the Hyades stars in the sky were well known. The British astrophysicist Arthur Eddington saw his chance. Taking up positions off the coast of Africa and in Brazil, Eddington and his colleagues simultaneously measured the cluster's light as it brushed past the sun. Though not exacting, the team's measurements matched up well enough with Einstein's predictions to show he was right. The experiment made front-page news, and overnight Einstein became world-famous.

Tests of such "gravitational lensing"—in which a massive body's spacetime curvature bends light from more distant objects—have continued ever since. One of the most recent experiments occurred in 2005. Edward Fomalont of the National Radio Astronomy Observatory and colleagues used a global network of radio telescopes to measure the bending of radio waves by the sun's gravity. Their precision was extraordinary: The study confirmed the amount of deflection predicted by GR to a level of 0.03 percent.

Sirius A & B
An artist's impression of Sirius B (blue dot in right of image) and its massive companion star, Sirius A. Sirius B's diameter is just 7,500 miles, less than that of Earth.
Courtesy NASA, ESA, H. Bond (STScI) and M. Barstow (University of Leicester)

Gravitational redshift

The third of Einstein's proposed tests is something he had first predicted back in 1907. He had determined that the wavelength of light (that is, any form of radiation on the electromagnetic spectrum, from radio waves to gamma rays) that passes through a gravitational field will shift toward the redder end of the spectrum—it will be redshifted. Why? The reason, Einstein argued, is that as a photon travels through a gravitational field, it loses energy. This results in a lower frequency, or the number of times per second that the light wave oscillates, and a corresponding shift toward the red. (A faster frequency means a shift into the spectrum's bluer end, or blueshifting.)

The predicted frequency shift was only two parts in a thousand trillion, but that's just what the pair measured.

The first test of gravitational redshift occurred in 1925. That year, the astronomer Walter Adams gauged the spectral signature from Sirius B. A white dwarf star, Sirius B is extremely dense and thus has a strong gravitational field. Adams' measurements agreed with predictions made using GR, but because the physics of such bodies was then only poorly understood, scientists couldn't rule out that the redshift stemmed from some other cause.

It wasn't until 1959 that the first truly conclusive experiment of redshift occurred right here on Earth. That year, physicists Robert Pound and Glen Rebka conducted a novel experiment inside the 74-foot-tall tower of Harvard's Jefferson Laboratory. Relying on an extremely sensitive phenomenon known as the Míssbauer effect, they were able to measure the change in wavelength of a beam of gamma rays they shot up the tower's elevator shaft. The predicted frequency shift from the bottom of the shaft to the top was only two parts in a thousand trillion, but as it happens that's just what the pair measured. The experiment offered one of the first high-precision tests of GR.

sunrise over Earth
Time dilation decreases with altitude, meaning it passes more quickly the weaker the gravitational field. Here, the Gulf of Mexico (foreground) and Florida appear in a photo shot from the Apollo 7 spacecraft in 1968.
Courtesy NASA

Time dilation

According to SR, as alluded to earlier, time will pass more slowly on a clock that is in motion compared to one that is stationary. GR further posits that clocks will run more slowly the stronger the gravitational field the clock is in.

To test both kinds of time dilation, as the phenomenon is known, physicist J. C. Hafele of Washington University in St. Louis and astronomer Richard Keating of the U.S. Naval Observatory devised a cleverly simple test in 1971. In order to secure highly precise measurements, they used atomic clocks, the ultra-accurate timekeepers that rely on the frequency of light waves emitted by particular atoms—in this case cesium atoms. The team flew four cesium clocks aboard two commercial jet flights. (Their budget didn't enable them to hire their own planes.) One flight went eastward, the other westward, and each included over 40 hours of flight. Both were compared to reference atomic clocks at the Naval Observatory on the ground.

The team's premise was this: Relative to an imagined master clock that is "stationary," the clock flying eastward, in the direction of the Earth's rotation, would be traveling more quickly than would the ground clock, which would be moving with the rotation but otherwise stationary. According to SR, the eastward flying clock should tick more slowly (again, versus a fictitious master clock) than the clock on the ground. At the same time, the flying clock, which would be subjected to lower gravity because of its altitude, should tick faster than the ground clock.

Hafele and Keating had worked out exactly how the effects of SR and GR should manifest themselves in both the east- and west-flying clocks. And their findings validated Einstein to a tee: According to their calculations using SR and GR, the flying clocks should have lost about 40 nanoseconds on the eastern flight and gained about 275 nanoseconds on the western flight. Their measurements? A loss of roughly 59 nanoseconds and a gain of around 273 nanoseconds—well within acceptable margins of error.

Echoing Einstein's own confidence, Hafele and Keating concluded their paper in Science with a dismissively bold statement: "[T]here seems to be little basis for further arguments about whether clocks will indicate the same time after a round trip, for we find that they do not." Their confidence was well-founded: Today, without such exquisite measuring of just those effects and continuous adjustments to factor them in, our GPS technology, for one, would not work.

A mosaic of radar images of Venus as collected by the Magellan spacecraft and other space- and ground-based instruments. The image is color-coded to represent differences in elevation.
Courtesy NASA/JPL-Caltech

Delay of light travel time

This is sometimes called the fourth "classical" test of GR, after the three suggested by Einstein himself. The astrophysicist Irwin Shapiro proposed bouncing radar signals off another planet and measuring the time it took them to return to Earth. There should be a measurable delay, Shapiro argued, between the round-trip travel time of signals sent when the planet was near the sun—and thus under greater influence of its gravity—than those when the planet was far away from the sun. Shapiro and colleagues recorded radar reflections off both Mercury and Venus. Their results, published in 1971, showed agreement with GR to the 5 percent level—again, close enough to be widely accepted by scientists.

Tests of this nature have become far more precise. In 2003, a team of Italian astrophysicists led by Bruno Bertotti of the University of Pavia measured how much the sun retarded radio waves sent from Earth to the Cassini spacecraft and back again as the spacecraft sped toward Saturn. Their results were accurate to 20 parts in a million and fully agreed with GR predictions.

Earth & moon
Laser-ranging experiments have shown that the Earth and moon are "falling" toward the sun with the same acceleration, just as general relativity predicts. The Galileo spacecraft took this image of the pair in a single frame from about 3.9 million miles away.
Courtesy NASA

The equivalence principle

In his equivalence principle, first formulated in 1907, Einstein held that one cannot tell the difference between gravity and acceleration, or between the absence of gravity and free fall. That is, given the same degree of force, the feeling of acceleration you would feel in a speeding-up rocket in the virtual zero gravity of deep space is exactly the same as the feeling of gravity you would feel while standing still on the Earth's surface. Likewise, the feeling of weightlessness you would feel in space is exactly the same as you would feel when falling from a great height.

Would general relativity still hold with massive, gravitationally bound objects like planets?

Tests of aspects of the equivalence principle occurred early on. Even before Einstein had devised the principle, a Hungarian baron named Roland von Eítvís and his colleagues had used a precise instrument known as a torsion pendulum to show that, in a gravitational field, materials with different masses and different components have the same acceleration to a few parts in a billion. That is, objects in a vacuum—whether a feather or a bowling ball—fall at the same rate. These and later so-called Eítvís experiments provided confirmation of the equivalence principle, and such experiments continue today.

But traditional Eítvís experiments concern laboratory-sized materials. Would GR still hold with massive, gravitationally bound objects like planets? To help check this, during the Apollo 11 moon landing Neil Armstrong deployed a reflector on the moon. This and other reflectors left by later moon missions allowed scientists on Earth to do laser-ranging experiments: shoot a laser beam at the moon and measure the time the beam takes to return. By 1971, scientists could measure these roundtrip times, which last about two and a half seconds, with a precision of one-billionth of a second.

Among other results, these laser-ranging experiments revealed that the Earth and the moon are falling toward the sun with virtually the same acceleration. ("Virtually" is almost superfluous here—the precision is to about 7 parts in 10 trillion.) In short, Einstein's equivalence principle holds for giant bodies, and theoretical calculations using GR indicate it should hold even for the most massive bodies of all. "In other words," Clifford Will writes in Was Einstein Right?, "according to general relativity, a black hole and a ball of aluminum fall with the same acceleration."

A pulsar just 12 miles across generated this X-ray nebula. Thought to be only about 1,700 years old, this young pulsar (bright spot in center of image) spins completely around almost seven times a second.
Courtesy NASA/CXC/CfA/P. Slane et al.

Binary pulsars

In 1974, University of Massachusetts physicists Russell Hulse and Joseph Taylor discovered an object in deep space—actually two in orbit around each other—that proved to be a veritable laboratory for tests of GR. It was a binary pulsar. Pulsars are rapidly spinning neutron stars that emit precisely timed radio pulses as they rotate. Scientists can use these signals for very accurate measuring of pulsars' orbital motions—and very accurate tests of GR.

The most famous of these was the measurement, first reported in 1979, of the tiny but steady shrinkage of the orbit caused by the loss of energy into gravitational waves (see below). These waves are one of the most striking of GR predictions, and the measurements matched the predictions perfectly. This earned Hulse and Taylor the 1993 Nobel Prize in Physics.

The Hulse-Taylor binary pulsar includes one pulsar and one "radio-quiet" neutron star. But in 2003, scientists discovered a double pulsar—two pulsars orbiting each other. This pair—designated PSR J0737–3039A/B—provides the best system so far discovered to make strong-gravitational-field tests of GR. A team led by Michael Kramer, a physicist at the Jodrell Bank Observatory in Macclesfield, U.K., conducted no fewer than four independent tests of GR with this double pulsar. The most precise analysis, that of the Shapiro delay (see above), confirmed the prediction made by GR's equations to within 0.05 percent. They also confirmed the gravity-wave-induced orbital shrinkage first seen by Hulse and Taylor. Such results showed that even in the unimaginably strong gravitational field of a pulsar—a star that may be only 10 miles across but weighs more than the sun—Einstein's nearly century-old theory holds up.

Gravity Probe-B
An artist's concept of the Gravity Probe B spacecraft, aimed at the reference star IM Pegasi. Gravity Probe B confirmed two predictions of general relativity.
Courtesy NASA Marshall Space Flight Center

Geodetic effect and frame-dragging

One important test of GR—actually two in one—was dreamed up in 1959 by three scientists taking a swim in a Stanford University pool. It became one of the longest-running projects in NASA history, with results finally announced only in 2011. The goal of the experiment, known as Gravity Probe B, was to test two key predictions derived from GR: one is that spacetime should be warped around a massive body; the other that a rotating body like the Earth will literally drag spacetime around with it as it spins, like a kitchen mixer drags pancake batter around as it spins.

The predicted angle of deviation would be miniscule—just the width of a human hair seen from a quarter mile away.

Both the geodetic effect and frame-dragging, as these two phenomena are known respectively, were measured by a single high-precision spacecraft launched in 2004. The craft held four exquisitely sensitive gyroscopes spinning at 4,000 revolutions per minute. Placed into a polar orbit, Gravity Probe B was aligned with a single star, IM Pegasi, about 300 light-years away. If gravity has no effect on spacetime, the NASA team argued, the ping-pong-ball-sized gyroscopes would always point in the same direction. But if GR is right, the gyroscopes' axes would ever so slightly and ever so slowly shift out of alignment with the star because of Earth's gravity and spin. Even after a year had passed, the predicted angle of deviation would be miniscule—just the width of a human hair seen from a quarter mile away.

In May 2011, Stanford's Francis Everitt, principal investigator of Gravity Probe B, along with NASA officials and others, announced the results: All four gyroscopes deviated exactly as the equations of GR figured they would. The idea born in a swimming pool over half a century before had finally paid off—for science and for GR.

galaxy cluster
The Hubble Space Telescope took the images that make up this photo of a cluster of galaxies. Known as Abell S0740, the galaxy cluster is over 450 million light-years away.
Courtesy NASA, ESA, and The Hubble Heritage Team (STScI/AURA)

Galaxy clustering

For years tests of GR on truly cosmic scales—as opposed to those of planets or our solar system—were inconclusive. Astrophysicist Reinabelle Reyes, a doctoral candidate at Princeton, and her team changed that in 2010.

Studying data collected from over 70,000 galaxies, Reyes' team discovered that the galaxies clustered together in exactly the manner that GR predicts. By combining measurements of the galaxies' clustering with other properties—including the way they bend each other's light and their motion relative to one another—the team was able to calculate a quantity known as EG, which physicists use when observing objects' expected interactions. (EG combines measurements of galaxy clustering, gravitational lensing, and the growth rate of structures.) GR predicted EG should be about 0.4. The team's value? 0.39. Yet another check in Einstein's favor.

merging black holes
Combining an optical image with X-ray data, this image shows two black holes (bright dots in center) in the midst of merging, a process that will take tens of millions of years. Astrophysicists believe such black-hole mergers are the most powerful sources of gravitational waves in the universe.
X-ray: NASA/CXC/MIT/C.Canizares, M.Nowak; Optical: NASA/STScI

Gravitational waves

GR has at least one last major hurdle to clear. In 1916, Einstein published a paper in which he predicted the existence of gravitational waves. These are disturbances in the fabric of spacetime caused by the acceleration of massive objects. Like ripples in a pond, they propagate outwards in all directions, though at the speed of light. In theory, cataclysmic events like the spiraling merger of two black holes should create such ripples in spacetime, and scientists should be able to detect those ripples when they sweep past Earth.

Despite the premature claim of a detection in 1969 and multiple high-tech attempts since, scientists have yet to confirm that gravitational waves exist (apart from the indirect checks using binary pulsar orbits—see above).

The most sensitive of gravitational-wave detectors, LIGO, which stands for Laser Interferometer Gravitational-wave Observatory, has been in operation since 2002. But gravitational waves are subtle—LIGO has been seeking disturbances as small as one hundred millionth the diameter of a hydrogen atom. New instruments are in the works, including an Advanced LIGO and LISA, the Laser Interferometer Space Antenna. If gravitational waves do exist, these new detectors should pick them up, scientists say.

Stronger than ever

Tests of general relativity continue apace. Who knows? Maybe one or more of them will eventually poke holes in Einstein's biggest idea, just as Einstein's theory of gravity poked holes in Newton's theory of gravity. But so far, with the 100th-year anniversary of GR's introduction to the world just four years away, Einstein can rest easy. No one has reported any experimental results that unequivocally violate GR—either its prediction of tiny, observable effects or the simplicity of its foundation and its consistency.

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