What Is General Relativity?

What Is General Relativity?[1]

In 1907, Albert Einstein had his “happiest thought” — people in free fall do not feel their own weight. This simple idea laid the foundation for his general theory of relativity, which Einstein presented 100 years ago this month.

The image above represents several situations, described below:


Imagine waking up in a box, completely weightless. Are you falling toward Earth or floating in outer space?


Now imagine waking up on the floor of the box.  Are you resting on Earth or accelerating in a spaceship?


In your accelerating spaceship, a beam of light would bend slightly. The Sun’s mass also bends starlight.

Einstein realized that falling freely in gravity feels the same as floating in space with no gravity. Gravity seems to be absent in free fall, at least in the small area around you. Since floating in space and falling in gravity feel the same, Einstein reasoned there must be no “force” of gravity at work in either state.

Einstein also realized that resting in gravity feels the same as accelerating at 1 g. Since acceleration and gravity feel the same, he argued that they must have the same cause.

Einstein proposed that the massive objects like the Earth curve space and time, and that what we call gravity arises from this curvature.

Acceleration feels the same as resting in a region of curved space and time.

A beam of light across the ship seems to bend slightly, because the ship moves forward as the light travels.

Einstein predicted that light should also be bent by gravity, since acceleration and gravity are equivalent.

Einstein’s prediction was confirmed during a solar eclipse in 1919, when distant background stars appeared to shift position.

Einstein Crosses and Rings

Astronomers have used the bending of light predicted by general relativity as a cosmic lens to study distant stars. A video produced for Einstein’s birthday in March explains:

Play Video 2:32

Sources: Max Planck Institute for Gravitational Physics; Michel Janssen, University of Minnesota

[1] Jonathan Corum and Jennifer Daniel, “What is General Relativity?” New York Times (November. 24, 2015), downloaded August 7, 2017


1919 Solar Eclipse

The Eclipse That Revealed the Universe[1]

Einstein presented his general theory of relativity 100 years ago, August 2017.

In 1919, British astronomers photographed a solar eclipse and proved that light bends around our Sun—affirming Einstein’s theory of general relativity.





A view of the 1919 solar eclipse, observed in Sobral, Brazil. Arthur Eddington set out to verify Einstein’s prediction that gravity could affect the course of starlight. Credit Arthur Eddington







So, this is what it is like to play cosmic pinball. The worlds move, and sometimes they line up. Then you find yourself staring up the tube of blackness that is the Moon’s shadow, a sudden hole in the sky during a total solar eclipse.

Such moments have left their marks on human consciousness—like the monoliths in the classic movie, “2001: A Space Odyssey”—since before history was recorded.

Few eclipses have had more impact on modern history than the one that occurred on May 29, 1919, more than six minutes of darkness sweeping across South America and across the Atlantic to Africa. It was during that eclipse that the British astronomer Arthur Eddington ascertained that the light rays from distant stars had been wrenched off their paths by the gravitational field of the Sun.

That affirmed the prediction of Einstein’s theory of general relativity, ascribing gravity to a warp in the geometry of space-time, that gravity could bend light beams. “Lights All Askew in the Heavens,” read a headline in this newspaper.

Eddington’s report made Einstein one of the first celebrities of the new 20th century and ushered in a new dynamic universe, a world in which space and time could jiggle, grow, warp, shrink, rip, collapse into black holes and even disappear. The ramifications of his theory are still unfolding; it was only two years ago that a rippling of space-time—gravitational waves produced by colliding black holes—was discovered.

The British astronomer Arthur Eddington, who discovered that light rays from distant stars would bend from the gravitational field of the Sun, an affirmation of one of the more dramatic predictions of Einstein’s theory of general relativity. Credit Oxford Science Archive, via Getty Images





But the first step wasn’t easy. How it happened illustrates that even the most fundamental advances in science can be hostage to luck and sometimes divine inspiration.

The bending of light by gravity was the most stunning and obvious prediction of Einstein’s theory. Astronomers had been trying to detect the effect at solar eclipses since before he had even finished formulating the theory. Nature and politics did not always cooperate.

One of the earliest to try was Erwin Finlay-Freundlich, an astronomer at the Berlin Observatory who was to become a big Einstein booster. Freundlich led an expedition to the Crimea in 1914 to observe an eclipse, but World War I began and he was arrested as a spy before the eclipse occurred. A team from the Lick Observatory in California did make it to the Crimean eclipse—but it rained.

“I must confess that I never before seriously faced the situation of having everything spoiled by clouds,” said William W. Campbell, the team’s frustrated leader. “One wishes that he could come home by the backdoor and not see anybody.”

Worse, Lick’s special eclipse camera was impounded by the Russians and not returned in time for the next eclipse, in Venezuela in 1916.

The next big chance to prove Einstein correct came in 1918, when the Moon’s shadow tracked right up the Columbia River between Washington State and Oregon. Lick sent another team of observers, but their camera was still not back from the Crimea and their improvised optics fell short, leaving the stars looking like fuzzy dumbbells as darkness fell.

So, the universe was still up for grabs in March 1919, when Eddington and his colleagues set sail for Africa to observe the next eclipse. Astronomically, the prospects were as good as they could get. During the eclipse, the Sun would pass before a big cluster of stars known as the Hyades, so there ought to be plenty of bright lights to see yanked askew.

Eddington was the right man for the job. A math prodigy and professor at Cambridge, he had been an early convert to Einstein’s new theory, and an enthusiastic expositor to his colleagues and countrymen.

A story went that he was once complimented on being one of only three people in the world who understood the theory. Admonished for false modesty when he didn’t respond, Eddington replied that, on the contrary, he was trying to think of who the third person was.

Instruments used during the solar eclipse expedition in Sobral, Brazil. Credit SSPL, via Getty Images







General relativity was so obviously true, he said later, that if it had been up to him he wouldn’t have bothered trying to prove it.

But it wasn’t up to him, due to a quirk of history. Eddington was also a Quaker and so had refused to be drafted into the army. His boss, Frank Dyson, the Astronomer Royal of Britain, saved Eddington from jail by promising that he would undertake an important scientific task, namely the expedition to test the Einstein theory.

Eddington also hoped to help reunite European science, which had been badly splintered by the war, Germans having been essentially disinvited from conferences. Now, an Englishman was setting off to prove the theory of a German, Einstein.

According to Einstein’s final version of the theory, completed in 1915, as their light rays curved around the Sun during an eclipse, stars just grazing the Sun should appear deflected from their normal positions by an angle of about 1.75 second of arc, about a thousandth of the width of a full Moon.

According to old-fashioned Newtonian gravity, starlight would be deflected by only half that amount, 0.86 second, as it passed the Sun during an eclipse.

A second of arc is about the size of a star as it appears to the eye under the best and calmest of conditions from a mountaintop observatory. But atmospheric turbulence and optical exigencies often smudge the stars into bigger blurs.

So, Eddington’s job, as he saw it, was to ascertain whether a bunch of blurs had been nudged off their centers by as much as Einstein had predicted, or half that amount—or none at all. It was Newton versus Einstein.

No pressure there.

And what if Eddington measured twice the Einstein deflection?, Dyson was asked by Edwin Cottingham, one of the astronomers on the expedition. “Then Eddington will go mad and you will come home alone,” Dyson answered.

To improve the chances of success, two teams were sent: Eddington and Cottingham to the island of Principe, off the coast of Africa, and Charles Davidson and Andrew Crommelin to Sobral, a city in Brazil. The fail-safe strategy almost didn’t work.

In Sobral, the weather was unusually cloudy, but a clearing in the clouds opened up only one minute before totality, the moment the Moon fully eclipsed the Sun. On Principe, it rained for an hour and a half on the morning of the eclipse, and Eddington took pictures through fleeting clouds, hoping that some stars would show up.

A few blurry stars were visible on a couple of his photographic plates, and a preliminary examination convinced Eddington that the positions of the stars had moved during the eclipse. He turned to his colleague and said, “Cottingham, you won’t have to go home alone.”

In the end, there were three sets of plates from which the deflection of starlight could be measured. How Eddington and his colleagues played them off against one another sealed the fate of Einstein’s theory.

The best-looking data had come from an Irish telescope at Sobral. The images indicated a deflection of 1.98 seconds of arc—more than Einstein had predicted.

Another Sobral telescope, known as an astrograph, also produced lots of star images, but they were blurred and out of focus, perhaps because heat from the Sun had affected the telescope mirror. The images gave a value of 0.86 for the deflection, about in line with Newton’s formula, but with large uncertainties.

Finally, there was the Principe telescope, which recorded only a handful of stars, from which Eddington heroically derived a reading of 1.61 seconds of arc.

Which result should Eddington use? If he averaged all three, he would wind up in the unhappy middle ground between Newton and Einstein.

If he just depended on the best telescope, as the astronomers and historians John Earman and Clark Glymour pointed out in an influential essay in 1980, the figure of 1.98 would have cast doubt on Einstein’s theory of general relativity.

In the end, Eddington wound up throwing out the Sobral astrograph data on the grounds that it was unreliable. Both of the remaining plates “point to the full deflection 1”.75 of Einstein’s generalized relativity theory,” Dyson and his colleagues wrote in their official report.

“Dear Mother, joyous news today,” Einstein wrote when he got wind of the result.

Astronomers and historians have argued ever since about whether Eddington’s belief that he already knew the answer led him to fudge the eclipse analysis by leaving out the warped astrograph.

In 2007, however, Daniel Kennefick, an astrophysicist and historian at the University of Arkansas, con-cluded after a long study of the records of the eclipse expedition that it was Dyson, the astronomer royal, who had decided to exclude the results from the astrograph. Dyson was well known to be skeptical of Einstein’s new theory.

Eddington and Dyson were right. The experiment was repeated during an eclipse in 1922 and at many other eclipses over the years, always with the same Einsteinian result. With improvements in technology, today even small universities can do the requisite observations.

During the eclipse coming this month, Bobby E. Powell, a physicist at the University of West Georgia, will be redoing the experiment with his students at a site near Lexington, SC. His is only one of half a dozen universities that will try it. He hopes to develop a lab manual for individuals or schools that might want to do it during the next eclipse in American skies, in April 2024.

In modern times, some of the most precise measurements of light-bending have come from radio observations of distant galaxies. In 2009 Edward Fomalont, of the National Radio Astronomy Observatory in Charlottesville, Va., and his colleagues used a set of antennas known as the Very Long Baseline Array to obtain results that supported Einstein’s predictions to within 0.02 percent.

Astronomers in the meantime have learned to use the light-bending and amplifying abilities of immense galaxies as telescopes—Einstein’s own telescope, if you like—to study exploding stars on the other side of the cosmos and to map the mysterious dark matter that pervades the universe.

In November 1919, news of Einstein’s triumph was announced to the world with all due pomp and circumstance at a joint meeting of Royal Society and the Royal Astronomical Society in London.

Presiding over the meeting, the physicist J. J. Thomson called general relativity one of the highest achievements of mankind, describing it “as a whole continent of new scientific facts.” Black holes and the Big Bang were still in the future.

Indeed, what emerged from the Moon’s shadow that cloud-speckled day in May was an entirely new universe.

[1] Dennis Overbye, “Out There,” New York Times (July 31, 2017). A version of this article appears in print on August 1, 2017, on Page D4 of the New York edition with the headline: “When We Knew Light Could Bend”. Downloaded August 6, 2017

A Brief History of Black Holes—(6)

A Brief History of Black Holes—(6) An Outrageous Legacy[1]

General relativity is one of the few fields in modern physics where theory has driven experimentation for almost the entire century. Einstein had a unique talent for not only proposing brilliant and fruitful thought experiments, but also real experiments that could test his theories. Perhaps his most famous prediction was how the gravity of the Sun would deflect the light from distant stars, an effect confirmed with spectacular success in 1919 during a solar eclipse, propelling Einstein to international celebrity. More impressive still was the 40-plus years between Schwarzschild’s (unintentional) prediction of black holes and the discovery of Cyg C-1.

To borrow a phrase from theoretical physicist Kip Thorne, perhaps the most outrageous piece of Einstein’s legacy was his prediction of gravitational waves, made a century ago, and triumphantly confirmed just this year (2017) by the Laser Interferometer Gravitational-wave Observatory (LIGO). In addition to confirming the basic idea that the “fabric” of space-time is not just a metaphor but a tangible substance, the LIGO discovery also provided a new test of general relativity in the most extreme environment—just outside a black hole. There were some surprises in store as well: the discovery of stellar-mass black holes 30 times the mass of the Sun, twice as big as any seen before. For the cherry on top, LIGO was even able to measure the spin of the final black hole at 70 percent of the maximum Kerr limit, arguably the most accurate and precise measure of spin to date.

Building on this unprecedented track record of success, most astrophysicists fully believe that general relativity’s description of the nature of black holes is the correct one. Lingering questions attempt to use our knowledge of black holes to improve our understanding of how gas magnetic fields, and x rays behave in the presence of such a tremendous gravitational force. This is the messy part of black hole research—Astronomer Royal Martin Rees famously described it as “mud wrestling”—and one where observation has been far ahead of theory for decades.

The first puzzle came right on the heels of the first detection of Cyg X-1. In 1973, from the most basic laws of conservation of energy and angular momentum, Igor Novikov and Kip Thorne derived a brilliant and elegant description of how gas slowly spirals in toward a black hole, releasing its gravitational potential energy as heat and radiation at temperatures of millions of degrees.

There are only two problems with the Novikov-Thorne model: It doesn’t work in theory and it doesn’t work in practice. It doesn’t work in theory because it doesn’t explain how exactly the gas loses angular momentum. It doesn’t work in practice because it doesn’t agree with observations of high-energy x rays coming from billion-degree gas.

Hot ionized gas experiences almost no friction or viscosity, so it should simply go around and around on perfectly circular orbits forever, never getting any closer to the event horizon. Novikov and Thorne fully appreciated this problem, and they absorbed it into their theory with a simple fudge factor, leaving the details to later work. In the end, it took almost 20 years to find the answer. In 1991, Steve Balbus and John Hawley discovered a powerful instability that comes from the twisting and pulling of magnetic field lines embedded in an accretion disk. Ionized gas is an excellent electrical conductor, which means it also can generate powerful magnetic fields. These fields, in turn, can pull back on the gas, slowing it down and allowing it to spiral in toward the black hole.

Two astronomers are working on continuing to develop the magneto rotational instability (MRI) experiment.

By 2001, supercomputers had become powerful enough to adequately simulate the Balbus-Hawley instability in accretion disks around realistic black holes, fully confirming their predictions. It took yet another decade before the simulations were sophisticated enough to include the effects of radiation, and study the interplay between the disk and corona. In doing so, we have finally reached the point where, starting from the most fundamental laws of nature, we can explain how the high-energy x rays, first seen in 1971, are actually generated around real black holes.

In exactly 100 years, black holes have progressed from being a mathematical curiosity, to the subject of purely theoretical physics, to a central area of astronomy research, where theory and computer simulations confront experiments and observations on a daily basis. With the recent opening of the gravitational-wave window on the universe, in the coming years we fully expect to learn even more about the birth, life and death of these remarkable objects. One thing we can say for certain: We will continue to be surprised by nature’s exotic imagination!

[1] Jeremy Schlichtmann, “A Brief History of Black Holes,” Astronomy (44, 10, October 2016, pp.30-35

Brief History of Black Holes (1)

A Brief History of Black Holes—(1) Foundation for What We Know[1]

The foundation for what we know about black holes came during the Great War. Imagine the scene: December 1915. Europe and the world are struggling under the dark cloud of World War I. Somewhere on the eastern front, an older German artillery lieutenant huddles in his great coat, fighting to stay warm and dry at the bottom of a trench.

With numb and trembling fingers, he opens the latest dispatches from home. One particularly bulky package attracts his attention. That night, throwing caution to the wind, he risks using an electric light to read the long and detailed report. Little does he know that it will prove to be arguably the most important work of creative genius of the 20th century.

The author of this pivotal document was a theoretical physicist named Albert Einstein. The recipient was his colleague Karl Schwarzschild, the director of the Astrophysical Observatory in Potsdam and an accomplished theorist and mathematician. Despite his astronomical career, Schwarzschild, then in his 40s, joined the war effort.

Just weeks before, Einstein had completed 10 long years of dedicated work, successfully expanding his special theory of relativity to include gravitational forces along with electricity and magnetism. In four landmark papers published in the Proceedings of the Prussian Academy of Sciences, Einstein laid out the mathematical foundation of the general theory of relativity, still considered one of the most beautiful and elegant scientific theories of all times..

The pinnacle of this magnum opus was published November 25, 1915, with the concise title “The Field Equations of Gravitation.” While perhaps a bit opaque to anyone without a firm grasp of tensor calculus, he field equations can be neatly summarized by the words of the great physicist John Wheeler: “Space-time tells matter how to move; matter tells space-time how to curve.”

In this artist’s depiction of Cygnus X-1, a stellar-mass black hole strips gas from the surface of its companion star as they orbit each other. Since the 1970s, it has since become the strongest black hole candidate, with scientists at near certainty that it is one. Initially detected in x ray, it has since been studied in various other spectra.

[1] Jeremy Schnittman, “A Brief History of Black Holes,” Astronomy (44, 10, October 2016, pp.30-35)

Eddington Observes Solar Eclipse to Test General Relativity

May 29, 1919: Eddington Observes Solar Eclipse to Test General Relativity

One of Eddington’s photographs of the May 29, 1919, solar eclipse. The photo was presented in his 1920 paper announcing the successful test of general relativity.

When Albert Einstein published his general theory of relativity (GR) in 1915, he proposed three critical tests, insisting in a letter to The Times of London that if any one of these three proved to be wrong, the whole theory would collapse.

  • Advance of the perihelion of Mercury
  • Deflection of light by a gravitational field
  • Gravitational red shift

Once he had completed his theory, Einstein immediately calculated the advance of the perihelion of Mercury, and he could hardly contain himself when GR produced the correct result. The next classical test was the deflection of light by a gravitational field, first performed by Sir Arthur Eddington in 1919.

Born to Quaker parents in December 1882, Arthur was just two years old when he lost his father to a typhoid epidemic that ravaged England. As a child, Eddington was enamored of the night sky and often tried to count the number of stars he could see. Initially Eddington was schooled at home, but when he did start attending school, he excelled so much in mathematics that he won a scholarship to Owens College in Manchester at age 16. He graduated with first class honors in physics, and promptly won another scholarship to attend Trinity College at Cambridge University.

Eddington completed his M.A. in 1905. First, he worked on thermionic emission at the Cavendish Laboratory, and then tried his hand at mathematics research, but neither project went well. He briefly taught mathematics before re-discovering his first love: astronomy. Eventually he found a position at the Royal Observatory in Greenwich, specializing in the study of stellar structure. By 1914 he had moved up to become director of the Cambridge Observatory; a Royal Society fellowship and Royal Medal soon followed.

During Eddington’s tenure as secretary of the Royal Astronomical Society, Willem de Sitter sent him letters and papers about Einstein’s new general theory of relativity. Eddington became Einstein’s biggest evangelist at a time when there was still considerable wartime hostility and mistrust toward any work by German physicists. He soon became involved in attempts to confirm one of the theory’s key predictions.

Since the masses of celestial bodies would cause spacetime to curve, Einstein predicted that light should follow those curves and bend ever so slightly. Isaac Newton had also predicted that light would bend in a gravitational field, although only half as much. Which prediction was more accurate? Scientists feared that measuring such a tiny curvature was simply beyond their experimental capabilities at the time.

It was Britain’s Astronomer Royal, Sir Frank W. Dyson, who proposed an expedition to view the total solar eclipse on May 29, 1919, in order to resolve the issue. Eddington was happy to lead the expedition, but initially the venture was delayed. World War I was raging, and the factories were too busy meeting the country’s military needs to make the required astronomical instruments. When the war ended in November 1918, scientists had just five months to pull together everything for the expedition.

Eddington took nighttime baseline measurements of the positions of the stars in the Hyades cluster in January and February of 1919. During the eclipse the Sun would cross that cluster, and the starlight would be visible. Comparison of the baseline measurements of a star’s position and the corresponding measurements made during the eclipse, when that star was just visible at the limb of the sun, would determine whether Einstein or Newton was right.

Then Eddington set sail for Principe, a remote island off the west coast of Africa, sending a second ship to Sobral, Brazil—just in case the weather didn’t cooperate and clouds obscured the view. It proved to be a smart decision. Eddington’s team was dismayed when heavy rains and clouds appeared on the day of the eclipse, although the skies cleared sufficiently by the time of the event to allow them to make their measurements. The Brazilian team had their own challenges: The tropical heat warped the metal in their large telescopes, forcing them to also use a smaller 10-centimeter instrument as backup.

Once the two teams had analyzed their results, they found their measurements were within two standard deviations of Einstein’s predictions, compared to twice that for Newton’s, thus supporting Einstein’s new theory. News of Eddington’s observations spread quickly and caused a media sensation, elevating Einstein to overnight global celebrity. (When his assistant asked how he would have felt had the expedition failed, Einstein is said to have quipped, “Then I would feel sorry for the dear Lord. The theory is correct anyway.”)

Not everyone immediately accepted the results. Some astronomers accused Eddington of manipulating his data because he threw out values obtained from the Brazilian team’s warped telescopes, which gave results closer to the Newtonian value. Others questioned whether his images were of sufficient quality to make a definitive conclusion. Astronomers at Lick Observatory in California repeated the measurement during the 1922 eclipse, and got similar results, as did the teams who made measurements during the solar eclipses of 1953 and 1973. Each new result was better than the last. By the 1960s, most physicists accepted that Einstein’s prediction of how much light would be deflected was the correct one.

Eddington succumbed to cancer in November 1944 after a long illustrious career. In addition to his many scientific contributions, he once penned a lyrical parody of The Rubaiyat of Omar Khayyam about his famed 1919 expedition:

Oh leave the Wise our measures to collate
One thing at least is certain, LIGHT has WEIGHT,
One thing is certain, and the rest debate –
Light-rays, when near the Sun, DO NOT GO STRAIGHT.