A Brief Guide to the Great Equations (29 page)

And, on November 25, in a talk called ‘The Field Equations of Gravitation’, he wrote it down as follows, in the familiar way:
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though it is sometimes written with
R
s instead of
T
s, and with additional terms.
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The equation comes in two parts. The left-hand side refers to a set of terms that characterize the geometry of space. The right-hand side refers to a set of terms that describe the distribution of energy and momentum. The left is the geometry side, the right is the matter side. As physicist John Wheeler liked to describe it, reading from left to right is space-time telling mass how to move; reading from right to left is mass telling space-time how to curve. Though the equation predicts only the slightest of deviations experimentally from the world as we know it – the positions of a few stars out of place – it amounts to a conceptual revolution from the world of Newton. In this new world, there is no absolute time nor space, and gravitation is not a force – not a tug between one object and another – but a property of space and time.

Einstein was utterly confident that it was right. He sent physicist Arnold Sommerfeld a postcard: ‘You will become convinced of the General Theory of Relativity as soon as you have studied it. Therefore I will not utter a word in its defence.’
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But while the core of general relativity was now clear to Einstein, it was still a maze to nearly all others. ‘[T]he basic formulas are good, but the derivations abominable’, Einstein wrote to Lorentz.
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Early in 1916, therefore, Einstein sat down to compose a logical route that others could follow. The result was a fifty-page paper published in a March issue of the
Annalen der Physik
, ‘The Foundation of the General Theory of Relativity.’ The paper was such a stunning success that it was reprinted in
booklet form, ran through several printings, and was translated into English. The final section states the three experimental predictions made by the theory:
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the spectral lines of light reaching us from the surface of large stars must appear displaced towards the red end of the spectrum.

a ray of light going past the Sun undergoes a deflection of 1.7 [seconds of arc]; and a ray going past the planet Jupiter a deflection of about .02 [seconds of arc].

The orbital ellipse of a planet undergoes a slow rotation… Calculation gives for the planet Mercury a rotation of the orbit of 43 [seconds of arc] per century, corresponding exactly to astronomical observation (Leverrier).

The first prediction was too difficult at the time to confirm, and the third was already contained in the theory when it first appeared. But the second prediction – that part having to do with starlight passing the sun – looked like it could be tested.

With a little help from nature.

For experimental science is the art of getting things you understand to tell you things you do not understand. You roll balls down an incline and time them. You time the swing of a pendulum. You measure how oil droplets behave in an electric field. What’s truly marvelous – the wonder of science – is that you get out of such events more than what you put into them. In some cases, you can stage these events as command performances, in the laboratory and entirely under your control. In other cases, you have to wait for nature to set the stage for you.

And an eclipse is one of these grand cosmic performances.

An alien, watching with a powerful telescope from a great distance, would see the earth and the moon, bathed in light from the sun, cast huge cone-shaped shadows as they revolve about each other. These motions can be predicted exactly, thanks to Newton’s laws. Every so often the earth or the moon enters the shadow cast by the other – sometimes completely, sometimes only partially. As seen from the earth, by an incredible coincidence, the moon’s apparent size is the same as the sun’s, so the moon completely blots out the sun’s light, throwing everything in the shadow-cone into darkness, bringing back the stars whose light is ordinarily blotted out during the day. Such eclipses thus set the stage for being able to tell whether this starlight is bent as it passes by the sun.

Einstein was anxious and excited about the prospect of testing his theory. How could he not have been? It was more than a formula – it was a proposal that the fundamental structure of the universe was different, and stranger, than human beings had ever thought. He had been frustrated by the setbacks of the earlier expeditions. But these had spared him the embarrassment of testing a result he would have had to revise.

After his monumental 1916 ‘General Theory’ paper outlining the trio of predictions, Einstein began actively promoting again the cause of testing the theory during an eclipse. He sent a copy of the paper to the Dutch astronomer and physicist Willem de Sitter, who in turn passed it to the secretary of the Royal Astronomical Society, Arthur
Eddington. Because the war had disrupted communications between the combatants, this was the only copy of Einstein’s paper to reach England. As a physicist, Eddington had been vexed by the Mercury discrepancy, and intrigued by Einstein’s theory, and proceeded to write several review articles about it. Moreover, as a Quaker and pacifist, he was attracted by the opportunity to overcome the hostility between German- and English-speaking scientists. His efforts met resistance. Oliver Lodge, the British physicist who had discovered a form of electromagnetic waves simultaneously with Hertz, and who continued to believe in the existence of ether, claimed that ether drift could account for Mercury’s perihelion. An American opponent of Einstein named Thomas J. J. See, who insisted that gravitation was a real physical force, wrote that ‘the whole doctrine of relativity rests on a false basis and will someday be cited as an illustration of foundations laid in quicksand.’
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Nevertheless, Eddington persisted, and began to drum up interest in an eclipse expedition in this fascinating and fundamental theory.
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Some recent social constructivist work, which tends to see all interest as self-interest, has drawn attention to Eddington’s efforts to garner scientific, media, and public attention to relativity, with the implication that Eddington was engaged essentially in manipulation, public relations, and self-promotion.
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But it is only natural that Eddington was excited by this work and wanted to share his excitement – and that the public and the media responded positively to this news of potentially fundamental significance. To think otherwise is to have an infantile view of scientists, and of the public. Had Eddington
not
wanted to share his excitement at scientific work that hinted at a revolutionary picture of the world –
that
would have made him pathological.

The latest eclipse expeditions fared no better than the earlier ones. The war scotched plans to mount an expedition to Venezuela to observe an eclipse in 1916. Another opportunity arose in 1918, when an eclipse took place in the U.S., but a series of unfortunate developments – including poor weather, not-yet-returned instruments that the University of California’s Lick observatory had lent to
the 1914 Russian expedition, and conflicts between group members – ended up with the results not being published.

Eddington helped enlist British Astronomer Royal Frank Dyson. Dyson was the first to propose an expedition to an upcoming total solar eclipse, on May 29, 1919. The path of the eclipse would run from North Brazil across the Atlantic, and pass Africa to the north. It would take place against a background of several bright stars. In November 1917, the Royal Society’s Joint Permanent Eclipse Committee and the Royal Astronomical Society organized two expeditions to two different locations to take photographs. One, led by A. C. D. Crommelin and C. R. Davidson, was to Sobral in northeast Brazil, the other, which Eddington joined, was to Principe, an island about 10 miles long and 4 miles wide, owned by Portugal, about 120 miles off Africa’s west coast. While the eclipse itself could be predicted, the weather could not be – and the weather at Sobral was especially worrisome because May was the last month of the rainy season.

The eclipse of May 29, 1919, was just another eclipse, yet another time that the earth entered into the cone-shaped shadow of its moon. But this one would turn out to be, scientifically, the most important eclipse in history.

In March 1919, the two expeditions left Greenwich, England, aboard the steamboat
Anselm
, and made a brief stop in Lisbon, Portugal, before arriving in Madeira. There the two groups split up. The Sobral group departed for Brazil on the
Anselm
, while the others stayed on at Madeira for 4 weeks to await a steamer to Principe.

When the Sobral expedition arrived at their a relatively barren location 80 miles inland, they set up their equipment in the racetrack of the local jockey club, after making sure that no races were planned before the eclipse. The Brazilian government supplied porters, bricklayers, carpenters, and interpreters, and an automobile – the first ever seen in Sobral – was brought all the way from Rio for the expedition’s use. The team built a support structure to shelter their two telescopes against gusts. A minor calamity occurred when a whirlwind suddenly appeared and overturned the structure, but carpenters pillaged
beams from elsewhere to fix it. A heavy rain fell on May 25, reminding the members of the expedition of the season. More disturbing was the discovery that the drive mechanism of the larger of the two telescopes was running unevenly, and that both instruments had focusing problems. On May 29, the moon’s shadow began to sweep across the earth’s surface. That morning, at Sobral, the members of the expedition awoke to an overcast sky. When the eclipse began, the sun was still behind clouds. But a minute before the eclipse became total, the sun emerged. For 6 minutes, Crommelin and Davidson took as many photographs as they could, exposing plates for 5 to 6 seconds each. ‘Eclipse splendid’, they telegrammed.

The other expedition landed in Principe and set up shop at a plantation on the northwest side of the island. The regularly overcast sky made the team members apprehensive. On May 29, the team members awoke to a heavy thunderstorm, and cloud cover hung around the rest of the morning. When the eclipse started, the sun remained completely obscured. About half an hour before totality, the team members spotted glimpses of the now-crescent-shaped sun, raising their hopes. But the cloud cover never cleared completely. Eddington and his colleague, E. T. Cottingham, helpless, took pictures of the clouds and brief glimpses of the stars, hoping against hope that they might show something. ‘Through cloud. Hopeful’, they telegrammed.

Over the next several months, groups set out computing the amount of deflection, taking into account the many sources of error.

In September, Einstein anxiously wrote to Lorentz to ask if he’d heard of the English results. On September 27, Lorentz telegrammed back:

Eddington found star displacement at rim of sun, preliminary measurement between nine-tenths of a second and twice that value. Many greetings, Lorentz

Einstein promptly sent a postcard to his mother, Pauline, deathly ill and with only a few months to live:

Dear Mother, joyous news today. H.A. Lorentz telegraphed that the English expeditions have actually demonstrated the deflection of light from the sun.
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Einstein also registered his excitement by sending a note to
Naturwissenschaften
.
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But now that the anxiety was over, he could collect himself and grew more sangfroid. When his student Ilse Rosenthal-Schneider came to visit him, he showed her the telegram, saying, ‘Here, perhaps this will interest you.’ She later recalled,

It was Eddington’s cable with the results of measurement of the eclipse expedition. When I was giving expression to my joy that the results coincided with his calculations he said, quite unmoved, ‘But I knew that the theory is correct’, and when I asked what if there had been no confirmation of his prediction, he countered: ‘Then I would have been sorry for the dear Lord – the theory
is
correct.’
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On November 6, 1919, the joint meeting of the Royal Society of London and the Royal Astronomical Society was presided over by Sir Joseph J. Thomson, who had discovered the electron about a quarter-century earlier. He opened the meeting by saying, ‘I call on the Astronomer Royal to give us a statement of the result of the Eclipse Expedition of May last.’
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Dyson:

The purpose of the expedition was to determine whether any displacement is caused to a ray of light by the gravitational field of the Sun, and, if so, the amount of the displacement. Einstein’s theory predicted a displacement varying inversely as the distance of the ray from the Sun’s centre, amounting
to 1.75’ for a star seen just grazing the Sun. His theory or law of gravitation had already explained the movement of the perihelion of Mercury – long an outstanding problem for dynamical astronomy – and it was desirable to apply a further test to it.