The Happiest Thought

Essay · physics · September 2026

General relativity is the one great theory of physics made by a single person, and the making took eight years of wrong turns, a borrowed geometry, a race to the finish and a calculation that gave its author palpitations. It was then confirmed by an eclipse, ignored for forty years, and revived by radio astronomers, pulsars and a generation of mathematicians who found black holes inside it. This is the story of how it was found, how it nearly died of neglect, and how it became the most precisely tested description of anything.

Reading time ≈ 26 min Bern 1907 → Berlin 1915 → Livingston 2015 A standalone essay

Bern, 1907

Einstein said that the idea came to him in the patent office in Bern in 1907, and that it was the happiest thought of his life: a man falling from a roof does not feel his own weight.[1] He was twenty-eight, two years past the papers on light quanta, Brownian motion and special relativity that had made his name among perhaps a hundred physicists, and he had been asked by Johannes Stark to write a review of relativity for a yearbook. In the last section of that review, almost as an afterthought, he set out what the falling man implied. If everything falls together, then an observer in free fall cannot tell that he is in a gravitational field at all; and an observer standing in a field cannot tell that he is not in a rocket accelerating upward through empty space. Gravity and acceleration are the same thing seen from different chairs. He drew two consequences in that same section, both of which would take a decade to test: clocks run slower where gravity is stronger, and light falling past a mass must bend.[2]

The review was the last thing he wrote on gravity for four years. Special relativity had made time part of geometry, and in 1908 Hermann Minkowski, who had taught Einstein at Zurich and thought him lazy, gave a lecture in Cologne announcing that “space by itself and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”.[3] Einstein at first called Minkowski’s four-dimensional formulation superfluous learnedness. He would need every word of it.

The long way round

Grossmann, you must help me

He came back to the problem in Prague in 1911, with a paper computing how much the Sun should bend the light of a star seen near its edge: 0.83 seconds of arc, later corrected to 0.87.[4] That number is, as it turned out, exactly half the right answer, because in 1911 he still treated space as flat and let only time be distorted by gravity. The paper matters for a different reason: it ended by suggesting that astronomers look for the effect at an eclipse, and one of them, Erwin Freundlich in Berlin, began trying. Freundlich’s expedition to the Crimea for the eclipse of August 1914 was interned by the Russian army on the first day of the war. Had it succeeded, it would have measured the wrong prediction and found it false.

What Einstein understood in 1912, back in Zurich at the Polytechnic where he had been a student, was that the problem was geometric and that he did not know the geometry. The clue was a rotating disc. Measure its circumference with rulers laid along the rim, and special relativity shortens them, so you count more rulers; measure the radius, and the rulers are not shortened. The ratio is more than π. A rotating frame, which the equivalence principle says is a gravitational field, has a geometry in which Euclid fails. He went to his friend and former classmate Marcel Grossmann, now professor of mathematics at the Polytechnic, and said, by his own later account, “Grossmann, you must help me or I shall go mad.”[5]

Grossmann went to the library and came back with Riemann. Bernhard Riemann had described in 1854 how to do geometry on a curved space of any number of dimensions using a table of numbers at each point, the metric, that tells you the distance between neighbouring points in every direction. Gregorio Ricci and Tullio Levi-Civita in Padua had worked out, by 1900, a calculus for such spaces, with objects that transform correctly under any change of coordinates, which is what Einstein needed if the laws were to look the same to every observer, falling or not. Grossmann taught it to him. The notebook Einstein kept through the winter of 1912 to 1913 survives, and it shows him within a few pages of the right equations, writing down the object now called the Ricci tensor and then abandoning it because he could not make it reproduce Newton’s gravity in the weak-field limit.[6] He and Grossmann published instead, in June 1913, an Entwurf, an outline, of a theory whose equations held only in some coordinate systems and not in others. It was wrong, and he spent two years convincing himself it was right.

The argument he invented to defend it is worth a paragraph, because it is the kind of mistake only a very good physicist can make. Suppose the equations did hold in all coordinates. Then take a region of empty space, a hole, and change the coordinates inside it while leaving them unchanged outside. The equations, being valid in any coordinates, would allow a second solution differing from the first only inside the hole. So the same matter distribution outside would fail to determine the field inside, and the theory would not be deterministic. Einstein concluded that generally covariant equations were physically impossible. The flaw, which took him until late 1915 to see, is that the two solutions are not different: they describe the same geometry in different labels, and a point in the hole has no identity apart from the fields that sit at it. That resolution, that coordinates are labels with no physical meaning, is now regarded as the deepest thing in the theory. In 1913 it was the thing keeping him from the theory.[7]

November 1915

Four Thursdays

He moved to Berlin in April 1914, to a professorship with no teaching duties arranged by Planck and Nernst, and his marriage ended within months of the move. In the summer of 1915 he lectured on the Entwurf theory in Göttingen for a week, to an audience that included David Hilbert, the most powerful mathematician alive, and came home saying he had convinced Hilbert of everything. By October he had convinced himself of nothing. The theory did not give the right rotation for a rotating frame, it did not give Mercury’s orbit, and the argument that had fixed the coordinates had been shown by Levi-Civita to be circular. He went back to the Ricci tensor he had abandoned in 1913.

What followed is the most concentrated month in the history of theoretical physics, and it is documented week by week because the Prussian Academy met on Thursdays and he reported to it every time.[8]

4 November · the return to covariance

He presents field equations built from the Ricci tensor, valid in all coordinates satisfying one restriction, and writes that he has “lost all confidence” in the theory of 1913. The equations are still not quite right.

11 November · a correction

A one-page addendum tightens the equations by assuming, wrongly, that the trace of the energy tensor vanishes. It is a step sideways, and he will withdraw it in two weeks.

18 November · Mercury

Using the equations as they stood, he computes the motion of a planet around the Sun to second order and finds that the perihelion of Mercury should advance by 43 seconds of arc per century beyond what Newton’s theory and the other planets account for. The anomaly had been known since Le Verrier found it in 1859 and had resisted every explanation, including an undiscovered planet named Vulcan. Einstein wrote later that he had palpitations of the heart and that for a few days he was beside himself with joy. The same paper corrects the 1911 light bending to 1.75 arcseconds.

25 November · the field equations

The final form, with a trace term on the right-hand side that makes the equations consistent with conservation of energy and momentum in every coordinate system. The paper is three pages. It ends: “With this, we have finally completed the general theory of relativity as a logical structure.”

The Mercury calculation is the hinge of the story, because it was the one test the theory could pass without waiting for anybody. Figure 1 shows what it says. The relativistic advance of a planet’s perihelion falls with the size of the orbit and rises with its eccentricity; Mercury, close and eccentric, gets 43 arcseconds per century, Venus about 9, the Earth about 4, and the number had been sitting in the astronomical tables for fifty-six years. Einstein did not fit it. He computed it from a theory with no free parameters, and it came out right to the precision of the observation.[9]

Figure 1. The relativistic advance of the perihelion, in arcseconds per century, against the size of the orbit, for a circular orbit around the Sun (line) and for the real planets (points), whose eccentricity lifts them slightly above the line. Mercury’s 43.0 arcseconds is the number Einstein computed on 18 November 1915; the observed anomaly, after every Newtonian perturbation is removed, was 43.1 ± 0.5 in Clemence’s 1947 analysis. Venus and the Earth give 8.6 and 3.8, both since confirmed by radar, and the eccentric asteroid Icarus gives 10.

Then there is Hilbert. He had been working on the same problem since Einstein’s summer visit, from a different direction, deriving the equations from a single principle of least action, and on 20 November, five days before Einstein’s final paper, he submitted a paper to the Göttingen academy that, in the version published the following March, contains the correct field equations. For eighty years this was described as a near dead heat that Hilbert had won by five days, and the two men’s correspondence that month is cold enough to suggest they thought so too. In 1997 the printer’s proofs of Hilbert’s paper were found in Göttingen, dated 6 December, and they do not contain the field equations in their final form; those were added in revision, after Einstein’s paper had appeared.[10] Hilbert himself never claimed otherwise. He said later that every boy in the streets of Göttingen knew more about four-dimensional geometry than Einstein, and that nevertheless it was Einstein who did the work.

1916 to 1917

The first solutions

Einstein had solved his equations only approximately, for weak fields. The first exact solution arrived within weeks, in a letter from the Russian front. Karl Schwarzschild, director of the Potsdam observatory and forty-two years old, was serving as an artillery officer, and in December 1915 he sent Einstein the exact geometry outside a spherical mass, adding that the war had been kind enough to let him “take this walk in the land of your ideas”.[11] Einstein presented it to the Academy in January. Schwarzschild was dead by May, of an autoimmune disease contracted at the front. His solution contains a radius, now named for him, at which the equations misbehave, and for forty years almost everyone, Einstein included, took the misbehaviour as a sign that nothing real could be that small.

Two more consequences came from Einstein himself in 1916 and 1917, and he distrusted both. In June 1916 he showed that the equations admit waves, ripples in the geometry travelling at the speed of light, and derived the rate at which an orbiting system should lose energy to them; the formula had an error of a factor of two, which he corrected in 1918 and Eddington corrected again in 1922.[12] In 1936 he submitted a paper to the Physical Review arguing that the waves did not exist after all, withdrew it in anger when the journal sent it to a referee, and was persuaded by the referee’s argument, delivered in person by Howard Robertson without saying he had been the referee, before it appeared elsewhere with the conclusion reversed.

In February 1917 he applied the equations to the universe as a whole. The universe he believed in was static and eternal, because that was what everyone believed, and his equations would not hold it still: matter attracts matter, and a static universe would fall in on itself. So he added a term, a constant he called Λ, that pushes outward at large distances, and adjusted it to balance the collapse.[13] Willem de Sitter showed within months that the equations with Λ also admitted an empty universe that expanded. Alexander Friedmann in Petrograd showed in 1922 that without Λ they admitted universes that expanded or contracted and nothing else, and Einstein published a note saying Friedmann had made an error, then a second note withdrawing the first. Georges Lemaître, a Belgian priest, derived the expansion again in 1927 and connected it to the redshifts of galaxies, and Einstein told him that his physics was abominable. Then Hubble published the redshift-distance relation in 1929, and in 1931 Einstein dropped Λ from the theory, reportedly calling it the greatest blunder of his life, though the phrase survives only in Gamow’s telling.[14] It would be back.

1919

Lights all askew in the heavens

The war had cut Germany off from British science, and the person who brought Einstein’s papers across was de Sitter, in neutral Holland, who sent them to Arthur Eddington in Cambridge. Eddington was the one astronomer in England who could follow the mathematics, a Quaker and a pacifist facing conscription, and the Astronomer Royal, Frank Dyson, secured his exemption on the grounds that he was needed for an expedition to test the German theory at the eclipse of 29 May 1919, when the Sun would stand in front of the Hyades, the richest field of bright stars it ever crosses.[15]

Two parties went. Eddington and Edwin Cottingham to Príncipe, in the Gulf of Guinea, where it rained on the morning of the eclipse and cleared enough for two usable plates; Andrew Crommelin and Charles Davidson to Sobral, in the north of Brazil, where the sky was clear and the main telescope’s mirror warped in the heat, blurring its images, while a small four-inch lens beside it worked. The measurement was of the shift in the stars’ positions between the eclipse plates and comparison plates of the same field taken at night months later, a shift of about the width of a coin seen from a mile away. There were three candidate answers: no deflection, the Newtonian 0.87 arcseconds, which is what you get by treating light as falling particles, and Einstein’s 1.75.

The results were read to a joint meeting of the Royal Society and the Royal Astronomical Society on 6 November 1919, with J. J. Thomson presiding beneath a portrait of Newton. Sobral’s four-inch gave 1.98 ± 0.12; Príncipe gave 1.61 ± 0.30; the warped Sobral astrograph gave 0.93 and was set aside as unreliable.[16] Thomson called it the most important result obtained in connection with gravitation since Newton. The Times ran “Revolution in Science” the next morning and the New York Times ran “Lights All Askew in the Heavens” four days later, and Einstein, who had been a professor known to physicists, became the most famous scientist in the world in the space of a week.

Whether Eddington had cooked the result by discarding the plate that disagreed was argued for decades, and the argument is settled: a reanalysis of the Sobral astrograph plates in 1979 with modern measuring machines gave 1.55 ± 0.34, consistent with Einstein, and the reasons given in 1919 for distrusting that instrument were the reasons a careful observer would give.[17] What is true is that the 1919 measurement was marginal, and that the next fifty years of eclipse expeditions did not improve on it much. Figure 2 collects them. The optical results scatter around Einstein’s line with errors of a tenth to a third of an arcsecond, and one 1929 measurement sits well above it. The question was closed not by eclipses but by radio astronomy, which does not need one: from 1969 the deflection of quasars passing behind the Sun could be measured every October, and by 2004 very-long-baseline interferometry had confirmed the prediction to a part in ten thousand.[18]

Figure 2. The deflection of starlight at the edge of the Sun, as measured from 1919 to 2004, with the errors the observers quoted. The magenta line is Einstein’s 1.75 arcseconds; the teal line is the 0.87 that a corpuscular theory of light, or Einstein’s own 1911 paper, would give. The two 1919 eclipse results straddle the prediction; the optical results of the next fifty years scatter around it with a tenth of an arcsecond or worse; the radio and VLBI results from 1975 onward sit on it with errors too small to draw, the 2004 value confirming the prediction to a part in ten thousand.

The Nobel committee, having given Einstein nothing in 1920 and 1921, gave him the 1921 prize in 1922 for the photoelectric effect, with a sentence in the citation explaining that relativity was not being honoured. Relativity has still not been honoured with a prize to its author. It was honoured in 1993, 2017 and 2020 through the people who tested it.

1920 to 1955

The low-water mark

What happened next is the part of the story that is usually left out, and it is the part that says most about how science works. For thirty-five years general relativity was a backwater. There were three confirmed effects, one of which, the gravitational redshift, was not convincingly measured until 1960, and all three were tiny corrections to Newton. There were no experiments to do. The mathematics was hard and the people who could do it were mostly in Germany, then mostly not. Physics had gone elsewhere, to the quantum theory that took shape between 1925 and 1927 and then to the nucleus, and a bright student in 1935 who wanted to work on gravity was told, at most universities, to want something else.

Einstein himself had gone elsewhere too, into a thirty-year search for a unified theory of gravity and electromagnetism that produced a dozen false starts and no physics, and into a running argument with the quantum theory that he had helped to found and would not accept. He was not entirely alone: Hermann Weyl in 1918 and Theodor Kaluza in 1921 tried the same unification by different routes, and Kaluza’s idea, that electromagnetism is gravity in a fifth dimension curled too small to see, would be revived by string theorists sixty years later. But the theory’s own predictions were not being followed up, and the most important of them was being actively denied.

That prediction was collapse. In 1930 Subrahmanyan Chandrasekhar, aged nineteen, on the ship from Madras to Cambridge, worked out that a white dwarf star heavier than about 1.4 solar masses could not hold itself up, and that nothing in known physics would stop it shrinking. Eddington, who had made Einstein famous, ridiculed the result at a Royal Astronomical Society meeting in 1935, saying there should be a law of nature to prevent a star from behaving in this absurd way, and Chandrasekhar, who won the Nobel prize for it in 1983, moved to Chicago and did not work on the problem again for thirty years.[19] In September 1939, in the week the war began, Robert Oppenheimer and his student Hartland Snyder published a paper following the collapse of a heavy star all the way down in Einstein’s theory: the star shrinks past its Schwarzschild radius, light from its surface takes forever to reach an outside observer, and the star “tends to close itself off from any communication with a distant observer; only its gravitational field persists.”[20] It is the first description of a black hole. Einstein published a paper in the same year arguing that Schwarzschild’s radius could not occur in nature. Oppenheimer went to Los Alamos and never returned to the subject. The paper was cited a handful of times in twenty years.

1955 to 1975

The renaissance

The revival had a date and a benefactor. Einstein died in April 1955. That July, a conference in Bern to mark fifty years of relativity gathered most of the people in the world who worked on it, and they fitted in one lecture hall. In January 1957 a second was held at Chapel Hill in North Carolina, paid for by a foundation set up by a businessman named Roger Babson who hoped someone would find a way to switch gravity off, and the money went instead to the first serious discussion of whether gravitational waves carry energy.[21] Richard Feynman, attending under a false name to avoid being bothered, settled the question with an argument about a bead on a rod: a passing wave would move the bead, friction would heat the rod, and so the wave must have carried the heat. The theory had energy in its waves after all, and by the mid-1960s Joseph Weber was trying to catch them with aluminium cylinders. His claimed detections of 1969 were never confirmed, but they started the field that succeeded in 2015.

Three things then happened in a decade that turned a mathematical curiosity into a working science. The first was experiment catching up. In 1959 and 1960 Robert Pound and Glen Rebka measured the gravitational redshift over the 22 metres of a tower at Harvard, using the Mössbauer effect to detect a shift of a few parts in 10¹⁵, and got Einstein’s value to ten per cent, the first laboratory test of the theory.[22] In 1964 Irwin Shapiro predicted a fourth effect, a delay in radar echoes from Venus and Mercury as the signal passed near the Sun, and measured it in 1968.[23] The second was the sky. Quasars, found in 1963, were sources of the luminosity of a hundred galaxies from regions smaller than the solar system, and nothing but gravitational collapse could power them; pulsars, found by Jocelyn Bell in 1967, were neutron stars, the stars Chandrasekhar’s argument had led to; and the microwave background, found in 1965, was the afterglow of Lemaître’s primeval atom. The universe, it turned out, was full of the strong-field situations the theory had been written for and nobody had looked at.

The third was mathematics. Roy Kerr in 1963 found the exact geometry outside a rotating mass, the solution real collapsed stars would have, and Roger Penrose in 1965 proved that once collapse passes a certain point a singularity is inevitable, with no assumption of symmetry, using methods from topology that physicists had not used before.[24] Stephen Hawking, from 1966, turned the same methods on the beginning of the universe. John Wheeler at Princeton, who had trained a generation of students to take the theory literally, gave the collapsed star its name at a lecture in December 1967, and by 1972 the X-ray source Cygnus X-1 was the first candidate for one.[25] In 1974 Hawking applied quantum field theory just outside the horizon and found that black holes radiate, which is where the story of this theory joins the story of the other one, and where the earlier essay on this blog took it up.

For thirty-five years there were three tiny effects, no experiments, and a founder who had gone elsewhere. Then the sky turned out to be full of the theory.the renaissance, in a sentence

1974 onward

The precision era

In the summer of 1974 Russell Hulse, a graduate student of Joseph Taylor’s using the Arecibo telescope, found a pulsar whose pulse period varied on an eight-hour cycle. It was in orbit around another neutron star, the two of them separated by about the radius of the Sun and moving at a thousandth of the speed of light, with a periastron advancing by 4.2 degrees a year, a hundred thousand times Mercury’s. It was the strong-field laboratory the theory had lacked, and it came with a clock accurate to a microsecond.[26] Einstein’s 1916 formula, with Eddington’s correction, says the orbit must shrink as it radiates gravitational waves, by about three and a half metres a year, and the shrinkage shows up as a cumulative shift in the time of closest approach that grows with the square of the elapsed time. Figure 3 is that shift. The measured points lie on the curve to a fifth of a per cent, which is the first evidence that gravitational waves exist and the reason Hulse and Taylor were given the 1993 Nobel prize.

Figure 3. The cumulative shift in the time of periastron of the Hulse–Taylor binary pulsar since its discovery, as general relativity predicts it: a parabola, because the orbit shrinks at a steady rate as it radiates gravitational waves, and the accumulated timing shift grows with the square of the elapsed time. The orbital period of 7.75 hours shortens by 76 microseconds a year, the separation by 3.5 metres, and by 2025 the pulsar reaches closest approach 107 seconds earlier than it would on a fixed orbit. The measured points, from forty years of timing at Arecibo, lie on this curve to 0.2 per cent.

From then on the tests came from engineering as much as from astronomy. The first satellite of the Global Positioning System was launched in 1978 with a clock deliberately set to run slow by 38 microseconds a day, the net of a 45-microsecond gravitational speed-up from being higher in the Earth’s field and a 7-microsecond slow-down from its orbital speed; the engineers, not all of whom believed the correction was needed, included a switch to turn it off, and it was never used.[27] Gravity Probe B, a satellite carrying four spinning quartz spheres, measured in 2011 the twisting of spacetime by the Earth’s rotation that Lense and Thirring had predicted in 1918.[28] The Cassini spacecraft on its way to Saturn in 2003 measured the Shapiro delay of its own radio signal to two parts in a hundred thousand, the tightest test of any of the classical predictions.[29]

The last two chapters closed the two questions Einstein had opened and doubted. In 1998 two teams measuring distant supernovae found that the expansion of the universe is speeding up, which in the theory means that Λ is not zero after all; the term Einstein had removed in 1931 was reinstated with a value of about 10⁻⁵² per square metre, and it is now the dominant constituent of the universe.[30] And on 14 September 2015, at nine minutes to eleven in the morning in Louisiana, the two LIGO interferometers recorded the waves that Einstein had predicted in 1916, retracted in 1936, and that Weber had failed to find: a signal lasting a fifth of a second from two black holes of about thirty solar masses each, merging 1.3 billion light years away, the waveform matching the numerical solution of the 1915 equations peak for peak.[31] Four years later the Event Horizon Telescope photographed the shadow of the black hole at the centre of M87. Oppenheimer’s object, cited a handful of times in twenty years, now has a picture.

Coda

What the history says about the theory

Three things stand out, and they are not the usual three. The first is that the theory was not derived from anything. Einstein had one physical principle, that falling is indistinguishable from floating, and a mathematical requirement, that the laws hold in any coordinates, and between them they fixed the equations almost uniquely, but only after he had spent two years arguing himself out of the requirement. The theory was found by a search through a space of possible theories, guided by consistency, taste and one old number from the astronomical tables. That is a strange way to discover something true, and this blog has spent some months on whether it should work at all.

The second is that confirmation and acceptance are different things. The eclipse of 1919 made Einstein famous and the theory respectable, but it did not make anyone work on it, and for a generation the theory’s most important prediction was rejected by its author and its most famous champion. What revived it was not a better test but a change in what astronomers could see. A theory can be right and idle at the same time, for decades, waiting for the instruments that can reach the regime it was written for.

The third is that the tests, when they came, did not stop. Every one of the effects in this essay has now been measured to at least a part in a thousand, several to a part in a hundred thousand, and the theory has never once been found wanting. That record is a problem, because the theory is known to be incomplete, and the incompleteness has to be hiding somewhere the measurements have not reached. Where that somewhere is, and what is thought to be there, is the subject of the essay this one was written to precede.

On method and tools

This piece was written collaboratively with Claude Fable 5.1 (Anthropic): human specification, editorial direction and critical review; machine synthesis, drafting, computation and figure generation.

The figures are computed, not traced. The script scripts/physics_history.py evaluates the relativistic perihelion advance 6πGM/(a c²(1 − e²)) per orbit for the planets from their orbital elements, the limb deflection 4GM/(c²R) for the Sun, and the cumulative periastron shift ½(ṁ_b/P_b)t² for PSR B1913+16 from the measured orbital period and its decay rate; the historical deflection measurements in Figure 2 are transcribed from the papers cited and the post-1975 values are converted from the published parameter γ using (1 + γ)/2. The numerical output is in docs/physics-history-results.json. Dates and quotations are from the sources below, chiefly the Collected Papers of Albert Einstein and Pais; where a story survives only second-hand, the text says so.

Authored by: Luis Matos Ferreira — Physicist, Developer, Writer

Related essays on this blog

1. The Smooth and the Grainy — where this theory and quantum mechanics contradict each other, and the attempts to join them.
2. An Act of Desperation — the companion history: how quantum mechanics was made, by many hands, in the same years.
3. Invented, Then Unavoidable — why physicists trust beauty, with this theory as the leading exhibit.

Sources

1. Einstein, unpublished manuscript for Nature, 1920, Einstein Archives 2-070, in Collected Papers of Albert Einstein (CPAE) vol. 7, doc. 31; the phrase is “der glücklichste Gedanke meines Lebens”.
2. Einstein, “Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen”, Jahrbuch der Radioaktivität und Elektronik 4, 411 (1907), section V.
3. Minkowski, “Raum und Zeit”, lecture to the 80th Assembly of German Natural Scientists and Physicians, Cologne, 21 September 1908; Physikalische Zeitschrift 10, 104 (1909). Einstein’s remark is reported by Sommerfeld; see Pais, Subtle is the Lord, Oxford, 1982, ch. 7.
4. Einstein, “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes”, Annalen der Physik 35, 898 (1911). On Freundlich’s 1914 expedition: Hentschel, The Einstein Tower, Stanford, 1997.
5. Einstein’s recollection is in his Kyoto lecture of December 1922, as recorded by Ishiwara; see Pais, ch. 12, and Kollros, Helvetica Physica Acta Supplementum 4, 271 (1956), for the wording.
6. The Zurich Notebook, CPAE vol. 4, doc. 10; Renn (ed.), The Genesis of General Relativity, 4 vols, Springer, 2007, for the analysis. Einstein & Grossmann, Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation, Teubner, 1913.
7. Stachel, “Einstein’s search for general covariance, 1912–1915”, in Howard & Stachel (eds), Einstein and the History of General Relativity, Birkhäuser, 1989; Norton, “How Einstein found his field equations”, Historical Studies in the Physical Sciences 14, 253 (1984).
8. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1915: 4 November, p. 778; 11 November, p. 799; 18 November, p. 831; 25 November, p. 844. CPAE vol. 6, docs 21–25. The palpitations are in a letter to Ehrenfest, 17 January 1916, CPAE vol. 8, doc. 182.
9. Le Verrier, Comptes rendus 49, 379 (1859); Clemence, “The relativity effect in planetary motions”, Reviews of Modern Physics 19, 361 (1947), observed 43.11 ± 0.45 against predicted 42.98.
10. Hilbert, “Die Grundlagen der Physik (Erste Mitteilung)”, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 1915, p. 395, submitted 20 November 1915, published 31 March 1916; Corry, Renn & Stachel, “Belated Decision in the Hilbert–Einstein Priority Dispute”, Science 278, 1270 (1997). Hilbert’s remark is quoted in Reid, Hilbert, Springer, 1970, p. 142.
11. Schwarzschild to Einstein, 22 December 1915, CPAE vol. 8, doc. 169; Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie”, Sitzungsberichte, 1916, p. 189, presented 13 January 1916.
12. Einstein, “Näherungsweise Integration der Feldgleichungen der Gravitation”, Sitzungsberichte, 1916, p. 688; “Über Gravitationswellen”, Sitzungsberichte, 1918, p. 154; Eddington, Proceedings of the Royal Society A 102, 268 (1922). On 1936: Kennefick, “Einstein versus the Physical Review”, Physics Today 58(9), 43 (2005).
13. Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie”, Sitzungsberichte, 1917, p. 142; de Sitter, Monthly Notices of the Royal Astronomical Society 78, 3 (1917).
14. Friedmann, Zeitschrift für Physik 10, 377 (1922) and 21, 326 (1924); Einstein’s notes, Zeitschrift für Physik 11, 326 (1922) and 16, 228 (1923); Lemaître, Annales de la Société Scientifique de Bruxelles A47, 49 (1927); Hubble, Proceedings of the National Academy of Sciences 15, 168 (1929); Einstein, Sitzungsberichte, 1931, p. 235. The “blunder” is from Gamow, My World Line, Viking, 1970; see O’Raifeartaigh & Mitton, Physics in Perspective 20, 318 (2018), on its provenance.
15. Eddington, Report on the Relativity Theory of Gravitation, Physical Society of London, 1918; Chandrasekhar, Eddington, Cambridge, 1983, on the conscription exemption.
16. Dyson, Eddington & Davidson, “A Determination of the Deflection of Light by the Sun’s Gravitational Field, from Observations made at the Total Eclipse of May 29, 1919”, Philosophical Transactions of the Royal Society A 220, 291 (1920); the meeting is reported in The Observatory 42, 389 (1919).
17. Harvey, “Gravitational deflection of light: a re-examination of the observations of the solar eclipse of 1919”, The Observatory 99, 195 (1979); Kennefick, No Shadow of a Doubt, Princeton, 2019.
18. Optical results 1922–1973 as tabulated in Will, Theory and Experiment in Gravitational Physics, 2nd ed., Cambridge, 2018, table 7.1; Fomalont & Sramek, Physical Review Letters 36, 1475 (1976); Lebach et al., Physical Review Letters 75, 1439 (1995); Shapiro, Davis, Lebach & Gregory, Physical Review Letters 92, 121101 (2004), γ = 0.99983 ± 0.00045.
19. Chandrasekhar, Astrophysical Journal 74, 81 (1931); the 1935 exchange is in The Observatory 58, 37 (1935); Miller, Empire of the Stars, Houghton Mifflin, 2005.
20. Oppenheimer & Snyder, “On Continued Gravitational Contraction”, Physical Review 56, 455 (1 September 1939); Einstein, Annals of Mathematics 40, 922 (1939).
21. DeWitt & Rickles (eds), The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference, Edition Open Access, 2011; Feynman’s argument is recorded there and in Feynman, Morinigo & Wagner, Feynman Lectures on Gravitation, 1995.
22. Pound & Rebka, “Apparent Weight of Photons”, Physical Review Letters 4, 337 (1960).
23. Shapiro, “Fourth Test of General Relativity”, Physical Review Letters 13, 789 (1964); Shapiro et al., Physical Review Letters 20, 1265 (1968).
24. Kerr, “Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics”, Physical Review Letters 11, 237 (1963); Penrose, “Gravitational Collapse and Space-Time Singularities”, Physical Review Letters 14, 57 (1965).
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26. Hulse & Taylor, “Discovery of a pulsar in a binary system”, Astrophysical Journal 195, L51 (1975); Weisberg & Huang, Astrophysical Journal 829, 55 (2016): P_b = 27906.98 s, ṁ_b = −2.398 × 10⁻¹², ratio of observed to predicted decay 0.9983 ± 0.0016.
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