# The Happiest Thought > In 1907 a patent clerk realised that a man falling off a roof feels no gravity at all, and called it the happiest thought of his life. Eight years later it was general relativity. Ride the lift that cannot tell gravity from acceleration, bend starlight past the Sun, and watch the clocks in your phone's satellites drift by 38 microseconds a day. Episode 08 of the Great Scientists series. Interactive film: https://www.planetpast.com/stories/scientist-einstein/ Publisher: PlanetPast (https://www.planetpast.com/) · Published 2026-10-13 · Physics, Space, History ## Prologue ### The happiest thought *An office, a falling man, eight years* Gravity is not a force. It is the shape of what you are falling through. In 1907 a patent clerk in Bern was writing a review article when something obvious occurred to him. A man falling from a roof does not feel his own weight. While he falls, he is weightless — gravity has vanished for him completely. Einstein called it the happiest thought of his life, because it suggested that gravity is not a force acting on things, but something about the frame you are in. Eight years later that hunch had become a set of equations saying that mass bends space and time, and that light follows the bend. ![A man falling from a roof feels no gravity. Everything else followed from that.](https://www.planetpast.com/stories/scientist-einstein/img/c00.jpg) - **1905**: four papers that changed physics - **8**: years from the thought to the equations - **38 µs**: a day: relativity in your phone > The happiest thought of my life. (Einstein on realising that a falling observer feels no gravity) Prologue · Why he matters #### The happiest thought Einstein’s route to **general relativity** started with one observation: a falling observer feels no gravity. Eight years later that became equations in which **mass curves spacetime** and light follows the curve. - **Born**: Ulm, 1879 14 March - **Died**: Princeton, 1955 18 April - **Nobel Prize**: 1921 for the photoelectric effect, not relativity How to use: pick a chapter below or press ← → to change step · ▶ plays the step · drag to rotate · three steps have buttons you can press. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein); [Wikipedia: the equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle) ## Chapter I · The clerk ### Technical expert, third class *Chapter I · 1902* The most productive year in physics happened on an office clerk’s evenings. Einstein finished his degree in 1900 and could not get an academic job. He applied across Europe and was refused. A friend’s father found him a post at the Swiss patent office in Bern: technical expert, third class, assessing applications for electrical devices. He was good at it, and it was undemanding enough to leave his mind free. He later called the office his worldly monastery. In 1905 he published four papers in a single year: on the quantum nature of light, on Brownian motion, on special relativity, and the short one with the equation about energy and mass. ![By then he was the most famous scientist alive. Fourteen years earlier he was grading patent applications.](https://www.planetpast.com/stories/scientist-einstein/img/s2-einstein.jpg) - 1879: Born in Ulm - 1900: Graduates; cannot get an academic post - 1902: Technical expert, third class, Swiss patent office - 1905: Four papers, one of them his doctorate - He applied for teaching jobs and was turned down - The patent job left his head free - He called the office his worldly monastery Chapter I · Step 1 #### Technical expert, third class Rejected for every academic post he applied to, Einstein spent **1902–1909** assessing patents in Bern. In **1905** he published four papers — light quanta, Brownian motion, special relativity, and **E = mc²**. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein); [Wikipedia: the 1905 annus mirabilis papers](https://en.wikipedia.org/wiki/Annus_mirabilis_papers) ### Four papers *Chapter I · The miracle year* Any one of them would have made a career. The first paper said light comes in discrete packets, which explained why shining light on metal knocks electrons out only above a certain colour. That is the paper that won him the Nobel Prize. The second explained the jittering of pollen grains in water as the result of being hit by molecules, which settled the argument about whether atoms are real. The third was special relativity: if the speed of light is the same for every observer, then time and distance cannot be. The fourth was three pages long and pointed out a consequence: mass is a kind of energy, and the exchange rate is the speed of light squared. $$E = mc^{2}$$ Mass is a form of energy. One gram holds about ninety thousand billion joules. - Light arrives in packets — the photoelectric effect - Pollen jitters because atoms are real - The speed of light is the same for everyone - Therefore time and length are not absolute - **1921**: the Nobel Prize — for the first of those Chapter I · Step 2 #### Four papers 1905: **light quanta** (his Nobel paper), **Brownian motion** (atoms are real), **special relativity**, and three pages on **E = mc²**. He was 26, and working full time in an office. Sources: [Wikipedia: the 1905 annus mirabilis papers](https://en.wikipedia.org/wiki/Annus_mirabilis_papers); [The Nobel Prize: Albert Einstein, 1921](https://www.nobelprize.org/prizes/physics/1921/einstein/facts/) ## Chapter II · The happiest thought ### You cannot tell the difference *Chapter II · 1907* Standing still on Earth and accelerating through space feel identical. Put yourself in a windowless box. Everything you drop falls to the floor at the same rate. You could be standing on the Earth. Or the box could be in deep space, with a rocket accelerating it upwards at nine point eight metres per second squared. From inside, there is no way to tell. Now cut the cable. Everything in the box floats, including you. You could be falling towards the Earth, or drifting in empty space with no gravity at all. Again, no way to tell. If no experiment can distinguish gravity from acceleration, then they are not two things. Press the buttons and try it. ![Inside a falling lift there is no experiment that can detect gravity.](https://www.planetpast.com/stories/scientist-einstein/img/c03.jpg) - Standing on Earth feels like accelerating in space - Falling freely feels like floating in deep space - No experiment inside the box can tell them apart - So gravity and acceleration are the same thing - **1907**: the thought - **1915**: the field equations Chapter II · Step 3 · **Interactive** #### You cannot tell the difference The **equivalence principle**: inside a sealed box, standing on Earth is indistinguishable from accelerating in deep space, and falling freely is indistinguishable from floating. Gravity and acceleration are the same thing. Press a situation and drop the ball. Watch the box, the ball and the reading. Sources: [Wikipedia: the equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle); [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity) ### Light must fall too *Chapter II · The consequences* If you cannot tell gravity from acceleration, light has to bend. The equivalence principle has consequences you can work out on the back of an envelope. Shine a torch straight across an accelerating box. While the light crosses, the box moves up, so the beam hits the far wall slightly low. From inside, the light looks bent. But the inside of an accelerating box is indistinguishable from a gravitational field. So gravity must bend light as well. The same argument says clocks lower in a gravitational field run slow. Einstein published the light-bending prediction in 1911 with a value that was half of the right answer. The full theory, in 1915, doubled it. - Shine a torch across an accelerating box - The far wall moves up while the light crosses - So the beam lands low — it has bent - If acceleration bends light, so must gravity - **1911**: he predicts light bending, with the wrong value - **1915**: the full theory doubles it - Clocks lower down run slower - Light climbing out of gravity loses energy - Both measured, both correct Chapter II · Step 4 #### Light must fall too Acceleration visibly bends a light beam inside the box; equivalence then forces gravity to bend light as well, and to **slow clocks** lower in the field. Einstein’s 1911 estimate was half the final 1915 value. Sources: [Wikipedia: the equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle); [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity) ## Chapter III · Space has a shape ### Matter tells space how to bend *Chapter III · 1915* Not a force between objects. A shape that objects follow. It took Einstein eight years and a crash course in differential geometry to turn the happiest thought into mathematics. What came out in November 1915 is one equation with two sides. On one side, the curvature of spacetime. On the other, the matter and energy in it. Matter tells spacetime how to curve, and the curve tells matter how to move. A planet in orbit is not being pulled. It is going as straight as it can through a region that is bent. The first thing he checked was Mercury. Its orbit drifts by forty-three arcseconds a century more than Newton allows, and the new equations produced that number exactly. He said it gave him palpitations. ![A crude analogy — but the central idea is right: mass changes the geometry.](https://www.planetpast.com/stories/scientist-einstein/img/c04.jpg) $$G_{\mu\nu} = \frac{8\pi G}{c^{4}} T_{\mu\nu}$$ - $G_{\mu\nu}$: the curvature of spacetime - $T_{\mu\nu}$: the matter and energy present Matter tells spacetime how to curve; spacetime tells matter how to move. - **43″**: per century of Mercury, explained exactly Chapter III · Step 5 · **Interactive** #### Matter tells space how to bend The **1915 field equations** relate the curvature of spacetime to the matter and energy in it. Orbits are not pulled — they are straight lines through curved geometry. The first test: Mercury’s **43″ per century**, produced exactly. Drag the mass slider buttons to deepen the well and watch the passing light ray and the orbit respond. Sources: [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity); [Wikipedia: tests of general relativity](https://en.wikipedia.org/wiki/Tests_of_general_relativity) ### Twice Newton’s answer *Chapter III · The test* A measurable difference, if you can find an eclipse. A theory that only explains what is already known is doing half a job. General relativity made a prediction nobody had measured. Starlight grazing the edge of the Sun should be deflected. Newtonian gravity, treating light as particles, gives about zero point eight seven arcseconds. Einstein’s theory gives one point seven five — exactly twice as much. An arcsecond is the width of a coin seen from four kilometres away, so this needs careful photography. And you cannot photograph stars next to the Sun. Unless the Moon gets in the way. - **0.87″**: Newton’s prediction for starlight at the Sun’s edge - **1.75″**: Einstein’s prediction - Starlight passing the Sun is deflected - You cannot see stars next to the Sun - Unless there is a total eclipse - Then photograph the field and compare Chapter III · Step 6 #### Twice Newton’s answer Starlight grazing the Sun: **0.87 arcseconds** under Newtonian gravity, **1.75** under general relativity. A factor of two — measurable, if you can photograph stars beside the Sun during a **total eclipse**. Sources: [Wikipedia: the 1919 Eddington eclipse experiment](https://en.wikipedia.org/wiki/Eddington_experiment); [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity) ## Chapter IV · The eclipse ### Two expeditions and a lot of cloud *Chapter IV · 1919* The measurement that made him famous was messier than the legend. In 1919 Britain sent two expeditions to photograph a total eclipse: one to the island of Príncipe off West Africa, the other to Sobral in Brazil. At Príncipe it rained, and cloud covered most of totality. Eddington got a usable result from one or two plates. At Sobral the main telescope produced blurred images, and the smaller backup instrument gave the better data. On the sixth of November the Royal Society announced that the measurements favoured Einstein. The next morning he was world-famous, and he had not left Berlin. The honest version is that it was a difficult measurement at the edge of what the equipment could do. Later eclipses, and then radio astronomy, confirmed it to far better precision. ![One of the eclipse negatives. The stars are the faint marks; the measurement is of how far they moved.](https://www.planetpast.com/stories/scientist-einstein/img/s6-eclipse.jpg) - Mar 1919: Two expeditions sail from England - 29 May 1919: Totality at Príncipe and at Sobral - 6 Nov 1919: The results are announced in London - Príncipe was clouded for most of totality - Sobral’s main telescope gave blurred images - The backup instrument saved the result - It was close, and it was contested for years Chapter IV · Step 7 #### Two expeditions and a lot of cloud The **29 May 1919** eclipse was photographed from **Príncipe** and **Sobral**. Cloud and blurred plates made it marginal; the backup instrument carried the result. Announced in London on **6 November 1919**, it made Einstein world-famous overnight. Modern measurements, especially with radio sources, confirm the 1.75″ deflection to a fraction of a per cent. The 1919 data were weaker than the headlines suggested — and they pointed the right way. Sources: [Wikipedia: the 1919 Eddington eclipse experiment](https://en.wikipedia.org/wiki/Eddington_experiment) ### Overnight *Chapter IV · The fame* A German theory, confirmed by an English telescope, a year after the war. The story travelled because of its shape. A German physicist’s theory had been confirmed by a British expedition, one year after four years of war between those two countries. Newspapers made it a parable about science crossing borders, and Einstein became the first scientist to be a global celebrity. He was uncomfortable with it and used it, campaigning for pacifism, for Zionism, and later against the rise of the Nazis. The Nobel Prize came in 1921, carefully awarded for the photoelectric effect. Relativity was still considered too speculative to honour. > Lights all askew in the heavens. Men of science more or less agog. (The New York Times, 10 November 1919) - A German theory confirmed by an English expedition - One year after the war ended - The press made it a story about peace - And made Einstein a celebrity - **1921**: Nobel Prize — for the 1905 light paper Chapter IV · Step 8 #### Overnight A German theory confirmed by a British expedition a year after the war made Einstein the first **celebrity scientist**. His **1921 Nobel Prize** was awarded for the photoelectric effect — relativity was still thought too speculative. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein); [The Nobel Prize: Albert Einstein, 1921](https://www.nobelprize.org/prizes/physics/1921/einstein/facts/) ## Chapter V · Fame and exile ### Out *Chapter V · 1933* He was on a lecture tour when the Nazis took power, and did not go back. By the late 1920s Einstein was both the most famous scientist in the world and, in Germany, a target. Nationalist physicists denounced relativity as Jewish physics. When the Nazis took power in 1933 he was abroad on a lecture tour. He resigned from the Prussian Academy, gave up his citizenship, and never returned. His house was raided, his property seized, his books burned, and a Nazi magazine published his photograph with the caption not yet hanged. He settled at the Institute for Advanced Study in Princeton and stayed for the rest of his life. - 1922: Lectures across Asia, including Japan - 1930s: Attacked in Germany as “Jewish physics” - 1933: Leaves Germany for good while abroad - 1940: Becomes an American citizen - His property was seized and his books burned - A bounty was published for his head - He never set foot in Germany again - He spent his last 22 years at Princeton Chapter V · Step 9 #### Out Denounced in Germany as “Jewish physics”, Einstein was abroad when the Nazis took power in **1933**. He renounced his citizenship, never returned, and spent his last 22 years at **Princeton**. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein) ### God does not play dice *Chapter V · The long disagreement* He helped start quantum mechanics, then refused to accept it. Einstein’s 1905 paper on light quanta is one of the founding documents of quantum theory. He then spent the rest of his life arguing that the theory was incomplete. His objection was not that the mathematics failed — it worked perfectly — but that it describes only probabilities, and he believed physics should describe what is actually there. In 1935 he and two colleagues published a thought experiment designed to show the theory was absurd. Experiments since the 1970s have shown that nature behaves exactly as the absurd version says, and that paper is now the foundation of research into entanglement. He was wrong, and he was wrong in a way that produced a whole field. > God does not play dice. (Einstein on quantum mechanics — Bohr’s reply: stop telling God what to do) - He helped start quantum theory in 1905 - Then spent thirty years objecting to it - The 1935 EPR paper was meant as a refutation - It became the foundation of quantum entanglement research - **30**: years spent on a unified theory that did not come Chapter V · Step 10 #### God does not play dice Einstein helped found quantum theory and then rejected its implications for thirty years. His **1935 EPR paper**, written to show the theory was absurd, became the foundation of **entanglement** research — and experiment has sided against him. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein) ## Chapter VI · The letter ### One signature *Chapter VI · 1939* He signed a letter, and spent the rest of his life regretting it. In the summer of 1939 Leó Szilárd came to Einstein with a draft letter warning President Roosevelt that nuclear fission might make an extraordinarily powerful bomb, and that Germany was working on it. Einstein signed. The letter helped start the American programme that became the Manhattan Project. He did no work on the bomb himself and was refused clearance to do so. After Hiroshima he campaigned against nuclear weapons for the rest of his life and said that if he had known the Germans would fail, he would never have lifted a finger. He died in Princeton in 1955, aged seventy-six, refusing surgery. - Szilárd drafted it; Einstein signed it - It warned Roosevelt that a uranium bomb was possible - He did no work on the bomb himself - He was denied security clearance > Had I known that the Germans would not succeed in producing an atomic bomb, I would never have lifted a finger. (Einstein, 1947) - **1955**: dies at 76; refuses surgery Chapter VI · Step 11 #### One signature In **1939** Einstein signed a letter drafted by **Leó Szilárd** warning Roosevelt that a uranium bomb was possible. He did no work on it and was denied clearance; afterwards he campaigned against nuclear weapons and called the signature his **one great mistake**. Sources: [Wikipedia: the Einstein–Szilárd letter](https://en.wikipedia.org/wiki/Einstein%E2%80%93Szil%C3%A1rd_letter); [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein) ## Epilogue ### Eleven kilometres a day *Epilogue* If nobody corrected for relativity, your map would be useless by lunchtime. Here is the part that touches you. A GPS satellite carries an atomic clock in a weaker gravitational field than yours, so general relativity says it runs fast — by about forty-six microseconds a day. It is also moving at fourteen thousand kilometres an hour, so special relativity says it runs slow, by about seven microseconds a day. The two do not cancel. The net effect is a gain of roughly thirty-eight microseconds every day, which would put your position out by about eleven kilometres after twenty-four hours. So the clocks are deliberately detuned before launch. Set the correction on and off and watch the error grow. - **+45.9 µs**: a day: clocks run fast, higher in the field - **−7.2 µs**: a day: clocks run slow, moving fast - **+38 µs**: a day net, and it must be corrected - Ignore relativity and positions drift - By roughly eleven kilometres a day - So the clocks are detuned before launch - Both of Einstein’s theories, running in your phone Epilogue · Step 12 · **Interactive** #### Eleven kilometres a day A GPS clock gains about **45.9 µs/day** from weaker gravity and loses about **7.2 µs/day** from orbital speed — a net **+38 µs**. Uncorrected, positions drift roughly **11 km per day**, so the clocks are detuned before launch. Toggle the correction and run the clock to watch the error accumulate. Sources: [Wikipedia: relativity corrections in GPS](https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System); [Wikipedia: special relativity](https://en.wikipedia.org/wiki/Special_relativity); [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity) ### A hundred years of passing *Epilogue* Waves in 2015, a photograph in 2019, and still no quantum version. General relativity has now been tested for over a century and has not failed once. In 2015 two detectors in America felt a ripple in spacetime from two black holes colliding more than a billion light years away, stretching a four-kilometre arm by less than the width of a proton. In 2019 a network of radio telescopes photographed the shadow of a black hole, and its size and shape matched the equations. The one place it still fails is where it meets quantum mechanics. Joining them is the unfinished problem he was working on when he died. The chapter stills here are AI-generated; the 1921 portrait, the eclipse plate and the black hole image are real. Sources are below. ![M87’s shadow, imaged in 2019. The size and shape match the 1915 equations.](https://www.planetpast.com/stories/scientist-einstein/img/s13-m87.jpg) - 1919: starlight bends - 1959: clocks confirmed to run slow lower down - 2015: gravitational waves detected - 2019: a black hole is photographed - Every test so far has agreed - It still does not fit with quantum mechanics - Which is the open problem he died working on Epilogue · Step 13 #### A hundred years of passing Light bending (1919), clocks slowing (1959), **gravitational waves** (2015), a **photographed black hole** (2019). General relativity has passed every test — and still does not join up with quantum mechanics. - 1905 four papers, including special relativity - 1915 general relativity - 1919 the eclipse measurement - Today 38 µs a day of correction in every satellite Chapter stills in this film are AI-generated illustrations. The 1921 photograph of Einstein, the 1919 eclipse negative and the Event Horizon Telescope image of M87 are real, credited where they appear. Sources: [Wikipedia: Albert Einstein](https://en.wikipedia.org/wiki/Albert_Einstein); [Wikipedia: the 1905 annus mirabilis papers](https://en.wikipedia.org/wiki/Annus_mirabilis_papers); [Wikipedia: general relativity](https://en.wikipedia.org/wiki/General_relativity); [Wikipedia: the equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle); [Wikipedia: the 1919 Eddington eclipse experiment](https://en.wikipedia.org/wiki/Eddington_experiment); [Wikipedia: tests of general relativity](https://en.wikipedia.org/wiki/Tests_of_general_relativity); [Wikipedia: relativity corrections in GPS](https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System); [Wikipedia: the first detection of gravitational waves](https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves); [Wikipedia: the M87 black hole image](https://en.wikipedia.org/wiki/Messier_87); [Wikipedia: the Einstein–Szilárd letter](https://en.wikipedia.org/wiki/Einstein%E2%80%93Szil%C3%A1rd_letter); [The Nobel Prize: Albert Einstein, 1921](https://www.nobelprize.org/prizes/physics/1921/einstein/facts/)