Insight Editions · No. 61
Einstein's Cosmos
How Albert Einstein's Vision Transformed Our Understanding of Space and Time
Michio Kaku
Michio Kaku recounts Albert Einstein's life and explains how relativity, quantum theory, cosmology, and the search for a unified field transformed modern physics.
A study guide to Einstein's Cosmos by Michio Kaku. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
The Book in Brief
The argument in brief
- Picture, principle, symmetry. Racing light led to the constancy of c and the Lorentz transformation. A falling man led to the equivalence principle and general covariance. When the third picture never came, the unified field theory stalled.
- The theories outran their author. General relativity contained expansion, black holes, gravity waves and lenses, which Einstein resisted or thought unobservable. Equations can be wiser than their makers.
- The quantum fight was about completeness. Einstein accepted quantum mechanics as correct but incomplete, and tried to absorb it into geometry rather than overthrow it. Bell tests later ruled out his local realism, yet the questions he forced still structure the field.
- The late years were prophetic. Kaluza-Klein, wormholes, condensates, entanglement and the cosmological constant have all returned to the centre of physics. Kaku's further claim, that strings complete the programme, remains a research bet, not a settled fact.
- Biography serves method. Patent office, Besso, Grossmann, Mileva, Elsa, exile and the bomb letter are told as the conditions under which the pictures were found or lost, not as gossip for its own sake.
Argument map: the three parts of the book, each built on (or missing) a physical picture.
| Ch | Title | Gist |
|---|---|---|
| Pref | A New Look at the Legacy | Pictures as organising principle; late work re-evaluated |
| 1 | Physics before Einstein | Newton's forces vs Maxwell's fields; the aether |
| 2 | The Early Years | Compass, geometry, light-beam daydream; Mileva; patent office |
| 3 | Special Relativity and the Miracle Year | Relative time, E = mc², photons, atoms; rise to Berlin |
| 4 | General Relativity | Equivalence principle, curved space, Mercury; war |
| 5 | The New Copernicus | 1919 eclipse, fame, anti-Semitism, Nobel, religion |
| 6 | The Big Bang and Black Holes | Cosmological constant, Hubble, Schwarzschild, waves, lenses |
| 7 | Unification and the Quantum Challenge | Kaluza-Klein, BEC, Bohr debates, EPR, wormholes |
| 8 | War, Peace, and E = mc² | Exile, Princeton, the bomb letter, Gödel, Gamow, death |
| 9 | Einstein's Prophetic Legacy | BEC, decoherence, tests, dark energy, strings |
Chapter payload flow: biography, theory, legacy.
A New Look at Einstein's Legacy
Why look again
Einstein is a pop icon "on a par with Elvis Presley and Marilyn Monroe" (biographer Denis Brian), Time's Person of the Century, ranked with Newton. Kaku gives two reasons for a fresh look.
- The predictions keep paying out. New instruments (satellites, lasers, supercomputers, gravity-wave detectors) are turning his predictions into other people's Nobel Prizes. Indirect proof of gravity waves from a double neutron star won the 1993 prize. Bose-Einstein condensates, predicted in 1924, won in 2001. Black holes and Einstein lenses are now everyday tools of astronomy. Even his "greatest blunder", the cosmological constant, turned out in 2001 to hold most of the energy in the universe.
- His method is being re-read. Einstein said that a theory not based on a picture simple enough for a child to grasp was probably worthless. Kaku makes these pictures the book's organising principle.
The "failure" that wasn't
Contemporaries saw the later search as folly. Abraham Pais: his fame "would be undiminished, if not enhanced, had he gone fishing instead" after 1925. Younger quantum physicists snickered while they collected Nobels. Kaku counters that superstring and M-theory have made unification the central quest of theoretical physics, so the late Einstein looks like a pioneer rather than a relic. The book's wager is that history will side with the hunter of a missing picture, even if the particular picture Kaku favours (strings) remains untested.
The preface also sets the voice: almost no mathematics, biography in service of ideas, and a running claim that crumbs from Einstein's plate keep winning prizes for others. That claim is the hinge for reading Part III generously without treating it as settled science.
Einstein predictions confirmed long after his death, as the preface lists them.
Three parts, three pictures: the preface's organising claim.
Physics before Einstein
A genius with a sense of humour
Asked for his formula for success, Einstein offered A = X + Y + Z: X is work, Y is play, and Z is "keeping your mouth shut". In Princeton he wiggled his ears at children. When a five-year-old asked whether he had been to the bathroom that day, he was "glad to have someone ask me a question I can answer". Jeremy Bernstein recalls the recurring word for him: "humanity". He was also generous to his predecessors, and kept pictures of Newton and Maxwell on his walls.
Newton's clockwork
Before Newton, earthly and heavenly motion were thought to obey different laws. After the plague closed Cambridge in 1665, the young Newton pictured an apple falling and a cannonball fired ever faster until it circled the Earth like the Moon. The same force that drops an apple holds the Moon in orbit. His laws of motion and gravity predicted Halley's comet and still steer NASA probes past Uranus and Neptune.
Newton's clockwork: one law of gravity predicts comets and finds new planets.
Newton's forces act instantaneously: if the Sun vanished, Earth would fly off at once and every clock in the universe would agree on the moment. Space and time are absolute. A second or a metre is the same on Earth, Mars and Jupiter, and an absolute frame settles whether the train or the trees are moving. The same inverse-square law that drops the apple predicted Halley's return and, when Uranus wobbled, pointed to the unseen pull of Neptune. Mechanics looked finished; the sky itself was a clock.
Maxwell's fields
In the 1860s James Clerk Maxwell explained electricity and magnetism with a new idea, the field. Einstein called it "the most profound and the most fruitful that physics has experienced since Newton". Iron filings around a magnet trace its lines of force, and static makes children's hair stand up along electric ones.
- Fields take time. Shake a magnet and the filings respond later. Like a spider web in the wind, a disturbance travels at a definite speed.
- Fields feed each other. Faraday showed that a moving magnetic field makes an electric field and vice versa. This is the basis of the dynamo in a dam and the motor in a vacuum cleaner.
- The wave is light. Maxwell put the two together into a self-sustaining wave of electric and magnetic fields and calculated its speed. It was the speed of light. "We can scarcely avoid the conclusion that light consists of the transverse undulations of the same medium..."
Two pillars, one contradiction: by 1900 the world-views of Newton and Maxwell could not be merged.
| Feature | Newton | Maxwell |
|---|---|---|
| Basic idea | Forces | Fields |
| Speed of influence | Instantaneous | Speed of light |
| Space and time | Absolute | Needs a medium (aether) |
| Picture | Apple and Moon | Vibrating spider web |
Clouds on the horizon
Success bred complacency. Max Planck was advised as a student to avoid physics because it was finished, and Lord Kelvin spoke of only a few "clouds" on the horizon. Then Marie Curie's radium glowed with seemingly endless energy from inside the atom, apparently in defiance of energy conservation, a hint that the atom was not the last word.
The deepest problem was the aether. Light crosses the vacuum, so what is waving? Physicists posited a stationary aether filling space, an absolute reference frame against which the Earth moved. But because light travels at about 186,000 miles per second, the aether had to be denser than steel (to carry such a fast wave) yet lighter than air, weightless, invisible and frictionless, a medium with miraculous properties that no experiment could catch. Michelson-Morley would later find no aether wind at all. Others tried to patch it with contractions and dragged aethers. Einstein, "with nothing to lose", went for the root: one pillar had to fall, and it would be Newton's absolute time.
The clash that set up 1905: Newton allows catching light, Maxwell forbids it.
Two successful theories that could not share a house.
Two successful theories, one clash
Newton's clockwork and Maxwell's fields each worked brilliantly in their domain. Ships, bridges and planetary tables ran on Newton; telegraphs, lights and radio ran on Maxwell. The crisis was not that either failed experiments in its own house, but that they could not share a house. Instantaneous forces versus a finite speed of light; absolute time versus a medium that experiments could not find. Kaku's point, which structures the whole book, is that revolutions begin at such contradictions, and that Einstein's gift was to refuse the patch and change the assumption everyone shared: universal time.
Why the aether could not be saved: each patch added a miracle property.
The Early Years
Childhood: two "miracles"
Born 14 March 1879 in Ulm to secular Jewish parents, Hermann (a struggling electrical entrepreneur who began in featherbeds before his brother Jakob pulled him into electrochemicals) and the musical Pauline Koch (daughter of Julius Koch, once a baker who made a fortune in grain). Hermann and Pauline were distressed that the baby's head was misshapen and prayed he was not damaged. Albert spoke so late his parents feared he was retarded; when he finally spoke, he used complete sentences, yet even at nine he talked poorly. He threw things at his younger sister Maja: "A sound skull is needed to be the sister of a thinker." His first reaction to the baby was "But where are the wheels?"
Contrary to myth, he was a good student in maths and science, but he hated rote drill and knuckle-slapping. Classmates called him Biedermeier ("nerd"); he showed no interest in sports. His seventh-grade Greek teacher, Herr Joseph Degenhart, told him it would be better if he simply were not there: smiling in the back row "violates the feeling of respect which a teacher needs". A headmaster, asked what profession Albert should pursue, predicted "he'll never make a success of anything". Decades later Einstein wrote that it is "nothing short of a miracle that the modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry".
Einstein's formative chain from two childhood miracles to the light-beam question.
- First miracle (age 4 or 5). A compass from his father: "Something deeply hidden had to be behind things."
- A religious phase (about 11). A distant relative tutored him in the Jewish faith; he refused pork and composed hymns to God on the way to school. Popular science books then convinced him much of the Bible "could not be true". He dropped religion as abruptly as he had taken it up. It was his first break with unthinking authority, though he kept a sense that whole regions lie just beyond science.
- Second miracle (age 12). Poor Polish medical student Max Talmud ate weekly dinners at the Einstein house and gave him a "holy geometry book" (Euclid). Albert found his own proof of Pythagoras, taught himself calculus until Talmud could no longer follow, and read Kant (Critique of Pure Reason), whose call for world government and digs at pompous philosophy ("usually a great deal of wind") he kept for life. He briefly considered becoming a philosopher; Hermann dismissed it as "philosophical nonsense".
- The factory. Dynamos and motors at his father's works (Hermann hoped for the Munich city-centre electrification contract and never got it) trained his gift for physical pictures. "All physical theories… ought to lend themselves to so simple a description that even a child could understand."
Dropout, exam failure, Aarau
When the Munich lighting contract was lost, Pauline's wealthy Genoa relatives backed a new firm on condition the family move to Italy so they could rein in Hermann's overgenerous impulses. They settled near a Pavia factory; fifteen-year-old Albert was left with distant relatives in a hated Munich school, facing Prussian military service and likely expulsion. A doctor's note citing a possible breakdown got him out. He turned up unannounced on the Milan doorstep: a "draft-dodging, high school dropout" with no skills. Long arguments followed; the compromise was the Zurich Polytechnic, which required no diploma, only a tough entrance exam. He was two years younger than most candidates and failed French, chemistry and biology, but shone so brightly in maths and physics that principal Albin Herzog promised admission the next year without re-examining, and physics head Heinrich Weber offered to let him audit. Herzog sent him for a year to school in Aarau, lodging with director Jost Winteler.
There he blossomed into the cocky, punning "cheeky Swabian", renounced German citizenship (stateless for five years; he loved the Swiss as "more humane"), and fell for Marie Winteler, two years older. Fellow student Hans Byland remembered a "laughing philosopher" whose sarcasm "mercilessly castigated all vanity". Girls found the violin-playing "passionate Latin virtuoso" easy to confide in. Marie and Albert walked, bird-watched and played piano-violin duets; he wrote "Beloved sweetheart… I only now realize how indispensable my dear little sunshine has become". Both families half expected a wedding. Marie felt inadequate beside his intensity and saw that she would have to compete with his first love: physics. (Maja later married Paul Winteler; Einstein's friend Michele Besso married the eldest daughter, Anna.)
The Polytechnic and Mileva
In the fall of 1895 (after Aarau) he entered the Polytechnic hungry for Maxwell, "the most fascinating subject at the time I was a student". He found that in Maxwell's theory light always moves at the same speed however fast you go: you can never catch the beam. Teachers preferred classical physics, so he cut classes and studied alone, relying on Marcel Grossmann's meticulous notes (still preserved; Grossmann told Pauline that "something very great" would happen to Albert). Heinrich Weber, once an ally, withdrew support: "you do not let yourself be told anything." Jean Pernet gave him the lowest grade after Einstein threw the lab manual away; an explosion from ignoring instructions injured his right hand. Pernet's assistant said the unorthodox solutions were always right. Hermann Minkowski called him a "lazy dog".
Mileva Maric, a Serbian four years older and only the fifth woman admitted to study physics there (Switzerland being the only German-speaking country then admitting women), became "Dollie" to his "Johnny". Over 430 letters survive; some later fetched $400,000 at auction. Friends could not see what he saw: she was moody, private, limped from a shorter leg, and her sister Zorka later became institutionalised. She had no illusions: "My sweetheart has a very wicked tongue and is a Jew into the bargain." Pauline was furious ("By the time you're 30, she'll be an old witch"; "This Miss Maric is causing me the bitterest hours of my life") and threw herself sobbing on a bed when he said "My wife." Marriage had to wait until he had a job.
1901: first paper (capillarity); temporary teaching at Winterthur; tutoring at Schaffhausen until director Jakob Nuesch fires him for "fomenting a revolution"; father's letter to Wilhelm Ostwald goes unanswered (Ostwald later nominates him for the Nobel).
1901-02: Mileva fails her finals a second time; career as a physicist ends; she is pregnant. Einstein is near starvation (Friedrich Adler recalled).
4 Feb 1902: daughter Lieserl born in Novi Sad; last mentioned in Sept 1903 with scarlet fever; her fate is unknown (death or adoption).
23 June 1902: starts at the Bern Patent Office, technical expert third class, a job found by Grossmann; Alfred Kleiner becomes Ph.D. advisor.
Oct 1902: father dies of heart disease after blessing the marriage; Albert's "deepest shock"; Maja notes Hermann never lived to see the fame.
Jan 1903: marries Mileva; son Hans born 1904. Visitor David Reichinstein finds him rocking a bassinet, bad cigar in mouth, book in hand, stove smoking.
The "worldly monastery"
Kaku sees three hidden benefits in the patent office. It drilled him to strip inventions to their essential principle ("pissing ink" by day). Many applications were electromechanical, the world of his father's factory. And the work left hours free to think: physics at night. He called it his "worldly monastery". A newspaper ad for private lessons (his first recorded press mention) brought Maurice Solovine, and with Conrad Habicht they formed the mock-grand "Olympian Academy", joyfully poor ("What a beautiful thing joyous poverty is!") and reading everything in coffeehouses and beer halls.
Why the Bern patent office suited Einstein: routine work, short days and time to think.
They pored over Ernst Mach (The Science of Mechanics), who attacked whatever could not be measured: atoms, absolute space, absolute time and the aether. Relative motions can be measured; absolute ones cannot. Meanwhile Michelson and Morley (1887) had split a light beam at right angles on a mercury-floated table so delicate that passing carriages shook it, and found no aether wind: light's speed was the same in every direction. Think of running with, against and across the wind; your speed should change. It did not.
| Response to Michelson-Morley | Idea | Problem |
|---|---|---|
| Earth at rest in aether | No wind to detect | Undoes Copernicus |
| Lorentz-FitzGerald contraction | Aether wind squeezes metre sticks and atoms | Ad hoc patch; aether gains yet another miracle property |
| Einstein (1905) | Drop the aether; rebuild space and time | Must give up absolute simultaneity |
Like Copernicus slicing Ptolemy's epicycles with Occam's Razor, Einstein would slice away the aether's pretensions with a children's picture. The ten-year question from Aarau was about to break.
School, Zurich and the years of hunger
Headmaster Weber's verdict, "you do not let yourself be told anything," and the later advice that he was "hopeless at physics" and should switch to medicine or law, hardened his distrust of rote authority. He loved the Swiss as "more humane" than others he had lived among. The child geometry book of age 12 was a "second wonder"; of Aaron Bernstein's popular science he wrote of reading "with breathless attention." His lifelong rule: physical theories, maths notwithstanding, should lend themselves to a description "even a child could understand."
After graduating (1900) luck soured: temporary posts, private lessons, the sense that "by the mere existence of his stomach, everyone was condemned to participate in that chase." Teaching at Winterthur (1901), then the letter that Mileva was pregnant; Lieserl was born 4 February 1902 in Novi Sad, last mentioned with scarlet fever in September 1903, and vanishes from the record. On 23 June 1902 he began at the patent office as technical expert, third class. Hermann Einstein died without suspecting that within two years his son would lay the foundations of his fame. The Olympia Academy with Solovine and Habicht lived Epicurus's line: "What a beautiful thing joyous poverty is!"
From Ulm to the patent office: the path into the miracle year.
Special Relativity and the "Miracle Year"
"A storm broke loose in my mind"
Kaku dramatises the puzzle with a police officer chasing a light beam. A roadside witness sees him neck and neck with it. The officer swears it raced away at full light speed however hard he accelerated. How can both be right?
How Einstein reached special relativity: keep both principles and let time give.
Around May 1905 Einstein spent hours with Michele Besso hammering at the clash between the relativity principle and the constant speed of light, and gave up. That night he pictured a Bern streetcar racing away from the clock tower at light speed: the tower clock would appear frozen while his own ticked on. Time beats at different rates depending on how fast you move, and events simultaneous for one observer need not be simultaneous for another. The officer's watch, and his brain, had almost stopped; that is why the beam still raced away at c from his point of view, while a roadside witness saw him neck and neck with it. Both reports are true in their own frames. Einstein kept the Lorentz-FitzGerald contraction, but as a shrinking of space itself, not of atoms squeezed by an aether wind, and the aether became unnecessary. The next morning he told Besso: "Thank you, I've completely solved the problem." He spent six weeks writing the paper, then went to bed for two weeks exhausted.
Kaku dramatises the same clash with a police officer chasing a light beam. A roadside witness sees him neck and neck with it. The officer swears it raced away at full light speed however hard he accelerated. How can both be right? Only if time and length adjust so that every inertial observer measures the same c.
If light moved at 20 mph, a passing car would be squeezed like an accordion to an inch, yet its passengers would notice nothing because their atoms are squeezed too. Length has no absolute meaning. Lorentz and FitzGerald had the right formula with the wrong physics. Henri Poincaré understood light's constant speed and the symmetry of Maxwell's equations, but would not give up the aether.
E = mc² and the rest of 1905
| 1905 paper | Claim | Payoff |
|---|---|---|
| Light quanta (9 June) | Light comes in packets with energy set by frequency | Photoelectric effect; 1921 Nobel |
| Brownian motion (18 July) | Molecular kicks jiggle pollen | First hard evidence for atoms |
| Special relativity (Sept) | Space and time are relative | End of the aether |
| E = mc² (late 1905) | Mass and energy convert | Stars, nuclear energy |
The four papers of the 1905 miracle year.
- Mass and energy. If clocks and rulers change with speed, so does mass; at light speed it would become infinite, which is why light speed cannot be reached. Energy of motion becomes mass, so a tiny amount of matter holds a fabulous amount of energy: a few teaspoons hold the energy of several hydrogen bombs. Einstein hoped the tiny "footnote" paper would explain radium's endless 4,000 calories an hour without fuel. "Whether the Almighty is laughing at it... that I cannot know." Laboratory verification took about twenty-five years. The equation later powered stars, reactors and the bomb; in 1905 it was only a consistency requirement of the new kinematics.
- The photon. Philipp Lenard found that the energy of ejected electrons depended on the light's colour (frequency), not its brightness: dim blue light ejects electrons that bright red cannot, the opposite of wave theory. Building on Planck's 1900 quanta (which Planck treated as a bookkeeping trick for oven walls), Einstein argued that light itself comes in packets (named photons by Gilbert Lewis in 1926). Each packet's energy is set by frequency. Kaku: the simplest photon-torpedo launcher is a flashlight. This paper, not relativity, won the 1921 Nobel; relativity was still too contested.
- Atoms. Pollen jiggling under Robert Brown's 1828 microscope could be explained by trillions of molecular collisions. Einstein turned the jiggling into a quantitative test and estimated atomic sizes; Jean Perrin later carried out the measurements (1908) that settled the debate. Ludwig Boltzmann, ridiculed for believing in atoms, killed himself in 1906, a year after the paper that would vindicate him.
His thesis, at first refused, earned him a doctorate on 15 January 1906. All of this was written at Kramgasse 49, Bern, a year to rival Newton's 1666.
From silence to Berlin: how the miracle year turned into a career.
Planck, Minkowski and symmetry
The only early response was a letter from Max Planck. He saw that c, like his own constant h, set a boundary of common sense: we find relativity and quanta strange because we live where speeds are low and objects are large. His assistant Max von Laue walked straight past the young clerk in the patent office waiting room, and quietly dropped Einstein's cigar into the Aare.
Hermann Minkowski, the professor who had called him a lazy dog, recast relativity as a four-dimensional space-time: "space and time separately have vanished into the merest shadows." Einstein scoffed at first ("superfluous erudition"; "Since the mathematicians have attacked the relativity theory, I myself no longer understand it") but later admitted that without it relativity "might have remained stuck in its diapers". The lesson was symmetry. Like a snowflake unchanged by a 60-degree turn, equations that stay the same when space and time rotate into each other (Lorentz covariance) unify ideas and compress Maxwell's eight equations into two. Unification through symmetry guided him for fifty years and became the compass for the later search for a unified field.
Henri Poincaré had understood light's constant speed and the symmetry group of Maxwell's equations, and had even sketched a relativity principle, but he would not give up the aether as a physical medium. Lorentz and FitzGerald had the right transformation formulae with the wrong physics (atoms squeezed by wind). Einstein kept the formulae, dropped the medium and changed the meaning of time.
Twins, tigers and promotions
Paul Langevin's twin paradox, debated at the 1911 Solvay Conference: a rocket twin returns ten years older to an Earth twin fifty years older. The situation is not symmetrical, because only the rocket twin accelerates and turns around. Atomic clocks flown on airliners confirmed time dilation in 1971. In the tiger-and-cage puzzle, the falling cage tilts in the tiger's frame because simultaneity differs. Punch ran the limerick of young lady Bright, who "came back the previous night".
1909: University of Zurich, after rival Friedrich Adler argued for him; at Salzburg he presents E = mc² and wave-particle duality.
1910: son Eduard born.
1911: Prague (office next to an asylum); first Solvay; meets Marie Curie.
1912: ETH professor; the Nobel goes to Nils Dalén for lighthouses.
1913-14: Prussian Academy and Kaiser Wilhelm Institute: "gambling on me as if I were a prize hen".
The marriage breaks
Fame cost him his family. Einstein compared life with Mileva to a cemetery; friends blamed either her bitterness or his absences, and Kaku declines to choose. The Berlin move of 1914 was the breaking point: she took the boys back to Zurich, and Einstein cried all the way home after losing custody. His double cousin Elsa Löwenthal, divorced with daughters Margot and Ilse, sociable and protective where Mileva was withdrawn, became his companion and later his second wife. The pattern of older partners (Marie, Mileva, Elsa) that began in Aarau continued.
At Salzburg (1909) he publicly presented both E = mc² and wave-particle duality, already stretching beyond the relativity paper alone. The climb from patent clerk to Prussian Academy ("gambling on me as if I were a prize hen") took less than a decade, but the personal cost was permanent estrangement from Mileva and, later, a tragic distance from Eduard.
Why 1905 was a miracle year
Four papers in one year, written at Kramgasse 49 after days at the patent office, rival Newton's plague-year output of 1666. Relativity alone would have made a career; with the photon, Brownian motion and E = mc² the clerk had remade light, matter and energy. Early silence (except Planck) shows how far ahead the work sat. Within a decade he had risen from technical expert third class to the Prussian Academy, and the personal cost (estrangement from Mileva, later Eduard's illness) tracked the fame.
Miracle year outputs and what each overturned.
Besso, the storm and the four papers
Around May 1905 Einstein laid the decade-old paradox before Michele Besso. The next day: "Thank you, I've completely solved the problem." The key was time: "Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity." He owed more to Maxwell, he said, than to anyone. On the Electrodynamics of Moving Bodies appeared in Annalen der Physik volume 17 (September 1905); he found the Lorentz contraction independently. A late-1905 footnote paper gave E = mc²; by 1907 he called it the theory's most important consequence, predicting a tiny mass loss in radium still too small to measure.
The photoelectric paper (Heuristic Point of View...) used Planck's 1900 quantum to explain Hertz's 1887 effect. Brownian motion (Movement of Small Particles..., after Robert Brown 1828) made atoms unavoidable. Minkowski's verdict: separately, space and time had "vanished into the merest shadows." Einstein shrugged that with mathematics "you can prove anything"; content mattered more.
Climb after silence
Planck sent Max von Laue to Bern in summer 1906. High-speed electron mass increase (1908) and a Zurich post followed. The 1909 Salzburg maiden lecture faced Planck in the room. First Solvay (1911, funded by Ernest Solvay) put him among the world's leaders. Returning to the Polytechnic (by then ETH) as professor was personal revenge on the place that had scorned the student. Berlin's offer made him feel like a "prize hen" who might not "lay another egg"; Academy members mostly displayed "peacock-like grandeur" but were "quite human." Elsa, the cousin who drew him to Berlin, kept the withdrawn life from becoming lonely.
After 1905: from silence to Berlin.
Who had which piece of relativity before 1905, and what Einstein changed.
General Relativity and "the Happiest Thought of My Life"
Two holes and a happy thought
Special relativity covered only steady motion, yet nearly everything accelerates. And it contradicted Newton, whose gravity acts instantly, while relativity says a change on the Sun should take eight minutes to reach us. Planck warned: "you will not succeed, and even if you succeed, no one will believe you", but if he did, "you will be called the next Copernicus".
The first consequence: a flashlight beam in an accelerating rocket droops, so gravity must bend light. The Sun could deflect starlight, which would be visible during a solar eclipse when compared with night photographs of the same stars.
From merry-go-round to marbles
Paul Ehrenfest's spinning disc: the fast-moving rim contracts while the slow centre does not, so the circumference becomes less than π times the diameter, like the Arctic Circle on a curved Earth. Space is curved.
Einstein's second picture: Newton's pull versus Einstein's push.
The merry-go-round argument: rotation warps geometry, so gravity must be curved space.
Put a rock on a bed and roll a marble past: it curves around the dip. Gravity does not pull; space pushes. Remove the Sun and a ripple of warped space spreads at light speed. Einstein told his son Eduard that a blind beetle on a curved branch doesn't notice the curve: "I was lucky enough to notice what the beetle didn't notice." Newton had confessed hypotheses non fingo about gravity's cause; now force was revealed as geometry, like ants tugged left and right as they walk over a crumpled sheet.
Riemann to the rescue, then three lost years
"Grossmann, you must help me or else I'll go crazy!" Marcel Grossmann found the tool: Bernhard Riemann's 1854 geometry of curved spaces in any dimension, built on non-Euclidean work by Lobachevsky, Bolyai and Gauss (who measured a mountain-top triangle in the Harz but never published). Once dismissed as the most "useless" branch of mathematics, tensor calculus became the language of the universe.
- General covariance. Equations must keep the same form in any coordinates, like a tabletop's area under a twisted fishing net. This leaves very few building blocks, chiefly the Ricci curvature.
- The 1912 mistake. Einstein had essentially the right theory in 1912, then dropped it, believing it broke Mach's principle because the same matter seemed to allow more than one field. The Einstein-Grossmann theory that followed did not even reproduce Newton.
- Rescue by war. Erwin Freundlich's expedition to the Siberian eclipse of 21 August 1914 was seized when war broke out. Had it gone ahead, it would have contradicted the wrong theory then in hand.
| Test | Prediction | Fate |
|---|---|---|
| Bending of starlight | 1.7 arc seconds (double the 1911 value) | Eclipse of 1919 |
| Gravitational red shift | Light loses energy climbing out of gravity | Lab-confirmed about 40 years later |
| Mercury's perihelion | Extra shift of about 43" per century | Matched (42.9") in Nov 1915 |
November 1915
Astronomers had explained wobbles in Uranus by finding Neptune (1846), but the search for Vulcan inside Mercury's orbit came up empty. Mercury's perihelion advanced by about 43" per century beyond Newton's prediction; no planet was there to cause it. In November 1915 Einstein returned to the Ricci curvature and saw that the multiple fields he had feared were mathematically equivalent. He then checked trial equations, ten of them instead of Newton's one, against the Newtonian limit, and got 42.9" for Mercury. "For some days, I was beyond myself with excitement." The final equation is about an inch long. Victor Weisskopf compared the reaction to a peasant seeing his first tractor: "But where is the horse?" Three years of wrong turns ended in a week of triumph; the 25 November presentation to the Prussian Academy fixed the field equations that still stand.
November 1915: three lost years end as the final field equations explain Mercury.
David Hilbert, who had heard six two-hour lectures by Einstein at Göttingen, wrote down the action and published, Kaku says, six days earlier; the Einstein-Hilbert action keeps both names. Kaku's moral: mathematicians work in self-consistent provinces, while physicists are driven by a few physical principles.
War, Adler, collapse, Elsa
Ninety-three intellectuals, Planck among them, signed the nationalist "Manifesto to the Civilized World". Physician Georg Nicolai circulated a counter-manifesto; only four signed, Einstein included: "what a sorry species of animal one belongs to." In 1916 his friend Friedrich Adler shot Austrian prime minister Count Stürgkh, then wrote a critique of relativity in his cell. His father cited it as proof of madness, and the death sentence became life imprisonment (Adler was freed in 1918). In 1917 Einstein collapsed with an ulcer, losing 56 pounds in two months. Elsa nursed him, and they married in June 1919.
Lost notebooks and the 1912 theory
Most biographies leap from the 1907 daydream to a finished theory in 1915, as if the equations arrived fully formed. The "lost notebooks" analysed in recent decades show otherwise: false starts, discarded tensors and three years spent on the wrong Einstein-Grossmann (Entwurf) theory. In 1912, guided by general covariance, Einstein had essentially the right Ricci-based equations, then abandoned them because he thought they broke Mach's principle (one mass distribution seeming to allow more than one field). He chased an incorrect idea until November 1915, when he saw that the multiple fields were mathematically equivalent and returned to the discarded equations.
Newton himself had asked whether bodies "bend" light rays, strongest at least distance. Einstein's 1911 papers put a number on the bend, still half the final value. He begged support for Erwin Freundlich's Siberian eclipse of 21 August 1914, even offering 2,000 marks of his own savings if everything else failed. War cancelled the trip; had it gone ahead, the wrong half-value theory then in hand would have been falsified in public.
Naming, Mercury and Hilbert
He began to call the 1905 work the "special theory of relativity" to mark it off from the more powerful "general theory" needed for gravity. Urbain Le Verrier had flagged Mercury's perihelion anomaly in 1859 (later refined near 43" per century); Neptune's discovery in 1846 had saved Newton for Uranus, but no Vulcan saved him for Mercury. After the 42.9" match Einstein wrote that his "boldest dreams have now come true" and that anyone who truly understood the theory could scarcely escape its charm. Max von Laue called it "of incomparable beauty."
David Hilbert joked that "physics is too important to be left to the physicists." He heard Einstein's six long Göttingen lectures, wrote an action principle and raced into print. Whatever the priority dispute, the lasting lesson Kaku draws is methodological: mathematicians seek self-consistent provinces; physicists are driven by a few physical principles until the math is forced to obey them.
War and the body
The "Manifesto to the Civilized World" bound "seventy million Germans" to the army and painted enemies as "Russian hordes allied with Mongols and Negroes". Einstein's counter-sign: "what a sorry species of animal one belongs to." Friedrich Adler's cry as he shot Count Stürgkh was "Down with tyranny! We want peace!" The cell critique of relativity became a legal shield against the gallows. Collapsing in 1917 with an ulcer, Einstein lost 56 pounds in two months; Elsa's nursing and their June 1919 marriage close the private arc of the public triumph.
1912 to 1915: the right theory found, lost and found again.
Equivalence principle as elevator: gravity and acceleration feel the same.
The New Copernicus
The eclipse
Arthur Eddington, Quaker, conscientious objector and secretary of the Royal Astronomical Society, was spared prison on condition that he lead the eclipse expedition, a political compromise that put a pacifist in charge of testing a German theory in wartime's aftermath. He went to Príncipe off West Africa; Andrew Crommelin went to Sobral, Brazil. On 29 May 1919 clouds parted just in time at about 1:30 pm. Star plates taken during totality would be compared with night plates of the same field: any shift of apparent position near the Sun's limb was the bending.
The 1919 eclipse test: three predictions, two expeditions, one verdict.
At the joint Royal Society and Royal Astronomical Society meeting on 6 November 1919, Sir Frank Dyson announced the confirmation, and J. J. Thomson called it "one of the greatest achievements in the history of human thought... a whole continent of new scientific ideas". Whitehead felt the air of "a Greek drama". Told that only three people understood the theory, Eddington paused: "I was wondering who the third might be." The Times headline: "Revolution in Science... Newton's Ideas Overthrown... Space 'Warped.'" The New York Times sent its golf correspondent, Henry Crouch.
A war-weary public embraced a pacifist Jew confirmed by a pacifist Quaker, a messenger from the stars with flaming hair and one-liners. Einstein joked that in Germany he was a "German man of science" and in England a "Swiss Jew", and that the labels would swap if he fell from favour. He soon felt he was "burning in Hell" with the postman as the Devil, in a "relativity circus".
Backlash
- Sceptics. The New York Times mocked British "intellectual panic". Charles Lane Poor of Columbia denied that the proofs existed. George Francis Gillette called relativity "cross-eyed physics" that would be "a joke" by 1940. Planck's rule applies: new truths win as opponents die out.
- Anti-Semites. Philipp Lenard, whose photoelectric data Einstein had explained, called him a "Jewish fraud" and backed "Aryan physics", joined by Johannes Stark. In August 1920 the Anti-relativity League hired Berlin's Philharmonic Hall to denounce him while he sat in the audience. At Bad Nauheim he was jeered under police guard.
- Murder. Rosa Luxemburg and Karl Liebknecht were killed in 1919. Foreign minister Walther Rathenau, Einstein's friend, was machine-gunned in June 1922. Lenard refused to close his institute and was nearly thrown in the river by workers. Rudolph Leibus offered a reward for killing Einstein and was fined sixteen dollars. Elsa wrestled an intruder at the door.
Tours, Zionism and the Nobel
Talks with Kurt Blumenfeld made him "conscious of my Jewish soul", and Chaim Weizmann recruited him to raise money for the Hebrew University.
1921: England: the Archbishop of Canterbury, Newton's tomb; Lord Rayleigh asks whether the Norman Conquest "has not yet occurred".
March 1922: Paris; some academics boycott him.
Late 1922: invited to Japan at Bertrand Russell's suggestion ("Lenin and Einstein"); en route, learns of the 1921 Nobel for the photoelectric effect, then lectures on relativity instead.
1923: prize money ($32,000) goes to Mileva under the divorce deal.
1930-31: Caltech, Hubble at Mt Wilson, Chaplin's City Lights premiere.
He had been passed over eight times (1910-21). Committee member Sven Hedin blamed Lenard's influence, and Robert Millikan recalled an evaluator who "couldn't understand" relativity and dared not risk it. Fame never faded: NYU's class of 1930 ranked him second only to Lindbergh, the Einstein Tower went up in Potsdam (1924), and he called himself an "artists' model". Chaplin: "they applaud you because no one understands you." Asked what it meant, Chaplin said: "Nothing."
Einstein's God
He mistrusted philosophy ("as if written in honey... Only mush remains") yet revered mystery: "Science without religion is lame, religion without science is blind." His 1929 image is a child in a vast library of books in unknown languages, sensing an order it cannot read. He separated the personal God who answers prayers from the God of Spinoza, expressed in the lawful harmony of nature, and believed only in the second.
Symbol and target
Fame made Einstein a symbol: pacifist, Jew, genius, refugee-to-be. Symbols attract both donations and death threats. The same tours that raised close to $1 million for the Hebrew University put him on stages where boycotts and jeers were real. Lenard's "Aryan physics" was not fringe crankery alone; it had Nobel prestige and state wind behind it after 1933. The 1919 confirmation had been a scientific event; by 1922 it was a political one. Einstein's reply to the hundred authorities, that one fact would suffice, is the methodological moral of the chapter: petitions do not bend starlight.
1919 eclipse path: from prediction to headline.
From confirmation to celebrity: the 1919 cascade.
The Big Bang and Black Holes
Newton's two headaches
In 1692 the minister Richard Bentley asked Newton why a finite universe of mutually attracting stars does not collapse. Newton's answer was an infinite, uniform universe. That raised Olbers' paradox: if stars fill infinite space, every line of sight ends on a star, so why is the night sky black? A finite static universe collapses; an infinite one should set the sky ablaze.
The fudge factor and its rivals
In 1917 Einstein found that his equations, applied to a uniform cosmos, would not sit still. He was "not revolutionary enough" to accept expansion (or contraction) as physical, so he added a cosmological constant, the only other term general covariance allows, proportional to the volume of space-time. It gives energy to empty space, a repulsion tuned to balance gravity exactly and hold a static universe. The term was mathematically natural; the motive was philosophical. When Hubble later showed expansion, Einstein dropped the constant and called it his greatest blunder. Decades on, the same term returned as dark energy.
| Model | Contents | Behaviour |
|---|---|---|
| Einstein 1917 | Matter + constant | Static, "matter but no motion" |
| de Sitter 1917 | Vacuum energy only | Expands with no matter |
| Friedmann 1922, Lemaître 1927 | Matter, expanding | Fate set by density |
Alexander Friedmann (who died of typhoid in 1925) and the Belgian priest Georges Lemaître showed that expansion arises naturally. Above a critical density (Kaku: about ten hydrogen atoms per cubic yard) the universe is curved like a sphere and recollapses. Below it, it is saddle-shaped and expands forever to a big freeze. At exactly the critical value it is flat.
Hubble settles it
Edwin Hubble first showed that nebulae such as Andromeda are other galaxies, so the universe went from one galaxy to billions in a year. Then, building on Vesto Slipher's 1912 red shifts and a 1928 talk with de Sitter, he found in 1929 that the farther a galaxy is, the faster it recedes (Hubble's law; the slope is the Hubble constant). At Mt Wilson in 1930 Einstein met him and called the constant his greatest blunder. When astronomers boasted that the 100-inch telescope revealed the universe's structure, Elsa replied: "My husband does that on the back of an old envelope."
From equations to an origin: how general relativity produced the big bang.
- The balloon. Galaxies are dots on an inflating balloon: from any dot, the others recede faster the farther away they are. A universe can be finite without a wall, like the Earth's surface; in a hypersphere, the farthest thing you can see is the back of your head.
- Age. Run the expansion backwards and you get an age (13.7 billion years from 2003 satellite data). Lemaître proposed a hot origin in 1931. Fred Hoyle, who favoured a rival theory, named it the "big bang" in 1949. Kaku: it was neither big (it began as a singularity) nor a bang (space itself expanded).
Black holes
In 1916, while serving on the Russian front and calculating artillery trajectories, Karl Schwarzschild found the first exact solution: a point mass. He died months later, aged 42, of a skin disease. Close to the mass is a "magic circle", the event horizon, from which not even light escapes. John Michell (1783) and Laplace had imagined Newtonian "dark stars".
From Schwarzschild's solution to observed black holes.
Waves and lenses
- Gravity waves. Fields that cannot outrun light must ripple. Einstein found approximate waves in 1916 and, with Nathan Rosen in 1937, an exact wave solution, but despaired of ever detecting them with the instruments of his day. The waves carry energy; orbiting masses spiral in as they radiate.
- Einstein rings. Prodded in 1936 by Czech engineer Rudi Mandl, who had pestered him with letters, he calculated that a foreground star could split and bend background light into a ring, a paper he dismissed as "of little value, but it makes the poor guy happy". Sixty years on, lenses became essential tools for weighing dark matter and magnifying the distant universe.
Falling into a black hole: two stories that are both true.
Cosmological constant: rejected, then rediscovered as dark energy.
Unification and the Quantum Challenge
Marble and wood
Almost as soon as special relativity was finished in 1905, Einstein aimed higher at general relativity.
He was not the first. Michael Faraday, working at the Royal Institution, dropped magnets from London Bridge and metal pieces from a lecture-room ceiling onto cushions, hoping magnetism or induced current would drag against gravity. Every trial failed. Faraday still wrote that the negative results "do not shake my strong feeling of the existence of a relation between gravity and electricity". Riemann, founder of curved space in any dimension, believed both forces were geometry, but he had neither a picture nor field equations, so the idea went nowhere.
Einstein's image was marble against wood. Marble is the elegant geometry of smoothly warping space-time, the stage on which stars and galaxies play. Wood is the gnarled jungle of matter and the quantum, growing in unpredictable ways as new particles keep being found. The defect in his own equations was that wood determines how marble bends. The strategy was therefore clear: make wood out of marble, so that particles become smooth kinks or knots in space-time rather than singularities where fields go to infinity. From a distance a kink looks like a particle; close up it is only a wrinkle in the rope.
| Attempt | Idea | Fate |
|---|---|---|
| Weyl (1918) | Add scale symmetry to Einstein-Maxwell | Lengths and atomic clocks change round a loop; too much symmetry |
| Eddington (1923) | "Pre-geometric" Ricci theory; distance emerges last | Pauli: "no significance for physics"; Einstein agreed |
| Kaluza (1921), Klein (1926) | Fifth dimension | Maxwell falls out of 5-D gravity; no electron found |
| Post-Riemannian geometry | Torsion, twisted spaces, "theory of connections" | No guiding principle; returned decades later in strings |
Hermann Weyl (1918) impressed Einstein at first ("a masterful symphony"). He folded Maxwell into the equations and demanded covariance under scale transformations that expand or contract all distances. The catch: travel a closed loop and you return shorter, or with clocks ticking at a new rate. Vibrating atoms would change frequency after a circuit. Nature does not use that much symmetry for the visible universe, so the theory was abandoned.
Arthur Eddington (1923) tried a Ricci-based theory with no metres or seconds until the last step ("pre-geometrical"). Electromagnetism was meant to emerge as a piece of curvature. Wolfgang Pauli said it had "no significance for physics"; Einstein panned it as empty of physical content.
Why unification stalled: the three-step method that worked twice had no third picture.
The fifth dimension
What rocked Einstein was a 1921 paper by an obscure Königsberg mathematician, Theodor Kaluza (Kaku spells him "Theodr"). Kaluza wrote Einstein's equations in five dimensions (four of space, one of time), which takes almost no work since the equations extend to any dimension, then split off the fifth. Out came gravity and Maxwell's eight equations: light as ripples in an extra dimension. Einstein wrote, "The idea of achieving [unification] by means of a five-dimensional cylinder world never dawned on me…. At first glance, I liked your idea enormously." Weeks later: "The formal unity of your theory is startling."
Oskar Klein (1926) suggested the fifth dimension is curled up smaller than an atom. Chlorine gas released in a room fills every nook and does not vanish into a hidden direction, so any extra dimension must be tinier than an atom. Kaku's image is fish under lily pads who treat their pond as two-dimensional; raindrop ripples from the third dimension look to them like a mysterious illuminating force. We are the fish. Light is the ripple we feel from the curled fifth dimension.
Einstein could not derive the electron and lost interest, half fearing the fifth dimension was a mathematical fiction. Kaku calls it a missed chance. More dimensions turn Maxwell's field into Yang-Mills fields; Klein glimpsed them in the late 1930s, but the work was forgotten in the chaos of war and rediscovered only in the mid-1950s. Those fields now underpin nuclear physics. Another twenty years later, Kaluza-Klein returned as string theory.
Public curiosity ran wild. A progress report to the Prussian Academy was pasted in Selfridges' window; Eddington wrote that large crowds gathered to read all six pages. Hundreds of reporters camped outside Einstein's home. Pauli, unsparing ("It is not even wrong"; "I do not mind if you think slowly, but I do object when you publish more quickly than you think"), said what God has torn asunder, let no man join. Ironically, Pauli later caught the bug himself.
Without a picture or principle, Einstein urged mathematicians into post-Riemannian geometries with torsion and twisted spaces. Those abstracts sat unused for about seventy years, until superstrings. He would have traded all the adulation for one simple physical image to guide the path.
Godfather of the quantum
- Bose-Einstein condensates (1924). Satyendra Nath Bose, an Indian physicist whose statistical papers had been rejected, treated photons as identical and asked Einstein to look. Bose had made unjustified assumptions, yet the final answer looked right. Einstein translated the paper into German, got it published, and extended it to atoms near absolute zero. All atoms of a given kind are indistinguishable; you cannot label hydrogen the way Boltzmann and Maxwell labelled rocks. Cool a gas to about a millionth of a degree above absolute zero and the atoms fall into one state, a "superatom" vibrating in lockstep like a stadium wave. Technology of the 1920s could not reach those temperatures; the prediction waited about seventy years.
- Matter waves. In a 1909 lecture Einstein had shown light's dual nature. Building on that programme, graduate student Prince Louis de Broglie (1923) gave matter itself wave properties and explained some atomic mysteries; Einstein promoted the idea, and de Broglie won the Nobel. Erwin Schrödinger, a well-known ladies' man, wrote the wave equation over Christmas 1925 at the Villa Herwig in Arosa with an unknown companion (the "lady of Arosa" remains unidentified among many candidates). Within months the equation made Bohr's hydrogen rules calculable and turned chemistry, Dirac boasted, into applied physics. High-school "orbitals" are its solutions.
- Dirac and antimatter. Paul Dirac made the wave equation relativistic, explained spin ½ (matching Stern-Gerlach), and from the overlooked square root in E = ±mc² predicted a mirror world of antimatter. Heisenberg called it "learned trash which no one can take seriously" until the positron appeared in 1932. Heisenberg later admitted antimatter was "perhaps the biggest jump of all the big jumps in our century." Kaku notes Einstein had entertained a related charge-reversal symmetry in 1925 but never pressed priority. Dirac's equation is engraved in Westminster Abbey near Newton's grave. Schrödinger and Dirac were polar opposites: one always with a companion, the other painfully shy and a man of few words.
- Probability. Max Born (1926): the Schrödinger wave does not describe the electron but the probability of finding it ("probability itself propagates in conformity with the laws of causality"). The absolute square of the wave is the chance at a point. Particles leave tracks; waves give odds. Heisenberg, after a night arguing with Bohr, walked through Faelled Park and saw that to locate an electron you must shine light on it, and the photons knock it. Uncertainty principle: position and momentum cannot both be known exactly (product at least Planck's constant over 4π). Even God cannot know both. Determinism (Newton's clock wound at the beginning of time) dies. Einstein to Born, December 1926: "Quantum mechanics calls for a great deal of respect. But some inner voice tells me that this is not the true Jacob…. He doesn't throw dice." On Heisenberg: "Heisenberg has laid a big quantum egg. In Göttingen they believe in it (I don't)." Schrödinger said that if his equation only gave probabilities he regretted having anything to do with it. Einstein said he would have become a "cobbler or employee in a gaming house" had he known his revolution would let chance into physics.
Einstein as godfather of the new quantum theory: each seed he planted or promoted.
Einstein versus Bohr
The camps split. Einstein, with Schrödinger and de Broglie, clung to determinism. The larger camp under Niels Bohr accepted uncertainty and average causality. They were polar opposites: Einstein the bookish child who wrote lyrical prose and bantered with journalists; Bohr the Danish soccer star who mumbled, repeated a single word when thinking, and dictated every paper first to his mother, then his wife (once interrupting his honeymoon), sometimes rewriting over a hundred times with the whole lab. Pauli, invited to Copenhagen, said he would come "if the last proof is sent away". Both men lived for physics; Bohr scribbled on goal posts; both needed sounding boards (Bohr was helpless without an assistant's ear).
The showdown was the Sixth Solvay Conference in Brussels, 1930. Einstein offered a photon box: open a shutter for a precise moment, release one photon, then weigh the box to get the energy exactly, beating uncertainty. Paul Ehrenfest watched Bohr reel: "To Bohr, this was a heavy blow…. Einstein, a majestic figure, walking calmly with a faint ironical smile, and Bohr trotting along by his side, extremely upset." All Bohr could mumble that evening was "Einstein… Einstein… Einstein." Overnight he found the flaw in Einstein's own general relativity: the lightened box rises in gravity, clocks run differently where gravity is weaker, and the restored uncertainties match Heisenberg exactly. When Einstein said God does not play dice, Bohr reportedly fired back, "Stop telling God what to do." Einstein admitted the theory "undoubtedly contains a piece of definitive truth." Wheeler called it "the greatest debate in intellectual history that I know about."
The Einstein-Bohr rounds: each thought experiment against uncertainty, and Bohr's reply.
Einstein wrote that he had thought a hundred times as much about the quantum problems as about general relativity. He accepted quantum mechanics as "the most successful physical theory of our period", nominated Schrödinger and Heisenberg for the Nobel (1929), and shifted strategy: not to prove the theory wrong, but to absorb it into a unified field theory, as relativity had absorbed Newton. Completeness, not overthrow, was the goal. Biographers who cast him as a reactionary dinosaur, Kaku says, miss the point.
Matter from geometry
In 1935, with Rosen, he cut the singularities out of two black-hole sheets and glued them together: a smooth "Einstein-Rosen bridge" that might be a particle. It was the first wormhole in physics, the scientific cousin of Alice's looking glass. The hope was a singularity-free geometry whose kinks ("solitons") would be electrons, so that chance never had to be put in by hand. Too much of particle physics (mass, spin, charge) failed to emerge, and the picture never came. By the late 1920s the two towers of physics stood side by side: relativity for the very large, quantum theory for the very small. Einstein's remaining decades would be spent trying to join them.
Quantum challenge: from Solvay to EPR.
War, Peace, and E = mc²
Exile
The Depression fed the Nazis. One Hundred Authorities against Einstein appeared in 1931; he replied that if relativity were wrong, one fact would suffice, not a hundred authorities. Leaving his summer house at Caputh in December 1932 for a visit to the United States, he told Elsa: "Turn around, you will never see it again." After 30 January 1933 the regime seized his property (the "weapon" found at Caputh was a bread knife), barred him from the Prussian Academy and burned his books on 10 May. A Nazi magazine captioned his photograph "Not yet hanged." Facing Hitler, he dropped absolute pacifism: "if I were a Belgian, I would not refuse military service." Visiting Churchill, he wrote in the guest book under address: "None." Stateless again in spirit, he became the world's most famous refugee scientist.
- The exodus. The civil service law forced out nine Nobel laureates and about 1,700 faculty members in a year. Szilard left with his savings in his shoes. Haber, a patriot who had developed poison gas, fled. Schrödinger, who was not Jewish, was beaten for confronting storm troopers. Bohr escaped Denmark in 1943.
- Planck's private plea to Hitler (May 1933) met a tirade: "There is simply no language in which one can talk to such men." His son was later executed after the plot against Hitler.
Princeton
Abraham Flexner's new Institute for Advanced Study (backed by $5 million of Bamberger department-store money) offered freedom from teaching and from the politics of a university faculty. Princeton was "a quaint ceremonious village of puny demigods on stilts". He asked for a "large wastebasket... so I can throw away all my mistakes"; a letter addressed only to "Dr. Einstein, America" reached him. Sailors, schoolchildren and cranks wrote constantly. There were private blows too: Eduard was diagnosed with schizophrenia (1930) and spent much of his life institutionalised; Paul Ehrenfest, witness to the Bohr debates, killed himself and his disabled son (1933); Elsa died (1936). Einstein lived "like a bear in my den" with sister Maja, stepdaughter Margot and secretary Helen Dukas, becoming the sockless, sweatered sage of legend while still filling notebooks with unified-field attempts.
From E = mc² to the bomb
As early as 1920-21 Einstein foresaw nuclear energy, its use in weapons and the practical difficulty: "firing at birds in the dark, in a neighborhood that has few birds". Rutherford, discoverer of the nucleus, still called nuclear power "moonshine". The chain that turned a 1905 footnote into a weapon ran through Chadwick's neutron (1932), Hahn and Strassmann's fission (1938), and Meitner and Frisch's calculation that the missing mass times c² equalled about 200 MeV per split.
From the 1939 letter to Hiroshima: Einstein's signature and his limited role.
The chain of discoveries that turned a 1905 footnote into a weapon.
Meitner saw that the missing mass of the fission fragments, multiplied by c², gave exactly the 200 million electron volts released. Bohr slapped his forehead: "Oh, what fools we all have been!" When Fermi and Joliot-Curie found two neutrons per split (2, 4, 8, 16...), Fermi pictured one bomb erasing the New York skyline. Szilard and Wigner drove to Long Island; Einstein's letter warned that "a single bomb of this type, carried by boat... might well destroy the whole port". Roosevelt: "Alex... see that the Nazis don't blow us up. This requires action." At first only $6,000 was allocated, until the British Frisch-Peierls report pushed the project forward in late 1941. Lise Meitner refused to join ("I will have nothing to do with a bomb!").
Einstein was never asked. Vannevar Bush said that showing him the project was "utterly impossible" given Washington's view of his history. Army intelligence doubted that "a man of his background" could become a loyal American. His FBI file ran to 1,427 pages under J. Edgar Hoover. The Navy did consult him on explosives ("in the navy without having to get a haircut"). In August 1945, told the news by Dukas at Saranac Lake, he said "Oh, Weh." Joseph Rotblat, the only scientist to quit Los Alamos on principle, later won the Nobel Peace Prize.
After the bomb
On Time's 1946 cover a mushroom cloud rose behind him, the public face of a weapon he had not built and had been barred from seeing. World War IV, he warned, would be fought with rocks. He chaired the Emergency Committee of Atomic Scientists, raised money for education about the bomb and pressed for world government as the only long-term brake on national arsenals. He later called signing the 1939 letter "the one great mistake in my life", a judgment Kaku softens but does not hide the arc of: warn, then regret, then campaign.
- Unification in isolation. Schrödinger announced his own "miracle" unified theory at a Dublin press conference (with de Valera present), but it was one Einstein had already discarded. Einstein: "an ostrich who forever buries its head in the relativistic sand"; "Subtle is the Lord, but malicious he is not", later "Maybe God is malicious." Pauli and Heisenberg caught the bug too. Bohr: "your theory is crazy... whether your theory is crazy enough". Pauli sent a blank sheet: if that was the theory, this was a Titian.
- Gödel's universe (1949). His neighbour Kurt Gödel found a rotating universe in which a round trip arrives before departure. Einstein dismissed it because the real universe expands rather than rotates, but the door to time travel stayed open.
- The echo of creation. George Gamow's group (Alpher and Herman, 1948) predicted a microwave afterglow of about 5 K; it was found at 2.7 K.
1951: Maja dies.
1952: Ben-Gurion offers him the presidency of Israel; he declines.
March 1955: Besso dies: "the separation between past, present, and future is only an illusion, however tenacious."
18 April 1955: dies of a burst aneurysm, unfinished unified-field calculations on his desk. Herblock's cartoon: "Albert Einstein lived here."
German bomb, Allied bomb, and the letter's aftermath
Szilard and Eugene Wigner drove to Long Island in 1939; the letter went to Roosevelt through banker Alexander Sachs. Early funding was only about $6,000 until the British Frisch-Peierls memorandum reached Washington in autumn 1941 and the all-out decision of 6 December 1941 followed. The Manhattan Engineer District was formalised in August 1942. Einstein, kept out, still consulted for the Navy on explosives in May 1943, joking he was "in the navy without having to get a haircut."
On the German side, Albert Speer shelved a crash bomb programme in 1942 when told it would take about three more years; Hitler wanted results in months. Operation Gunnerside (February 1943) wrecked the Vemork heavy-water plant after a failed 1942 glider raid. Saturation bombing forced Heisenberg's group into a rock cellar at Haigerloch; they never sustained a chain reaction. Lise Meitner refused bomb work: "I will have nothing to do with a bomb!"
Private losses and unfinished quests
Eduard ("Tedel") broke down after a failed romance in 1930; Einstein said he had "seen it coming... ever since Tedel's youth" and later felt the illness had "severed the strongest tie he had with a human being." Ehrenfest's 1933 murder-suicide, Elsa's death in 1936, Mileva's death in 1948 (about 85,000 francs found stuffed in her bed, used for Eduard's care), Maja in 1951, and Michele Besso in March 1955 mark the narrowing circle. Offered the presidency of Israel after Weizmann's death (1952), he declined: he would "rather walk naked down Broadway" than take the ceremonial post, in the anecdote Kaku retells of his distaste for official pomp.
At the Institute he told visitors he needed a large wastebasket for mistakes, and that anything really new is invented in youth; later one becomes "more experienced, more famous, and more stupid." On his seventieth birthday (1949) the festschrift felt to him like "an impeachment" for refusing quantum orthodoxy. Pauli later presented a Heisenberg-Pauli unified attempt at Columbia with a blank transparency: if that was the theory, this was a Titian. Gödel's 1949 rotating cosmos allowed closed timelike curves; Einstein rejected it cosmologically (the real universe expands) but could not close the mathematical door. He died on 18 April 1955 of a burst aneurysm, still trying, in his phrase, to "read the mind of God."
Exile to Princeton: private losses around the public legend.
Conscience after Hiroshima
Einstein had been kept outside the Manhattan Project, yet the public linked his face to the mushroom cloud. He used that fame to push for international control of atomic energy and for a world government strong enough to police national arsenals. Joseph Rotblat's principled exit from Los Alamos, later honoured with the Nobel Peace Prize, stood as the path Einstein morally preferred but could not take from outside. The Emergency Committee raised funds and published; the Doomsday Clock tradition of the Bulletin is the institutional heir of that anxiety.
After the bomb: Einstein's public campaign versus his private unfinished theory.
Einstein's last decade: science, conscience and unfinished work.
Einstein's Prophetic Legacy
The quantum legacy
When Einstein wrote on Bose-Einstein condensation in 1924, he did not expect to see it. One would need temperatures near absolute zero before quantum states collapsed into a giant superatom.
- Superatoms made. In 1995 Eric Cornell (NIST) and Carl Wieman (Colorado; Kaku spells "Weiman") cooled about 2,000 rubidium atoms to twenty-billionths of a degree into a Bose-Einstein condensate. Wolfgang Ketterle (MIT) made larger sodium ones that showed interference, proving the atoms acted as the predicted superatom, and in 1997 an atom laser: a laser hit the condensate and turned the atoms into a synchronised beam, the matter analogue of coherent light. All three shared the 2001 Nobel "for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms". Kaku floats uses in nanotechnology (atomic films for semiconductors), quantum computing that might replace silicon, and even condensates as a piece of dark matter.
- The cat returns. In the 1930s-40s, while quantum physicists collected Nobels "like apples picked off a tree", deeper questions were brushed under the rug. Now that "easy" questions about metals and semiconductors are picked clean, Einstein's hard ones return. Single atoms are movable (IBM spelled its name with them; scanning tunneling microscopes build atomic abacuses), so Bohr's "wall" between the quantum and everyday worlds looks shaky. The fate of computer technology, a large fraction of world wealth, may hang on the answer if future transistors are single atoms.
| Answer to the cat | Claim | Problem |
|---|---|---|
| Copenhagen (Bohr) | A wall separates micro from macro; observation collapses the wave | Where is the wall when we move single atoms? |
| Consciousness (Wigner) | A mind collapses it; "Wigner's friend" watches the watcher | Infinite chain; some read it as cosmic consciousness or God |
| Many worlds (Everett, 1957) | The universe splits at each quantum event | Wheeler later called it "metaphysical baggage" |
| Decoherence | Branches stop interfering; waves never collapse | Ends up as many worlds on different "radio stations" |
Wigner went further: "The very study of the external world led to the conclusion that the content of the consciousness is the ultimate reality." Planck: "Science cannot solve the ultimate mystery of Nature… we ourselves are part of the mystery." Everett, Wheeler's student, said the cat is dead in one universe and alive in another; a cosmic ray that miscarries Churchill's mother splits us from a world where the Nazis won; a quantum nudge that misses the Yucatan comet leaves Manhattan to dinosaurs. Wheeler abandoned the idea.
John Bell (1964; Kaku says 1965) at CERN turned EPR into a test. Alain Aspect in Paris (1982; Kaku says 1983) confirmed quantum mechanics: "Einstein was wrong about his criticism of the quantum theory." Most now find Copenhagen incomplete. Decoherence is favoured by several Nobel laureates. A cat of about 10²⁵ atoms has dead and live waves that coexist but no longer sense each other, like radio stations sharing a room (Steven Weinberg's image). Waves never "collapse"; they separate. The cost: parallel worlds where the Nazis won or dinosaurs survived exist "in this very room" on other frequencies. Feynman: "nobody understands quantum mechanics."
Answers to Schrodinger's cat: each school and its cost.
Relativity under the microscope
1970: radio positions of quasars 3C 279 and 3C 273 bend as predicted.
1971: atomic clocks flown east and west (compared with the Naval Observatory) test both theories of relativity at different speeds and altitudes.
1977: Jesse Greenstein sees time slow on a dozen white dwarfs.
1989-93: Hipparcos (ESA) finds starlight bent from halfway across the sky, even from stars 1,500 times fainter than the Big Dipper; no eclipse needed in space.
1993: Nobel for Hulse and Taylor: pulsar PSR 1913+16, a double neutron star about 16,000 light-years away, orbits every 7 hours 45 minutes. Like spoons stirring molasses, the stars leave gravity-wave wakes, lose energy and spiral in by a millimetre per revolution, about a yard a year in an orbit 435,000 miles across, matching Einstein to 99.7%. They will merge in about 240 million years.
- Gravity waves direct. LIGO (two sites at Hanford, one at Livingston; with VIRGO in Pisa, TAMA near Tokyo, GEO600 in Hanover) uses laser arms like a giant Michelson-Morley instrument. Final cost about $292 million plus $80 million for upgrades, the largest NSF project. A wave shifts the arm lengths and makes an interference pattern; only a wave bigger than Earth fires detectors worldwide at once. Kaku expected LISA, three spacecraft 3 million miles apart in an equilateral triangle, around 2010, delicate enough to sense a shift of one-hundredth an atom's width and peer to the first trillionth of a second after the big bang, perhaps reading the unified field itself.
- Lenses and rings. Einstein proved in 1936 that galaxies can focus distant light. First lens: quasar Q0957+561 (1979). First ring: MG1131+0456 (1988); about twenty fragments followed. The first complete ring (1938+666, 1997, Hubble plus Britain's MERLIN) is a second of arc across, a penny seen from two miles. Ian Brown (Manchester): at first it looked like a defect; then "a perfect Einstein ring!" Colleagues: "It's a bulls-eye!"
- The baby picture. Penzias and Wilson found the microwave background in 1965 with the Bell Labs Horn antenna while blaming pigeon droppings; R. H. Dicke identified it as Gamow's echo. COBE (1989) and George Smoot's Berkeley team mapped ripples from about 400,000 years after the bang. The media said "face of God"; Kaku says a baby picture. The ripples match quantum fluctuations demanded by uncertainty; without them the principle would have suffered a setback. Stretched by expansion, they seed today's lumpy galaxy clusters.
How Einstein's 'unobservable' predictions became instruments.
Dark energy and black holes
Supernovae (1998-2000) showed that the expansion is accelerating, ruling out a big crunch (and Hawking's backward-running time, which he retracted: people diving back onto boards and eggs leaping into shells). Previously some hoped enough matter would reverse expansion into a blue-shifted crunch, perhaps oscillating. The "greatest blunder" returned as dark energy, the largest store of energy in the cosmos. More vacuum means more push, a runaway. It fits Alan Guth's inflation: a large early cosmological constant drove exponential growth, then ordinary Friedmann-Lemaître expansion. Balloon data suggest approximate flatness; we are ants on a huge balloon. WMAP (2003): 4% atoms, 23% dark matter, 73% dark energy. Copernicus again: not even our atoms are typical. Dark matter already showed ordinary matter is a minority; dark energy dwarfs both.
Hubble and the VLA confirmed over fifty black holes, perhaps one in half of all galaxies. Gas whirls at about a million mph around those in M87 and NGC 4258; a central dot a light-year across can spin a galaxy 100,000 light-years wide. In 2002 a Milky Way black hole was weighed (Kaku: 2 million suns; modern figure about 4.3 million), so the Sun orbits a black hole roughly a tenth of Mercury's orbital radius. In 2001 a wandering Galactic black hole was tracked by lensing; any approach to the solar system would "eat up the entire solar system and not even burp." Roy Kerr's 1963 spinning solution collapses to a ring; centrifugal force can hold it open. Fall through and gravity is large but finite: in principle a shortcut to another universe, if the passage stayed open. Crossing the event horizon of a large Kerr hole might be "unforgettable" rather than instantly lethal.
The universe's energy budget, then and now.
Time machines
After Gödel, van Stockum's 1936 infinite spinning cylinder turned out to allow time travel. Kip Thorne's 1988 traversable wormhole needs negative energy, which exists in tiny amounts in the Casimir effect (1948): two plates in vacuum attract because some wave modes are excluded between them. Join two pairs of Casimir plates with a wormhole, fly one pair near light speed (or park it in a gravity well), and stepping through takes you into the past. Hawking asked where the tourists from the future are and proposed chronology protection, but "everything not forbidden is compulsory" (T. H. White's ants). Paradoxes are resolved either by Novikov's self-consistency ("We cannot send a time traveler back to the Garden of Eden") or by the timeline forking into a parallel universe.
The unified field theory reborn
The Standard Model covers three forces but is "supremely ugly", like a whale, an aardvark and a giraffe taped together, and blows up when gravity is added. Kaku's candidate is superstring theory: particles are notes on a vibrating string, physics is harmony, the universe a symphony.
Time-machine and odd geometries allowed by Einstein's equations.
Tests. The LHC might find sparticles; the neutral photino could be dark matter; LISA might hear the big bang; and if our universe is a membrane in hyperspace, gravity leaking into a parallel universe a millimetre away could alter the inverse-square law or explain dark matter. The real obstacle, Kaku says, is theoretical: solve the theory fully and it will prove a theory of everything "or a theory of nothing".
Kaku's verdict: Einstein founded general relativity, was godfather to the quantum theory and paved the way for unifying both. Crumbs from his plate keep winning Nobels; the derided unification programme is again centre stage.
Reading the legacy in 2026
Kaku wrote in 2003-04. The scorecard since then splits cleanly. Relativity's "unobservable" predictions (waves, shadows of black holes, precision clocks) paid out. Quantum questions Einstein forced (Bell, decoherence, condensates) became industries. Unification via strings did not find sparticles, extra dimensions or a unique vacuum. A fair reading of Chapter 9 keeps the prophetic arc for relativity and quantum foundations, and treats the string ending as advocacy: valuable as a map of hopes, not as a verdict.
Legacy scorecard: confirmed, pending, not found.
Relativity's delayed payoffs
Bose-Einstein condensation (1924 paper) waited until 1995; Cornell, Wieman and Ketterle shared the 2001 Nobel, and Ketterle's group made an "atom laser" in 1997. Bell's 1965 inequality turned Einstein's EPR critique into a laboratory programme. Everett's 1957 many-worlds answer to the cat remains contested; Feynman's line still stands: "nobody understands quantum mechanics."
Clock and light tests filled in: white-dwarf gravitational redshifts (Greenstein, 1977); jet-borne atomic clocks East and West (1971); Hipparcos (1989-93) measuring solar deflection on stars 1,500 times fainter than the Big Dipper. Hulse and Taylor (Nobel 1993) watched PSR 1913+16 spiral in every 7 h 45 m, radiating gravity waves. Einstein rings moved from theory (1936) to quasar Q0957+561 (1979), radio ring MG1131+0456 (1988) and near-perfect circles with Hubble and MERLIN (1997): "a perfect Einstein ring!"
COBE (1989) mapped the microwave afterglow Penzias and Wilson found in 1965. Dark energy, cousin of the cosmological constant Einstein introduced in 1917 and later disliked, returned as the largest energy budget after 1998-2000. A ~2 million solar-mass black hole was pinned to the Milky Way centre by 2002. Thorne's 1988 wormhole time-travel solutions and the Casimir effect (1948, measured) keep the speculative door that Gödel opened in 1949.
Strings as Kaku's heir
String theory, Kaku's candidate "final theory," curves space around a moving string exactly as 1915 gravity requires, and, like Kaluza-Klein (1921), can house electromagnetism in extra vibrating dimensions. Particle zoos with Greek names made Fermi wish he had been a botanist; Glashow joked the Nobel should go to whoever did not find a new particle. Einstein's own late method: "ferret out some general principle from nature"; "pure thought can grasp reality, as the ancients dreamed." Kaku's closing tribute reframes the fishing jab: after 1925 Einstein still stood on the two pillars, relativity and quantum theory, that every fundamental account must still join.
From paper predictions to instruments: selected relativity payoffs.
Main Points
- Think in pictures: Einstein's breakthroughs began with images a child could grasp, not with equations.
- Hunt for contradictions between successful theories: Newton against Maxwell, then Newton against relativity, opened each revolution.
- Picture, principle, symmetry is the method: a contradiction suggests a principle, which fixes a symmetry, which constrains the equations.
- Time and space are relative; the speed of light is not: drop universal time and the aether disappears.
- Mass is frozen energy (E = mc²): later the key to fission, the stars and the bomb.
- Gravity is geometry: matter curves space-time and space-time steers matter.
- Trust a good principle over a nagging doubt: Einstein had the right equations in 1912 and lost three years to a mistaken objection.
- Experiment decides: 1919 made him famous; newspaper editorials and "100 authorities" changed nothing.
- Equations can be wiser than their authors: expansion, black holes, waves and lenses were all in the theory before anyone believed them.
- Yesterday's blunder can be tomorrow's discovery: the cosmological constant came back as dark energy.
- Quantum mechanics won the debate; Einstein won better questions: Bell tests ruled out local hidden variables, and entanglement became a technology.
- Einstein wanted quantum theory completed, not overthrown, as relativity had absorbed Newton.
- Without a guiding picture, even genius drifts: the unified field theory failed for lack of data on nuclear forces.
- Science is social: Besso, Grossmann, Planck, Minkowski and Eddington were each essential.
- Isolation can help: the patent office gave Einstein freedom and a habit of stripping problems to their essence.
- Fame is double-edged: it brought crowds and influence, and made him the chief target of anti-Semites.
- Principles must meet reality: Einstein's pacifism yielded to the Nazi threat; he signed the bomb letter, then campaigned against the bomb.
- Personal costs were real: two marriages, a lost daughter and a son institutionalised sit alongside the triumphs.
- Unification through symmetry still drives physics, from Minkowski's space-time to supersymmetry.
- Judge long research programmes on decades, not years: the "wasted" late Einstein looks prophetic, though strings remain untested in 2026.
- Fame is a tool and a trap: it funded Zionist causes and arms control, and made him the chief target of "Aryan physics".
- A low-status job can be a gift: the patent office trained him to strip problems to essentials and left hours free.
- Priorities matter: antimatter, condensates and gravity waves looked like curiosities until instruments caught up.
- Moral principles meet history: absolute pacifism bent when Hitler rose; the bomb letter followed, then lifelong regret and campaigning.
- Check the popular story: Hilbert priority, EPR date, Mercury's 43", Wieman's spelling and string triumphalism all need a closer look.
Three pictures revisited: method, geometry, unfinished quest.
Frameworks and mental models
| Name | What it says | Use it when |
|---|---|---|
| Thought experiment | Imagine an idealised scene and follow the logic | Testing an idea before data exists |
| Picture, principle, symmetry | Image, then rule, then constraint on equations | Building a theory or model from scratch |
| Two pillars must agree | Contradiction marks where the breakthrough lies | Choosing which problem to attack |
| Correspondence | New theory must reduce to the old where the old works | Checking a new idea (Mercury, Newtonian limit) |
| Occam's Razor | Cut away ad hoc patches (aether, epicycles) | A theory needs ever more fixes |
| Marble vs wood | Seek elegant geometry beneath messy detail | Looking for a unifying structure |
| Absorb, do not overthrow | New theory completes the old in a limit | Facing a successful but incomplete theory |
| Equations wiser than authors | Solutions can outrun the maker's taste | A theory yields "absurd" predictions |
| One fact beats 100 authorities | Experiment, not petitions, decides | A consensus attacks a result |
Who's who
| Person | Role |
|---|---|
| Michele Besso | Friend and sounding board for 1905 |
| Marcel Grossmann | Notes, patent job, Riemann's geometry |
| Mileva Maric | Classmate, first wife, mother of Hans and Eduard |
| Elsa Einstein | Cousin and second wife |
| Max Planck | Quantum founder; Einstein's first champion |
| Hermann Minkowski | Recast relativity as space-time |
| Arthur Eddington | Led the 1919 eclipse test |
| Edwin Hubble | Expanding universe (1929) |
| Karl Schwarzschild | First exact solution; black holes |
| Niels Bohr | Copenhagen school; Einstein's great opponent |
| Erwin Schrödinger | Wave equation; the cat |
| Theodor Kaluza, Oskar Klein | Fifth dimension |
| Leo Szilard | Drafted the 1939 letter |
| Kurt Gödel | Time-travel universe (1949) |
| Philipp Lenard | Nobel physicist turned anti-Semitic foe |
| Satyendra Nath Bose | Statistics paper Einstein translated; BEC |
| John Bell | Theorem that made EPR testable |
| Kip Thorne | Traversable wormholes; LIGO science |
| Alan Guth | Inflation; large early cosmological constant |
About this book
Einstein's Cosmos: How Albert Einstein's Vision Transformed Our Understanding of Space and Time by Michio Kaku, 2004. This is a chapter-by-chapter study of the book, with summaries, maps, tables and diagrams; short quotations keep their page references. It is shared free for personal study, is not for sale, and is not endorsed by the author or publisher. Please read and buy the original.
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