Insight Editions · No. 235
Beyond Einstein
The Cosmic Quest for the Theory of the Universe
Michio Kaku and Jennifer Thompson
The history of unification told through simple physical pictures, from Newton’s falling moon to Maxwell, Einstein and Feynman, ending with the superstring as the candidate theory of everything.
A study guide to Beyond Einstein by Michio Kaku and Jennifer Thompson. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
All four forces and all matter may be notes on one vibrating string, which Kaku presents as the only theory that marries quantum mechanics with gravity.
Three centuries of unification, from Newton to M-theory (1995), plus cosmology, dark matter, extra dimensions and time travel.
10⁻³³ cm string length; 10¹⁹ GeV Planck energy; 10 and 11 dimensions; 19 free parameters in the Standard Model; SSC cancelled 1993.
Readers who want the logic of a theory of everything without equations, updated with 30 years of experiments.
The Book on One Page
Kaku and Thompson argue that physics is converging on the unified field theory Einstein failed to find, and that the superstring is its only serious candidate. The book is a history of unification told as a sequence of simple physical pictures: Newton's falling moon, Maxwell's dominoes, Einstein's trampoline, Feynman's Tinker Toys and, finally, a vibrating string whose notes are the particles.
- The problem. The twentieth century built two great theories that do not fit together: general relativity (gravity, the cosmos) and quantum mechanics (matter, three forces). Joining quantum theory to relativity produces infinities; joining it to gravity, with point particles, fails outright.
- The lesson of fifty years. Gauge symmetry tamed the infinities three times: QED (1949), the electro-weak theory (1971) and QCD. The more symmetry a theory has, the better behaved it is. The resulting Standard Model works perfectly and is ugly: three generations, nineteen free parameters, no gravity.
- The candidate. String theory, found by accident in 1968 and abandoned for demanding 26 or 10 dimensions and a graviton, was reborn in 1984 when Green and Schwarz showed it free of anomalies. It contains supersymmetry, conformal symmetry and E(8) × E(8), enough to cancel every divergence, with gravity as its lowest note.
- The test bed. With the SSC cancelled in 1993, Kaku turns to cosmology: the Big Bang restores lost symmetries, dark matter may be superpartners, cosmic strings may have seeded galaxies, and the extra six dimensions may have curled up when a ten-dimensional universe cracked.
- The fringe. Antimatter, parity and CP violation explain why matter survived; Gödel and NUT universes, Einstein-Rosen bridges and universes from nothing await quantum-gravity calculations that strings are supposed to make possible.
- The 1995 coda. M-theory unites the five superstring theories through duality in eleven dimensions.
- The 2026 verdict. Higgs found, top found, gravitational waves heard, black holes photographed; but no superpartners, no proton decay, no WIMPs, and some 10⁵⁰⁰ possible vacua instead of a unique answer. The book's history and physics hold up; its optimism about imminent confirmation does not.
| Ch | Title | One-line payload |
|---|---|---|
| Intro | Einstein's Unfinished Symphony | A boy's question about Einstein's last theory finally has a candidate answer. |
| 1 | Superstrings: A Theory of Everything? | Particles are notes of a string; strings may unite four forces, but testing needs Planck energies. |
| 2 | The Quest for Unification | Newton, Maxwell and Einstein each unified via a simple picture; Einstein failed by abandoning pictures. |
| 3 | The Quantum Puzzle | Quantum mechanics rules matter but rests on point particles, which explode into infinities with relativity. |
| 4 | The Riddle of Infinities | Gauge symmetry renormalized QED, the electro-weak force and QCD. |
| 5 | The Top Quark | The top completes the Standard Model, a triumph that is ugly, arbitrary and gravity-free. |
| 6 | The Birth of the Superstring Theory | Found by accident in 1968, killed by 26 dimensions, revived in 1984 by anomaly cancellation. |
| 7 | Symmetry: The Missing Link | Nature demands symmetry; broken symmetry explains why four forces appear today. |
| 8 | Supersymmetry | Boson-fermion symmetry cancels divergences, needs Grassmann numbers, and is still unseen. |
| 9 | Before the Big Bang | Forces freeze out as the universe cools; the Big Bang may be a ten-dimensional universe cracking. |
| 10 | The Mystery of Dark Matter | Zwicky and Rubin proved invisible mass; superpartners are a leading candidate. |
| 11 | Cosmic Strings | Galaxy clumping from COBE ripples, early dark matter, or giant defects of symmetry breaking. |
| 12 | Journey to Another Dimension | Kaluza-Klein, Flatland, hypercubes and black holes as bridges between universes. |
| 13 | Back to the Future | Antimatter, parity and CP violation explain why matter exists; time travel awaits quantum gravity. |
| 14 | Beyond Einstein | Symmetry and beauty as guides; a final theory gives the rules, not mastery of the game. |
| P | M-Theory | Duality reveals five string theories as one eleven-dimensional theory. |
Einstein's Unfinished Symphony
Kaku traces the book to a fourth-grade boy in Palo Alto who read, in 1955, that Einstein had died before finishing his greatest work, the unified field theory. Nobody, not teachers, librarians or later even physicists, could tell him what it was. Thirty years later the 1984 superstring breakthrough made that childhood question answerable, and this book is the answer he wanted to read as a boy.
The origin story
The boy reasoned simply: if Einstein was that great, his unfinished project must have been the crowning work of his career. The libraries held only incomprehensible quantum-mechanics texts, none of which even mentioned the unified field theory, and most physicists he later met shrugged it off as premature or presumptuous. Kaku himself grew cynical while working on string theory when it was still a theory of the strong interactions only.
- The neglected prophets. In the 1970s nobody took John Schwarz and Joël Scherk seriously when they proposed that a refined string theory might be Einstein's lost unified theory.
- The vindication. In 1984 a theoretical breakthrough (the Green-Schwarz anomaly cancellation, told in Chapter 6) made superstrings look like the best, and perhaps the only, candidate.
- The partnership. Kaku and the writer Jennifer Trainer Thompson had already co-written Nuclear Power: Both Sides; this second collaboration pairs a theoretical physicist's insider view with a writer's craft.
What makes this book different
The authors set superstrings inside three hundred years of physics rather than treating relativity, quantum theory or cosmology in isolation. The emphasis is on matter: how quarks, leptons, Yang-Mills particles and gluons can all be read as different vibrations of one string. The companion volume, Kaku's Hyperspace, covers the other half of the story, space and time, parallel universes, time warps and the tenth dimension.
The book's organising promise is that one object, a vibrating string, can explain both the zoo of particles and the four forces. Every later chapter is a step towards earning that claim.
This edition adds a 1995 Postscript on M-theory, which the authors called the most advanced version of string theory and possibly decisive for proving it. Three decades later M-theory remains mathematically central and experimentally untested; the boy's question has a richer answer, but not yet a confirmed one.
Superstrings: A Theory of Everything?
Kaku sets out the stakes: superstring theory replaces point particles with vibrating loops about 10⁻³³ cm long and claims to unite all four forces, including the gravity that defeated Einstein. It is the first framework in which quantum mechanics and general relativity fit together, and it makes wild predictions about ten dimensions, a sister universe and dark matter. Its fatal weakness is the flip side of its ambition: the energies needed to test it directly exist only at the beginning of time.
The claim and the hype
The chapter opens with the 1980s excitement. Edward Witten of Princeton predicted that superstrings would dominate physics for fifty years, called the theory "a miracle, through and through," and compared the moment to the birth of quantum theory. Science magazine likened it to the Holy Grail and to the step from real to complex numbers. Two of its creators, John Schwarz (Caltech) and Michael Green (Queen Mary College, London), half-jokingly called it a Theory of Everything (TOE).
The intoxicating idea is compression. The German Handbuch der Physik fills a whole library shelf; if superstrings are right, all of it could in principle be derived from a single equation.
Matter as music
Since Democritus coined atomos, science has assumed that the ultimate building blocks are points. Superstring theory says they are tiny vibrating strings, about 100 billion billion times smaller than a proton, far too small for any instrument; matter only looks point-like because our probes are crude.
The guiding analogy is the violin string. Thousands of years of trial and error produced the rules of harmony, yet all of them follow from one picture: a string resonating at different frequencies. No note, C or B flat, is more fundamental than another; what is fundamental is the vibrating string itself.
- Particles are notes. Each particle and each force carrier is a mode of vibration of the string; none is more fundamental than another.
- Gravity is the lowest note. The graviton comes from the lowest vibrational mode of a closed loop.
- Diversity is explained. Higher excitations give the other forms of matter, which is why the universe can hold billions of distinct particle types and substances.
The music created by the string is matter itself.Kaku and Thompson
The four forces
A force is anything that can move an object. Over two thousand years physics narrowed the list to four, and their dissimilarity is the puzzle the book sets out to solve.
| Force | What it does | Everyday or cosmic evidence | Key fact in the chapter |
|---|---|---|---|
| Gravity | Attractive; binds solar systems and galaxies | Falling apples, planetary orbits, stars kept from exploding | Dominant over trillions of miles; hardest to quantise |
| Electromagnetism | Holds electrons around nuclei; governs chemistry | Combed hair lifting paper; light, radio, X-rays | Beats gravity on earth down to about 10⁻¹³ inch (nuclear size) |
| Strong force | Binds protons and neutrons in nuclei | Starlight, the sun, the atomic bomb | Explains why only about 100 elements exist; bombs release over a million times dynamite's energy per pound |
| Weak force | Drives radioactive decay | Geiger-counter clicks, the earth's internal heat, reactor heat | Too fleeting to feel directly |
Two arguments in this section are worth keeping. First, the strong force versus electric repulsion balance explains the periodic table's limit: beyond about a hundred protons, even the strong force cannot contain the protons' mutual repulsion. Second, the sun would be a cinder if it burned coal; only nuclear energy lets stars shine for billions of years, so without the strong force there is no life.
One substance, many faces. Boil a glass of water and it becomes steam; freeze it and it becomes ice; it is still water. Turn a lump of uranium into a bomb and rock becomes light. Kaku's punchline: the four forces may be phases of one force, just as ice, water and steam are phases of one substance, and the "temperature" that switches between them is energy.
Unification so far
- Electricity and magnetism were shown to be one force in the nineteenth century (Maxwell, Chapter 2).
- Electro-weak unification earned the 1979 Nobel Prize for Steven Weinberg, Sheldon Glashow and Abdus Salam.
- Grand unified theories (GUTs) propose to join the electro-weak force with the strong force.
- Gravity has resisted for sixty years: quantum mechanics handled the other three forces brilliantly and "failed dismally" for gravity.
The missing link: two hands that do not match
The twentieth century produced two towering theories. Quantum mechanics rules the very small: it explains atoms, nuclear physics, the hydrogen bomb, transistors and lasers, and could in principle compute every chemical property without a lab. General relativity rules the very large: black holes and the Big Bang. Each uses different mathematics, each is astonishingly accurate in its own domain, and they are incompatible.
Kaku's image is a body whose right hand looks and works nothing like the left. Physicists who believe nature is simple cannot accept that. Superstrings need both theories to work and are, in Kaku's words, the first and only framework in which a quantum theory of gravity makes sense: the missing piece of a sixty-year jigsaw.
Stranger than science fiction
At a 1958 talk by Wolfgang Pauli, Niels Bohr told him: "We all agree that your theory is crazy. The question which divides us is whether it is crazy enough." Superstrings, Kaku says, are crazy enough. Three predictions preview the rest of the book.
Ten dimensions and a sister universe
Einstein's relativity gave the Big Bang, dated here at 10 to 20 billion years ago, but cannot say why the universe exploded or what came before. Superstring theory proposes that the universe began in ten dimensions, was unstable, and cracked into two pieces: our four-dimensional universe and a six-dimensional one that curled up to about 100 billion billion times smaller than a nucleus. The violence of that fission is the Big Bang. The analogy is a vibrating soap bubble that fissions into smaller bubbles. Interdimensional travel was possible only at the very beginning.
Dark matter
Telescopes find only the hundred or so familiar elements everywhere in the cosmos. The ten-to-four-dimensional transition may have created a new kind of matter: it has weight but is otherwise invisible, tasteless, odourless, detectable only through gravity. It could resolve the missing mass problem: visible stars and galaxies hold too little mass to halt cosmic expansion, yet other estimates suggest the universe might recollapse. There may be more dark matter than ordinary matter.
Two 1995-era statements need care. The age of the universe is now pinned at 13.8 billion years, not "10 to 20." And the link between dark matter and the ten-dimensional fission is Kaku's speculation, not a derivation; dark matter is observed, but no string calculation predicts which particle it is. The "sister universe" picture of a single cracking event is also a popular simplification of compactification, not a standard result.
Super skeptics
The theory's claims invite doubt, and Kaku quotes the doubters fairly:
- Sheldon Glashow (Harvard): years of effort by "the best and the brightest" have yielded "not one verifiable prediction."
- Gerard 't Hooft, at Argonne National Laboratory, compared the fanfare to American TV commercials: all advertisement, little substance.
- Freeman Dyson: "The ground of physics is littered with the corpses of unified theories."
The defence has two parts. No experiment contradicts the theory, and it has no rival: earlier unified theories died because they could not marry gravity to quantum mechanics, and superstrings do not suffer from that disease.
| Skeptics (1980s–90s) | Defenders | |
|---|---|---|
| Evidence | Not one verifiable prediction | No experiment contradicts it |
| History | Unified theories have all died | They died of the disease strings cure |
| Tone | Hype, like TV adverts | Uniquely elegant and consistent |
The SSC and the turn to cosmology
The Superconducting Super Collider, planned through the 1980s, would have been the largest scientific machine in history, smashing particles at trillions of electron volts and drawing as much power as a city. Congress cancelled it in 1993. Even the SSC could not have tested GUTs or strings directly; at best it would have probed their periphery. Hopes shifted to the Large Hadron Collider (LHC) at CERN, then precariously funded, which might find the lowest vibrations of the superstring, a new class of particles. Because unification energies exist only at the origin of time, Kaku argues the final verdict may come from cosmology.
- LHC delivered, from 2010, and found the Higgs boson (announced 4 July 2012, mass about 125 GeV).
- No superpartners have appeared through Run 2 and Run 3 (13.6 TeV since 2022): gluinos are excluded up to roughly 2.2–2.4 TeV and first-generation squarks to about 1.8 TeV in simple models. The "lowest vibrations of the superstring" Kaku hoped for have not shown up.
- Next machines: the High-Luminosity LHC is due around 2030; CERN's Future Circular Collider (about 91 km) completed its feasibility study in 2025, with a decision expected later this decade; China proposes CEPC.
- Cosmology did become the main testing ground, as Kaku predicted: precision data from Planck, DESI, gravitational-wave detectors and the Event Horizon Telescope now constrain physics at energies no collider can reach.
Chapter 1's argument has four steps: the forces look unrelated; three have been unified by quantum field theory; gravity resists; only strings accommodate gravity consistently. The weakness is entirely experimental, and the chapter is honest about it.
The Quest for Unification
Kaku rereads the history of physics as a sequence of unifications: Newton joined heaven and earth, Maxwell joined electricity and magnetism (and found light), Einstein joined space with time and matter with energy, then gravity with geometry. Every great unification rests on a simple physical picture, and Einstein failed at the last one because he abandoned pictures for mathematics and tried to unite gravity with light instead of with the nuclear forces and the quantum.
Newton: uniting heaven and earth
In the late 1600s the church held two sets of laws: perfect, harmonious laws for the heavens and coarse ones for the earth. Dissent was dangerous: Giordano Bruno was burned at the stake in Rome in 1600 for saying the sun was one star among innumerable suns with their own earths, and Galileo was forced to recant heliocentrism (allegedly muttering, "But the earth does move!").
Isaac Newton, aged 23, was sent home from Cambridge when the Black Plague shut the universities. Watching falling objects, he asked a heretical question: does the moon also fall? His answer was yes. The moon falls continuously, but the earth's surface curves away beneath it as fast as it falls, so it never lands. The Principia set down the laws for satellites and planets.
Newton's mountain cannon. Throw a rock from a high mountain: it lands farther away the harder you throw. Throw it fast enough and it circles the whole earth and hits you in the back of the head. The moon is that rock. The picture predates artificial satellites by three centuries, and the same laws flew probes to Mars and past Uranus and Neptune.
- First unification. One law of gravitation governs falling rocks and orbiting planets, linking human destiny with the stars.
- Measuring the cosmos. While the church taught a motionless earth, Newton could estimate the earth-moon and earth-sun distances.
- The pictorial principle. Kaku's recurring thesis begins here: the mathematics of unification may be obscure, but its essence is always pictorially simple.
Maxwell: electricity, magnetism and light
Two centuries later, in the mid-1860s (during the American Civil War), European experiments showed that changing magnetic fields create electric fields and vice versa. Shove a bar magnet into a coil and a current flows; run a current through a coil and it becomes a magnet. The same principle runs every hydroelectric plant: falling water spins coils in a magnetic field and the current travels hundreds of miles to wall sockets.
James Clerk Maxwell, a little-known thirty-year-old Scot at Cambridge around 1860, claimed electricity and magnetism are two sides of one coin. He pictured them as force fields filling space, like the spiderweb of lines around a bar magnet, and asked what would happen if a vibrating magnetic field made an electric field, which made a magnetic field, and so on without end.
Black and white dominoes. Line up alternating black and white dominoes and tip the first: a wave runs down the line. Remove all the black ones and the wave stops. Maxwell's wave works the same way: neither field alone can travel; only the alternation of electric and magnetic fields makes a self-propagating wave.
Computing the speed of this self-sustaining wave, Maxwell got the speed of light. Light, therefore, is a chain of electric fields turning into magnetic ones: the first genuine unified field theory. Most physicists balked because there was no ether to carry the wave. In 1889, ten years after Maxwell's death, Heinrich Hertz generated a spark, sent an electromagnetic wave across a room and detected it, the crude ancestor of radio.
- One spectrum. Radar, ultraviolet, infrared, radio, microwaves, TV and X-rays are all the same wave at different frequencies.
- A concrete number. At 99.5 FM, the fields in the radio wave turn into each other 99.5 million times per second.
- A hidden time bomb. Maxwell's equations already implied that moving clocks run slow, contradicting Newton's uniform cosmic time; nobody noticed for half a century.
Einstein the unemployed revolutionary
Kaku groups Einstein's life's work into three theories: special relativity, general relativity and the unfinished unified field theory.
- 1900 Graduates from the Zurich Polytechnic; rejected for academic posts, scrapes by tutoring; his father writes of his son's depression and sense of being a burden.
- 1902 A friend's recommendation lands him a job at the patent office in Bern.
- 1905 Special relativity, aged 26.
- 1915 General relativity.
- 1919 Eclipse expeditions confirm light-bending (29 May).
- 1921 Nobel Prize, given for the photoelectric effect, not relativity.
- 1925–1955 Thirty years on the unified field theory; dies with it unfinished.
The patent office helped twice: it left him time to think, and it trained him to strip vague proposals down to their essential idea, the same habit of physical pictures that served Newton and Maxwell.
Racing a light beam
The childhood question: what would a light beam look like if you raced alongside it at light speed? You should see a frozen wave of fields. But Maxwell's equations allow no stationary light waves; light always moves at the same speed whatever your own speed.
The 101 mph light beam. Suppose light moved at 101 mph and you rode a train at 100 mph. Common sense says you would clock the beam at 1 mph and study it at leisure. Maxwell's equations say you measure 101 mph. Einstein's resolution: on the moving train clocks run slower and rulers shrink, including the scientist's brain, so the measurement comes out at 101 mph. Now imagine light moved at 5 mph, a stroller's pace: cars would be flattened like pancakes (and appear rotated), their passengers nearly frozen in time, regaining shape and pace as they braked at a traffic light. Relativity offends common sense only because light, which circles the earth seven times a second, is so fast compared with us.
Einstein later said flatly that special relativity "owes its origin to Maxwell's equations." He went further than anyone because he saw an underlying symmetry linking space with time (space-time) and matter with energy, so that a rock (uranium) can become a flash of light. Kaku's footnote defines the book's master concept: an equation has symmetry if it remains unchanged when its components are shuffled or rotated.
Space warps: general relativity
Special relativity said nothing about gravity, and Newton's gravity acts instantaneously, violating the light-speed limit.
The vanishing sun. If the sun vanished, Newton says the earth would fly off at once. Einstein says nothing outruns light, so the earth should keep orbiting for about eight minutes, the light-travel time, before it notices. A new theory of gravity was needed.
His 1915 answer pictures space-time as a trampoline. A bowling ball (the sun) makes a dip; a marble (the earth) rolling nearby circles the depression. Newton would invoke an invisible force; Einstein says the marble simply follows the curved surface. Gravity is not a force at all but the bending of space-time by matter-energy. Remove the ball and ripples spread across the net at light speed: gravitational waves, which solve the vanishing-sun puzzle.
- Eclipse test. On 29 May 1919, expeditions to Brazil and Africa compared star positions near the eclipsed sun with their night positions; the shift made world headlines.
- Einstein's certainty. Asked what he would have said had it failed: "Then I should have been sorry for the dear Lord, but the theory is correct."
- Nobel confidence. He promised his ex-wife the Nobel money in the divorce settlement years before winning it; a split committee gave the 1921 prize for the photoelectric effect instead of relativity.
- Laboratory confirmation. In 1959 and 1965, Robert Pound and colleagues at Harvard sent gamma rays down 74 feet of a building and measured gravity's shift of their wavelength, as Einstein predicted.
- Pound-Rebka numbers. The predicted shift over 74 feet is about 2.5 parts in 10¹⁵, a few parts in a thousand trillion, not "one part in a hundred trillion." It is also a gravitational redshift, not a bending of light's path.
- The 1905 reception. The relativity paper was published in Annalen der Physik and quickly taken up by Max Planck; it was not "largely ignored." What Bern rejected (in 1907) was Einstein's habilitation thesis.
- Institute name. Oppenheimer directed the Institute for Advanced Study, not "Studies."
The trampoline ripples are now observed. LIGO detected gravitational waves from two merging black holes on 14 September 2015 (announced 2016; Nobel 2017). In 2017 the neutron-star merger GW170817 arrived within 1.7 seconds of its gamma-ray flash after a 130-million-year journey, showing gravity travels at light speed to about one part in 10¹⁵: Einstein's eight-minute answer, confirmed. By 2026 LIGO-Virgo-KAGRA have catalogued hundreds of mergers.
From revolutionary to relic
Einstein then hunted bigger game: uniting his geometric gravity with Maxwell's light. He spent his last thirty years on it, largely alone. In the 1940s and 1950s colleagues called him over the hill and out of touch with quantum theory; some sneered that he was senile. Even J. Robert Oppenheimer, his own director, called the quest futile.
- "A sort of petrified object," Einstein said of himself, "rendered blind and deaf by the years."
- The ostrich. In 1954: he must seem like "an ostrich who forever buries its head in the relativistic sand in order not to face the evil quanta."
- The board of wood. He had little patience with scientists who look for the thinnest part of a board and drill many holes where drilling is easy, and said physicists a century later would appreciate his labours.
Meanwhile physics was riveted by atomic and nuclear physics, heralded as no science ever had been by the atomic bomb. Through the 1930s to 1950s Niels Bohr (Copenhagen) and Werner Heisenberg (Göttingen) built quantum mechanics while Einstein pursued light and gravity.
| The popular myth | Kaku's reading | |
|---|---|---|
| On quantum theory | Einstein's biggest blunder was rejecting it | He accepted its validity but thought it incomplete, as Newton's gravity was incomplete |
| On his late work | Senile dead end | Surprisingly modern: he expected particles to appear as solutions of a unified geometric theory |
| Why the myth persists | Historians' verdict | Historians cannot read the mathematics of his late papers |
Einstein's mistake
Physicists now understand why Einstein failed. He worked in physical pictures (he joked that he put clocks everywhere in the universe but could not afford one for his home), and the mathematics came later as translation. A biographer recalled that his method "taught me the difference between knowledge and understanding." In his last decades he abandoned the picture: lacking a guiding principle ("one must again ferret out some general principle from nature"), he retreated into twisted geometries, mathematical structures without physical content.
Why Einstein failed, in three points
- No physical picture. He traded intuition for mathematics devoid of physical content.
- Wrong partner force. He tried to unite gravity with electromagnetism instead of including the nuclear forces, then the least understood.
- Wrong attitude to the quantum. The key to unification is the marriage of relativity and quantum mechanics, the theory of matter he distrusted. Einstein understood forces superbly and matter poorly.
Kaku's verdict: Einstein was right to seek unification through symmetry and wrong in tactics. Superstrings may be the missing physical picture, a graphic theory in which infinitely many particles are modes of one vibrating string.
The Quantum Puzzle
The second pillar of modern physics, quantum mechanics, is a theory of matter: energy comes in discrete packets, particles behave as waves, and only probabilities can be predicted. It powers the transistor, the laser and all of chemistry, yet it offends common sense and offended Einstein. Its real limitation, Kaku argues, is not philosophical but structural: built on point particles, it breaks down with infinities the moment it is married to relativity, and only strings remove the points.
Two giants with interwoven fates
Kaku pairs Einstein (relativity, forces, the very large) with Werner Heisenberg (quantum mechanics, matter, the very small). Both were German-born iconoclasts who did their best work young: Einstein at 26, Heisenberg at 24, after a PhD at 21, with a Nobel Prize at 32. Germany was the pilgrimage site of physics; J. Robert Oppenheimer went to Göttingen in the late 1920s because American physics was primitive.
- Divergent paths in 1933. Einstein, a Jew, fled Nazi Germany; Heisenberg stayed and worked on Hitler's atomic bomb project.
- The letter. Heisenberg's presence in Germany helped persuade Einstein to write to Franklin Roosevelt in 1939 urging an American bomb.
- The assassination plan. A former OSS agent later revealed that the Allies drafted plans to assassinate Heisenberg if needed.
The scientific contrast is just as sharp. Relativity asks about the beginning and end of time and the edge of the universe; Heisenberg, Erwin Schrödinger and Niels Bohr asked what the smallest object is and whether matter can be divided forever.
| General relativity | Quantum mechanics | |
|---|---|---|
| Domain | Galaxies, the expanding universe | Atoms, nuclei, subatomic particles |
| Main subject | Force fields that fill space smoothly | Matter, moving well below light speed |
| Fields are | Continuous, gossamer-like tendrils | Quantised into discrete units (photons) |
| Fails at | Explaining atoms | Large-scale cosmos, high speeds |
Neither suffices alone: Einstein pushed relativity to breaking point, and quantum mechanics without relativity cannot handle galaxies or fast particles. Merging them consumed half a century; only superstrings offer a possible synthesis.
Planck, the reluctant revolutionary
The quantum was born in 1900 from black-body radiation: why does heated steel glow red, then white? Treating light as a pure wave that can vibrate at any frequency predicted infinite energy at high frequencies, the ultraviolet catastrophe.
A Sunday in Berlin, 1900. The experimentalist Heinrich Rubens mentioned his latest black-body data to Max Planck over a social visit. After Rubens left, Planck found a mathematical trick that fitted the data and mailed him a postcard that evening. Presenting it in December 1900, Planck half-disbelieved his own idea that energy is exchanged in discrete packets: "Experience will prove whether this hypothesis is realized in nature."
The packets are invisible in daily life because they are fixed by a tiny number, Planck's constant h ≈ 6.6 × 10⁻²⁷ erg·s (the book rounds it to 6.5), and each packet carries energy E = hν. Physicists found granular light preposterous.
In 1905 Einstein, still obscure and far bolder than Planck, used quanta to explain the photoelectric effect: particles of light knock electrons out of metal, with energies he calculated from h. Experiments confirmed it; Planck won the Nobel Prize in 1918, Einstein in 1921. Kaku's application: the television camera, whose reusable photoelectric surface records moving images, unlike film that can be exposed only once.
Quantum cookbooks
- 1900 Planck: energy comes in quanta.
- 1905 Einstein: light quanta explain the photoelectric effect.
- 1923 Louis de Broglie, a French prince and graduate student, gives matter waves a frequency and wavelength.
- 1926 Schrödinger writes the wave equation; Heisenberg's equivalent matrix form appears almost simultaneously. The "old quantum theory" becomes mature quantum mechanics.
- 1927 Heisenberg's uncertainty principle.
- 1935 Schrödinger's cat.
Before 1926, predicting even simple chemistry was hopeless; after it, physicists went from ignorance to near-complete understanding of simple atoms. The Schrödinger equation is a cookbook: it states exactly what to mix and for how long to get the properties of any molecule, including ones never seen in nature, given a large enough computer.
What quantum mechanics built
- Conductors and insulators. In a metal lattice, outer electrons are only loosely bound and roam the whole lattice, so tiny fields push currents through it; in rubber and plastic they are held tight.
- The transistor. Semiconductors switch between conductor and insulator, so they act like a water faucet for current. John Bardeen, William Shockley and Walter Brattain shared the 1956 Nobel Prize.
- Neon and fluorescent light. Current kicks electrons to higher orbits; falling back, they emit light. Ordinary light, sunlight included, is incoherent, a jumble of frequencies and phases.
- The maser and laser. Charles Townes predicted that excited atoms could be made to decay in synchronisation, producing coherent radiation never seen in nature. He made a pulse of coherent microwaves in 1954 (Nobel 1964); the idea soon worked for light. Lasers cut metal, carry communications, clear arteries through glass fibres, play discs and read bar codes.
- Others. Electron microscopes exploit electron waves to see viruses; X-ray diffraction unlocks DNA; fusion machines may one day give nearly unlimited power.
- Holographic 3D television, which Kaku expected our grandchildren to watch in spherical sets, never arrived; consumer 3D TV flopped and was abandoned by manufacturers around 2017.
- Fusion: the US National Ignition Facility achieved ignition (more fusion energy out than laser energy in) in December 2022 and has since repeated it at higher yields. ITER has slipped badly, with research operations now planned for the mid-2030s; private fusion firms have raised billions.
- DNA's structure had in fact been solved by X-ray diffraction in 1953; the book's "eventually" refers to understanding life itself.
- Quantum technology is the new frontier: quantum computers exploit superposition and entanglement directly, a use of "Schrödinger's cat" physics the 1995 book does not foresee.
Anyone who is not shocked by quantum theory has not understood it.Niels Bohr
Uncertainty and the death of determinism
In 1927 Heisenberg proposed that one cannot know both the position and velocity of a particle at once: Δx · Δp ≥ ħ/2. A wave is smeared out; you cannot point to exactly where an ocean wave is and how fast it moves. Kaku explains it as disturbance: to see an electron you must bounce photons off it, and the photon knocks it away. No better apparatus helps.
The "measurement disturbs the electron" story is Heisenberg's own 1927 microscope heuristic, but it is misleading. Uncertainty is a property of the wave function itself: a particle does not have a sharp position and momentum to be disturbed. Kaku's opening sentence (a wave is smeared, a consequence of the Schrödinger equation) is the better explanation.
Newtonian determinism pictured a cosmic clock wound up by God and ticking by three laws of motion. Pierre Simon Laplace pushed it to the limit: knowing every atom's initial motion, one could compute eclipses, Halley's comet, and also wars, human decisions, which restaurant you will eat in ten years from now and what you will order, even heaven or hell. Asked by Napoleon why Celestial Mechanics never mentioned the Creator, Laplace said: "I have no need for that hypothesis."
Heisenberg calls this nonsense. Individual events are unpredictable; only probabilities can be computed, but those are computed with astonishing accuracy for large numbers.
The exam bell curve. Nobody can predict how one student will do on a college entrance exam, yet the bell-shaped curve for millions of students barely changes year to year. Quantum mechanics is the same: it cannot say when one uranium nucleus will decay, so it describes that nucleus as a mixture of intact and decayed states, and from that strange assumption predicts the decay rate of billions of nuclei with high precision.
Schrödinger's cat
Setup (1935). A cat sits in a sealed box with a bottle of poison gas wired to a Geiger counter beside a lump of uranium ore. If one nucleus decays, the counter fires, the bottle breaks, the cat dies. Since the nucleus is a mixture of decayed and intact states, the cat's wave function is a mixture of dead and alive. Punchline: opening the box, the act of measurement, decides the cat's fate; worse, quantum mechanics implies that objects have no definite state until observed. Einstein: "No reasonable definition of reality could be expected to permit this."
Philosophy and science
Physicists have always cared about philosophy. Einstein called science without epistemology "primitive and muddled" and as a young man co-founded the Olympian Academy reading group; Schrödinger nearly quit physics for philosophy; Planck wrote on free will in The Philosophy of Physics.
The old riddle returns: does a tree falling in an empty forest make a sound? Bishop Berkeley and the solipsists said no; all of science since Galileo and Newton said yes, because laws exist objectively. Quantum physicists, on the strength of their equations, take a leap: observation creates reality, though the founders applied this only to the subatomic world. Heisenberg recalled 1927 conversations with Bohr ending near despair, then walking alone in the park asking: "Could nature possibly be as absurd as it seemed?"
Einstein's three objections
- Probability cannot be a foundation. "I am convinced that God does not play dice" (to Max Born).
- Incompleteness. "Every element of the physical reality must have a counterpart in the physical theory"; quantum mechanics describes only group behaviour, not individual events.
- Objective reality and causality. He held to an observer-independent world "although, up to now, success is against it," comparing himself to Spinoza, who believed in universal causation before science could show it.
He called himself "an obstinate heretic" and noted in 1948 that "momentary success carries more power of conviction for most people than reflections on principle." His precedent: Newton's gravity succeeded for two centuries before proving incomplete. Kaku stresses again that Einstein accepted the equations; he regarded them as the surface of a deeper, objectively real unified field theory.
Experiments have since ruled against Einstein's specific hope. Bell's theorem (1964) showed that any theory with local hidden variables must disagree with quantum predictions, and loophole-free Bell tests in 2015 (Delft, Vienna, NIST) confirmed quantum mechanics. Alain Aspect, John Clauser and Anton Zeilinger won the 2022 Nobel Prize for this work. A deeper theory could still exist, but it cannot be both local and realistic in Einstein's sense.
Pragmatism rules
By the 1930s and 1940s perhaps 99 percent of physicists were in the quantum camp. A minority, including Nobel laureate Eugene Wigner, argued that measurement requires consciousness, so the universe's existence depends on an observer: human, alien or God, and perhaps the world sprang into being at the first measurement.
The pragmatic majority answers with a camera: a photon crossing the galaxy is indeterminate until it exposes a film, and the film needs no mind. Observation does not imply consciousness.
Superstrings sharpen the cat problem rather than solving it. A full quantum description of strings requires the wave function of the entire universe, space-time included, so treating a cat in a box as a self-contained system may be incomplete. The final answer may need a much more detailed understanding of cosmology.
Most physicists simply live with the strangeness. John von Neumann, asked at Los Alamos about a problem solvable "by the method of characteristics," told a puzzled young physicist: "In mathematics you don't understand things, you just get used to them."
Why quantum mechanics alone fails
By the 1930s quantum mechanics was a Mack truck flattening old problems; Paul Dirac annoyed chemists by saying it reduced all of chemistry to equations. But it worked only at low speeds. Electrons in hydrogen move at about 1/100 the speed of light, so relativity could be ignored; the early success of quantum mechanics was in this sense a fluke of slow atoms.
The Toyota on the race track. A car that runs well below 100 mph may spin out of control past 150 mph. Car engineering is not wrong; you need a redesigned car for high speeds. Quantum mechanics is the same: no deviations at low velocity, failure at high velocity, so it must be married to relativity.
The first marriage, quantum field theory, was a disaster for decades: every calculation of electron collisions gave infinity. The culprit is the point particle.
The inverse square law says fields weaken with distance, so they grow without limit as you approach a point; at its surface the field is 1/0, and every calculated energy fills with such infinities. The assumption Heisenberg and Schrödinger made, that quantum mechanics rests on point particles, was too stringent. A new quantum mechanics can be built on superstrings, which banish points altogether.
The Riddle of Infinities
For half a century the marriage of quantum mechanics and special relativity produced infinite answers. Kaku follows the safe-cracking that fixed it, force by force: Feynman's QED (1949), the electro-weak theory made finite by 't Hooft (1971), and quantum chromodynamics for quarks. The single lesson of fifty years is that gauge symmetry cancels infinities: the more symmetry a theory has, the better behaved it is, which is why the superstring, with the largest symmetry ever found, is so promising.
Feynman the safecracker
Kaku opens with a question: what do safecrackers and physicists share? Both sift random-looking clues for hidden patterns. Richard Feynman was both. Since the 1930s physicists had been trying to crack the safe of quantum field theory; only in the last twenty years did they see that the clues form a pattern, an underlying mathematical symmetry.
"Wise Guy" at Los Alamos. During the atomic bomb project Feynman cracked three vaults in a row holding the bomb's secret equations. In one he left a note on yellow paper bragging how easy it was, signed "Wise Guy"; in the last, "Same Guy." Frederic de Hoffman opened them, turned grey-yellow-green, and shouted that it was "the same guy who's been trying to get into Building Omega!" Feynman confessed. The point for Kaku: the same knack for spotting the key factor let Feynman crack the infinities.
The S-matrix: why the sky is blue
At MIT Feynman asked what the most important problem in theoretical physics was, and answered: removing the infinities from quantum field theory. The target quantity is the S-matrix (S for scattering), a set of numbers giving how many particles scatter at what angle and energy when they collide. Know the S-matrix completely and you can in principle predict the properties of any material.
- Blue sky. Nineteenth-century physicists used a crude S-matrix for sunlight scattering off air: blue scatters more than red, and daytime sky light is mostly scattered light. On the airless moon the daytime sky is black.
- Red sunset. At sunset you look at the sun itself through a long horizontal path of air; by the time the light arrives, only the reds are left unscattered.
- Chemistry and life. 1930s physicists computed the S-matrix for colliding hydrogen and oxygen and showed water forms; with all atomic S-matrices one could predict every molecule, DNA included.
The obstacle: in 1930 J. Robert Oppenheimer found that quantum mechanics joined to special relativity gave an infinite S-matrix, and wrote that unless the infinities were removed the theory must be discarded.
Tinker Toys and Feynman diagrams
In the 1940s Feynman doodled collisions. Each doodle was shorthand for pages of algebra, letting him condense the mathematics and isolate the infinities. Critics thought the diagrams silly or a prank, since he could not derive his rules, and some preferred the equivalent formulations of Julian Schwinger (Harvard) and Shinichiro Tomonaga (Tokyo). Freeman Dyson explained the confusion: Feynman "wrote down the solutions out of his head without ever writing down the equations"; others' minds "were analytical; his was pictorial."
Feynman's Tinker Toy kit for QED
- Straight stick: a moving electron.
- Wavy stick: a moving photon.
- Joint: one wavy stick meeting two straight ones, the interaction.
- Trees (no closed loops): finite, and match experiment.
- Loops: give infinities, because the theory still rests on point particles, the old 1/0 problem.
- The S-matrix is the sum of all possible diagrams, an infinite series.
Two electrons can exchange one photon, two photons or many; anyone can draw hundreds of such diagrams with a little practice.
Renormalization: infinity minus infinity
QED has two parameters, the electron's charge and mass. Maxwell's equations have an extra symmetry, gauge symmetry, which let Feynman regroup diagrams so that the infinities could be absorbed into redefined charge and mass. The "bare" charge and mass are assumed infinite to begin with; they swallow the loop infinities and come out finite. This is renormalization: in effect, ∞ − ∞ = finite.
Global versus gauge symmetry (Kaku's footnote). If a wave equation is unchanged when you make the same rotation at every point in space and time, it has global symmetry. If it is unchanged when you make a different rotation at each point, it has the richer local or gauge symmetry. Gauge symmetry is probably the only way to remove the sicknesses of quantum field theory.
Paul Dirac objected for years, likening it to a card sharp shuffling diagrams until the infinite cards vanished: "Sensible mathematics involves neglecting a quantity when it turns out to be small, not neglecting it because it is infinitely great and you do not want it!" But in the 1950s QED computed the hydrogen energy levels with precision no other theory approached. After the three versions were proved equivalent, Feynman, Schwinger and Tomonaga shared the 1965 Nobel Prize. In hindsight the real achievement was exploiting Maxwell's gauge symmetry; the interplay between symmetry and renormalization, found again and again, is one of the great mysteries of physics.
QED is now the most precisely tested theory in science: the electron's magnetic moment was measured in 2023 to about 0.13 parts per trillion, in agreement with QED calculated to five loops (over 12,000 Feynman diagrams). The muon's cousin measurement, Fermilab's muon g-2, released its final result in June 2025; with an improved lattice-QCD prediction, the long-advertised anomaly has largely evaporated.
Renormalization fails: the weak force
In the 1950s and 1960s blackboards filled with trees and loops, and physicists hoped lightning would strike twice. It did not: without understanding gauge symmetry, they explored hundreds of blind alleys for two decades.
The neutrino and the lepton families
Weak interactions involve electrons and their partners, neutrinos; together these are leptons. The neutrino has no charge, "probably" no mass, and is nearly undetectable.
- 1930 Wolfgang Pauli predicts the neutrino to explain energy missing in radioactive decay.
- 1933 Enrico Fermi publishes its theory and names it ("little neutral one"); Nature rejects the paper as too speculative.
- 1937 The muon appears in cosmic rays: an electron over 200 times heavier. I. I. Rabi: "Who ordered that?"
- 1953 The neutrino is detected at a nuclear reactor.
- 1962 Brookhaven shows the muon has its own muon neutrino.
- 1977–78 Experiments at Stanford and Hamburg find a third heavy electron, the tau, about 3,500 electron masses, with its own tau neutrino.
Neutrino telescope and neutrino bomb. Neutrinos come up through your floor every second after crossing the earth from China; some would pass through a solar system of solid lead. A neutrino telescope could look through hundreds of miles of rock for oil, minerals and earthquake origins, except that film able to stop a neutrino does not exist. Heinz Pagels offered the pacifist's weapon, a neutrino bomb: as costly as a nuclear weapon, it explodes with a whimper, terrifies everyone, and its neutrinos fly harmlessly through everything.
Several dates and claims are off. The reactor neutrino experiment of Reines and Cowan began in 1953 but the confirmed detection came in 1956 (Nobel 1995). The muon was found in 1936–37 by Anderson and Neddermeyer. The tau was discovered by Martin Perl at SLAC in 1975 (Nobel 1995), and the tau neutrino was directly observed only in 2000 at Fermilab. Glashow proposed the SU(2) × U(1) structure in 1961; Weinberg (1967) and Salam (1968) added symmetry breaking. Kaku also omits Martinus Veltman, 't Hooft's adviser and co-laureate (1999), and the 1973 discovery of asymptotic freedom by Gross, Wilczek and Politzer (Nobel 2004), which is what made QCD credible.
- Neutrinos have mass. Super-Kamiokande showed atmospheric neutrinos oscillate between flavours in 1998, and SNO solved the solar neutrino problem in 2001 (Nobel 2015). Oscillation requires mass. KATRIN (2025) caps the electron-neutrino mass at 0.45 eV, over a million times lighter than the electron.
- Neutrino telescopes exist. IceCube, a cubic kilometre of Antarctic ice, has detected astrophysical neutrinos since 2013 and mapped the Milky Way in neutrinos (2023). Geoneutrinos from the earth's radioactive interior were detected by KamLAND (2005) and Borexino, a modest version of Kaku's look-through-the-earth dream.
The W-particle theory and its sickness
Borrowing from QED, physicists proposed that electrons and neutrinos interact by exchanging W-particles: a straight stick (electron), dotted stick (neutrino) and spiral (W). The theory was nonrenormalizable, because it lacked Maxwell-style gauge symmetry, and it languished for three decades.
The electro-weak breakthrough
In 1967–68 Steven Weinberg, Abdus Salam and Sheldon Glashow noticed the resemblance between the photon and the W. Einstein had tried to unite light with gravity; perhaps the right move was to unite light with the weak force. They used the most powerful gauge symmetry available, the Yang-Mills theory (1954), with symmetry group SU(2) × U(1), which put weak and electromagnetic forces on the same footing and treated the electron and neutrino as two sides of one coin. It did not explain the three families.
Nobody believed Weinberg's guess that it was renormalizable. Then in 1971 the 24-year-old Dutch graduate student Gerard 't Hooft proved it was. He checked by computer: "the output of the program was an uninterrupted string of zeros. Every infinity canceled exactly."
- 0 papers citing Weinberg-Salam from 1968 to 1970.
- 162 papers on it in 1973, after 't Hooft.
- 1979 Nobel Prize for Weinberg, Salam and Glashow.
- 3 physics Nobel laureates from the Bronx High School of Science at the time, more than any other school.
Glashow, the revolutionary anarchist
Weinberg and Glashow were best friends at Bronx Science and wrote for its Science Fiction Club magazine, but a friend told The Atlantic: "Steve is a royalist, Shelly a revolutionary anarchist." Weinberg works alone and is private; Glashow is gregarious, a "futzer" who arrives each morning with four or five wild ideas, mostly wrong, and lets others tear them apart. Howard Georgi said his new particles were another way "to throw rocks at the establishment." Kaku's lesson: brilliance is not enough; theoretical physics needs a generator of bizarre ideas. As a Harvard undergraduate, Kaku sat Glashow's electrodynamics final and heard him announce mid-exam that he could not solve problem five himself.
In his 1979 Nobel lecture Glashow said that in 1956 particle physics was "a patchwork quilt" of separately taught subjects, and that now strong, weak and electromagnetic interactions all arise from a single principle in what was being called a standard theory.
Mesons and the particle zoo
Would lightning strike a third time, for the strong force? Yes, after decades of confusion.
- Yukawa's meson (1935). Hideki Yukawa proposed that nucleons are held together by exchanging pi mesons, predicted their mass, and first argued that short-range forces come from massive exchanged particles, an idea that inspired the W.
- Discovery (1947). Cecil Powell found the meson in cosmic rays at close to Yukawa's mass; Yukawa won the Nobel in 1949, Powell in 1950.
- The zoo. Through the 1950s and 1960s accelerators found hundreds of hadrons. In the 1930s the universe had seemed to need four particles (electron, proton, neutron, neutrino) and two forces.
- 1958 Berkeley's first particle almanac: 19 pages, 16 particles.
- 1960 An expanded almanac, plus a wallet card.
- 1995 Over 2,000 pages, hundreds of particles.
- Fermi: "If I could remember the names of all these particles, I would have been a botanist."
- Oppenheimer: the Nobel should go to the physicist who did not discover a new particle that year.
Worlds within worlds: from Mendeleev to quarks
The model is chemistry. In 1869 Dmitri Mendeleev reduced billions of compounds to elements in a periodic table; knowing only about 60 elements, he used the holes to predict new ones, later found where he said. In the 1930s quantum mechanics reduced the table itself to three particles: electron, proton, neutron.
- The Sakata school. In the 1950s Shoichi Sakata of Nagoya University, citing Hegel and Engels, argued for a sublayer of three particles beneath the hadrons, obeying a symmetry he called SU(3). Dialectical materialism suggested infinite layers (the "onion theory"): stars make galaxies, atoms make molecules, nucleons make nuclei. Sakata wrongly chose the proton, neutron and lambda as his three.
- The Eightfold Way. In the early 1960s Murray Gell-Mann (Caltech) and Yuval Ne'eman found hadrons falling into patterns of eight, named as a joke after the Buddhist path to wisdom; holes in the chart predicted new particles.
- Quarks. Gell-Mann and George Zweig traced the patterns to three quarks, a name from Joyce's Finnegans Wake, obeying SU(3) with corrected combinations. Gell-Mann won the 1969 Nobel Prize.
Quantum chromodynamics
What glues quarks together? In the early 1970s physicists applied the electro-weak recipe: use a Yang-Mills field. Its particle, the gluon, acts like a sticky glue; the resulting color force theory is quantum chromodynamics (QCD), widely believed to be the final theory of the strong force, with early computer work indicating that the field does bind quarks.
The three-times-lucky recipe
- QED (1949): Maxwell's gauge symmetry makes electrons and photons finite.
- Electro-weak (1967–71): Yang-Mills SU(2) × U(1) makes the weak force finite.
- QCD (1970s): Yang-Mills SU(3) makes the strong force finite.
- Next: would lightning strike a fourth time and unite all three? Kaku's answer is the GUT.
QCD has passed every test. Lattice QCD supercomputer calculations now reproduce the proton mass and hadron spectrum to a few percent, and the quark-gluon plasma has been made at Brookhaven's RHIC and the LHC. Proving rigorously that Yang-Mills theory confines quarks with a mass gap remains one of the Clay Institute's $1 million Millennium Prize Problems.
The Top Quark
The top quark, announced at Fermilab in 1994–95, completed the Standard Model, the most successful theory in the history of science. Kaku uses the moment to inventory that model and condemn it as ugly: three electromagnetic, weak and strong theories taped together, three redundant generations, nineteen arbitrary parameters, and no gravity. The Standard Model is a triumph that physicists treat as a way station, and even its natural successor, the GUT, cannot include gravity.
Fifteen minutes of fame
When the top quark was announced, The New York Times put it on the front page; NBC news asked passers-by what a top quark was (one gave a surprisingly accurate answer), and comedians worked it into their acts. It was the first subatomic particle with a public moment.
The stakes were high. The bottom quark turned up at Fermilab in 1977, implying a partner; fifteen years of failed searches followed, and conference jokes about the missing top grew nervous. Without it, the Standard Model would collapse "like a house of cards." Steven Weinberg: "A lot of us would have been embarrassed if it were not."
How the top was caught. Fermilab's Tevatron circulated protons one way and antiprotons (negatively charged antimatter twins) the other, then merged the beams at almost 2 trillion electron volts. Automatic detectors and computers recorded collision debris, spiderwebs of curved tracks from a single point. Sifting the data left 12 collisions with a top fingerprint, implying a mass of 174 billion electron volts (GeV), the heaviest elementary particle known, nearly a gold atom (197 nucleons); the bottom weighs about 5 GeV. Over 440 scientists from 36 institutions hedged with a one-in-400 chance of error. Spokesman William Carithers: the excess was "too large to ignore, but too small to cry Eureka." Later, that team and a rival group on the same accelerator jointly announced 38 top events and the end of doubt.
The chronology is compressed. CDF submitted its "evidence" paper in April 1994; the definitive discoveries by CDF and DØ were announced together on 2 March 1995. The "trillion photographs" are electronic collision records, not photographs. The modern top-quark mass is about 172.5 GeV.
Generations of quarks
The quark census
- First generation: up and down. Three combine into nucleons: proton = up + up + down, neutron = down + down + up. All visible matter.
- Second generation: strange and charm. Found in the heavy debris of atom smashing; a near carbon copy of the first, only heavier.
- Third generation: bottom (1977) and top (1994–95).
- Three colors each (a label, nothing to do with ordinary colour).
- Count: 6 flavours × 3 colours = 18, doubled by antiquarks to 36 quarks.
Why nature repeats the same family three times, differing only in mass, is one of the deepest unsolved mysteries; Kaku calls it useless redundancy.
The Standard Model, and why it is ugly
No experiment up to about a trillion electron volts had deviated from the Standard Model, yet physicists dislike it because it was made by gluing three theories together by brute force, like three jigsaw pieces taped together that obviously do not fit.
| Sector | Matter particles | Force carriers | Count in Kaku's tally |
|---|---|---|---|
| Strong (QCD) | 36 quarks: 6 flavours, 3 colours, plus antiquarks | Gluons (Yang-Mills) | 8 gluon fields |
| Weak | Leptons: electron, muon, tau and three neutrinos | W⁺, W⁻, Z (massive Yang-Mills) | Kaku says 4 |
| Electromagnetic | Charged particles | Photon (Maxwell field) | 1 |
| Symmetry breaking | Higgs particle | Not yet found in 1995 |
Three reasons the Standard Model cannot be final
- A bizarre collection of quarks, leptons, gluons and W and Z bosons.
- Exactly three generations in both quarks and leptons, identical except for mass.
- Nineteen arbitrary parameters (lepton masses, W and Z masses, the relative strengths of forces) inserted by hand and fixed only by measurement.
Einstein's guiding question was: if you were God, how would you build the universe? Certainly not with nineteen dials and a horde of duplicates; ideally with one or no adjustable parameters and one object from which every particle, and perhaps space and time, is made. The analogy is again Mendeleev's table: successful but full of arbitrary constants until three particles explained it.
- The Higgs boson was found at the LHC by ATLAS and CMS on 4 July 2012 at about 125 GeV; Peter Higgs and François Englert won the 2013 Nobel Prize. Every Standard Model particle has now been seen.
- The model has grown. Neutrino masses add about seven more parameters, taking the count to roughly 26.
- Still no clean deviation at the LHC's 13.6 TeV. Kaku's verdict, successful but ugly and incomplete, stands; the known gaps are gravity, dark matter, dark energy, neutrino mass and the matter-antimatter imbalance.
- Note: the weak force has three carriers (W⁺, W⁻, Z); Kaku's "four" includes the photon of the combined electro-weak theory.
GUTs: lightning a fourth time
The next step is to merge the Yang-Mills fields into one. The simplest grand unified theory, SU(5), was written by Howard Georgi and Sheldon Glashow at Harvard in 1974. It shuffles the electron, neutrino and quarks into one family and the photon, W-particles and gluons into one family of forces.
The unification energy is far beyond any accelerator, but SU(5) makes one test possible today: a quark can turn into an electron by emitting another particle, so the proton must decay and has a finite lifetime. Detectors deep underground had found no conclusive decay.
Kaku lists the GUT's problems:
- Hard to test except through proton decay.
- No reason for three families (electron, muon, tau).
- Scores of arbitrary constants: quark and lepton masses, the number of Higgs particles; it resembles a Rube Goldberg device.
- Fatal: no gravity. Yang-Mills gauge theory "hit a brick wall" with gravity; a fifth lightning strike needs symmetries larger than Yang-Mills, which is where the superstring enters.
Proton decay has still not been seen. Super-Kamiokande has pushed the lifetime for the classic decay p → e⁺ + π⁰ beyond about 2.4 × 10³⁴ years, which rules out minimal SU(5) (it predicted roughly 10³⁰–10³¹ years). Supersymmetric and SO(10) GUTs survive. Hyper-Kamiokande (about 8 times larger, operations from around 2027–28) and DUNE will push an order of magnitude further.
The chapter ends Part I with a clean diagnosis: gauge symmetry has unified three forces and keeps them finite, but cannot swallow gravity. Part II, "Supersymmetry and Superstrings," starts from that wall.
The Birth of the Superstring Theory
String theory has the strangest history in science: found by accident in an old maths table in 1968, proposed for the wrong problem (the strong force), abandoned for a decade because it demanded 26 or 10 dimensions and kept producing an unwanted graviton, then resurrected in 1984 when Green and Schwarz showed it was free of anomalies. The defects that killed it as a theory of hadrons, gravity and extra dimensions, turned out to be exactly what a theory of everything needs.
Two rival philosophies
In the 1960s renormalization looked contrived, and a backlash formed around Geoffrey Chew of Berkeley. His S-matrix theory discarded elementary particles and Feynman diagrams and demanded only that the S-matrix be self-consistent, betting that the constraints were so tight that only one solution was possible: the bootstrap approach.
| Quantum field theory | S-matrix theory (Chew) | Superstring theory | |
|---|---|---|---|
| Basic unit | Few point particles | None; infinitely many particles, none elementary | One string |
| Particles | Small elementary set | Infinite, all equal | Infinite, all modes of the string |
| Calculation | Feynman diagrams | Self-consistency, very hard to compute | String diagrams, computable |
| Infinities | Need renormalization | Avoided by fiat | Loops probably finite by themselves |
Kaku's thesis: the superstring takes the best of both. Like field theory it has elementary units that interact through Feynman-like diagrams, but with no renormalization tricks; like the S-matrix theory it holds infinitely many particles, none more fundamental, but unlike it you can actually calculate.
Guessing the answer: Veneziano and Suzuki, 1968
At CERN in 1968, Gabriele Veneziano and Mahiko Suzuki, working independently, asked: if Chew's postulates are so restrictive, why not guess the S-matrix? Leafing through tables of functions, they found Euler's Beta function and saw that it satisfied almost all of Chew's postulates. Never before had a major discovery come from flipping through a maths book; Kaku suspects their youth helped, since an older physicist would have dismissed the idea.
- The missing postulate. The Beta function violated unitarity, the conservation of probability, and hundreds of papers tried to fix it.
- Adding spin (1971). John Schwarz and André Neveu at Princeton and Pierre Ramond at the National Accelerator Laboratory added particles with spin: the Neveu-Schwarz-Ramond (NSR) model, ancestor of the superstring.
- The physical picture (1970). Yoichiro Nambu of Chicago showed the formula's magic comes from interacting strings; applied to NSR, this became the superstring.
Leonhard Euler worked in the eighteenth century (he died in 1783); the book's "in the 1800s" is wrong, and the formula was over two centuries old in 1968. The string interpretation was found independently by Holger Bech Nielsen and Leonard Susskind (1969–70), whom Kaku does not mention. "Bethe-Saltpeter" should read Bethe-Salpeter.
The Nambu mode
Nambu is quiet and reserved, the opposite of the playful Einstein, the prankster Feynman and the enfant terrible Gell-Mann, and he has rarely claimed priority. Kaku says he first published what became the Bethe-Salpeter equation and the early ideas of spontaneous symmetry breaking, long credited as the Goldstone theorem and only lately named Nambu-Goldstone. With strings, Nambu clearly wrote the basic equations. Laurie Brown of Northwestern called him a trailblazer years or decades ahead; physicists say that to know the next decade's physics, read Nambu.
Three modes of discovery
- Yukawa mode: rooted in experimental data; Yukawa reached the meson by analysing what was known.
- Dirac mode: a wild mathematical leap, as in Dirac's antimatter and magnetic monopole; general relativity belongs here.
- Nambu mode (coined by colleagues at his 65th-birthday celebration): interpret the data closely using imaginative, even wild, mathematics. The superstring owes its origin to it.
A life between East and West
- Family. After the 1923 Tokyo earthquake the family moved to Fukui, seat of the Shin-shu Buddhist sect. His grandfather sold household shrines; his father rebelled, studied English literature and wrote a thesis on William Blake, and quietly kept Marxist classics as they became dangerous to own in the militarist 1930s.
- Training. He built radios as a boy, studied at the University of Tokyo, and detested the militarism.
- Post-war Japan. Tomonaga, isolated by war, had laid the foundations of QED five years before Schwinger, as Freeman Dyson recorded with astonishment.
- To America. Oppenheimer invited him to Princeton; he left Japan in 1952, shocked by a normal society (firebombed Tokyo suffered more damage than Hiroshima), visited Chicago in 1954 and became a professor there in 1958.
- "In a pig's eye!" At the 1957 Rochester Conference Feynman shouted this at Nambu's proposed isoscalar meson, which was soon found and named the omega meson.
Nambu shared the 2008 Nobel Prize for discovering spontaneous symmetry breaking in particle physics, the mechanism behind the Higgs. He died in 2015. Veneziano, Ramond, Schwarz and Green all lived to see string theory become a mainstream discipline; Green and Schwarz shared the 2014 Breakthrough Prize.
Nambu's string
Older ideas from Yukawa and Heisenberg pictured particles as pulsating blobs, but every blob or membrane theory broke a principle: shake one side and the vibration crosses the blob faster than light. Nambu's string avoids this because vibrations along it travel at or below light speed, with each vibration mode a separate particle.
The mysterious music box. Given a box that emits tones and knowing nothing of music, you would first name the notes (C, F, G), then find relations among them (groups of eight, the octave), then derive the laws of harmony, and finally guess a single source: a vibrating string. Physics did the same with hadrons: catalogue (the particle zoo), find patterns (Eightfold Way, Beta function), then guess the string.
To satisfy unitarity, Bunji Sakita, Keiji Kikkawa and Miguel Virasoro (Wisconsin) proposed adding loops, reintroducing Feynman diagrams for strings to the horror of S-matrix purists. The programme was completed by Kaku and Loh-Ping Yu as Berkeley graduate students, and by Claude Lovelace (CERN) and V. Alessandrini.
Fun with origami
Strings are open (with ends) or closed (loops). A moving point traces a line (a Tinker Toy stick); a moving open string traces a paper strip, and a closed string a paper tube. Collisions become strips and tubes that merge smoothly, so Tinker Toys give way to origami. Kaku's Berkeley adviser Stanley Mandelstam explained string collisions with scissors, tape and paper.
In 1974 Kaku and Keiji Kikkawa wrote string theory as a full string field theory, a quantum field theory of strings rather than points, needing only five kinds of joint:
The loop test: Möbius strips and Klein bottles
Divergences appear only in loops. In ordinary field theory they can be shuffled away, but in any theory of gravity each term must be finite by itself: one infinite diagram ruins everything. Astonishingly, string loop diagrams are finite through a marvellous sequence of cancellations. Proving it requires odd geometry: the one-loop diagram for open strings includes a Möbius strip (a strip twisted and glued so it has one side; an ant on the inside finds itself outside), and for closed strings a Klein bottle (a tube twisted 180° and joined to itself, a one-sided surface). Once geometric curiosities, both are essential to the cancellation.
The death of the string, 1974
Three fatal defects (as a theory of the strong force)
- Too many particles: the closed string's lowest note was a massless graviton, the open string's a photon. What were gravity and light doing in a theory of hadrons?
- Tachyons: particles faster than light, implying causality violation (going back to meet your mother before you were born).
- Dimensions: Claude Lovelace (CERN) found the model worked better in 26 dimensions; Richard Brower and Charles Thorn (MIT) proved it collapsed otherwise; the NSR superstring needed 10. An inconsistent theory eventually predicts 1 + 1 = 3.
Four dimensions (length, breadth, depth, time) describe anything from an ant to the sun; parallel universes were a science-fiction device. By around 1974 most physicists, Kaku included, deserted strings, recalling Bohr's "crazy enough" remark but unable to stretch that far. Through 1974–1984 only Michael Green (Queen Mary College, London) and John Schwarz (Caltech) kept at it.
A vice made a virtue. Joël Scherk (Paris) and John Schwarz proposed that the unwanted graviton and photon were the real graviton and photon: the right theory applied to the wrong problem, a theory of the universe, not of hadrons. Schwarz: "No one accused us of being crackpots, but our work was ignored." (The book dates this to 1976; their paper appeared in 1974, and Tamiaki Yoneya reached the graviton result independently the same year.)
Children of the string, 1974–1984
The parent was shunned as "too symmetrical to be realistic," but its offspring dominated physics:
- Quark confinement. Ken Wilson (Cornell) proposed that gluons condense into sticky taffy strings with quarks at the ends, so quarks are never seen alone, as steam condenses into droplets. His computer method (lattice gauge theory) spurred NSF supercomputers; he won the Nobel for phase transitions (the book says 1983; it was 1982).
- Supersymmetry. First found in the ten-dimensional string, it worked in four dimensions too and cured diseases of GUTs (Chapter 8).
- Supergravity. Peter van Nieuwenhuizen, Dan Freedman and Sergio Ferrara at Stony Brook (1976) made the first non-trivial extension of Einstein's equations in sixty years; it is contained within the superstring.
- Kaluza-Klein revival. In the early 1980s quantum effects made higher-dimensional theories respectable again.
1984: anomalies and the resurrection
Anomalies are tiny but deadly mathematical defects that appear when quantum mechanics meets relativity; like a slight error in a potter's mix of clay and minerals, they eventually crack the finished theory. They also add constraints, so many that, as Chew hoped, the final answer may be unique.
- Why 10 dimensions. Alexander Polyakov showed the dimension is fixed by the need to cancel an anomaly.
- The threat. Edward Witten and Luis Alvarez-Gaumé (Princeton) showed that field theories of gravity coupled to matter are riddled with fatal anomalies.
- The rescue. In 1984 Green and Schwarz showed the superstring has enough symmetry to ban anomalies altogether.
- The stampede. Steven Weinberg "dropped everything... Including several books" to learn strings, conceding "the mathematics is very difficult." Papers grew from a trickle to over a thousand by 1995.
Kaku's parallel is Alexander Fleming in 1928, who noticed that mould contaminating his staphylococcus cultures killed the bacteria and saw that the nuisance mattered more than the experiment: penicillin, and a 1945 Nobel Prize for "the triumph of accident and shrewd observation." The superstring's unwanted graviton and extra dimensions were its penicillin mould.
Symmetry: The Missing Link
To a physicist beauty means symmetry, and Kaku's claim is that nature does not merely prefer it but demands it: symmetry is the only known way to make relativistic quantum theories free of divergences and anomalies. The mathematics came from Galois and Lie, was resisted for decades by physicists, and triumphed in the gauge revolution. The superstring works because it contains every known symmetry and more, and the four forces look different today only because the universe is old and cold enough for that symmetry to have broken.
What symmetry means
A crystal is beautiful because it rotates back into itself at certain angles: a cube at 90° about any axis, a sphere under every rotation. In physics, "rotations" are really shufflings (space into time, electrons into quarks), and an equation is symmetric if it is unchanged after the shuffle.
The world looks broken: jagged rocks, meandering rivers, clouds, a blizzard of particles. But the Yang-Mills era showed that at the fundamental level nature demands symmetry, as an ironclad condition for merging relativity with quantum mechanics. Physicists once assumed many consistent quantum-relativistic theories could exist; the conditions for removing divergences and anomalies now look so strict that perhaps only one theory is allowed. The superstring contains the symmetries of the electro-weak theory, the GUTs and general relativity, and others not yet discovered.
Galois and the birth of group theory
The mathematics of symmetry is group theory, a group being a set of objects linked by precise rules. Its founder was Évariste Galois (born 1811).
- The problem. The quadratic x² + bx + c = 0 is solved with square roots. Can the quintic ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0? As a teenager Galois used symmetry alone to show no, settling a centuries-old question.
- Rejections. He was turned down by the École Polytechnique after a lecture over the examiners' heads; Cauchy lost his paper; in 1830 the referee Fourier died and the paper was lost; Poisson dismissed the third as incomprehensible.
- Politics. A radical in the Revolution of 1830, he was expelled from the École Normale and arrested in 1831 at a rally against King Louis Philippe.
- Death. A year later he was killed in a pistol duel, reportedly over a woman and possibly arranged by a police agent provocateur, aged barely twenty. The night before, he wrote his results to Auguste Chevalier; they were published fourteen years later.
Two attributions need correcting. The impossibility of solving the general quintic by radicals was first proved by Niels Henrik Abel in 1824 (building on Ruffini); Galois's achievement was the deeper theory of which equations are solvable. And the exceptional groups E₆, E₇, E₈ (and G₂, F₄) were not found by Lie: Wilhelm Killing (1888) and Élie Cartan (1894) classified the simple Lie algebras into four infinite families plus five exceptional ones, not "seven varieties." The police-agent duel story is a legend that historians doubt.
Sophus Lie, a Norwegian, turned group theory into a mature subject in the late 1800s, cataloguing continuous groups now called Lie groups. Mathematicians thought they had finally produced knowledge with no physical use whatsoever. A century later these groups underpin the whole physical universe.
Lie groups: the language of symmetry
| Group | What it rotates | Example in physics |
|---|---|---|
| O(3) | Ordinary 3-D rotations (O = orthogonal) | Beach ball; atoms, because the Schrödinger equation is rotation-invariant |
| U(1) | Complex numbers; one photon | Maxwell's equations |
| SU(2) | Two particles into each other | Heisenberg's 1932 proton-neutron shuffle; electron-neutrino in Weinberg-Salam |
| SU(2) × U(1) | Combined | Electro-weak theory |
| SU(3) | Three subnuclear particles | Sakata, then quarks; QCD colour |
| SU(5) | Electron, neutrino, three quarks | Smallest GUT |
| SU(N) | N particles | N quarks, N as large as desired |
| E(N), N ≤ 8 | No physical object; pure algebra | E(8) × E(8) symmetry of the superstring |
The exceptional groups stop at E(8) for purely mathematical reasons; no snowflake or crystal has E(N) symmetry. Kaku notes a strange numerology linking 8, 10 and 26 (E(8), the superstring's ten dimensions, the bosonic string's twenty-six). If we understood why these numbers recur, we might understand why the universe has four dimensions.
Hostility toward unification
Kaku's charge is that the physics majority has repeatedly been stubborn, almost pigheaded, resisting larger Lie groups and unification.
Schwinger's lost unification. In 1941, forty-two years before the W-particle was found, Julian Schwinger told Oppenheimer that the weak and electromagnetic forces could be united; Oppenheimer "took it very coldly." Schwinger, a prodigy (City College at 14, Columbia graduate at 17, PhD at 20, Harvard full professor at 28), persisted. In 1956 he showed a nearly complete electro-weak theory to I. I. Rabi, who replied, "Everybody hates that paper." When it conflicted with experimental data, Schwinger handed it to his graduate student Sheldon Glashow. The data were wrong. Abdus Salam: "If those experiments hadn't been wrong, he might have gotten the entire thing then and there."
The same frost met Sakata's SU(3) sublayer in the 1950s. Kaku's diagnosis is psychological and cultural:
The plodding and the brash detective. A careful, bright-but-not-genius detective has spent months on contradictory clues. A young detective walks in, spots a pattern and says, "I know who the killer is!" The veteran, resentful and a little envious, lists a hundred reasons why it is premature, and may even convince the newcomer, as Oppenheimer convinced Schwinger. Punchline: what if the young detective is right? Kaku blames a Western mechanistic habit of studying parts, which isolates laws but hides larger patterns, for the decades of prejudice against Einstein's programme.
Yang-Mills theory
Chen Ning (Frank) Yang was born in 1922 in Hefei, China, son of a mathematics professor; he studied at Kunming and Tsinghua, came to the US in 1945 (taking "Frank" from Benjamin Franklin), and earned his PhD in 1948 at Chicago, drawn by Enrico Fermi (who first controlled a chain reaction in 1942).
From 1947 Yang asked whether Maxwell's U(1) symmetry could be generalised to SU(2). Heisenberg's proton-neutron shuffle used the same angle everywhere, on the moon as on earth. Yang asked: what if the angle were different at each point in space? Working this out with Robert Mills at Brookhaven in 1954, he found the local symmetry demands a new meson-like particle, much like the W.
The reaction to one of the century's most important papers was indifference. The theory had too much symmetry:
- Massless particles. It predicted massless carriers, while the W had to be heavy.
- Renormalizability unknown. It was probably not renormalizable, though nobody could prove it.
For almost twenty years it was explored and discarded, one of the great missed opportunities in science. Peter Higgs found that some of its symmetries could be broken to give the particles mass; then in 1971 't Hooft proved the Higgs-broken Yang-Mills theory renormalizable, setting off a "volcanic explosion." Applied as SU(2) × U(1) it gave the electro-weak force; as SU(3), the gluon theory; as SU(5) or larger, the GUTs.
That's the most exciting idea I know: that nature is much simpler than it looks.Steven Weinberg
C. N. Yang died in Beijing on 18 October 2025, aged 103; he shared the 1957 Nobel Prize with T. D. Lee for parity violation, not for Yang-Mills theory, which never received its own prize. Mills died in 1999. The symmetry-breaking mechanism is credited to Higgs, Englert and Brout, and Guralnik, Hagen and Kibble (all 1964); its particle was found in 2012.
From GUTs to strings
GUTs explained hundreds of particles with a few quarks, leptons and Yang-Mills particles, but accelerators kept finding more: a fourth quark in 1974, then more carbon-copy quarks. History was repeating the 1950s particle flood, and carbon copies mean the GUT cannot be fundamental. The superstring replaces the proliferation with one string and the symmetry E(8) × E(8), which contains the GUT symmetry; the three families become different vibrations of the same string.
| Family | Electron family | Muon family | Tau family |
|---|---|---|---|
| Lepton | Electron | Muon | Tau |
| Neutrino | Electron neutrino | Muon neutrino | Tau neutrino |
| Up-type quark | Up | Charm | Top |
| Down-type quark | Down | Strange | Bottom |
The book's own family table mispairs the quarks, listing up, strange and top in one row and down, charm and bottom in another. The correct generations are (up, down), (charm, strange), (top, bottom), as in the table above.
Origami and conformal symmetry
The superstring rests on two great symmetries: conformal symmetry (here) and supersymmetry (Chapter 8). Point-particle Feynman diagrams are attached blindly in all possible ways; QED needs only a few for spectacular agreement, but a quantum theory of gravity needs tens of thousands of diagrams for one loop, most of them divergent. String diagrams can be stretched and shrunk like rubber without changing their value, so at one loop the tens of thousands of diagrams collapse into one. This symmetry is powerful enough to cancel thousands of divergences and yield a finite S-matrix.
Broken symmetry and its restoration
If nature were fully symmetric there would be one force, not four, and no atoms, chemistry or life. It is the breaking of symmetry that makes the universe interesting.
Freezing water. Liquid water looks the same however you rotate it, and so do its equations. Cool it and ice crystals form in random directions, a jagged solid. The equations keep the symmetry; the solutions do not. The transition happens because nature seeks the lowest energy state, as water runs downhill; a system starting in the wrong state, a false vacuum, drops to a lower one. Heat the ice and the symmetry (O(3)) returns.
We cannot reheat the universe, but we can study the Big Bang, when temperatures restored the superstring's full symmetry. We see four forces today because the universe is so old and so cold. At the origin we would have seen supersymmetry, which raises the chapter's closing question: if it is so simple, why did it elude physicists so long?
Supersymmetry
Supersymmetry is the strangest symmetry ever found: it turns bosons (force particles, integral spin) into fermions (matter particles, half-integral spin), so every known particle should have a superpartner. It emerged from string theory, cancels divergences pairwise, produced supergravity, and needs a new arithmetic, Grassmann numbers, where a × b = −b × a. Its weakness, frankly admitted, is that not one superpartner has been seen; Kaku pins his hopes on bigger colliders and on the Big Bang itself.
John Schwarz, the persistent architect
John Schwarz of Caltech figures most prominently in the story. His father was an industrial chemist and his mother a physicist at the University of Vienna who had secured a job with Marie Curie, who died before she could start. The Hungarian-Jewish family fled Europe in 1940; John was born in 1941 in North Adams, Massachusetts.
- Harvard, maths turned physics (graduated 1962): mathematics was fun, but "I really didn't see the point"; nature's questions were more satisfying.
- Berkeley, PhD 1966 under Geoffrey Chew, alongside David Gross, with junior faculty Weinberg and Glashow ("there was a certain aura about him").
- Princeton, with the young Frenchmen André Neveu and Joël Scherk. In 1971 Neveu and Schwarz saw that the Veneziano-Suzuki formula could not describe all the spinning particles in nature.
Spin: bosons and fermions
Everything spins, from galaxies (millions of years per turn) to particles (millions of turns per second). A record player can spin at 33⅓ or 78 rpm, but quantum spin comes only in discrete amounts, measured in units of ħ = h/2π. Quantum mechanics sorts all particles into two classes.
| Fermions (after Enrico Fermi) | Bosons (after Satyendra Bose) | |
|---|---|---|
| Spin | Half-integral: ½, 3/2, 5/2 | Integral: 0, 1, 2 |
| Role | Matter: you, walls, sky | Forces: light, gravity |
| Examples | Electron, proton, neutron, neutrino, quark (all ½) | Photon (1), W (1), pi meson (0), graviton (2) |
Nambu's string was only a bosonic string. Neveu, Schwarz and Ramond added a fermionic string, and their theory, slightly modified, is today's superstring. Its S-matrix had even better properties than Veneziano's, and marvellous coincidences make physicists suspect a hidden symmetry.
The discovery of supersymmetry
In 1971 Bunji Sakita (City College of New York) and Jean-Loup Gervais (École Normale, Paris) found it: the NSR theory has a symmetry that rotates a bosonic object into a fermionic one. Soviet physicists Yu. A. Gol'fand and E. P. Likhtman found it simultaneously, unnoticed in the West. The first version was two-dimensional, because a moving string sweeps out a 2-D strip. It implies that every boson has a fermion partner and vice versa.
"Be your own severest critic." During the lean mid-1970s, when the 26- and 10-dimension requirements had killed strings and only Schwarz and Michael Green persisted, Richard Feynman told Schwarz that any theorist must be his own severest critic, probably as a kindly hint to abandon a dead end. It backfired: "I tried to be very critical, but I couldn't find anything wrong with it!"
Joël Scherk, whom Kaku met at Berkeley in 1970 (they wrote the first paper on the singularity structure of multiloop string diagrams), was a gentle, unconventional soul at home in the Haight-Ashbury and Telegraph Avenue counterculture. He returned to France via weeks in a Japanese Buddhist monastery and the Trans-Siberian Railway, developed severe diabetes, and died in 1980; Kaku reports it as suicide amid personal problems.
Supergravity
The boson-fermion symmetry was too good to waste. In 1974 Bruno Zumino and Julius Wess extracted it from the string into an ordinary four-dimensional point-particle field theory (a spin-0 boson with a spin-½ fermion) and showed it kills many divergences.
Folding the wedding dress. A seamstress finds a wedding dress lopsided the night before the wedding. She can compare every piece with the patterns and trim, or she can fold the dress in half and cut off whatever sticks out. Supersymmetry folds Feynman diagrams: a loop with a fermion inside diverges, a matching loop with a boson inside diverges with the opposite sign, and the two cancel, leaving a finite result.
In 1976 three physicists at Stony Brook gave the graviton (spin 2) a fermion partner, the gravitino (spin 3/2), creating supergravity: the first non-trivial extension of Einstein's equations in sixty years, a halfway house between Einstein and the superstring (it is what a closed superstring becomes as its length shrinks to zero). A magazine photographed Peter van Nieuwenhuizen and Dan Freedman leaping in the air as if defying gravity.
| What GUTs need | What supergravity offers | |
|---|---|---|
| Symmetry group | At least SU(5) | At most O(8) |
| Particle content | All quarks and leptons | Cannot hold both at once |
| Divergences | Must vanish for gravity | Not all cancelled |
Supergravity has had a quiet second act. Computations by Zvi Bern and collaborators showed that maximal (N = 8) supergravity is unexpectedly finite through five loops (2018), far better than power counting predicted; whether it stays finite at seven loops is still open. Supergravity also lives on as the low-energy limit of M-theory (Postscript).
The Princeton string quartet
By the late 1970s supergravity was recognised as a small piece of the superstring. After the 1984 Green-Schwarz anomaly result, it was clear an enormous symmetry group was needed to kill gravity's divergences. In 1985 David Gross, Jeffrey Harvey, Emil Martinec and Ryan Rohm at Princeton (the "Princeton string quartet") found the heterotic string with symmetry E(8) × E(8), compatible with all earlier GUTs and so with all known experiments. E(8) dwarfs SU(5), swallowing every GUT and predicting thousands of new particles. Kaku calls it the leading candidate for a theory of the universe.
Supernumbers: why supersymmetry was found so late
Since humans counted sheep on their fingers, numbers have meant tangible things that obey commutativity: 2 × 3 = 3 × 2 = 6. Roman tax collection and trade built arithmetic on that intuition. Supersymmetry needs numbers that break it.
Grassmann numbers and supernumbers
- Rule: a × b = −b × a (anticommuting).
- Consequence: a × a = −a × a, so a² = 0, yet a ≠ 0.
- Consistency: the arithmetic is fully self-consistent.
- Physics: Grassmann numbers describe fermions, so your body's particles can only be described by them.
- Unification: supersymmetry joins real numbers and Grassmann numbers into supernumbers.
- The blind spot: Sophus Lie catalogued groups but missed supergroups, which need Grassmann numbers; an unconscious prejudice delayed supersymmetry for decades.
Supersymmetry at the beginning of time
There is no experimental evidence. If supersymmetry held at our energies, the spin-½ electron would have a spin-0 partner (the selectron) of equal mass; none exists. Critics call it "a solution looking for a problem." Advocates answer that the symmetry is broken at low energy and we need bigger machines.
From cosmic-ray balloons to colliders
In the 1920s particle physics meant cosmic rays: balloons carried photographic plates aloft, and physicists spent months scanning emulsions for tracks of unpredictable energy (Yukawa's pi meson was found this way). In the 1930s Ernest Lawrence at Berkeley built the cyclotron, a few inches across, making made-to-order beams. Kaku likens it to humanity's shift from foraging to agriculture: controlled harvest instead of chance.
The Superconducting Super Collider, as planned
- Cost: over $11 billion; staff about 3,000 scientists and engineers.
- Magnets: 6.6 tesla, about 130,000 times the earth's field, superconducting, cooled by liquid helium at 4.35 K.
- Tunnel: about 20 feet wide, underground; two beam tubes under 2 feet across.
- Beams: protons circling 3 million times, accelerated within 15 minutes, to collide at 40 TeV.
- Reach: GUT and string unification energies are a quadrillion times higher; only glimmers expected.
- Fate: cancelled by Congress in 1993.
The book gives the SSC tunnel as "perhaps two hundred miles long." The design circumference was about 87 km (54 miles) in Ellis County, Texas, and some $2 billion had been spent and 22.5 km of tunnel bored when it was cancelled.
The torch passed to CERN's LHC: two proton beams colliding at 14 TeV, recreating temperatures of 10¹⁶ degrees found 10⁻¹² seconds after the Big Bang. The hope is sparticles, supersymmetric particles that would be low-energy vibrations of the superstring. Satellites probing black holes and Big Bang remnants offer another route: "echoes of creation" as the laboratory.
No sparticles. The LHC has run since 2010 (7–8 TeV, then 13 TeV, and 13.6 TeV from 2022, just short of the 14 TeV design). ATLAS and CMS have excluded gluinos below roughly 2.2–2.4 TeV, light squarks below about 1.8 TeV and many other superpartners in the simplest models. Supersymmetry survives only at higher masses or in hidden ("compressed", "split") forms, which weakens its original motivation, solving the hierarchy problem naturally. Many physicists now speak of a naturalness crisis. The High-Luminosity LHC (from about 2030) will gather about ten times more data.
Antaeus: theories must touch ground
Maurice Goldhaber's parable: Antaeus was invincible while touching his mother, the earth, and was defeated once lifted off it. "Theories in physics are like that. They have to touch ground for their strength."
| The critic | The defender |
|---|---|
| Julian Schwinger on GUTs: "Unification is the ultimate goal... But that it should be unification now, surely that's the original definition of hubris." | John Schwarz: if correct, it is "a theory about physics at every scale"; we need mathematical tools to extract the low-energy consequences. |
| Even the SSC could not reach the Planck scale of 10¹⁹ GeV. | The bottleneck is not machines but our grasp of how ten dimensions became four. |
Kaku's closing move turns from accelerators to cosmology: the greatest laboratory is the universe at the beginning of time. Part III, "Beyond the Fourth Dimension," follows that move.
Before the Big Bang
Cosmology turns the Big Bang into a laboratory for unification: run the expanding universe backwards and the four forces merge one by one as temperatures soar. Kaku covers the evidence (Hubble's expansion, the 3-degree background radiation), the exotic objects (neutron stars, black holes, Hawking radiation), inflation and the unsettling idea of a false vacuum. His boldest claim is that the Big Bang was the aftershock of a ten-dimensional universe that was unstable and cracked into our four dimensions and six curled-up ones.
Einstein's biggest blunder and the expanding universe
Every culture has a creation myth; the Norse ended theirs in Ragnarok, the death of the gods. Physics can now say something about creation itself, and string theory even claims to say what came before it.
- 1917 Einstein's equations insist the universe expands. Believing it eternal and static, he adds a fudge factor (the cosmological constant), later calling it his "biggest blunder."
- 1922 Alexander Friedmann (USSR) finds the simplest, most elegant expanding solution; nobody takes it seriously.
- 1929 Edwin Hubble, using the 100-inch Mount Wilson telescope, finds millions of galaxies beyond the Milky Way, all receding.
- 1931 Einstein drops the fudge factor.
- Hubble's law. The farther a galaxy, the faster it recedes, measured by the Doppler effect: an approaching source has a higher frequency, a receding one lower (the drop in a passing train's whistle). Galaxies show a red shift, never a blue one.
- The balloon. Glue spots on a balloon and inflate it: every spot recedes from every other, so each one sees itself at the centre.
- Olbers' paradox. In 1826 Heinrich Olbers argued that infinitely many stars should make the night sky blinding. In an expanding universe, red shift drains energy and stars have finite lives, so the sky is dark.
Einstein's "blunder" came back. In 1998 two supernova teams found the expansion is accelerating (Nobel 2011), driven by dark energy that behaves like his cosmological constant and makes up about 68% of the cosmic energy budget. In March 2025 DESI, mapping nearly 15 million galaxies and quasars, reported a 2.8–4.2σ preference (depending on the supernova data combined) for dark energy that weakens over time; not yet a discovery, but a live threat to the simple constant. Note also that Georges Lemaître (1927) independently derived expansion and connected it to observed red shifts before Hubble.
The GUT history of the early universe
The universe is unsymmetrical today because it is old and cold. Going back in time, temperatures rise until each broken symmetry is restored, so the Big Bang becomes a test of how symmetry breaks.
- The Planck era. At 10⁻⁴³ seconds, with the universe 10⁻³³ cm across, matter was unbroken superstrings and the whole cosmos could fit in a proton.
- Gravity breaks first. At 10³² K (a thousand trillion trillion times the sun's temperature) gravity condensed out "like water droplets from vapour."
- Then the strong force, while the universe was about the size of a bowling ball.
- Then the electro-weak force at 10¹⁵ K, about 10⁻⁹ seconds, leaving a soup of free quarks, leptons and photons. Gluons condensed into the sticky glue binding quarks into hadrons.
- Transparency. At about 300,000 years and 3,000 K, hydrogen atoms could survive; before that space was opaque like dense fog, afterwards light could travel light-years.
- Order of breaking: gravity, then strong, then weak, leaving electromagnetism unbroken.
Matter first appeared 10⁻³⁸ seconds or so after the Big Bang, and will all disappear maybe 10⁴⁰ seconds from now.Sheldon Glashow
Steven Weinberg confessed "the feeling of unreality in writing about the first three minutes as if we really know what we are talking about." These are theories, but the evidence keeps confirming the overall event.
The echo of the Big Bang
In the 1940s George Gamow predicted that radiation from the Big Bang should still fill space, the same in every direction. In 1948 Ralph Alpher and Robert Herman estimated its temperature at 5 K.
Pigeons in the horn, 1965. At Bell Labs, Holmdel, New Jersey, Arno Penzias and Robert Wilson found their Holmdel Horn Antenna, built for satellite communications, picking up a stubborn microwave hiss from every direction. They rechecked everything and even cleaned out pigeon droppings; the hiss stayed. Its spectrum matched the predicted curve at about 3 K. It remains the most conclusive evidence for the Big Bang; the pair won the 1978 Nobel Prize.
- COBE (1989–92) measured a near-perfect black-body spectrum at 2.725 K and found tiny ripples (Nobel 2006 for Mather and Smoot); WMAP and Planck (final results 2018) mapped them in detail.
- Precision numbers: age 13.8 billion years (not "10 to 20"); transparency at 380,000 years; ordinary matter 5%, dark matter 27%, dark energy 68%.
- Tension: the expansion rate from the early universe (~67 km/s/Mpc) disagrees with local measurements (~73), the unresolved Hubble tension.
Neutron stars and black holes
A star is a nuclear furnace burning hydrogen into helium ash; Hans Bethe worked out the reactions in 1939 (Nobel 1967). It lives by balancing outward nuclear fire against inward gravity.
The death of a star
- Fuel exhausted after billions of years; gravity wins.
- Neutron star: atoms crushed into touching neutrons, solid nuclear matter; the sun's mass squeezed to the size of Manhattan. The 1054 supernova seen by Chinese astronomers in daylight left one at the heart of the Crab Nebula.
- Black hole: if the star is several solar masses or more, even neutrons yield and the star crushes to a point; light cannot escape but orbits, like Newton's thrown rock.
The black hole vanishes like the Cheshire cat, leaving only its smile: the warped space-time. Its severe warping resembles the early universe. Kaku says that falling in, you would seem to slow until frozen, taking thousands of years to reach the centre, where time supposedly stops; in reality general relativity probably breaks down there and string theory must take over.
The slow-motion fall is what a distant observer sees: you appear to freeze at the horizon. The infalling traveller feels nothing special at the horizon and reaches the centre in a finite and short proper time (seconds for a stellar black hole). Kaku also writes that "numerous black holes" inhabit the galactic centre; the centre holds one supermassive black hole, Sagittarius A, of about 4 million* solar masses.
- Theory: J. Robert Oppenheimer and Hartland Snyder, 1939.
- M87: the Hubble Space Telescope found a black hole there in summer 1994, 50 million light-years away.
- NGC 4258: identified in January 1995 by radio telescopes, 21 million light-years away.
- Cygnus X-1: an X-ray source about 6,000 light-years away whose output only gravitational collapse can explain.
- 1997: Hubble data hinted at black holes in thousands of middle-sized galaxies.
The Cheshire cat's smile has been photographed. The Event Horizon Telescope imaged the shadow of M87 (6.5 billion solar masses) in April 2019 and Sagittarius A in May 2022. Reinhard Genzel and Andrea Ghez won the 2020 Nobel for tracking stars orbiting Sgr A*, sharing it with Roger Penrose** for proving black holes form generically. LIGO hears black holes merge, and supermassive black holes appear in nearly every large galaxy.
Stephen Hawking, quantum cosmologist
Some call Stephen Hawking Einstein's successor because he applied quantum corrections to black holes and found what Einstein never anticipated: black holes evaporate. By the uncertainty principle, there is a small probability that light leaks out against gravity; the hole loses energy and may shrink to a mini black hole as small as a proton.
- Origins. His father, a medical researcher in London, introduced him to biology. At about 15 he ran dice-throwing ESP experiments, until a lecture on Rhine's Duke experiments showed good technique gave no results: "it was all a fraud."
- Illness. An indifferent Oxford student, he was diagnosed in his first graduate year at Cambridge with amyotrophic lateral sclerosis (Lou Gehrig's disease).
- Method. Unable to write, he does relativity's hundred-page calculations in his head, thinking in pictures like Einstein and Feynman.
- Outlook. "When one's expectations are reduced to zero, one really appreciates everything that one does have." Fame is "rather a nuisance."
Hawking died on 14 March 2018. Hawking radiation has never been observed from a real black hole (it is far too faint), though analogue versions have been seen in laboratory fluids and optical systems. The black hole information paradox it created drove decades of string-theory work; the 2019 "island" and Page curve calculations suggest information does escape.
Inflation: the flatness and horizon puzzles
Einstein's equations left two puzzles. Flatness: the universe has almost no measurable curvature, though the equations favour some. Horizon (uniformity): galaxies a billion light-years away in opposite directions look the same, yet light has not had time to carry information between them.
Blow up the balloon. Alan Guth (MIT), improved by Paul Steinhardt (Pennsylvania) and Andrei Linde (Moscow), proposed that between 10⁻³⁵ and 10⁻³³ seconds the universe expanded exponentially, growing by about 10⁵⁰ before the ordinary Big Bang. Inflate a balloon trillions of times and its surface looks flat. And our entire visible universe began as a tiny speck small enough to mix uniformly before inflation stretched it to its present size, which is why it is uniform.
Inflation's predictions of a nearly flat universe and nearly scale-invariant ripples have been confirmed by WMAP and Planck, though modern estimates of the growth factor are usually quoted as at least 10²⁶ (60 e-folds), not a fixed 10⁵⁰. Its signature primordial gravitational waves have not been found: the BICEP2 claim of 2014 turned out to be galactic dust, and the tensor-to-scalar ratio is now below about 0.036. Steinhardt himself has become a leading critic of inflation.
Is our universe unstable?
The earth will probably die in fire: the sun, out of hydrogen, will burn helium and swell into a red giant, which Kaku says will reach the orbit of Mars, vaporising the earth in several billion years. GUTs and strings allow something worse.
The dam and the bubble. Water behind a dam sits in a false vacuum: not its lowest energy, held back by a barrier. Quantum mechanics lets it tunnel through. If our whole universe sits in a false vacuum, a quantum transition could start, like boiling: a bubble of true vacuum appears and expands at nearly light speed, so nobody sees it coming. You might be doing your laundry when it arrives and the quarks in your body dissolve into plasma under new laws of physics and chemistry. Kaku reassures: 10 to 20 billion years of stability suggest we are already in the lowest state.
The Higgs measurements undercut that reassurance in an interesting way. With a Higgs mass of 125 GeV and a top-quark mass of about 172.5 GeV, the Standard Model's vacuum appears metastable: a lower state exists, but the expected lifetime is vastly longer than the age of the universe (estimates exceed 10¹⁰⁰ years). New physics could change the verdict. On the sun: current models have it swell to roughly the earth's orbit in about 5 billion years, not to Mars.
What came before
The false-vacuum idea answers the chapter's question. Perhaps the ten-dimensional universe was a false vacuum. In time it made the quantum leap: like a bursting dam, ten-dimensional space-time ruptured into a four-dimensional universe (ours) and a six-dimensional one.
The six extra dimensions are all around us but curled to the Planck length, too small to see; that may be why the universe looks four-dimensional. Experimental proof is far off; meanwhile cosmology's most mysterious clue is dark matter.
The 10-to-4 "cracking" is Kaku's own vivid gloss, not a calculation anyone has completed. String theory does not yet explain why six dimensions curled up, and since 2003 the theory has been found to allow an enormous range of possible vacua (often quoted as 10⁵⁰⁰), which makes a unique story of our origin harder, not easier.
The Mystery of Dark Matter
With the SSC dead, Kaku turns to the cosmos as physics' laboratory. Its first great clue is dark matter: an invisible substance, by 1995 estimates 90 percent of the universe, revealed only by its gravity. Kaku tells how Zwicky found it in the 1930s and was ignored, how Ostriker and Peebles and above all Vera Rubin made it undeniable, and why sparticles from string theory are a leading candidate. If dark matter turns out to be superpartners, the superstring could be tested in the sky instead of in a collider.
What is the world made of?
The twentieth century's great chemical achievement was finding that a little over one hundred elements explain everything from DNA to exploding stars, and that distant galaxies contain exactly the same elements as our backyard. That seemed the final word. Then the data showed that over 90 percent of the universe is unseen matter that has weight but no visibility: hold a clump in your hand and you would see nothing. Its nature also decides the cosmic future: a fiery Big Crunch or a Cosmic Whimper (Big Chill).
How much does a galaxy weigh?
Two ways to weigh a galaxy, which disagree
- Count the stars. Multiply average stellar density by volume (as one estimates hairs on a head; blondes have fewer than brunettes), then multiply by the average stellar mass, found from binary stars whose orbital periods give masses via Newton's laws.
- Watch the motion. Measure how fast stars, gas or whole galaxies orbit, and use Newton's laws to infer the mass holding them.
In the 1930s Fritz Zwicky of Caltech studied the Coma cluster, about 300 million light-years away, whose galaxies moved so fast they should fly apart. The mass needed to bind them was twenty times the luminous mass. He proposed dunkle Materie, dark matter, out of faith that Newton's laws hold at galactic scales, a faith with precedent: unseen planets were predicted from orbital wobbles.
Neptune was predicted in 1846 from wobbles in the orbit of Uranus, not Saturn. Pluto was found in 1930 during a search motivated by supposed perturbations that later proved spurious; it is far too small to have caused them. Zwicky's 1933 estimate was actually several hundred times the luminous mass (with the distance scale of the day); "twenty" reflects later corrections.
Zwicky met indifference, even hostility: Hubble had established galaxies beyond the Milky Way only about nine years earlier, and astronomers expected the anomaly to fade. In the 1970s radio astronomers found hydrogen gas around galaxies orbiting too fast and discounted it.
The halo (Ostriker and Peebles, 1973)
Astronomers pictured a galaxy like the solar system: inner bodies fast, outer slow. Mercury, named for the speedy god, moves at 107,000 mph; Pluto lumbers at 10,500 mph, and at Mercury's speed it would escape the sun. Jeremiah Ostriker and James Peebles at Princeton showed that such a galaxy is unstable; it becomes stable only inside a massive invisible halo holding about 90 percent of its mass. This too was met with indifference.
One woman's challenge: Vera Rubin
What turned the tide was the persistent work of Vera Rubin and colleagues at the Carnegie Institution in Washington, against a sceptical and overwhelmingly male profession.
- 1930s Age ten, she maps meteor trails over Washington; her electrical-engineer father helps her build a telescope at 14.
- College A Swarthmore admissions officer suggests she paint astronomical subjects instead (a family joke ever after: "Have you ever thought of a career in which you paint?"). At Vassar, a high-school physics teacher says, "You'll do all right as long as you stay away from science."
- Graduate school Princeton does not even send her a catalogue; it admits no women in astronomy until 1971. She declines Harvard to follow her husband Robert Rubin, a physical chemist, to Cornell; Harvard's reply bears the scrawl "Damn you women. Every time I get a good one ready, she goes off and gets married."
- Cornell Courses from Hans Bethe and Richard Feynman; her master's thesis on galaxies deviating from uniform Hubble expansion is rejected as far-fetched, later deemed prophetic.
- Home "I actually cried every time the Astrophysical Journal came into the house."
- 1954 PhD at Georgetown via night classes; her thesis shows galaxies are distributed clumpily, not smoothly.
- 1970s Seeking a quiet, unglamorous topic, she measures rotation in Andromeda: gas at the rim moves as fast as gas near the centre.
- Since 1978 About 200 galaxies show the same flat rotation curve. Zwicky was right.
- 1981 Elected to the National Academy of Sciences, where only 75 of 3,508 members since 1863 had been women.
Her daughter, a cosmic-ray PhD, was the only woman at a conference in Japan: "between her generation and mine, not an awful lot has changed." Rubin wrote a children's book, My Grandmother Is an Astronomer.
Rubin died in December 2016 without a Nobel Prize, a widely criticised omission. The Vera C. Rubin Observatory in Chile released its first images in June 2025 and is surveying the southern sky, partly to map dark matter through weak lensing. Jim Peebles shared the 2019 Nobel Prize for theoretical cosmology.
Bending starlight
Halos may be six times the size of the visible galaxy. Two lensing methods weigh them:
- Microlensing. In 1986 Bohdan Paczyński (Princeton) realised a clump of dark matter passing in front of a star would magnify it briefly. Two groups reported such brightenings in 1994.
- Cluster lensing. Anthony Tyson and colleagues at AT&T Bell Labs found clusters bending light from dim blue background galaxies far more than their stars could; about 90 percent of their mass is dark.
Hot and cold dark matter
| School | Candidate | Argument for | Status in the book |
|---|---|---|---|
| Hot dark matter | Neutrinos, light and fast | The universe may be flooded with them; a small mass could close the gap | Los Alamos (Feb 1995) claims electron-neutrino mass of about a millionth of the electron's, unconfirmed |
| Cold dark matter | WIMPs (weakly interacting massive particles), e.g. axions (named after a detergent) | Heavy, slow, exotic | No detection |
| MACHOs | Massive compact halo objects: red dwarfs, neutron stars, black holes, Jupiters | Ordinary matter, just dim | At best 20%; Hubble found too few red dwarfs in late 1994 |
| Sparticles | Superpartners: sleptons, squarks (spin 0), photino, gluino | Natural in string theory; the photino is a leading WIMP | Too heavy for existing machines |
The SSC's death need not doom tests of the superstring: new telescopes and satellites could narrow dark-matter candidates within a decade, and if they turn out to be sparticles, belief in the superstring would get an enormous boost.
- Dark matter is certain; its identity is not. The Bullet Cluster (2006) showed mass separated from hot gas in a cluster collision, a strong argument against modified gravity alone. Planck gives dark matter about 27% of the cosmic budget, about 85% of all matter (not 90% of the universe; dark energy holds the largest share).
- WIMPs keep failing to appear. LZ in South Dakota released world-leading limits in December 2025 from 417 live days, with no WIMP signal; it also began seeing boron-8 solar neutrinos, the "neutrino fog" that will eventually swamp such searches. XENONnT and PandaX-4T agree.
- The photino of 1995 is now usually the neutralino, a mixture of superpartners; LHC limits squeeze it hard.
- Axions have become a leading alternative, hunted by ADMX and others. MACHOs were largely ruled out by microlensing surveys (MACHO, EROS, OGLE) by the 2000s.
- The 1995 Los Alamos (LSND) neutrino claim was never cleanly confirmed; neutrino masses are real (Chapter 4) but too small to be the dark matter.
How will the universe die?
Cosmologists use omega (Ω), the matter density relative to the critical density.
The three fates (as framed in 1995)
- Ω > 1: gravity reverses the expansion; collapse to a Big Crunch.
- Ω < 1: expansion forever to near absolute zero, the Cosmic Whimper.
- Ω = 1: perfectly balanced and flat; requires about three hydrogen atoms per cubic metre (Kaku's figure).
- 0.1: Ω favoured by 1995 data.
- 1: Ω predicted exactly by inflation.
- 1%: critical density in visible stars.
- 15%: maximum for non-luminous ordinary matter, set by nucleosynthesis.
- 10%: reached even with galactic halos, so halos cannot solve the missing mass problem (which Kaku distinguishes from the galactic dark matter problem).
The puzzle was solved in an unexpected way. The universe is flat (total Ω = 1 to within about 0.2%), but most of the missing density is dark energy (about 68%), not matter (about 31%). The critical density is about five to six hydrogen atoms per cubic metre. Because the expansion is accelerating, the standard forecast is the Big Chill; if DESI's hint of weakening dark energy holds up, the far future becomes uncertain again, and a slow recollapse is not excluded.
A second puzzle remains: galaxies clump into gigantic clusters. Its solution may involve another kind of string, cosmic strings.
Cosmic Strings
Cosmology's second clue is clumpiness: the background radiation was almost perfectly smooth at 300,000 years, yet galaxies sit in walls, clusters and voids hundreds of millions of light-years across. Kaku lays out three ways to grow that structure: COBE's ripples, dark matter that clumps early, and cosmic strings, giant defects left by symmetry breaking. Cosmic strings borrow the mathematics of superstrings but are a different object: frozen fault lines of the early universe, possibly light-years long.
Strings the size of galaxies
Superstrings are unimaginably small, but some physicists proposed that soon after the Big Bang gigantic cosmic strings, larger than galaxies, floated through space. Their wriggling wakes might have seeded the galactic clusters, so our solar system might owe its existence to them. (Star Trek: Generations used a roaming energy ribbon that wrecks starships and traps Kirk and Picard in a time warp, transporting anyone who touches it to a wish-fulfilling dream world.)
Why is the universe so clumpy?
| The microwave background | The galaxy maps | |
|---|---|---|
| Epoch | 300,000 years after the Big Bang | Clumping by about 100 million years |
| Look | Smooth in every direction; no ripples found by balloons, rockets or ground instruments | Clumps and voids spanning several hundred million light-years, up to 5% of the visible universe |
| Implication | A uniform explosion | Not enough time to clump from such smoothness |
Clumpiness was glimpsed by Harlow Shapley (Harvard, 1933) and Fritz Zwicky (1938), but the data were crude. Automated, digital surveys later charted over ten thousand galaxies at a time.
- 1987 Alan Dressler (Carnegie) and six collaborators find galaxies within about 200 million light-years streaming towards an unseen mass, the Great Attractor, roughly towards Leo.
- 1989 Margaret Geller and John Huchra (Harvard) find the Great Wall, about 500 million light-years across; a Southern Wall follows from about 3,600 galaxies.
- Early 1990s Tod Lauer (NOAO, Tucson) and Marc Postman (STScI) survey a volume 30 times larger, 119 clusters out to 500 million light-years, and find the Great Attractor is part of a bigger flow at about 700 km/s towards Virgo.
The face of God: COBE
The COBE satellite (launched 1989) was designed to find the seeds of structure: tiny hot and cold spots in the background radiation. Berkeley physicists spent months subtracting Milky Way static and the motion of the earth and sun. In April 1992 the result made front pages worldwide: tiny irregularities too faint for earlier experiments. Reporters were told, half in jest, that they were looking at the face of God. Calculations showed these ripples, growing over a billion years, were enough to make the clumps.
Three ways to make clumps
The soufflé in a tornado. Donald Goldsmith's image: before 300,000 years, ordinary matter is like a soufflé baked in a tornado, torn apart as soon as it rises by fierce radiation. Wait until the winds die and soufflés survive. Dark matter ignores the wind: it feels gravity but not light, so it could start clumping almost immediately, and after 300,000 years ordinary matter falls into the ready-made dark clumps.
Topological defects
Cosmic strings come from the physics of phase transitions. Melting, freezing and boiling are not smooth: they start at microscopic defects, lines and walls in the atomic lattice that seed the new phase.
- Ice. Micrographs of freezing water show line-like and wall-like defects around which crystals grow.
- Iron. In a magnetic field, domain walls separate regions whose atoms point the same way; as the field grows the walls merge until all atoms align.
- Superconductors. Magnetic fields are normally expelled, but certain superconductors let them in as thin strings of condensed field (flux tubes).
In the cooling early universe, fields may have frozen into strings, walls and textures. Cosmic strings have no ends: they are closed loops or infinitely long, a tangled web threading the cosmos, under enormous tension, wiggling violently and crossing each other.
- Galaxy seeds? Strings hundreds of thousands of light-years across were first thought to seed galaxies; computer simulations seemed to rule this out.
- Gravity-wave wakes. In the 1980s it was proposed that strings, like motorboats on a lake, leave wakes of gravitational waves that condense into sheets of matter resembling galaxy walls.
- Superconducting strings. With a primordial magnetic field, strings could carry huge currents and push matter away rather than attract it; either way, matter ends up uneven.
What the next experiments would settle
- A million-galaxy atlas. Donald York (Chicago) led a multi-university effort to chart up to one million galaxies, to test whether the anomalies persist.
- Finer COBE. COBE resolved only 7 degrees of arc (a large grapefruit at arm's length), ten times the largest superclusters. A satellite resolving 0.5 degrees was needed, since balloons fly too briefly and the atmosphere blurs ground instruments.
- Inflation on trial. COBE neither proved nor disproved inflation, which says quantum fluctuations at the Big Bang were magnified across millions of light-years.
- Cold dark matter's identity: sparticles, axions or something else.
- Kaku's wish list was fulfilled. The Sloan Digital Sky Survey (York's project, operating from 2000) mapped millions of galaxies; WMAP (2001–10) and Planck (2009–13) resolved the background radiation to a few arcminutes. George Smoot, who coined the "face of God" line, and John Mather won the 2006 Nobel Prize for COBE.
- The verdict: inflation plus cold dark matter. The ripple spectrum fits nearly scale-invariant quantum fluctuations from inflation, grown by cold dark matter. Cosmic strings cannot be the main seed: Planck caps their tension at roughly Gμ < 10⁻⁷.
- Strings are not dead. String theory itself predicts cosmic superstrings (stretched fundamental strings and D-branes). In 2023 NANOGrav and other pulsar-timing arrays reported a background of nanohertz gravitational waves; merging supermassive black holes are the favoured source, but cosmic-string networks remain one of the alternatives being tested.
- Bigger structures. The Sloan Great Wall (2003) and the Laniakea supercluster (2014), which contains the Great Attractor, dwarf the 1989 Great Wall.
Kaku's broader point holds: once the SSC died, cosmology became the testing ground for physics beyond the Standard Model. It also points the reader towards the theory's strangest feature, higher-dimensional space-time.
Journey to Another Dimension
Extra dimensions began with Theodor Kaluza's 1919 letter to Einstein: write gravity in five dimensions and Maxwell's light falls out for free. Oskar Klein hid the fifth dimension by curling it to the Planck length, but nobody could say why it curled, and the idea slept for fifty years until string theorists revived it. Kaku then teaches the reader to think in higher dimensions through Flatland, hypercubes and curved space, and ends at black holes as bridges to other universes. Higher dimensions make physics simpler: more room means more symmetry, and more symmetry means unification.
Kaluza-Klein: light from a fifth dimension
- April 1919 Theodor Kaluza, an unknown mathematician at Königsberg (now Kaliningrad), writes to Einstein: a five-dimensional theory of gravity contains enough room for electromagnetism. Einstein: "The idea of achieving [a unified field theory] by means of a five-dimensional cylinder world never dawned on me. At first glance I like your idea enormously"; weeks later, "The formal unity of your theory is startling."
- 1919–1921 Einstein sits on the paper for two years, then recommends it to the Prussian Academy.
- 1926 Oskar Klein (Swedish) proposes the fifth dimension is a circle of Planck size, about 10⁻³³ cm, a hundred billion billion times smaller than a nucleus.
- 1926–1955 Einstein returns to it periodically without progress.
- 1970s Joël Scherk and Eugène Cremmer use the Kaluza-Klein trick to reduce 26 or 10 dimensions to 4.
Where did the fifth dimension go? Open a bottle of gas in a sealed room: by random collisions the molecules diffuse into every available dimension, yet they fill only three. Klein's answer: the fifth dimension is real but curled into a circle so tiny that molecules are too big to fit, so they spread through only the familiar ones.
The solution raised a new question: why would one dimension ball up while the others stretch to infinity? Einstein, Kaku says, worked late in life down two avenues: his own geometric version of electromagnetism, which grew mathematically complex and died, and Kaluza-Klein, beautiful but useless without an answer to that question.
String theorists had an advantage Kaluza and Klein lacked: quantum mechanics. Nature prefers its lowest-energy state, so if the ten-dimensional string vacuum is a false vacuum, it would tunnel to a lower state, ideally six curled dimensions plus our four. Nobody had proved this; Kaku calls it one of the outstanding problems for young physicists.
The curling of six dimensions is described today by Calabi-Yau manifolds (introduced to string theory in 1985 by Candelas, Horowitz, Strominger and Witten). The problem Kaku flagged is still open in a new form: moduli stabilisation. Since the KKLT construction (2003), string theory appears to allow an astronomically large set of stable vacua, so it explains how dimensions can curl but not why ours curled this way. Experiments have tested larger extra dimensions directly: gravity obeys the inverse-square law down to about 50 micrometres in torsion-balance tests, and the LHC has found no Kaluza-Klein particles or microscopic black holes.
Mr. Square and Flatland
Science fiction makes higher-dimensional worlds look like ours with a twist; the mathematics is stranger. The best entry is downward, through Edwin A. Abbott's Flatland (1884), a Victorian satire by a Shakespeare scholar, theologian and headmaster of the City of London School.
The trial of A. Square. In Flatland, rank rises with the number of sides: women are Straight Lines, workers and soldiers Triangles, gentlemen Squares, nobles Pentagons and Hexagons, the highest Circles. Lord Sphere from Spaceland passes through, seen only as circles that grow and shrink. He peels Mr. Square off his plane and shows him the third dimension, where a Cube appears as a square within a square that keeps changing shape. Back home Mr. Square preaches the third dimension, is tried for sedition before the Council, and is jailed for life inside a line drawn around him. He could simply step out through the third dimension, but cannot conceive it.
What a ten-dimensional being could do to us
- See inside us and operate without cutting the skin, as Spacelanders see Flatlanders' organs.
- Poke a finger into our homes, which we would see as a sphere of flesh hovering in mid-air.
- Lift a prisoner out of a locked cell and set him down elsewhere: he vanishes and reappears, a true teleporter via a higher dimension.
Visualising higher dimensions
Mathematicians handle higher dimensions algebraically, but two Flatland tricks help.
- Unfolding. A hollow cube unfolds into six squares in a cross, which a Flatlander can see but never refold. A hypercube unfolds into three-dimensional cubes in a cross, the tesseract. Salvador Dalí's Crucifixion (Corpus Hypercubus) at the Metropolitan Museum of Art hangs Christ on an unfolded hypercube while Mary Magdalene looks up.
- Shadows. A wire cube's shadow on a plane is a square within a square; rotate the cube and the shadow writhes in ways a Flatlander cannot follow. A wire hypercube's shadow in our space is a cube within a cube, gyrating incomprehensibly as it turns.
The rule: higher-dimensional beings see lower-dimensional objects whole; lower-dimensional beings see only slices or shadows of higher ones.
The Flatlander and the carrot. Lift Mr. Square into our space like a paper doll. His eyes face sideways and see only a plane. As he drifts past a carrot he sees a small orange circle appear from nowhere, grow, turn into a green circle (the leafy top) and vanish: successive slices of one object he can never see whole. Grabbed by a ten-dimensional being, we would first see three spheres of flesh circling and closing in, then a parade of 3-D objects appearing, changing colour, growing, shrinking and disappearing.
The curvature of space-time
A space warp is the distortion of space-time by matter-energy, Einstein's gravity. We think space is flat for the same reason the earth looked flat: we are small relative to its curvature. A bug on a sphere thinks it flat, yet can walk all the way round: a sphere's surface is unbounded but finite. Our universe may live on the skin of an expanding hypersphere, galaxies receding like spots on a balloon. Asking where the Big Bang happened is like asking where on the balloon's surface the inflation started: nowhere on the surface.
| Surface | Sum of a triangle's angles | Curvature |
|---|---|---|
| Flat plane | Exactly 180° | Zero |
| Sphere | More than 180° | Positive |
| Saddle or trumpet | Less than 180° | Negative |
Educated people in Columbus's day did not think the earth was flat; its sphericity had been known since antiquity, and the dispute was over its size. Kaku's claim that "we need five dimensions to explain where the Big Bang took place" overreads the balloon analogy: general relativity needs no embedding space, and the Big Bang happened everywhere. Lobachevsky was not destitute: he was rector of Kazan University, though his work was ignored; János Bolyai found the same geometry independently and goes unmentioned.
Non-Euclidean geometry
- Gauss's triangle. Carl Friedrich Gauss had assistants stand on three mountain tops and measured the angles: 180°, so space is flat or its curvature too small to see.
- Euclid's fifth postulate (about 300 B.C.): through a point not on a line, exactly one parallel can be drawn. For two thousand years mathematicians tried to derive it from the other four; every proof contained an error.
- Lobachevsky (1829). Nikolai Lobachevsky assumed it unprovable and built a geometry where it is false: the birth of non-Euclidean geometry. Gauss had reached the same result earlier but never published, fearing the backlash.
- Riemann (1854). Bernhard Riemann generalised it to any number of dimensions and any curvature. Poor and supporting relatives, he finally won a Göttingen professorship in 1859 and died of tuberculosis in 1866, aged 39. Riemannian geometry became the mathematics of general relativity; Einstein "borrowed wholesale" from it.
Where is the farthest star?
The back of your own head. Suppose the universe is a small hypersphere and light travels all the way around it. Peer through a telescope at the farthest object and you see yourself, peering through a telescope; the farthest star is Sol. Tilt the telescope slightly and you see an image of yourself looking at another copy of yourself, an infinite regress of observers, all made by light that has circled the universe many times.
Black holes as gateways
Einstein's trumpet-shaped picture of a black hole was not self-consistent alone: he had to join two trumpets neck to neck, which looks like a gateway between two universes, the Einstein-Rosen bridge. To Einstein it was a curiosity: gravity is infinite at the neck, crushing atoms and nuclei, so no communication is possible.
| Non-spinning (Schwarzschild) | Spinning (Kerr, 1963) | |
|---|---|---|
| Collapse to | A point | An infinitely thin ring |
| Gravity on entry | Infinite at the centre | Finite if you pass through the ring along its axis; crushing from the side |
| Bridge | Closed by infinite gravity | A probe might pass to another universe, or, per Hawking and Penrose, another part of ours |
| Realism | Idealised | Most black holes should spin, by conservation of angular momentum |
Rockets sent through a Kerr ring at right angles might emerge on the far side of the universe. Whether such bridges survive depends on quantum corrections, impossible to compute in general relativity; superstrings may finally decide whether quantum effects seal the bridge, as many physicists expect.
- Kerr's interior is unstable. Later work (Poisson and Israel's mass inflation, 1990, and successors) shows the inner horizon of a realistic rotating black hole is violently unstable, so the clean passage through the ring almost certainly does not exist in nature.
- Traversable wormholes need exotic matter. Morris and Thorne (1988) showed a wormhole stays open only with negative energy; quantum effects allow small amounts, and Gao, Jafferis and Wall (2016) built a traversable wormhole in AdS that never permits faster-than-light signalling.
- ER = EPR. Maldacena and Susskind (2013) proposed that entangled particles are connected by microscopic Einstein-Rosen bridges, a now-central idea in quantum gravity. A 2022 quantum-processor "wormhole" simulation drew wide publicity and equally wide criticism that it was a toy model, not a real wormhole.
Back to the Future
Taking his cue from Alice stepping through the looking glass, Kaku asks what physics says about alternate universes: made of antimatter, mirror-reversed, time-reversed, or reached by time travel. The answers run from settled experiment (antimatter, parity violation, CP violation) to the frontier (Gödel and NUT universes, a universe from nothing). CP violation is the chapter's hinge: a tiny asymmetry between matter and antimatter is why anything at all survived the Big Bang, and only a quantum theory of gravity such as strings can rule on time travel.
Through the looking glass
Lewis Carroll was Charles Lutwidge Dodgson, an Oxford mathematician and logician. Kaku repeats the tale that Queen Victoria, charmed by Alice, asked for his next book and received a treatise on abstract mathematics. Carroll's message to children: other worlds with different rules are possible. GUTs and strings have a surprising amount to say about which ones.
The Queen Victoria anecdote is apocryphal; Dodgson himself denied it in print. And the world behind the mirror is Looking-Glass Land, not Wonderland, which Alice entered down a rabbit hole.
Antimatter
Paul Dirac (born 1902) graduated from Bristol in electrical engineering at 18, found no job, could not afford Cambridge, and took a second degree in applied mathematics in 1923. Hearing of Heisenberg's work in 1925, he plunged in with little prior physics.
The minus sign (1928). At 26, Dirac wanted a relativistic equation for the electron, since Schrödinger's works only at low speeds. Kaku frames the key as E = ±mc²: Einstein ignored the minus sign because his theory concerned forces, but an equation for matter could not. Negative-energy solutions described particles identical to ordinary ones but with opposite charge: the anti-electron, which could orbit an antiproton to make antiatoms, antimolecules, antiplanets and antistars. Dirac cautiously suggested the proton might be the electron's partner, but left the door open.
- Discovery. Carl Anderson (Caltech) found a cosmic-ray track of an electron curving the wrong way in a magnetic field: the positron.
- Honours. Dirac won the Nobel Prize in 1933 at 31 and Newton's Lucasian chair; Anderson won in 1936.
- Heisenberg's verdict. Antimatter was "the most decisive discovery in connection with the properties or the nature of elementary particles."
- Energy. Matter-antimatter annihilation is up to 100 percent efficient, against about 1 percent for a nuclear bomb (Kaku's figures); a chunk of antimatter would explode beyond any hydrogen bomb. Antimatter bombs are possible in principle but prohibitively expensive; antimatter rocket fuel would need natural antimatter deposits.
- The "dirac". Dirac was so taciturn that Cambridge students defined the dirac as a unit of volubility: one word per year.
The relativistic relation is E² = p²c² + m²c⁴, whose square root has two signs; "E = ±mc²" is a simplification. Fission converts about 0.1 percent of mass to energy and fusion about 0.7 percent, so Kaku's "1 percent" is generous. Dirac shared the 1933 prize with Schrödinger.
Antimatter is now made and stored routinely at CERN's Antiproton Decelerator. Antihydrogen atoms were first produced in 1995 and trapped for minutes by ALPHA (2011). In 2023 ALPHA showed that antihydrogen falls down under gravity like ordinary matter, ruling out "antigravity." Its spectrum matches hydrogen's to parts in a trillion. Positron annihilation is used daily in hospital PET scanners.
Going backward in time
In the early 1940s Feynman, then a Princeton graduate student, saw that in QED antimatter moving forward in time is indistinguishable from matter moving backward in time. Push an electron left with a field; reverse its time and it moves right, exactly as a positive charge would. Anderson's positron was, in this reading, an electron going backward in time. An electron-positron annihilation diagram becomes one electron that moves forward, emits a photon, and turns back in time.
Wheeler's one-electron universe. John Wheeler excitedly told his student Feynman why all electrons are identical (no fat, green or long ones): there is only one. Out of the Big Bang comes a single electron that runs forward billions of years to Doomsday, which flips it backward in time; at the Big Bang it flips again, zigzagging like a Ping-Pong ball. Anyone living in between sees countless electrons (forward legs) and positrons (backward legs). Moving back and forth in space cannot copy an object, but moving back and forth in time can, like the hero of Back to the Future watching himself leave in the time machine. Your electrons would be billions of years older than mine. (The modern version would be a one-string universe.)
Is it true? Formally yes, but no QED experiment can tell matter-backward from antimatter-forward, so no usable signal goes into the past. Antimatter in space may come from the future, but we cannot use it to message the past.
The idea predates Feynman: Ernst Stueckelberg proposed it in 1941. Wheeler's one-electron picture also fails on its face, as Feynman pointed out at the time: it predicts equal numbers of electrons and positrons, whereas the universe is overwhelmingly matter.
Mirror universes and parity
In the looking-glass world people are left-handed, hearts sit on the right and clocks run counterclockwise. The equations of Newton, Maxwell, Einstein and Schrödinger are unchanged by mirror reversal, so physicists believed in conservation of parity: a left-handed and a right-handed universe are equally possible.
Feynman's radio problem. We make radio contact with aliens who understand everything. We say our hearts are on the left. "What is left?" As in left hand. "Which is our left tentacle?" Turn clockwise. "What is clockwise?" When a clock's hands point up, they move to the right. "We understand up and clocks, but not right." Stand on your north pole and the planet turns... "How do you tell the North Pole from the South?" We give up. Punchline: if parity holds, no radio message can define left and right.
In 1956 Chen Ning (Frank) Yang and Tsung-Dao Lee, at the Institute for Advanced Study, showed parity is violated in the weak interaction. Chien-Shiung Wu at Columbia confirmed it: cobalt-60 nuclei in a magnetic field emit decay electrons preferentially in one direction. Pauli: "God must have made a mistake!" Lee and Yang won the 1957 Nobel Prize. Now we can radio the aliens: put cobalt-60 in a magnetic field, see which way the electrons go, and you know north, hence clockwise and right.
The handshake. We fly to meet the aliens, agreeing to shake right hands. They extend their left tentacles. In a flash we realise they are made of antimatter: they ran the experiment with anti-cobalt-60, whose positrons went south. Shaking hands would annihilate us all.
The aliens say cobalt-60 has "sixty protons." It has 27 protons; 60 is the mass number (27 protons plus 33 neutrons). And Wu was left out of the Nobel Prize that her experiment secured, now widely regarded as an injustice.
CP violation: why anything exists
After parity fell, physicists hoped for the combined symmetry CP (C, charge conjugation, swaps matter and antimatter; P swaps left and right). If CP held, an antimatter mirror universe would still be indistinguishable, and you still could not define left by radio without knowing what the aliens were made of. In 1964 Val Fitch and James Cronin at Brookhaven found CP violated in the decay of certain mesons (Nobel 1980).
| Symmetry | What it swaps | Status | Discovered broken |
|---|---|---|---|
| P (parity) | Left and right | Violated in weak decays | 1956–57 (Lee, Yang, Wu) |
| C (charge) | Matter and antimatter | Violated in weak decays | 1957 |
| CP | Both together | Slightly violated | 1964 (Cronin, Fitch) |
The disappointment became a blessing. The visible universe contains almost no antimatter; why? Early ideas kept matter and antimatter apart by some unseen force. GUTs and strings offer the simplest answer:
The matter in our bodies is a fossil of that annihilation; without CP violation, there is no universe.
CP violation has since been measured in B mesons (BaBar and Belle, 2001; Nobel 2008 for Kobayashi and Maskawa's explanation), in charm mesons (LHCb, 2019) and, in 2025, for the first time in baryons (LHCb, in Λb decays). The puzzle is that the Standard Model's CP violation is billions of times too small to explain the cosmic excess, so new sources are sought, for example in neutrinos, where T2K and NOvA see hints and DUNE and Hyper-Kamiokande will measure it. Andrei Sakharov's 1967 conditions for creating matter (baryon-number violation, C and CP violation, departure from equilibrium) frame the search.
Time travel?
Most solutions of Einstein's equations explain real things: Schwarzschild (black holes), Reissner-Nordström (charged black holes), Robertson-Walker (the Big Bang). Others are disturbing.
- Gödel (1949). Kurt Gödel found a rotating-universe solution that is acausal: time loops back on itself, like a film replayed forever. Einstein, in February 1949, called it "an important contribution to the general theory of relativity, especially to the analysis of the concept of time," admitted the problem had troubled him since 1915, and suggested such solutions might be "excluded on physical grounds."
- NUT (1960s). E. T. Newman, T. W. J. Unti and L. A. Tamburino (Pittsburgh) found solutions with time travel and spiral-staircase geometry: walk 360° around a star and you arrive not at your start but on a different sheet of space-time, like climbing a spiral staircase to the next floor.
- Reassurance. You will probably not, as in Back to the Future, make your mother fall in love with you before you are born; NUT regions, if real, lie beyond our light horizon.
The quantum theory reopened these doors: by the uncertainty principle there is always some probability of leaping into such a universe, and without calculable quantum gravity nobody could say how small. Kaku's claim: with superstrings "all quantum effects are now totally calculable," so the question of bridges, other universes and time travel can be answered once and for all, though nobody had done the calculation.
The question is still open. Kip Thorne and colleagues (1988) showed how a traversable wormhole could be made into a time machine, given exotic negative energy; Stephen Hawking's chronology protection conjecture (1992) argues quantum effects always destroy time machines before they form. Semiclassical calculations support Hawking in many cases, but no full string-theory calculation settles it. Kaku's "only a matter of time" has so far been more than thirty years.
Everything from nothing?
Stopping traffic in Princeton. During the war George Gamow, walking with Einstein, passed on Pascual Jordan's idea: a star's mass is positive energy, its gravitational field negative energy, so the total may be zero, and nothing forbids a quantum jump from vacuum to a whole star. Einstein stopped in his tracks in the middle of the street; cars had to brake to avoid them (Gamow, My World Line).
In 1973 Edward Tryon of Hunter College proposed independently that the entire universe is a vacuum fluctuation, since its total energy appears to be near zero. Inflation theorists take this seriously. For strings, it would mean the original ten-dimensional universe had zero energy; once someone computes how ten dimensions cracked into four, the energy stored can be checked. Kaku calls the problem well defined and "only a matter of time."
Time travel, NUTs, everything from nothing: Einstein could wave such solutions away "on physical grounds," but that was speculation. Kaku's selling point for strings is that they make the quantum corrections calculable, and he ends by inviting young readers to settle these questions.
Beyond Einstein
Kaku closes with the big picture. If the superstring proves a finite quantum theory of gravity, it is the only candidate unified theory and completes Einstein's quest. Its success would vindicate beauty and symmetry as guides, answer Dirac's objection to renormalization, and read the history of unification as a four-stage mystery novel. But knowing the rules is not mastering the game: a final theory would open physics rather than end it, and humanity, barely a Type 0 civilisation, is only beginning.
The end of a three-hundred-year story
The ancient questions (what lies beyond the farthest star, how the universe began, what came before time) may at last get detailed, numerical answers. Unification, once beautiful but impractical, has been the dominant theme of theoretical physics for twenty years; Glashow describes the isolated strands of physics being woven into a single elegant fabric.
In no other branch of science is there even an abstract possibility of being finished.John Schwarz
Schwarz's point: chemistry, biology and even condensed-matter, atomic and plasma physics are open-ended, but particle theory asks so specific a question that complete success would finish it, with "one concise and beautiful answer that encompasses the whole story."
The oldest record. Historians prize a yellowed manuscript a few centuries old; archaeologists, artefacts thousands of years old; geologists, gems formed hundreds of millions of years ago; astronomers, starlight billions of years old. The superstring reaches further than all of them, to the beginning of time, when all forces were one primal superforce: phenomena at the centre of our existence but beyond all human experience.
Symmetry and beauty
Physics has come full circle: before Newton the universe was thought perfectly ordered; by the 1800s, in the run-up to relativity and quantum mechanics, physics looked chaotic; now order returns on a higher plane. Symmetry alone cannot deduce the laws, but beauty grounded in evidence has been a remarkably accurate guide. Schwarz: at the deepest level, "for reasons that nobody seems to understand, the more elegant and simple your scheme is, the more success it seems to have."
Physics has also become more coherent. A newcomer once needed books on black holes, lasers, quarks, quantum mechanics and electromagnetism, and a student twenty volumes; now one book can present the field in a few pictorial ideas, which Kaku names as the theme of Beyond Einstein.
The minefield that symmetry must clear
Marrying quantum mechanics with relativity produces:
- Anomalies: small defects that make a theory inconsistent.
- Divergences: infinite answers.
- Tachyons: faster-than-light particles.
- Ghosts: particles with negative probability.
- Other diseases.
The superstring works because it has the largest symmetry ever found in a physical model, arising naturally from strings rather than points. Many universes fit relativity, and many fit quantum mechanics, but together so few survive that only one ironclad solution is probably possible.
It also answers Dirac, who never accepted Feynman's sleight of hand with infinities: superstrings need no renormalization, since all loop diagrams are believed finite by symmetry.
This chapter is the book at its most confident and most dated. "Only one solution is probably possible" turned into its opposite: since 2003 string theory appears to admit an enormous number of vacua, and uniqueness is no longer claimed. All-loop finiteness of superstring perturbation theory remains strongly believed but not fully proved (major progress came from Eric D'Hoker, Duong Phong and Edward Witten). And the appeal to beauty has critics: Sabine Hossenfelder's Lost in Math (2018) and Peter Woit's Not Even Wrong (2006) argue that elegance has misled fundamental physics since the 1980s.
Like a mystery novel
| Stage | In a mystery novel | In physics | Era |
|---|---|---|---|
| 1 | The characters are introduced | Forces identified: Newton, Maxwell, Planck, Heisenberg. Slow, because no crime was defined; only Einstein saw the goal, alone and blind to the nuclear force | Centuries to 1930s |
| 2 | Patterns link suspects to the crime | SU(3) in strong, SU(2) in weak interactions; Lie groups and quarks, with no idea why | 1950s–1960s |
| 3 | Theories proposed, false starts and reversals | Gauge symmetry unifies three forces; S-matrix detour gives birth to strings, which are misunderstood and discarded | 1970s |
| 4 | Clues fall into place; the conclusion | The superstring emerges without rival; experiment still pending | 1984–1995 |
Becoming grandmasters
Will physicists put themselves out of work? Glashow's fable answers no.
Arthur at Washington Square. An intelligent alien lands in New York's Washington Square and watches two old men playing chess. He sets himself two tasks: learn the rules, then become a Grandmaster. Particle physicists and cosmologists are on the first task, since only there are the rules partly unknown. Condensed-matter physicists, chemists, geologists and biologists know the rules and face the second. One task is more fundamental, the other more relevant; both are immense.
A cancer researcher told, correctly, that the laws governing DNA's atoms are completely known gains nothing: cell biology involves trillions of trillions of atoms, beyond any computer's ability to solve the Schrödinger equation. "Quantum mechanics solves all of chemistry in principle" says everything and nothing. A unified theory gives the rules of the game, not the art of winning; it would open vast new regions of study, not end physics.
The "rules versus Grandmaster" distinction is a useful discipline outside physics too. Knowing the governing rules of a system (an architecture standard, a regulatory framework, a model's training objective) is a different achievement from knowing how the system behaves at scale. Most practical failures happen in the gap between the two, where emergent behaviour lives.
On the threshold of the stars
We are making credible statements about the origin of time while technologically in our infancy, just beginning to probe nearby planets. Giordano Bruno burned in 1600 for calling the sun a star; perhaps two million years after leaving the forests, we reason about events billions of years ago. One might have expected only an advanced civilisation to find the unified theory.
Kardashev's scale of civilisations (Nikolai Kardashev)
- Type I: controls the resources of a planet. Controls weather, makes the Sahara bloom, harnesses hurricanes, redirects rivers, farms oceans, reshapes continents, predicts or creates earthquakes, extracts deep minerals. Kaku's estimate: a few hundred years away.
- Type II: controls the power of a star. Colonises the solar system and neighbours, mines asteroids, builds machines to mine the sun. Several thousand years away.
- Type III: controls a galaxy, with interstellar travel; think of Isaac Asimov's Foundation series.
Newton and Maxwell never imagined moon rockets or electrified cities; their societies could not absorb their theories' potential. Because technology grows geometrically and imagination extrapolates linearly, old science fiction always looks quaint, and science will always be stranger than science fiction. We cannot yet exploit a unified field theory, but we can explore it. "Far from the end, it is only the beginning."
Kaku says our rockets "can barely escape" the sun's pull; in fact Voyager 1 crossed into interstellar space in 2012 and Voyager 2 in 2018. On the Kardashev scale, astronomers who use Carl Sagan's logarithmic version put humanity at about 0.73. Kaku went on to develop the Type I to III theme at length in Physics of the Future (2011) and The Future of Humanity (2018).
M-Theory
In 1995 string theory underwent its third incarnation. Edward Witten and Paul Townsend found that the five apparently different superstring theories are one theory seen from different angles, linked by a new symmetry, duality, and that its true home is eleven dimensions, where strings coexist with membranes. Witten named it M-theory. For Kaku this is the strongest sign yet that the final theory is near: "we can see the dim outlines of the lion, and it is magnificent."
Twenty-first-century physics that fell into the twentieth
Kaku's diagnosis of the theory's difficulty: superstring theory is 21st-century physics that fell into the 20th century by accident, and the 21st-century mathematics needed to solve it has not been invented. Nobody can catalogue all its solutions, the conformal field theories.
Ramond's Egyptian tomb. Pierre Ramond compares string theory to a tomb buried in sand. You trip over a stone fragment, which turns out to be the handle of an entrance; digging reveals a staircase, then ever more beautiful chambers, and finally the Pharaoh's tomb: the fundamental principles. The point: string theory is being discovered backwards, from solutions towards principles.
| General relativity | String theory | |
|---|---|---|
| Starting point | A physical principle: the Equivalence Principle | An accident: a formula found in 1968 |
| Then | Field equations deduced | Solutions found piecemeal |
| Finally | Solutions discovered | The underlying principle still unknown |
Three incarnations
- 1968 Dual Resonance Model: Veneziano and Suzuki's scattering formula, with no idea why it worked.
- Around 1970–72 Nambu explains it as a vibrating string.
- 1984 Green and Schwarz show it is the only consistent candidate for a theory of everything; millions of solutions follow, some close to our universe, none exact. By the early 1990s progress stalls and physicists leave the field.
- 1995 Witten (IAS) and Paul Townsend (Cambridge) start an avalanche of papers: the theory lives in 11 dimensions, with strings and membranes. M stands for magic, majesty, mother, mystery or membrane.
The Postscript dates Nambu's string interpretation to "around 1972"; Chapter 6 gives 1970, which is closer to the truth (Nambu, Nielsen and Susskind, 1969–70).
The embarrassment of five theories
By 1995 there were five consistent superstring theories in ten dimensions. Einstein had asked whether God had any choice in creating the universe; if quantum theory and relativity together allowed only one solution, why five?
The five ten-dimensional superstring theories
- Heterotic E(8) × E(8): the Princeton string quartet's theory, apparently the most realistic; usually what "the superstring" meant.
- Heterotic SO(32).
- Type I (open and closed strings).
- Type IIA.
- Type IIB.
Result of 1995: all five are the same theory, viewed from the eleventh dimension. "Perhaps God had no choice after all."
The Roman general on the mountain. Roman armies without telephones sent runners between battlefields, creating chaos. The fix was to go into the third dimension: seize a mountain top, from which all the small fronts appear as one coherent battle. From the eleventh dimension, the five string theories are likewise seen to be one.
Duality
Maxwell's equations are unchanged if you swap electric and magnetic fields: the electric field is dual to the magnetic. For 130 years this was thought unique to electromagnetism. It turns out to be one of string theory's most powerful symmetries: take one string theory's dual and you often get a completely different string theory, proving the five equivalent. Most startling, the dual of the ten-dimensional Type IIA theory is an eleven-dimensional theory: M-theory.
- Supergravity resurrected. The low-energy limit of M-theory is the old eleven-dimensional supergravity, dismissed in the 1980s; M-theory supplies the higher-order terms that may make it finite.
- Branes resurrected. 1980s supermembranes of various dimensions, discarded in favour of strings, are essential after all. A membrane vibrating in p dimensions is a p-brane ("pea-brain").
- New power. Problems once intractable became trivial: an almost complete classification of string solutions in eight and six dimensions; the next target is four.
The blind wise men and the lion. Einstein said that when Nature shows a tail, there is a lion at the other end: the tail is the clues (the four forces), the lion the unified theory. A lion races past three blind wise men. One grabs the tail: "It's a string!" Another the ear: "It's a membrane!" The third a leg: "It's a three-brane!" Each is right about his sector; what connects the sectors is duality.
Where it leaves the quest
Nobody yet had a complete description of M-theory, and with millions of four-dimensional solutions no "Eureka!" was imminent. But duality is the first guiding principle for sifting them; before it, physicists got lost. If duality and M-theory show that one solution is precisely our universe of quarks and electrons, it will be "one of the greatest scientific discoveries of all time." Kaku ends: "I believe that one day soon we shall hear it roar."
Thirty years after the Second Superstring Revolution
- D-branes (1995). Joseph Polchinski identified the branes as D-branes, surfaces where open strings end, which became the main tool of the field.
- Black-hole entropy (1996). Andrew Strominger and Cumrun Vafa counted D-brane states to reproduce the Bekenstein-Hawking entropy of certain black holes, string theory's most celebrated quantitative success.
- AdS/CFT (1997). Juan Maldacena conjectured that string theory in anti-de Sitter space is exactly equivalent to a quantum field theory on its boundary, a holographic duality and the most cited paper in high-energy physics. It now powers work on quark-gluon plasma, condensed matter, the information paradox and the idea that space-time emerges from entanglement.
- The vacuum explosion (2003). KKLT and others found that M-theory admits perhaps 10⁵⁰⁰ four-dimensional vacua. Instead of picking out our universe, the theory seemed to allow almost anything, prompting anthropic arguments and fierce criticism.
- The swampland (2005 onward). Vafa and others turned the question around, seeking criteria that low-energy theories must meet to come from quantum gravity. The 2018 de Sitter conjecture suggested string theory may not allow a stable positive cosmological constant, so DESI's 2025 hints of evolving dark energy drew intense string-theory interest.
- Still no definition, still no test. M-theory has no complete non-perturbative formulation beyond special backgrounds (matrix models, AdS/CFT), no LHC superpartners or extra dimensions have appeared, and no unique prediction distinguishes it. Its biggest payoffs have come as mathematics and as a toolkit for quantum gravity and quantum field theory, not as the confirmed theory of everything Kaku foresaw.
The Postscript's logic still stands as a description of what M-theory did: it turned five rival theories into one and promoted duality to a master symmetry. What changed is the expected payoff. Duality did not lead to our universe being singled out; it led to holography, which may prove the deeper discovery.
Master Takeaways
- Unification is the spine of physics. Newton joined heaven and earth, Maxwell electricity and magnetism, Einstein space with time and gravity with geometry, Weinberg-Salam-Glashow the weak force with light; the superstring proposes the last step, gravity with everything.
- Symmetry cancels infinities. Every successful quantum theory of a force (QED, electro-weak, QCD) was made finite by gauge symmetry; the superstring has the largest symmetry known, which is why its loop diagrams are believed finite without renormalization.
- Point particles are the root disease. A point's field goes as 1/0 at its surface; replacing points with strings of length about 10⁻³³ cm smooths interactions and removes the infinities that blocked quantum gravity.
- The Standard Model is a success and a stopgap. It matches every experiment yet has three duplicate generations, nineteen (now about 26) free parameters and no gravity, so it cannot be final.
- String theory's "defects" were its strengths. The unwanted graviton and the demand for extra dimensions killed it as a theory of hadrons and made it a candidate theory of everything.
- The test is the weak point. Unification happens near 10¹⁹ GeV, a quadrillion times beyond any collider; after the SSC's cancellation the evidence must come from cosmology, and thirty years on no direct confirmation exists.
- Great theories rest on simple pictures. Kaku's reading of Einstein's failure is that he abandoned physical pictures for formal mathematics and tried to unite gravity with light instead of with the nuclear forces and the quantum.
- Broken symmetry makes the world interesting. The four forces look different because the universe is cold and old; heating it toward the Big Bang would restore electro-weak, then GUT, then string symmetry.
- Supersymmetry pairs every boson with a fermion. It cancels divergences pairwise and needs anticommuting Grassmann numbers, but no superpartner has been seen, at the LHC or anywhere else.
- Quantum mechanics predicts only probabilities. Uncertainty, Schrödinger's cat and the measurement problem remain philosophically open; Bell tests have since ruled out the local realism Einstein hoped for.
- Dark matter is real and still unidentified. Zwicky, Ostriker-Peebles and Vera Rubin's flat rotation curves established it; WIMP, MACHO and neutrino explanations have mostly failed.
- CP violation is why we exist. A one-in-a-billion excess of matter survived the Big Bang's annihilation, but the Standard Model's CP violation is far too small to explain it.
- Extra dimensions can hide by curling up. Kaluza (1919) and Klein (1926) showed a fifth dimension yields electromagnetism and can be Planck-sized; strings need six such dimensions, and why they curl is still open.
- Lower dimensions teach higher ones. Flatland, unfolded hypercubes and hypercube shadows show that lower-dimensional beings see only slices and shadows of higher objects.
- Exotic solutions need quantum gravity to judge. Einstein-Rosen bridges, Kerr rings, Gödel and NUT universes are legal in relativity; whether quantum effects forbid them is unsettled.
- Duality is the 1995 master symmetry. It shows the five superstring theories are one eleven-dimensional M-theory and later produced holography (AdS/CFT).
- A final theory gives the rules, not mastery. Glashow's chess fable: knowing the laws that govern DNA's atoms does not cure cancer; unification opens new fields rather than ending physics.
- Beauty is a powerful but fallible guide. It worked from Newton to the Standard Model; its record since the 1980s, in supersymmetry and string uniqueness, is far weaker.
Frameworks & mental models
| Name | What it says | Use it when |
|---|---|---|
| Chain of unifications | Each leap merged two apparently different things under one principle | Tracing how a field matures from fragments to theory |
| Matter as music | Particles are vibration modes of one string; no note is more fundamental | Explaining how one simple rule can generate diversity |
| Symmetry cancels infinities | More symmetry means fewer pathologies in quantum theories | Judging which candidate theory is likely to be consistent |
| Global vs local (gauge) symmetry | Same transformation everywhere vs a different one at each point; local symmetry forces new force carriers | Understanding why forces exist at all |
| Broken symmetry and the thermostat | Equations keep symmetry; cold solutions break it; heating restores it | Reading the early universe as a high-energy laboratory |
| Yukawa, Dirac and Nambu modes | Data-driven, mathematics-driven, or wild mathematics disciplined by data | Choosing a research style |
| Rules vs Grandmaster | Knowing fundamental laws differs from mastering their consequences | Separating fundamental from applied questions |
| Flatland reasoning | Study lower dimensions to grasp higher ones: slices and shadows | Visualising anything beyond direct intuition |
| Antaeus principle | Theories lose strength when they lose contact with experiment | Auditing a beautiful but untested idea |
| Kardashev scale | Civilisations ranked by energy use: planet, star, galaxy | Placing technology in a long-run perspective |
On the whole book. As history and as an introduction to unification, Beyond Einstein is clear and largely reliable, though it compresses dates (the tau, the neutrino detection, the top quark, Scherk-Schwarz) and occasionally misattributes (Lie for the exceptional groups, Galois for the quintic). Its physics of 1995 is sound. Its weakness is advocacy: it presents string theory as "without rival," expects superpartners at the LHC, a unique solution, finite calculable quantum corrections "only a matter of time," and dark matter made of photinos. Three decades later none of these has come true, and string theory faces some 10⁵⁰⁰ possible solutions and serious critics. Read it as the best case for strings made at the height of their promise, and read the update boxes for what happened next.
Who's who
| Person | Role | Why they matter here |
|---|---|---|
| Isaac Newton | Gravitation, 1687 | First unification: heaven and earth |
| James Clerk Maxwell | Electromagnetism, 1860s | Light as electric and magnetic fields; first field theory |
| Albert Einstein | Relativity, 1905 and 1915 | Space-time and gravity as geometry; failed unified field theory |
| Max Planck | Quantum, 1900 | Energy comes in packets |
| Werner Heisenberg | Quantum mechanics, uncertainty | Founder of the theory of matter |
| Erwin Schrödinger | Wave equation, the cat | The "cookbook" of chemistry |
| Paul Dirac | Relativistic electron, antimatter | Predicted antimatter; critic of renormalization |
| Richard Feynman | QED, diagrams | Tamed infinities; antimatter as matter going backward in time |
| C. N. Yang and Robert Mills | Gauge theory, 1954 | The symmetry framework behind all forces |
| Gerard 't Hooft | Renormalization of Yang-Mills, 1971 | Made the electro-weak theory finite |
| Weinberg, Salam, Glashow | Electro-weak theory | 1979 Nobel; second great unification |
| Murray Gell-Mann | Quarks, Eightfold Way | Order in the particle zoo |
| Veneziano and Suzuki | Beta-function formula, 1968 | Accidental birth of string theory |
| Yoichiro Nambu | String interpretation | Wrote the basic string equations |
| John Schwarz and Michael Green | Superstrings, 1984 anomaly cancellation | Revived strings as a theory of everything |
| Joël Scherk | Strings as gravity | Proposed the reinterpretation with Schwarz |
| Michio Kaku | String field theory, 1974 (with Kikkawa) | Co-author and insider |
| Gross, Harvey, Martinec, Rohm | Heterotic string | E(8) × E(8) candidate |
| Fritz Zwicky and Vera Rubin | Dark matter | Discovered and established it |
| Stephen Hawking | Black-hole evaporation | Quantum corrections to gravity |
| Kaluza and Klein | Fifth dimension | Ancestors of extra-dimensional unification |
| Edward Witten | M-theory, 1995 | Unified the five string theories |
Connect it
- Abstraction layers. Kaku's "worlds within worlds" (compounds, elements, nucleons, quarks, strings) is the same move an enterprise architect makes when a sprawl of systems is explained by a smaller set of shared platforms; the test of a good layer is whether it predicts the holes in the chart, as Mendeleev's did.
- Symmetry as a design constraint. Physicists found that consistency constraints, not taste, forced symmetry on their theories. Architecture standards earn their keep the same way: an interface contract that holds at every point (local, not global) removes whole classes of integration failures.
- Beauty versus evidence in AI. The string story is a cautionary tale for any field, AI included, where an elegant framework runs ahead of measurement; Goldhaber's Antaeus principle argues for keeping every model grounded in evaluations against real outcomes.
- Rules versus mastery. Glashow's chess fable maps onto large models: knowing a network's architecture and training objective (the rules) does not tell you how it behaves in a bank's production workflow (the game).
About this book
Beyond Einstein: The Cosmic Quest for the Theory of the Universe by Michio Kaku and Jennifer Thompson, 1995. 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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