DEEP READ · 110
From the Big Bang to Black Holes · Stephen Hawking · 1988
The twentieth century left us two spectacularly successful theories that refuse to get along: general relativity for the very large, quantum mechanics for the very small. Hawking's book is the story of where they collide. Run general relativity backwards and the universe slams into a beginning where every law of physics breaks down; bring quantum mechanics in, and that beginning may smooth away — leaving a universe that is finite but has no edge, and needs no first push. Along the way he turns black holes from one-way graves into hot objects that glow and slowly evaporate, which is his own hardest contribution to science.
Hawking (1942–2018) held the Lucasian Chair of Mathematics at Cambridge — Newton's old post — and was diagnosed with ALS (motor neurone disease) at 21; by the time he wrote this book he could speak only through a voice synthesizer. Published in 1988, it spent 237 weeks on the Sunday Times bestseller list and sold more than ten million copies. It is the best-selling book on cosmology ever written, and quite possibly the most-bought, least-finished book of its era.
The book opens with a joke. A well-known scientist (some say Bertrand Russell) finishes a public lecture on how the Earth orbits the Sun and the Sun orbits the center of the galaxy. A little old lady at the back stands up: rubbish, the world is a flat plate resting on the back of a giant tortoise. The scientist smiles: and what is the tortoise standing on? "You're very clever, young man," she replies, "but it's turtles all the way down!"
Hawking uses the story to plant the book's deepest rule: on what grounds do we think orbiting planets are better than a tower of turtles? His answer is a frank positivism. A theory is only a model in our heads, plus rules connecting the quantities in the model to the things we observe. A good theory does two things: it describes a large class of observations with very few arbitrary elements, and it makes definite predictions that future observations could prove wrong.
That is Karl Popper's falsifiability, inherited wholesale: a thousand agreeing observations never prove a theory true — they only mean it hasn't failed yet — while one solid contradiction forces a rewrite. Newton's gravity was treated as truth for two centuries until the orbit of Mercury, whose closest approach to the Sun drifts by an extra 43 arcseconds per century, refused to fit. Einstein took over.
This rule changes how you should read everything that follows. When Hawking later says time may have no boundary, or that "imaginary" time may be the more fundamental kind, he isn't claiming to have seen what the universe really is. He's saying that this mathematical model predicts better and more economically. Keep that in mind and you won't mistake his cosmology for a metaphysical manifesto — and you'll understand why, late in life, he said it is pointless to ask whether a model is "real," only whether it agrees with observation.
In Newton's world, time is a river flowing independently of everything, and "now" is the same for everyone. Einstein's special relativity of 1905 dismantled that. Accept one thing — that every observer measures the same speed of light, a conclusion forced by the Michelson–Morley experiment of 1887 — and absolute time has to go. Two observers in relative motion will disagree about whether two events happened at the same time and about how much time passed, and both will be right. Hence the twin paradox: the twin who takes a fast rocket on a round trip comes home younger than the one who stayed behind. Space and time are welded into a single four-dimensional spacetime.
Hawking's main tool for picturing spacetime is the light cone. Drop a stone into a pond and ripples spread out at a fixed speed. Stack the circles from each successive moment on top of one another and you get a cone opening upward. Light spreading out from an event traces exactly such a cone in a spacetime diagram:
Light cone (schematic): the sloping edges are the speed of light. Events in the "elsewhere" can't exchange even a light signal with P, so they can't be cause or effect of it.
Its power is that it settles causality in a single line: an event can only influence what lies in its future light cone, and can only be influenced by what lies in its past one. Hawking's example: if the Sun went out right now, we wouldn't know for about eight minutes — the time sunlight takes to reach us. For those eight minutes, the Sun's death sits in our "elsewhere." As far as we are concerned, it hasn't happened yet.
Einstein's general relativity of 1915 goes one step further: gravity isn't a force at all — mass and energy bend spacetime itself. The standard picture is a bowling ball on a taut trampoline: a marble rolling past curves around the dip, not because the ball is "pulling" it but because the marble is following the straightest available path across a curved surface. Planets do the same, tracing geodesics — the nearest thing to straight lines — through curved four-dimensional spacetime. Three kinds of evidence back this up: those 43 arcseconds of Mercury, starlight bent as it grazed the Sun during the 1919 eclipse, and the fact that time runs slower where gravity is stronger. A clock high up ticks faster than one on the ground, and GPS satellites have to correct for this every day; without the correction their positions would drift by kilometers within a day.
The light cone sets the stage for the rest of the book. Once spacetime can bend, gravity can tilt the cones. Where it's strong enough, every light ray points inward — that's a black hole. Run the universe backward and all the cones may converge on a single point — that's a singularity.
In 1929 Edwin Hubble found that the light from nearly every galaxy is shifted toward the red end of the spectrum — a redshift, like the falling pitch of a receding siren — and the farther away a galaxy is, the faster it's receding. The universe is expanding. Not galaxies flying outward through a fixed space, but space itself being stretched, like dots on a balloon being inflated: from any dot, every other dot appears to be moving away.
Hawking points out something few people think about: we could have guessed long before Hubble that the universe can't be static, infinite and eternal. If it were infinite, unchanging and filled with stars, every line of sight would eventually end on the surface of a star, and the night sky would blaze as bright as the Sun. This is Olbers' paradox. The mere darkness of the night hints that the universe has a finite age. Einstein himself didn't believe the cosmos could change, and added a cosmological constant to his equations to hold it still, while the Russian mathematician Alexander Friedmann had already found expanding solutions to the original equations in 1922. In 1965 Arno Penzias and Robert Wilson stumbled on a faint microwave hiss arriving evenly from every direction — the cosmic microwave background, the cooled afterglow of the Big Bang — and the expanding universe became settled science.
Now play the tape backward. The universe gets smaller, hotter and denser. But what's at the very end of the rewind? Many assumed that because the real universe isn't perfectly symmetric, galaxies running backward would miss one another and slip past rather than all piling into one point. Hawking and Penrose, in work culminating in 1970, proved they wouldn't miss. As long as general relativity holds and the energy density of matter is positive, then however lumpy the details, there must have been a singularity in the past — a point where density and spacetime curvature are infinite. These are the singularity theorems.
The weight of the result is that it amounts to a confession: at the singularity the equations of general relativity spit out infinities, which is the theory's way of saying "I'm out." A theory that predicts where it fails is admitting it's incomplete. That gives the second half of the book a clear motive: to talk seriously about the beginning, you need a theory that works at tiny scales — quantum mechanics. Hawking even writes that what he now hopes to persuade people of is that, once quantum effects are included, there may be no singularity after all. He proved the theorem; then he set out to get around it.
Early in the nineteenth century the French mathematician Pierre-Simon Laplace imagined a demon: know the position and velocity of every particle in the universe at one instant, and you can compute the whole past and future. This is scientific determinism.
Werner Heisenberg's uncertainty principle of 1927 ended that dream. Here's the mechanism. To see where a particle is, you have to shine light on it. The shorter the light's wavelength, the more precisely you can locate it — but Max Planck had shown that light comes in discrete packets, quanta, and the shorter the wavelength, the more energetic each packet. So the sharper your look, the harder you kick the particle and the more you scramble its velocity. The more precisely you measure position, the less precisely you can know velocity, and the product of the two uncertainties can never fall below a fixed tiny amount set by Planck's constant. This isn't a limit of our instruments. It's a property of the world.
The quantum mechanics that grew out of this no longer predicts a single definite outcome, only the probabilities of many. Particles also behave like waves. In the famous double-slit experiment, electrons are fired one at a time at a barrier with two slits, yet the screen behind slowly builds up the alternating light-and-dark bands that only waves produce — as if each electron passed through both slits and interfered with itself.
Hawking uses this chapter to set up two tools he'll need later. First, virtual particles: the uncertainty principle applies to energy and time too, which means the "vacuum" can't be truly zero — a field's value and its rate of change can't both be exactly zero — so particle–antiparticle pairs constantly pop into existence and annihilate almost instantly. Second, the four forces of nature — gravity, electromagnetism, the weak and the strong nuclear forces — are all described in quantum theory as the exchange of particles. Electromagnetism and the two nuclear forces can already be described within one family of theories. Gravity alone still won't come in. That is the great unresolved problem of the book.
How this changes your view: the picture of the universe as a perfectly ticking clock is wrong at the bottom level. The foundation of the world is probabilistic. And when that fundamental fuzziness meets the extremes of black holes and the beginning of time, it doesn't just tweak the answer — it can overturn it.
A star holds itself up against its own gravity with the outward pressure of nuclear fusion. When the fuel runs out, a massive star collapses inward with nothing to stop it. In 1930 the Indian-born astrophysicist Subrahmanyan Chandrasekhar calculated that a stellar remnant above roughly 1.4 solar masses can't be supported even by the pressure arising from the Pauli exclusion principle — the rule that no two electrons may occupy the same state. That threshold is the Chandrasekhar limit. Heavier still, and not even a neutron star can hold: the remnant becomes a black hole.
The boundary of a black hole is its event horizon. Inside it, spacetime is bent so far that the light cones tip entirely inward; everything, light included, can only move toward the center. Hawking compares it to a one-way membrane, or the line above a waterfall past which no boat, however hard it's rowed, can make it back upstream.
In 1970–71 Hawking proved the area theorem: the area of a black hole's horizon can never decrease. When two black holes merge, the new horizon is at least as large as the two old ones combined. That looks uncannily like the second law of thermodynamics, which says entropy — disorder — never decreases. A Princeton graduate student, Jacob Bekenstein, seized on this: perhaps the area simply is the black hole's entropy. Hawking was annoyed and thought it impossible. Anything with entropy has a temperature, and anything with a temperature must radiate — whereas a black hole, by definition, lets nothing out.
Then in 1974 his own calculations showed that black holes do radiate. The intuitive picture he offers: virtual particle pairs are forever appearing in the vacuum. If a pair appears right at the horizon, the partner carrying negative energy may fall in while the positive-energy partner escapes. To a distant observer it looks as though the black hole has emitted a particle, and the hole loses mass by swallowing negative energy. (Hawking is clear that this is a heuristic; the real result comes from doing quantum field theory in curved spacetime.) This is Hawking radiation.
The counterintuitive part is that the smaller the black hole, the hotter it is and the faster it evaporates. A black hole of one solar mass sits at about a ten-millionth of a degree above absolute zero — far colder than the 2.7-kelvin glow of the cosmic background — so it absorbs more than it emits and won't evaporate in practice. But if the early universe produced primordial black holes with the mass of a mountain (around a billion tonnes) squeezed into the size of a proton, those should be in their final, explosive moments right now.
Why it matters: it was the first result to require general relativity, quantum mechanics and thermodynamics all at once. The formula for a black hole's temperature contains the gravitational constant G, Planck's constant ħ, the speed of light c and Boltzmann's constant k. Any genuine theory of quantum gravity has to reproduce it, and for nearly fifty years it has been the test every candidate theory must pass.
This is Hawking's most ambitious chapter and the hardest to follow. In 1983 he and James Hartle put forward the no-boundary proposal.
Start with imaginary time. In mathematics the imaginary number i satisfies i² = −1. In relativity, the formula for distance in spacetime gives the time part the opposite sign from the space parts; that sign difference is exactly what makes time different from space. Measure time in imaginary numbers and the minus sign turns into a plus — time becomes mathematically indistinguishable from a direction in space. Physicists already used this as a calculational trick for quantum processes (it's called a Wick rotation). Hawking proposed taking it seriously as a description of the universe's earliest moments.
Then the analogy. The surface of the Earth is finite but has no edge. You can walk forever and never fall off the end of the world. The South Pole is where latitude begins, but nothing strange happens there; physics at the pole is as ordinary as anywhere else, and asking what lies south of it makes no sense. If, in imaginary time, the four-dimensional geometry of the universe is a smooth closed surface like that, then the Big Bang is like the South Pole — the start of time, but not a singularity where the laws break down. "What happened before the Big Bang?" becomes a malformed question. The state of the universe is fixed entirely by the laws of physics, with no need to specify extra "initial conditions" at an edge.
An anecdote in the book shows what was at stake. In 1981 Hawking attended a cosmology conference at the Vatican. When the Pope received the participants, he told them it was fine to study how the universe evolved after the Big Bang, but they should not inquire into the Big Bang itself, because that was the moment of Creation. Hawking writes that he was glad the Pope didn't know he had just given a talk proposing that spacetime might be finite but without boundary — that there might be no moment of Creation at all. Then comes the book's most quoted passage (paraphrased): so long as the universe had a beginning, we could suppose it had a creator; but if it is completely self-contained, with no boundary or edge, it would have neither beginning nor end — it would simply be. What place, then, for a creator?
How this changes the way you think: the seemingly airtight argument "everything has a cause, so there must be a first cause" quietly assumes that time is a line with an endpoint. If time itself rounds off near the start, the first cause loses its footing. That holds, of course, only if the model is right — and it has never been tested against observation.
At the microscopic level, the laws of physics barely care which way time runs. Play a film of billiard balls colliding in reverse and it still obeys mechanics. So why don't broken cups reassemble themselves? Hawking distinguishes three arrows of time:
| Arrow | Points toward | In plain terms |
|---|---|---|
| Thermodynamic | Increasing entropy (disorder) | Ordered arrangements are rare and disordered ones are vast in number, so systems almost always drift from order to mess |
| Psychological | The direction in which we feel time pass and remember | Forming a memory costs energy and raises the entropy around it, so it must point the same way as the thermodynamic arrow |
| Cosmological | The direction in which the universe expands | Under the no-boundary proposal the universe starts smooth and ordered, so entropy starts low and climbs |
Why the three arrows line up: the universe began in an extraordinarily ordered state and has been getting messier ever since, and our memories ride along on that slide.
His image for entropy is a jigsaw puzzle in a box. There's one arrangement in which the picture is complete and an astronomical number in which it isn't, so shaking the box almost certainly scrambles it. A computer storing a memory works the same way: putting its memory into order costs energy that is dumped as heat, raising the total disorder of the surroundings by more. We remember only the past because remembering is itself an entropy-raising process, and it can only be written in the direction entropy grows.
This chapter also holds the most honest moment in the book. Hawking admits he first believed that if the universe someday recollapsed, the arrow of time would reverse in the contracting phase, and people would "remember the future." His colleague Don Page and his student Raymond Laflamme persuaded him he was wrong. His point, in paraphrase: it's better to admit you were wrong than to pretend you weren't. That page says more about what he means by science than any manifesto could.
1. The rules: a theory is a falsifiable model, judged only by how much it explains with how little and whether it makes testable predictions.
2. Two pillars: general relativity (spacetime bends; gravity is geometry) governs the large; quantum mechanics (uncertainty, probability, virtual particles) governs the small. Each has passed every test, yet they are fundamentally incompatible.
3. Relativity's confession: the universe is expanding; run it backward and the singularity theorems guarantee a beginning where the laws fail. Black holes hide singularities too. The theory breaks down at its own edges.
4. The first marriage: use both theories at a black hole's horizon and you get Hawking radiation — black holes have temperature and entropy, and they evaporate. The two pillars can cooperate locally, and any future unified theory now has a question it must answer.
5. Scale it up to everything: apply quantum mechanics to the universe itself and, with imaginary time, you get a cosmos that is finite but unbounded. The singularity smooths away, and the arrow of time gets an explanation along the way.
6. The ultimate goal: a complete unified theory. Hawking was then cautiously optimistic that it might not be far off; find it, he wrote, and we would "know the mind of God."
So what the book actually establishes is a single thing: our two best descriptions of the universe must collide at the beginning of time and at the center of a black hole, and any serious talk about "the beginning" has to start from that collision. It rests on three pieces of solid material — the observations of expansion and the microwave background, the mathematics of the singularity theorems, the calculation of Hawking radiation — plus one bold proposal that has never been tested.
Misreading 1: "Hawking proved God doesn't exist." Believers and atheists alike quote "the mind of God" and "what place, then, for a creator?" The first is a figure of speech; Hawking later said plainly that he didn't believe in a personal God. The second is a rhetorical question resting on an untested model. The book proves no theological conclusion. It only shows that "the universe must have a beginning, so it must have a cause" is not a logical necessity.
Misreading 2: "Hawking radiation has been observed." It hasn't. Radiation from astrophysical black holes is far too faint, drowned out by the cosmic background, and no primordial black hole has ever been found. All we have are tabletop analogue experiments that mimic a horizon with sound waves, fluids or ultracold atomic gases (Bose–Einstein condensates) — the results reported by the Israeli physicist Jeff Steinhauer from 2016 onward, for instance. They support the mathematical mechanism, but they aren't black holes. That's why Hawking never won a Nobel Prize: the Nobel requires observational confirmation.
Misreading 3: "The no-boundary proposal is Hawking's settled cosmology." It's an elegant hypothesis that sits comfortably alongside inflation (a burst of exponential expansion in the first instant, invoked to explain why the universe is so flat and uniform), but it has no unique, confirmed observational prediction. In 2017 Neil Turok and colleagues published calculations arguing that, handled more rigorously, the proposal yields unstable universes unlike ours, and the dispute is still open. The book's most famous chapter is scientifically its least secure.
Criticism 1: "The most famous unread bestseller." In 2014 the mathematician Jordan Ellenberg used the positions of readers' Kindle highlights to estimate how far people actually get through popular books. He jokingly called the measure the "Hawking Index"; this book scored about 6.6%. Hawking's publisher had warned him that every equation would halve his sales, so the only one left is E=mc². The price: without equations, many passages leave readers nodding along rather than understanding. The book's fame far outstrips the degree to which it is understood.
Criticism 2: the "final theory is near" optimism didn't pan out. Hawking wrote that there were grounds for cautious optimism that we might be nearing the end of the search. More than three decades later, string theory still has no testable predictions and quantum gravity remains unsolved. Hawking himself softened his position in a 2002 lecture, "Gödel and the End of Physics," suggesting that — in light of Gödel's incompleteness theorem, which says any sufficiently powerful mathematical system contains statements it can neither prove nor disprove — a finite final theory might not exist at all.
Criticism 3: parts of it are dated. The 1998 discovery that the universe's expansion is accelerating (driven by what's called dark energy) stripped most of the meaning from the original edition's discussion of whether the universe would eventually recollapse, and dark matter barely appears. The biggest revision concerns black holes (see the next section). It's a map of the 1988 frontier, not a textbook for today.
The information paradox: a war he started and then conceded. Hawking radiation has a disturbing consequence. If the radiation is purely thermal, depending only on the black hole's mass, charge and spin, then an encyclopedia and an equal mass of coal thrown into a black hole would come out as exactly the same radiation — the information that fell in would be wiped out. But a bedrock principle of quantum mechanics is that information can't be destroyed; physical processes are, in principle, reversible. In 1976 Hawking argued that the information really is lost and quantum mechanics would have to change. That launched a nearly thirty-year "black hole war" with Leonard Susskind and others, and in 1997 a public bet with the physicist John Preskill. In 2004 Hawking conceded, accepting that the information probably escapes with the radiation somehow, and paid up with a baseball encyclopedia as the bet required. Today's mainstream view — from the holographic principle to recent calculations involving so-called "islands" — broadly sides with the position he conceded to. Without this episode, you'd take the black holes of A Brief History of Time as Hawking's last word.
Model-dependent realism: the positivism of chapter one, pushed all the way. In The Grand Design (2010, with Leonard Mlodinow), Hawking proposed model-dependent realism: there is no reality independent of our models, and different models can each be correct within their own domain, the way different maps each work for their own region. That led him to suspect there might be no single final theory, only a family of overlapping ones (he pinned his hopes on "M-theory"). The same book claims that because there is a law like gravity, the universe can and will create itself from nothing — a far bolder step than the rhetorical question in A Brief History of Time, and it drew far more criticism.
Put together: A Brief History of Time is the midpoint of Hawking's thinking, not its endpoint. Its hardest parts — the singularity theorems and Hawking radiation — still stand. Its most romantic parts — the no-boundary universe, the final theory just around the corner, the implicit assumption that information is lost — are exactly the ones he later revised most.
1. A theory is just a model plus rules linking it to observation; it can never be proven, only refuted.
2. There is no cosmic clock: because light's speed is the same for everyone, time is different for everyone.
3. Gravity isn't a force — it's mass bending spacetime, and planets are simply going straight through curved space.
4. An event can only affect what lies in its future light cone — for the eight minutes after the Sun goes out, it hasn't happened to us yet.
5. The night is dark, the galaxies are receding, and the whole sky glows faintly warm: the universe has an age, and it was once small and hot.
6. General relativity predicts its own breakdown at the singularity — a theory that can point to where it fails is telling you it's incomplete.
7. The more precisely you pin down position, the less you know about velocity: uncertainty isn't a flaw in the instruments; it's a property of the world.
8. Black holes aren't black: they have a temperature and an entropy, they evaporate, and the smaller they are the hotter they burn — the first handshake between gravity and the quantum.
9. So long as the universe had a beginning, we could suppose it had a creator; but if it is finite without boundary and simply is, what place, then, for a creator? (paraphrased)
10. Even if there is only one possible unified theory, it is just a set of equations — what is it that breathes fire into the equations and makes a universe for them to describe? (paraphrased)