Insight Editions · No. 29
The Theory of Everything
The Origin and Fate of the Universe
Stephen Hawking
Stephen Hawking's lectures explain the expanding universe, black holes, the big bang, the arrow of time, and the search for a unified account of nature.
A study guide to The Theory of Everything by Stephen Hawking. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
2. The Expanding Universe
Galaxies and redshift
Only in 1924 did Edwin Hubble show our galaxy is not the whole universe. Using stars of known luminosity, he measured distances to nine other galaxies. We now see some hundred thousand million galaxies, each with about a hundred thousand million stars. We live in a spiral galaxy about 100,000 light-years across, rotating once every several hundred million years. Star colours give temperature; missing colours give composition. In the 1920s galaxy spectra proved redshifted, and in 1929 Hubble found a galaxy's redshift is directly proportional to its distance: the universe is expanding.
Newton's gravity could have predicted this in the seventeenth century, but belief in a static universe ran deep: Einstein added a cosmological constant to keep it static. "Only one man, it seems, was willing to take general relativity at face value": Alexander Friedmann.
Friedmann assumed the universe looks the same in every direction, from every galaxy. The 1965 discovery by Penzias and Wilson of uniform microwave radiation, predicted by George Gamow's hot early universe, supports the first assumption; the second we believe "only on grounds of modesty." Three solution types follow:
- Slow expansion: gravity stops it and it recollapses; space is finite but unbounded, bent round on itself.
- Fast expansion: it expands forever, slowing a little.
- Critical rate: just fast enough to avoid recollapse.
Friedmann's work became known in the West only after Robertson and Walker found similar models in 1935. Which applies depends on density: visible stars give under one hundredth of the critical density; including dark matter, about a tenth.
The big bang and its rivals
All Friedmann solutions have a time, "between ten and twenty thousand million years ago," when galaxies were at zero distance: the big bang singularity, where all theories break down. Many disliked a beginning. The steady state theory (1948) of Hermann Bondi and Thomas Gold, refugees from Nazi-occupied Austria, and Fred Hoyle had new matter continually created, about one particle per cubic kilometre per year. A Cambridge radio survey led by Martin Ryle found more faint sources than the theory allowed, and the 1965 microwave background killed it.
Evgenii Lifshitz and Isaac Khalatnikov (1963) argued that irregularities would avoid a singularity, so the big bang was an artefact of perfect symmetry. They withdrew the claim in 1970.
Roger Penrose (1965) showed that a star collapsing under its own gravity is trapped in a region whose surface shrinks to zero: a singularity. Hawking, then a research student needing a thesis, saw that reversing time turns collapse into expansion. His joint paper with Penrose in 1970 proved there must have been a big bang singularity, provided general relativity is correct and the universe contains as much matter as observed. There was opposition, partly from Soviet physicists following Lifshitz and Khalatnikov, partly from those who found singularities repugnant. Ironically, Hawking later argued that quantum effects can remove the singularity.
- "Ten to twenty thousand million years" is now pinned at 13.8 billion.
- The universe is not headed for any of the three classic fates by density alone: expansion is accelerating, which the 1980s lectures could not know.
- The singularity theorems assume classical general relativity; Hawking's own later work suggests the singularity is replaced by quantum physics.
- Planck (2018) still anchors ΛCDM: about 13.8 billion years, ~5% ordinary matter, ~27% dark matter, ~68% dark energy, spatially flat.
- Hubble tension (Oct 2026): Local ladders still cluster near H0 ≈ 73.2-73.5 km/s/Mpc (H0DN ~73.5 ± 0.81; corrected Pantheon+/DES-DOVEKIE ~73.26 ± 0.81, ~6.9σ vs CMB ΛCDM 67.24 ± 0.35). JWST Cepheid tests reject crowding explanations at high significance; some TRGB analyses sit lower (~69), so the gap is not closed.
- DESI DR2 hints dark energy may evolve (few-σ, below 5σ discovery); finals expected around 2027. Early dark energy models can ease H0 tension in some fits but are not established.
- Penrose shared the 2020 Nobel Prize for black hole formation from general relativity.
Deeper notes from the lecture
Hubble's distance method used stars of known luminosity as standard candles: measure apparent brightness, infer distance. Our galaxy is about 100,000 light-years across; stars in the spiral arms orbit roughly once per 100 million years. Spectra give temperature (glowing body colours) and composition (missing absorption lines). The Doppler car-horn analogy is Hawking's sound version of redshift.
Einstein's cosmological constant was built-in antigravity in the fabric of space-time, tuned to cancel attraction. Friedmann (1922) predicted expansion years before Hubble. The balloon-with-spots image: no spot is the centre; farther spots recede faster.
- Visible stars: under 1/100 of critical density
- Including dark matter in galaxies and clusters: about 1/10 of critical
- Expansion rate then: roughly 5 to 10 percent per thousand million years
- Even if recollapse awaits, not for at least another 10,000 million years
Penzias and Wilson (1965) found microwave noise the same in every direction, day and night, after ruling out bird droppings. Dicke and Peebles were already hunting Gamow's leftover glow; the Nobel (1978) went to the discoverers. Uniformity to about one part in ten thousand confirmed Friedmann's isotropy assumption. We believe the "same from every galaxy" assumption "only on grounds of modesty."
The first Friedmann model bends space like Earth's surface: finite, unbounded. You could not circumnavigate before recollapse without travelling faster than light. Lifshitz and Khalatnikov's 1963 hope that sideways velocities avoid a singularity was withdrawn in 1970. Penrose's 1965 collapse theorem, time-reversed by research-student Hawking, became the joint 1970 paper: a big bang singularity if GR is correct and there is as much matter as we see.
Arguments in full: distances, models, beginnings
Hubble could not use parallax on other galaxies: they appear fixed as Earth orbits the Sun. He used standard candles, stars whose luminosity is known from nearby examples, then inferred distance from apparent brightness. Nine galaxies were enough to prove our Milky Way is not the whole universe. Today the count is of order 1011 galaxies, each with of order 1011 stars. Our Sun is an ordinary yellow star near the outer edge of a spiral arm.
Spectra do more than give colour. Relative brightness of colours matches a glowing body, so temperature follows. Missing lines match chemical elements in the star's atmosphere. In the 1920s those same missing sets appeared in other galaxies, all shifted toward the red by the same relative amount: the Doppler interpretation is recession. Police radar uses the same idea on radio pulses reflected from cars.
Why expansion was missed
Newton's gravity already implies a static universe either collapses or needs a balance. Expanding above a critical rate never recollapses; below it, gravity wins. The rocket analogy in the lecture: under about seven miles a second, the rocket falls back; above, it escapes. That logic was available from the late seventeenth century. Belief in a static cosmos blocked it. Einstein's 1915 general relativity predicted a non-static universe; he added a cosmological constant, built-in antigravity in the fabric of space-time, tuned to cancel attraction. Only Alexander Friedmann took the equations at face value and, in 1922, predicted Hubble's later result.
Friedmann's two assumptions and three models
- The universe looks the same in every direction (isotropy on large scales).
- It looks the same from any other place (homogeneity; believed "only on grounds of modesty").
Three solutions follow. Closed: expansion slows, stops, recollapses; space is finite and unbounded, like Earth's surface in three dimensions; time has a beginning and an end. Open: expansion forever at a nonzero asymptotic speed. Critical: expansion forever but slowing toward zero. Circumnavigating a closed model before recollapse would require faster-than-light travel.
CMB as lucky confirmation
Penzias and Wilson (Bell Labs, 1965) found excess microwave noise isotropic day and night after ruling out bird droppings and atmospheric thickness. Dicke and Peebles at Princeton, following Gamow, were already hunting a redshifted leftover glow. The Nobel (1978) went to the discoverers. Uniformity to about one part in ten thousand confirmed Friedmann's first assumption. Balloon-with-spots: no centre; farther spots recede faster, matching Hubble's law.
Density, dark matter, and fate (lecture numbers)
Visible stars give under 1/100 of critical density. Galaxy and cluster dark matter push that to about 1/10. Expansion rate then: roughly 5 to 10 percent per thousand million years. Hawking's 1980s conclusion: probably expands forever; even if not, recollapse is at least 10,000 million years away. Modern acceleration (dark energy) was unknown then.
Steady state and the singularity fight
Bondi, Gold, and Hoyle (1948) proposed continuous creation (~one particle per cubic kilometre per year) so the universe looks the same at all times. Testable: source counts should be uniform in volume. Martin Ryle's Cambridge radio survey found more weak (distant) sources than strong ones, implying more sources in the past. The 1965 microwaves required a denser past. Steady state fell.
Lifshitz and Khalatnikov (1963) hoped sideways velocities let a bounce replace the bang; they withdrew in 1970. Penrose (1965) proved collapse singularities. Research-student Hawking time-reversed the argument for expanding Friedmann-like universes. The joint 1970 paper: a big bang singularity if classical GR is correct and there is as much matter as observed. Opposition from Soviets and from those who found singularities "repugnant" did not defeat the theorem. The Catholic Church in 1951 had already welcomed the big bang as compatible with Genesis; many physicists disliked a beginning for the opposite reason.
Penzias and Wilson were designing a satellite antenna. Excess noise refused to go away. Dicke's group had the theory; the Bell Labs pair had the detection. Outcome: cosmology gained its fossil glow, and Friedmann's isotropy stopped being a rough guess.
- Edwin Hubble: distances to other galaxies; 1929 redshift-distance law
- Alexander Friedmann: 1922 expanding models from GR
- Arno Penzias / Robert Wilson: accidental CMB discovery, Nobel 1978
- Bob Dicke / Jim Peebles: predicted the leftover glow
- Bondi, Gold, Hoyle: steady state (1948)
- Martin Ryle: radio counts that broke steady state
- Roger Penrose / Stephen Hawking: singularity theorems culminating 1970
Expansion as measured fact (depth)
Lecture 2 turns geometry into data: galaxies recede; spacetime stretches; the Big Bang is a hot dense early state, not an explosion into empty space. Hubble’s law, microwave background and light-element abundances form the modern triad. Hawking’s 1980s numbers on fate (recollapse odds) are historical; dark energy later flipped the late-time story.
Local ladders still sit near H0 ≈ 73 km/s/Mpc while early-universe ΛCDM fits sit near 67. JWST Cepheid checks have not erased the gap; some TRGB analyses sit mid-range. Treat the tension as open: new physics, systematics, or both.
Draw a rubber-sheet sketch: galaxies as coins; expansion as sheet stretch. Mark why “centre of explosion” is the wrong picture.
Lecture 2 working notes. Recession velocity proportional to distance is the linear Hubble flow at modest z; at high z use careful distance measures. CMB is leftover heat; acoustic peaks encode geometry and contents. Light elements from Big Bang nucleosynthesis constrain baryon density. Dark energy (1998+) changed fate tables Hawking’s lectures used. Hubble tension (2026) is the live fight between early and late H0.
People hear “Big Bang” and picture a bomb in a room. The better picture is the room itself stretching. There is no privileged centre in standard FLRW models.
HUBBLE-FRIEDMANN-SINGULARITY. Observed recession; predicted by Friedmann's three models; forced by the Hawking-Penrose theorems if classical GR holds. Hold the three words and Lecture 2's chain is complete.
Pick a density: below critical, critical, or above. Sketch whether neighbouring galaxies' separation grows forever, asymptotes, or returns to zero. Then add one modern twist: accelerating expansion can change the classical "recollapse" branch even if density looks high.
The singularity theorems sound like "time must begin." Invert them: they assume classical general relativity and enough matter. Hawking's later quantum work was precisely an attempt to remove the singularity the theorems forced. Do not treat the 1970 result as the last word on the beginning.
Hubble found galaxies receding in proportion to distance; Friedmann's models had predicted it. The microwave background defeated the steady state theory, and the Hawking-Penrose theorems showed that classical general relativity requires a big bang singularity.
3. Black Holes
Dark stars to dead stars
John Wheeler gave the idea its name, "black hole" (the book says he coined it in 1969). The idea goes back to John Michell's 1783 paper: a massive, compact star's gravity could stop light escaping, so we would not see it. Laplace said much the same soon after but dropped it from later editions of his book.
A star forms when gas collapses and heats until hydrogen fuses into helium; heat then balances gravity. When fuel runs out, it contracts. In 1928 Subrahmanyan Chandrasekhar, sailing to Cambridge to study with Arthur Eddington, worked out that the exclusion principle can support a cold star only up to about 1.5 solar masses, because relativity caps the particles' speeds: the Chandrasekhar limit. Lighter stars become white dwarfs or neutron stars; heavier ones face collapse. Eddington refused to believe it; Chandrasekhar won the Nobel Prize in 1983, partly for this work.
From Oppenheimer's 1939 work: as a star shrinks, gravity bends light cones inward until, at a critical radius, light cannot escape. That boundary is the event horizon. An astronaut on the surface, signalling each second by his watch, would send his 11:00 signal just as the star crossed the horizon. His companions would see the gaps between signals grow longer, the light grow redder and fainter, and the 11:00 signal never arrive. The star would fade from view, leaving only a black hole. Tidal forces would kill the astronaut anyway, stretching him like spaghetti.
Singularities and censorship
Penrose's and Hawking's work (1965 to 1970) showed there must be a singularity inside a black hole, where the laws break down. Penrose proposed cosmic censorship: "God abhors a naked singularity." Singularities are hidden behind horizons, so their lawlessness cannot affect us outside. The strong version says singularities lie entirely in the future (like collapse) or the past (like the big bang).
Werner Israel (Dublin, 1967) showed non-rotating black holes must be perfectly spherical, depending only on mass. Brandon Carter (1970) and Hawking extended this, and David Robinson (1973) proved a rotating hole must be the Kerr solution. A black hole's size and shape depend only on its mass and rotation, not on what collapsed to form it. Wheeler summed it up: "A black hole has no hair." Enormous information about the original body is lost.
Looking for them
Black holes are rare cases where theory ran far ahead of evidence. In 1963 Maarten Schmidt at Mount Palomar found the redshift of a quasar, so distant and luminous that only collapse of a galaxy-centre mass seemed able to power it. In 1967 Cambridge student Jocelyn Bell found regular radio pulses (briefly nicknamed signals from "little green men"); these pulsars proved to be rotating neutron stars, the first proof such dense objects exist.
In Cygnus X-1 a visible star orbits an unseen companion emitting X-rays, from matter heated as it spirals in. The companion's minimum mass was about six solar masses, too much for a white dwarf or neutron star. In 1975 Hawking bet Kip Thorne that it was not a black hole, as insurance: if black holes did not exist, his work was wasted but he would win four years of Private Eye; if they did, Kip got a year of Penthouse. "We were 80 percent certain that Cygnus was a black hole."
Hawking adds that very small primordial black holes might have formed from irregularities in the early universe; those above a thousand million tons could be detected only by their gravity.
- Wheeler popularised "black hole" in a 1967 lecture; it first appeared in print in January 1964 (Ann Ewing, Science News Letter), coiner unknown.
- The modern Chandrasekhar limit is about 1.4 solar masses.
- "No hair" is now known to be subtle: quantum effects (Hawking radiation) and proposals of "soft hair" (Hawking, Perry and Strominger, 2016) reopen how much information a black hole keeps.
- Hawking conceded the Cygnus X-1 bet in 1990. Radio work (2021) puts the hole near 21 solar masses.
- Gravitational waves: hundreds of mergers in GWTC catalogs since GW150914 (2015; Nobel 2017).
- EHT: M87* (2019) and Sgr A* (2022); 2017 to 2021 M87* polarisation images (released 2025) show a stable ~43.9 μas ring with a polarisation spiral that flipped by 2021. Genzel and Ghez shared the 2020 Nobel with Penrose for Sgr A*'s mass.
- JWST still finds surprisingly massive holes in the first billion years.
Deeper notes from the lecture
Michell's 1783 dark star and Laplace's similar remark set the classical escape-velocity intuition. A living star balances fusion heat against gravity; when fuel ends, the exclusion principle can hold a cold remnant only up to Chandrasekhar's limit (lecture figure ~1.5 solar masses; modern ~1.4). Eddington's refusal delayed acceptance; the Nobel came in 1983.
Oppenheimer's 1939 picture: light cones tip inward; at the critical radius the outgoing cone lies along the horizon. Outside watchers see signals redshift and slow; the star fades to black. Tidal stretch ("spaghetti") kills the falling astronaut. Penrose's cosmic censorship hides singularities; the strong form keeps them in the past (big bang) or future (collapse).
Israel (1967), Carter (1970), Hawking, and Robinson (1973) lock the uniqueness theorems: non-rotating holes are spherical; rotating ones are Kerr. Wheeler's phrase: a black hole has no hair. Quasars (Schmidt 1963) need galaxy-centre collapse to explain their power; pulsars (Bell 1967) proved neutron stars real. Cygnus X-1's unseen companion, at least ~6 solar masses in the lecture, was the leading stellar-mass candidate; Hawking's 1975 insurance bet with Thorne was conceded in 1990.
- Chandrasekhar limit: ~1.5 M☉ (book); ~1.4 M☉ (modern)
- Cygnus X-1 minimum then: ~6 M☉; modern mass ~21 M☉ (2021)
- Primordial holes above ~10⁹ tons: detectable only by gravity if not evaporating
Arguments in full: from Michell to Cygnus X-1
The term black hole is John Wheeler's (1969). The idea is older. John Michell (1783) argued a star massive and compact enough would trap light if light were corpuscular; we would still feel its gravity. Laplace put a similar note in early editions of The System of the World and later dropped it. Newtonian light-as-cannonball is inconsistent with fixed light speed; a consistent theory waited for Einstein 1915.
Star life and the Chandrasekhar limit
A star forms when hydrogen gas collapses, heats, and fuses to helium; heat pressure balances gravity like air in a balloon. More massive stars burn faster: the Sun has fuel for roughly another five thousand million years; the heaviest may last only ~100 million years. When fuel ends, the star cools and contracts.
Subrahmanyan Chandrasekhar, on the voyage to Cambridge (1928), used the Pauli exclusion principle: matter particles cannot share position and velocity, so they generate a repulsion that can support a cold star. Relativity caps velocity differences at c, so above about 1.5 solar masses (the Chandrasekhar limit) that support fails. Below the limit: a white dwarf (radius of a few thousand miles, hundreds of tons per cubic inch), like the companion of Sirius. A parallel neutron star state (supported by nucleon exclusion) has radius ~ten miles and hundreds of millions of tons per cubic inch.
Eddington refused the collapse implication; Einstein wrote against zero-size stars. Chandrasekhar shifted topics under pressure; his 1983 Nobel partly rewarded the early limit work. Oppenheimer (1939) treated collapse in GR; war and nuclear physics shelved the topic until the 1960s observational boom.
Horizon, astronaut clock, censorship
As a star shrinks, light cones tip inward. At a critical radius light cannot escape: the event horizon. An astronaut signalling each second reaches 11:00 as the surface crosses the horizon; distant companions see gaps stretch, light redden and fade; the 11:00 signal never arrives. The hole still gravitates. Penrose-Hawking: a singularity of infinite density inside. Cosmic censorship (weak): singularities stay hidden behind horizons for outside observers. Strong form: singularities lie entirely in the future (collapse) or past (big bang). Naked singularities and wormhole shortcuts look unstable once an astronaut is present.
No hair: Israel, Carter, Kerr, Robinson
Werner Israel (1967): a non-rotating hole must be the spherical Schwarzschild solution (known since 1916/17), fixed by mass alone. Early reading: only perfect spheres make holes (hence naked singularities). Penrose and Wheeler: like a fluid ball, collapse radiates away bumps. Roy Kerr (1963): rotating solutions fixed by mass and spin. Brandon Carter (1970) and Hawking (1971) then David Robinson (1973) closed the proof: the end state is Kerr. Maxim: "A black hole has no hair." Mass and rotation (and, in fuller modern form, charge) exhaust what outside observers can measure.
How we found them
Maarten Schmidt (1963): quasar 3C273 redshift too large for local gravity; an expanding-universe distance implies enormous luminosity, natural if a galactic nucleus collapses. Jocelyn Bell and Anthony Hewish (1967): pulsars, first joked as LGM 1-4 ("Little Green Men"), then rotating neutron stars. Neutron stars sit only a few times above the black-hole critical radius, so deeper collapse became plausible.
Cygnus X-1: a visible star orbits an unseen companion emitting X-rays from a hot accretion spiral. Lowest mass ~six solar masses, above white-dwarf and neutron-star limits. Hawking's 1975 bet with Kip Thorne: if not a hole, Hawking wins four years of Private Eye; if a hole, Thorne gets one year of Penthouse. Then ~80% confident; later ~95%; he conceded in 1990.
Primordial low-mass holes need early-universe compression, not stellar collapse. Mountain-mass (~109 tons) holes are hard to see by gravity alone; smaller ones glow (next lecture). Absence of many such holes constrains how chaotic the early universe was.
Bell's pulsed radio sources were briefly labelled LGM. The less romantic truth, rotating neutron stars, was "bad news for writers of space westerns" and good news for black-hole believers: collapse to ten-mile objects is real.
- John Michell / Laplace: eighteenth-century dark stars
- Chandrasekhar: mass limit for cold stars; Nobel 1983
- Eddington: resisted the limit
- Oppenheimer: 1939 GR collapse
- Wheeler: named black holes (1969)
- Israel / Kerr / Carter / Robinson: no-hair theorems
- Schmidt: quasars; Bell / Hewish: pulsars
- Kip Thorne: Cygnus bet counterparty
Collapse, horizon, no-hair (depth)
Stars above a mass limit cannot rest on degeneracy pressure; collapse forms a region where escape speed exceeds light. The event horizon is a causal boundary, not a marble surface. “No-hair” slogans (mass, charge, spin) summarise how little exterior observers learn. Singularities are where classical theory fails, not where physicists stop thinking.
EHT images (M87*, Sgr A*) and LIGO/Virgo/KAGRA ringdowns make horizons astrophysical objects, not only pen-and-paper solutions. Masses and spins are routine catalogue entries; information puzzles remain theoretical.
Lecture 3 working notes. Escape velocity, Schwarzschild radius, horizon redshift and no-hair are the teaching core. Realistic holes rotate (Kerr). Astrophysics adds accretion disks, jets and mergers. EHT sees shadow-scale emission; GW hears ringdowns. Information and singularity theorems push into lecture 4 and quantum gravity.
Compute a rough Schwarzschild radius for Earth and for the Sun (rs = 2GM/c²). Notice Earth would need to be crushed to centimetres; the Sun to kilometres. Numbers make “collapse” concrete.
HORIZON ≠ SURFACE. You can cross in finite proper time; outside observers see freeze and redshift.
LIMIT-HORIZON-HAIR. Chandrasekhar limit (collapse if heavier); event horizon (light cones tip in); no hair (only mass and spin remain). Three words carry Lecture 3.
For a star of 10 solar masses after fuel ends, write the sequence: contract, pass the critical radius, fade from outside view, singularity inside. Circle the step an outside observer never sees completed (the 11:00 signal). That is the horizon as information cutoff.
"No hair" invites the claim that a black hole remembers nothing. Quantum radiation and soft-hair proposals reopen how much information survives. The classical slogan is sharp; treating it as final information theory is the shadow.
Stars above the Chandrasekhar limit can collapse past the point where light escapes, forming black holes hidden behind event horizons. Black holes have no hair: only mass and spin survive. Quasars, pulsars and Cygnus X-1 turned the theory into astronomy.
4. Black Holes Ain't So Black
The area theorem
In November 1970, getting into bed (slow because of his disability), Hawking realised that light rays forming the event horizon can never approach each other, or they would collide and fall in. So the area of the event horizon can never decrease; when two black holes merge, the final area is at least the sum of the two.
Entropy and the second law
This resembles entropy, the measure of disorder, which by the second law of thermodynamics never decreases in an isolated system: gases mixed from two boxes never spontaneously separate. But throwing high-entropy matter into a black hole would seem to reduce the outside entropy. Princeton student Jacob Bekenstein proposed that horizon area measures entropy. Hawking was irritated: if black holes had entropy, they would have a temperature and must glow, yet nothing escapes. In 1972 he wrote a paper with Brandon Carter and Jim Bardeen arguing the analogy failed.
Visiting Moscow, Hawking discussed black holes with Yakov Zeldovich and Alexander Starobinsky, who argued that rotating black holes should emit particles. Hawking devised a better mathematical treatment and found, to his surprise, that even non-rotating black holes emit at a steady rate. He feared it would help Bekenstein's entropy argument, but the black hole was emitting particles at exactly the correct rate to prevent violations of the second law. He presented it at an Oxford seminar at the end of November 1973; the paper appeared in 1974.
How a black hole radiates
The uncertainty principle forbids a field from being exactly zero, which would fix both its value and rate of change. So empty space is full of virtual particle pairs appearing, separating and annihilating; their indirect effects on electron orbits are measured. One partner has positive energy, the other negative. Near a black hole, the negative-energy partner can fall in and become real; its partner may escape as radiation. The inflow of negative energy reduces the hole's mass (E = mc2).
- A hole a few times the sun's mass: about one ten-millionth of a degree above absolute zero, far colder than the microwave background, so it absorbs more than it emits. It will lose mass only once the background cools below its temperature.
- A primordial black hole of about a thousand million tons (a mountain's mass, smaller than a proton) would be at about 120 billion degrees and emit about 6,000 megawatts, enough for ten large power stations.
- Those formed in the early universe with this mass would be finishing now in a final burst of gamma rays.
The search for primordial black holes
The gamma-ray background limits them to no more than about 300 per cubic light-year on average. If concentrated in galaxies a million times more, the nearest might be as far as Pluto, yet even then catching their few quanta would need a larger detector than any built. The Earth's atmosphere could serve as a detector: a final burst would create showers of electrons and positrons whose flashes could be seen, as distinct from lightning. A negative search still tells us the early universe was smooth.
Where the two theories meet
Radiation from black holes was the first prediction depending on both general relativity and quantum mechanics. It caused opposition at first (John Taylor called it nonsense at the Oxford seminar), but most physicists came round. It also implies the approximations fail when a hole shrinks to a fraction of a gram, so from 1975 Hawking turned to a full sum over histories approach to quantum gravity.
- The "6,000 megawatts" figure assumes mainly photons, neutrinos and gravitons; real primordial hole outputs depend on which particles exist at that temperature.
- Hawking assumed information was lost in evaporation; he conceded the information paradox bet in 2004, and the 2019 to 2020 "Page curve" and "islands" calculations suggest information escapes.
- Pluto was reclassified as a dwarf planet in 2006.
- Still never observed from an astrophysical black hole.
- Analogues (2025 to 2026): optical-fibre experiments report single-photon-stimulated analogue Hawking radiation with heralded single-photon output (Nature Communications, May 2026); related work claims backreaction of the emitted radiation on the optical horizon. BEC spin-sonic proposals continue. Spontaneous quantum Hawking radiation remains hard to isolate; treat lab results as analogue evidence, not sky detection.
- The area theorem was tested with loud mergers including GW250114 (2025).
- No confirmed primordial black hole burst; gamma-ray limits only.
Deeper notes from the lecture
The area theorem (November 1970) came as Hawking got into bed: horizon generators cannot converge, so area cannot shrink; mergers only grow total area. Bekenstein's area-as-entropy move annoyed Hawking because temperature would imply glow. The 1972 Bardeen-Carter-Hawking paper argued the analogy was incomplete.
Moscow 1973: Zeldovich and Starobinsky on rotating holes emitting; Hawking's calculation showed non-rotating holes emit too. Oxford seminar late November 1973; paper 1974. John Taylor called it nonsense; most physicists later accepted it. Temperature scales as 1/M: solar-mass holes at ~10⁻⁷ K absorb CMB; mountain-mass primordials at ~10¹¹ K emit gigawatts and would be dying now.
Virtual pairs near the horizon: negative-energy partner can fall in and become real relative to infinity; positive escapes. Energy accounting uses E = mc². Searching for bursts: gamma-ray background caps average density (~300 per cubic light-year in the lecture); atmosphere as calorimeter; null result constrains early-universe smoothness. From 1975 Hawking pushed a sum-over-histories approach to quantum gravity because the approximations fail below a fraction of a gram.
"Black holes ain't as black as they are painted." , Hawking's lecture title and claim
Arguments in full: area, entropy, glow, explosions
Area theorem night
November 1970, shortly after daughter Lucy's birth, Hawking was getting into bed (slow because of disability) and defined a black hole as the set of events that cannot escape to infinity. The horizon is made of light rays that forever hover, "like running away from the police and managing to keep one step ahead." Those rays cannot approach each other or they would collide and fall in, leaving the boundary. Like the edge of a distant shadow, horizon generators stay parallel or diverge. Therefore horizon area never decreases; matter falling in increases it; two holes merging yield final area at least the sum. He rang Penrose the next day.
Second law and Bekenstein
Entropy of an isolated system never decreases (statistical, not absolute). Join systems and combined entropy exceeds the sum. Gas filling a box, oxygen mixing with nitrogen: disorder wins. A black hole seems to offer a cheat: throw high-entropy gas in and outside entropy falls. Bekenstein proposed horizon area is the hole's entropy so the sum never falls. Fatal flaw then: entropy implies temperature, temperature implies radiation, but holes were defined not to emit. Hawking, Carter, and Bardeen (1972) stressed the analogy and the flaw; Hawking admits irritation at Bekenstein "misusing" the area result. Bekenstein was basically right.
Moscow to Oxford
September 1973, Moscow: Zeldovich and Starobinsky argued rotating holes emit by the uncertainty principle. Hawking believed the physics, disliked the maths, rebuilt it, and announced at Oxford end of November 1973. Surprise: even non-rotating holes emit steadily. Spectrum matches a hot body; temperature falls as mass rises. Emission rate is exactly what the second law needs.
Virtual pairs picture
Empty space cannot have fields fixed at exactly zero (uncertainty). Fluctuations are virtual particle pairs that appear, separate, and annihilate. Near a hole, the negative-energy partner can fall in and become real; the positive-energy partner can escape as radiation. Smaller holes: shorter distance for the negative partner, higher temperature. Outgoing positive energy is balanced by negative energy inflow, so mass falls (E = mc²). Horizon area shrinks, but radiation entropy more than compensates.
Explosions and primordial hunt
Gamma-ray background limits average density of such holes to at most ~300 per cubic light-year, under one millionth of cosmic mass density. Preferential clustering in galaxies might put the nearest ~ as far as Pluto, still hard to see. Final bursts need large space-borne detectors or atmosphere Cerenkov flashes at separated sites (Porter and Weekes in Arizona found flashes, none confirmed as primordial). Null results still teach: early universe was smooth, uniform, high-pressure, or we would see more holes.
Reception
First public announcement near Oxford met incredulity; session chair John G. Taylor called it nonsense and wrote against it. Later calculations by many groups confirmed the thermal spectrum. Hawking radiation was the first prediction that truly needed both GR and quantum mechanics.
"The black hole was emitting particles at exactly the correct rate to prevent violations of the second law."
- Solar-mass-scale T ~ 10−7 K vs CMB ~2.7 K
- Evaporation time ~ 1066 years
- Primordial ~109 ton hole: lifetime ~ cosmic age; power ~ 10,000 MW
- Gamma background: ≤ ~300 little holes per cubic light-year
Hawking radiation and evaporation (depth)
Quantum fields near horizons yield a thermal flux: black holes have temperature inversely related to mass and can evaporate. Tiny holes would be hot; stellar and supermassive holes are cold. Analogue systems and calculations keep refining the story; the information paradox (unitary quantum mechanics vs thermal evaporation) remains a live research frontier.
Lab analogue horizons (fluids, optics, BECs) report Hawking-like spectra in several setups. They support the mechanism’s robustness; they do not yet settle information recovery in real gravity.
| Mass scale | Qualitative T |
|---|---|
| Primordial tiny | possibly hot / explosive |
| Stellar ~10 M☉ | far below CMB |
| Supermassive | colder still |
Lecture 4 working notes. Hawking temperature T ∝ 1/M; luminosity rises as mass falls for small holes. Pair-production folk pictures help intuition and mislead on bookkeeping; trust the QFT-in-curved-spacetime calculation outline. Evaporation time for stellar holes exceeds the age of the universe by enormous factors. Information paradox options (remnants, holography/AdS-CFT intuition, soft hair, modifications) remain unsettled.
COLD WHEN BIG. Ordinary holes are colder than the CMB; they grow by accretion more than they evaporate today.
AREA-ENTROPY-GLOW. Horizon area never decreases; Bekenstein reads area as entropy; Hawking finds the holes glow at the rate that saves the second law. Area-entropy-glow is the discovery path, including Hawking's own resistance.
State the virtual-pair story in four beats: pair appears near horizon; negative-energy partner falls in; positive escapes; hole mass drops. Then invert mass: smaller hole, higher temperature, runaway. That is evaporation.
Hawking radiation is often sold as observed fact. Invert: no astrophysical detection exists; lab analogues are stimulated or contested. The calculation is central to theory; claiming the sky has confirmed it is the shadow.
Horizon area never decreases, like entropy, and Bekenstein's idea that it is entropy implied a temperature. Hawking found black holes do radiate, via virtual pairs, at exactly the rate that saves the second law. Small black holes get hotter and explode; none has yet been seen.
5. The Origin and Fate of the Universe
An audience with the pope
In 1981 Hawking attended a cosmology conference at the Vatican. The pope told the participants it was fine to study the universe's evolution after the big bang, but not the big bang itself, the moment of Creation. Hawking was glad the pope did not know he had just presented a paper suggesting space-time might be finite without boundary, so that there was no moment of Creation. "I had no desire to share the fate of Galileo," with whom he felt kinship, having been born exactly 300 years after Galileo's death.
The hot big bang and four open questions
The standard story: infinite temperature at the big bang; after one second about ten thousand million degrees; after about 100 seconds, a thousand million degrees, when protons and neutrons formed helium; then cooling, galaxies, stars. The sun, a second- or third-generation star about five thousand million years old, contains about 2% heavier elements forged in earlier stars. The model fits observation but leaves questions:
- Why was the early universe so hot?
- Why is it so uniform on large scales, when distant regions had no time to exchange heat?
- Why did it start so close to the critical rate of expansion, a precision of one part in a hundred thousand million million at one second?
- Why, despite this uniformity, does it contain lumps such as stars and galaxies?
Hawking notes the anthropic answer: we can only live in a region suitable for us. But that would make the rest of the universe random, while we see uniformity everywhere.
Inflation
Alan Guth at MIT proposed that the early universe, very hot, cooled without breaking the symmetry between forces, like supercooled water below 0 °C. The leftover energy acts like a cosmological constant, driving expansion by a factor of a million million million million million in a tiny fraction of a second. This smooths out irregularities, sets the rate near critical, and explains the hot, uniform result. Since gravitational energy is negative and matter energy positive, the total can be zero; doubling both still gives zero. As Guth said, "the universe is the ultimate free lunch." That explains the roughly 1080 particles in the observable universe.
Guth's original version ended inflation suddenly, like ice crystals forming, making irregular bubbles. In October 1981 in Moscow, young Andrei Linde proposed a slow breaking of symmetry. Hawking pointed out his bubbles would be larger than the universe. Linde's chaotic inflation (1983) improved on both.
Imaginary time and the no-boundary condition
To predict how the universe began, we need laws that hold at the beginning; classical general relativity breaks down there. Quantum gravity uses Feynman's sum over histories, computed in imaginary time, a well-defined mathematical device in which time behaves like a direction in space and space-time becomes Euclidean.
With Jim Hartle, Hawking worked out the conditions if space-time has no boundary. In imaginary time, the universe would be like the surface of the Earth: finite, with no edge, and the beginning like the South Pole, a point where the usual laws still hold. It is "just a proposal," not deducible from other principles, judged by its predictions. In real time, the history would start at a minimum size, expand in an inflationary way, and carry small quantum non-uniformities that grow into galaxies. Perhaps imaginary time is the fundamental time, and real time something we invent to describe the universe.
If the universe has no beginning or end, Hawking asks: "What place, then, for a creator?"
- The pope's remark is Hawking's paraphrase. John Paul II's published address of 3 October 1981 did not forbid research; it said science alone cannot settle the ultimate beginning, which needs metaphysics and revelation.
- Inflation is widely accepted but contested (Steinhardt and others argue it predicts a multiverse and is hard to falsify).
- The no-boundary proposal remains a proposal; whether it really yields inflation and a smooth start is debated (Feldbrugge, Lehners and Turok, 2017).
- Inflation's flatness and nearly scale-invariant fluctuations still fit Planck-class data. Primordial tensor modes unseen: BICEP/Keck r < 0.036; BICEP2's 2014 claim was dust.
- No-boundary research continues: 2026 path-integral work argues consistent evaluation can drive closed-universe probabilities near 1, reshaping how the proposal is scored; older critiques (Feldbrugge, Lehners, Turok 2017) still contest whether it yields a smooth inflationary start.
- Hawking and Hertog (2018) and Hertog's On the Origin of Time (2023) revise the picture toward holographic cosmology.
Deeper notes from the lecture
Hot big bang timeline in the lecture: infinite T at t=0; ~10¹⁰ K at one second; ~10⁹ K by ~100 seconds when helium forms; later galaxies and stars; Sun ~5×10⁹ years old with ~2% heavier elements from earlier stars. Four open questions: heat, large-scale uniformity (horizon problem), near-critical expansion (flatness to one part in 10¹⁴ at one second in Hawking's figure), and the origin of lumps.
Guth's supercooling leaves vacuum energy acting like a cosmological constant; expansion by about 10³⁰ in a fraction of a second. Gravitational energy negative, matter positive: total can stay zero while both grow ("ultimate free lunch"), accounting for ~10⁸⁰ particles in the observable universe. Guth's sudden end made Swiss-cheese bubbles; Linde's slow roll and later chaotic inflation (1983) improved the exit. Hawking's Moscow remark: Linde's early bubbles would outgrow the universe.
Imaginary time turns the path integral into a well-posed Euclidean sum. Hartle-Hawking: like Earth's surface, finite without edge; the beginning is a regular point (South Pole). Real-time history: minimum size, inflation, small quantum ripples → galaxies. Hawking floats that imaginary time may be fundamental. Closing question: if no boundary, "What place, then, for a creator?"
Arguments in full: hot bang, inflation, no boundary
Vatican spark
1981 Vatican cosmology meeting: the Pope said study after the bang was fine, but not the bang itself (moment of creation). Hawking had just spoken on a no-boundary idea and was glad the Pope had not heard the talk. Sympathy with Galileo: born 300 years after Galileo's death.
Hot big bang timeline (lecture)
| Time | Temperature / event |
|---|---|
| Bang | Zero size, infinite T (classical) |
| 1 s | ~1010 K; photons, e±, neutrinos, some p, n |
| ~100 s | ~109 K; deuterium then helium; ~1/4 mass to helium |
| Hours | Nucleosynthesis ends |
| ~106 years | Atoms form; then galaxies from denser patches spinning up like skaters pulling in their arms |
| Stars | H→He; massive stars → C, O; supernovae seed next generations |
| Sun | ~5×109 years old; ~2% heavier elements; second/third generation |
Agreement with helium abundance and the microwave background makes the picture trusted back to about one second.
Four open questions
- Why so hot at the start?
- Why so uniform on large scales?
- Why expansion so near critical? (one part in 1014 at one second either way: early recollapse or empty now)
- Origin of the small density ripples that become galaxies?
Classical GR cannot answer: laws break at the singularity. The anthropic principle: we observe a region fit for life. Without inflation-like smoothing, matching microwave temperatures in all directions and the critical expansion looks like divine fine-tuning.
Inflation: Guth, bubbles, Linde
Alan Guth: early universe stuck in a supercooled unbroken-symmetry state; leftover energy acts like a cosmological constant; expansion by ~1030 in a fraction of a second. Wrinkles smooth like a balloon; expansion driven near critical. Total energy can stay zero because positive matter energy cancels negative gravitational energy; doubling both still gives zero. "The universe is the ultimate free lunch." Observable-universe particle count ~1080.
End of inflation: symmetry breaks, latent heat reheats, then a hot-bang-like expansion. Guth's original bubble nucleation failed: bubbles raced apart too fast to percolate. Andrei Linde (after Hawking's Moscow seminar, Oct 1981): slow breaking inside a huge bubble. Hawking argued symmetry should break everywhere at once. Slow-breaking overpredicted microwave variations. Linde's 1983 chaotic inflation dropped the phase-transition crutch and fit fluctuation amplitudes better. Inflation enlarges the set of viable starts but does not make every start work.
Quantum gravity and no boundary
Singularity theorems say classical GR fails; quantum gravity is required. Time and space become alike; perhaps Euclidean time is fundamental and "real" time a useful fiction. Histories of the universe are entire curved space-times.
No boundary proposal (Vatican talk; worked out with Jim Hartle at Santa Barbara): space-time is finite yet without edge, like Earth's surface. "The boundary condition of the universe is that it has no boundary." Not deduced from a deeper principle; judged by predictions. Most histories negligible; a preferred family looks like Earth latitudes in imaginary time (North Pole = zero size, not singular). In real time: start at a minimum size, inflate, expand large, later look singular again. Astronauts in black holes still hit sticky ends in real time. Quantum fluctuations under no-boundary give the minimum nonuniformity; inflation amplifies them into galaxies. If fully self-contained: "What place, then, for a creator?"
Audience with the Pope after the 1981 conference. Boundary drawn at the bang. Hawking's no-boundary talk had already crossed it in mathematical language the audience missed. He notes the Galileo parallel and moves on.
- Hot bang alone: same T in all directions and near-critical expansion look miraculously chosen.
- Inflation: many messy starts stretch into a flat, uniform patch; ripples from quantum noise.
Inflation, beginning, fate (depth)
Inflation stretches quantum fluctuations into seeds of structure and helps with horizon/flatness puzzles. The no-boundary proposal and related quantum-cosmology ideas try to remove a classical singular beginning. Fate talk moved when dark energy was discovered: accelerated expansion dominates late-time stories Hawking’s lectures could not assume.
DESI DR2 community discussions of evolving dark energy (~2.8-4.2σ hints) are acceptance tests for frozen Λ. Not a slogan flip: a probe schedule for w(z).
Lecture 5 working notes. Inflation’s job list: horizon, flatness, monopoles (if any), nearly scale-invariant perturbations. Quantum cosmology (no-boundary and rivals) tries to replace “before” with a path-integral boundary condition. Fate: heat death under accelerated expansion is the default late-time story if dark energy stays roughly Λ-like; evolving-w hints (DESI) are probes, not verdicts.
HOT-FLAT-INFLATE-POLE. Hot big bang leaves heat, uniformity, flatness and lumps open; inflation answers them; the no-boundary South Pole removes the edge. Hot-flat-inflate-pole is Lecture 5.
List Guth's four puzzles, then write one sentence each on how a 10^30-fold stretch solves uniformity and flatness. Leave "why so hot" and "where lumps come from" as quantum leftovers. That is inflation's division of labour.
"No boundary, no creator" is Hawking's rhetorical close, not a theorem. The proposal is judged by predictions; rivals (and 2017 critiques) argue it may not yield the smooth inflationary start claimed. The shadow is converting a research proposal into settled metaphysics.
The hot big bang leaves the universe's heat, uniformity, flatness and lumps unexplained. Inflation answers them by a burst of exponential growth, and the no-boundary proposal, using imaginary time, offers a beginning without a singularity or a creator's choice.
6. The Direction of Time
Laws without a direction
Hawking opens with L. P. Hartley's The Go-Between: "The past is a foreign country. They do things differently there." His question is why the past is so different from the future: why do we remember the past but not the future, and is that connected with the expansion of the universe?
- C: swap particles for antiparticles.
- P: take the mirror image, swapping left and right.
- T: reverse the motion of every particle, running the film backward.
The laws governing matter in all normal situations are unchanged under C and P together, so mirror-image beings made of antimatter would live exactly as we do. Hawking's advice: if an alien offers you his left hand, don't shake it; you might both vanish in a tremendous flash of light. And since the laws are unchanged under CP and under CPT, they must be unchanged under T alone.
Yet everyday life is lopsided. Film a cup of water falling off a table and smashing, and anyone can tell whether the film runs forward or backward: in reverse, the pieces gather themselves off the floor and jump back onto the table as a whole cup. "If it were" ever seen, Hawking jokes, "the crockery manufacturers would go out of business." The usual explanation is the second law of thermodynamics: disorder, or entropy, always increases. It is Murphy's Law: things get worse. An intact cup is a state of high order, a broken cup on the floor a disordered one, so time runs from the first to the second and not back.
| Arrow | Direction | Hawking's explanation |
|---|---|---|
| Thermodynamic | Disorder increases | Ordered states are rare; a shaken jigsaw almost always ends disordered |
| Psychological | We remember the past, not the future | Recording memory, as in a computer, increases total disorder |
| Cosmological | The universe expands | Set by the boundary conditions of the universe |
Hawking's plan for the lecture: show that the psychological arrow is determined by the thermodynamic one, so the two always agree; that with the no-boundary assumption both are tied to the cosmological arrow, though they need not point the same way; and that only when all three agree can there be intelligent beings to ask why.
The thermodynamic arrow: counting arrangements
The second law rests on a simple count: there are far more disordered states than ordered ones. A jigsaw in its box has exactly one arrangement that makes the picture and a vast number that do not. Start in the ordered state and shake the box: the pieces will probably take a disordered arrangement simply because there are so many more of them. Some groups may still form parts of the picture, but the more you shake, the more those groups break up, until the pieces are completely jumbled. Disorder increases provided the system starts in a state of high order.
That proviso is the whole story. Suppose, Hawking says, God had decided the universe should finish in a state of high order and did not care how it started. Then early times would be disordered and disorder would decrease: broken cups would reassemble. But any humans watching would, he argues, have a backward psychological arrow: they would remember the late events and not the early ones, and would still see disorder increasing.
The psychological arrow: how a memory records
We do not know how the brain works in detail, but we do know how computer memory works, and Hawking assumes the arrow is the same for both; otherwise a computer that remembered tomorrow's stock prices would make a killing.
- A memory element (Hawking's example: a superconducting loop that either carries a current or does not) can be in two states, labelled one and zero.
- Before recording, it is disordered: one and zero are equally likely.
- After interacting with the system it records, it is definitely in one state: the memory has passed from disorder to order.
- Making sure it is in the right state takes energy, dissipated as heat, which increases disorder in the universe.
- The increase in disorder is greater than the gain in order in the memory, so every recording raises total disorder.
So the direction in which a computer remembers the past is the direction in which disorder increases, and we remember things in the direction in which disorder increases. This makes the second law "almost trivial": disorder increases with time because we measure time in the direction in which disorder increases. "You can't have a safer bet than that."
Why order at the beginning?
But why should the universe be highly ordered at the end of time we call the past, rather than disordered throughout, which might seem more probable? One answer is that God simply chose a smooth, ordered start and we should not ask why. Hawking replies that the whole history of the universe can be called God's work, and it appears to follow laws we can discover, so it is not unreasonable to hope that similar laws hold at the beginning.
Classical general relativity cannot supply them: it predicts a singularity of infinite density and curvature where all known laws break down, so in effect it predicts its own downfall. A lumpy, disordered start would have left disorder nothing to do but stay constant (no thermodynamic arrow) or decrease (an arrow opposite to expansion). Neither matches what we see.
| Start | Thermodynamic arrow | Matches observation? |
|---|---|---|
| Smooth, ordered | well defined, disorder grows | yes |
| Lumpy, completely disordered, disorder constant | none | no |
| Lumpy, completely disordered, disorder decreasing | opposite to the cosmological arrow | no |
A quantum theory of gravity is needed. It sums over all possible histories of the universe, each carrying two numbers, the size of a wave and its phase (crest or trough); the probability of a property comes from adding the waves for every history that has it. The trouble is that we do not and cannot know the boundary conditions in the past, unless the condition is that there is no boundary: every history finite but without edges or singularities, like the surface of the Earth with two more dimensions. Then the beginning of time is a regular, smooth point.
That implies the universe began expanding very smooth and ordered, but not perfectly uniform, which the uncertainty principle forbids: density and velocity fluctuations had to be present, and the no-boundary condition makes them as small as they could be. An inflationary phase enlarged the universe enormously. The fluctuations stayed small at first, then grew: slightly denser regions had their expansion slowed by the extra mass, stopped, and collapsed into galaxies, stars and beings like us. A smooth, ordered universe became lumpy and disordered, giving the thermodynamic arrow, and with it our psychological arrow, pointing the way the universe expands.
Does the arrow reverse?
What if the universe stops expanding and recollapses? Would survivors see cups jumping back onto tables, or remember tomorrow's prices? Recollapse is at least ten thousand million years off, but there is a quicker test: jump into a black hole, whose collapse resembles the late stages of a collapsing universe. An astronaut there might win at roulette by remembering where the ball went before betting, except that he would soon be turned to spaghetti, and trapped behind the event horizon he could neither report the reversal nor bank his winnings.
At first Hawking believed disorder would decrease if the universe recollapsed, because he thought it had to return to a smooth, ordered state when small again. The contracting phase would be the time reverse of the expansion: people would die before they were born and grow younger as the universe shrank. The symmetry was attractive, and a simple model seemed to support it. Don Page pointed out the no-boundary condition did not require the contracting phase to mirror the expanding one, and his student Raymond Laflamme found a model in which collapse was very different. "I realized that I had made a mistake." The no-boundary condition in fact implies that disorder keeps increasing during contraction: the thermodynamic and psychological arrows do not reverse in a recollapse or inside black holes. Some people, like Eddington, never admit they are wrong; others claim they never really held the view. Hawking says it is much better to admit it in print, as Einstein did in calling the cosmological constant the biggest mistake of his life.
Why, then, do the thermodynamic and cosmological arrows point the same way now? The weak anthropic principle: in a contracting phase, conditions would not suit intelligent beings, so we find ourselves in the expanding phase.
- The past hypothesis (why entropy was so low at the start) remains open; Penrose still argues inflation does not solve it.
- Direct T violation in weak decays is established; it does not explain the everyday arrow.
- Accelerating expansion makes a future recollapse unlikely, so the reverse-arrow thought experiment is mostly historical.
- Explaining the low-entropy start (the "past hypothesis") remains an open problem; Penrose argues inflation does not solve it.
- CPT symmetry holds, but T alone is violated in some weak interactions (directly observed with kaons and B mesons), though this does not explain the everyday arrow.
- With accelerating expansion, the recollapse scenario now looks unlikely.
Deeper notes from the lecture
Hartley's line sets the mood: the past is a foreign country. C, P and T symmetries: laws look the same under CP and under CPT, hence under T alone in ordinary situations. Everyday counterexample: smashed cup film. Second law as Murphy's Law. Jigsaw count: one ordered picture, myriad disordered heaps; shake and disorder wins if you start ordered.
God-chooses-ordered-end thought experiment: disorder would decrease, but beings there would still experience a psychological arrow pointing toward rising disorder. Computer memory (superconducting loop 0/1): recording orders the bit but dumps more heat disorder into the environment; we remember along rising entropy. "You can't have a safer bet than that."
Classical GR predicts its own downfall at a singularity, so it cannot set the ordered start. No-boundary: histories finite without edges; start smooth with minimal uncertainty-principle ripples; inflation stretches them; gravity grows lumps; thermo and psycho arrows align with expansion. Black-hole "test" of reversal is fatal and unreportable. Page and Laflamme kill the pretty time-symmetric recollapse; Hawking publishes the correction, citing Einstein on the cosmological constant.
Ask of any process: does disorder rise (thermo)? Does a record form only that way (psycho)? Are we in the cosmic phase where both can hold (cosmo)? Intelligent observers, on this account, show up only where all three agree.
Three arrows (depth)
Thermodynamic, psychological and cosmological arrows usually align. Entropy increase explains why memory and cause-talk point one way. A universe that begins in a low-entropy state sets the thermodynamic arrow; without that special beginning, the story stalls. Time’s direction is not an extra microscopic law; it is boundary conditions plus statistics.
| Arrow | Points | Tied to |
|---|---|---|
| Thermodynamic | entropy up | low-entropy past |
| Psychological | memory of past | recording in irreversible media |
| Cosmological | expansion | may reverse in some models (not ours late-time) |
Lecture 6 working notes. Microscopic laws are mostly time-symmetric (with tiny CP exceptions not explaining the arrow). The arrow needs special initial conditions. Psychological arrow rides on thermodynamic recording. Cosmological arrow currently aligns with expansion. A bouncing cosmos would need a careful entropy story or the arrows misalign.
THERMO-PSYCHO-COSMO. Disorder grows (thermo); memory records with the same rise in disorder (psycho); no-boundary plus anthropic place us in expansion (cosmo). Three arrows, one alignment.
Film a cup smash in your head. Name which arrow tells you the film is forward (thermo), which tells you that you remember the smash not the reassembly (psycho), and which cosmic phase you must be in for both to match expansion (cosmo).
Hawking first taught that arrows reverse in recollapse. Page and Laflamme corrected him; he admitted the mistake in print. The shadow is clinging to the pretty time-symmetric story after the calculation says otherwise, or refusing to publish the correction.
- The laws are unchanged under CPT, yet everyday time has a direction.
- Thermodynamic arrow: disorder grows because there are far more disordered states, given an ordered start.
- Psychological arrow: recording a memory raises total disorder, so we remember in the direction disorder grows.
- Cosmological arrow: the no-boundary condition gives a smooth, minimally fluctuating start; inflation and gravity turn it lumpy, aligning the arrows with expansion.
- The arrows do not reverse in a recollapse or a black hole; Hawking admits in print that he first thought they would.
7. The Theory of Everything
Partial theories and cautious optimism
A unified theory is too hard all at once, so physics proceeds by partial theories. Einstein's search failed because too little was known about nuclear forces. Physicists have predicted the end before: in 1928 Max Born told visitors physics would be over in six months, after Dirac's equation for the electron. Still, Hawking sees "grounds for cautious optimism."
Infinities plague quantum theories; in others they can be removed by renormalization, but not in gravity, carried by a spin-2 graviton. Supergravity promised cancellations but was too hard to check.
Particles become vibrating strings, and their histories are tubes: two strings joining look like the legs of a pair of trousers. In 1974 Joël Scherk and John Schwarz showed strings could describe gravity. Infinities are thought to cancel in versions such as the heterotic string. Strings need ten or twenty-six dimensions, the extras curled up too small to see or to fly a spaceship through, like a hose that looks one-dimensional from afar.
Why only four dimensions large? The anthropic principle: two space dimensions seem too few for complex beings, and with more than three, orbits of planets around the sun would be unstable. Other problems: many ways to curl up the dimensions, and no clear prediction.
Three possibilities
- A complete unified theory exists and we will find it if smart enough.
- Only an infinite sequence of better theories.
- No theory: beyond some point events are random.
Gravity may end the "boxes within boxes": a particle above the Planck energy (about 1019 GeV) would become a black hole.
Forces on the ladder
Hawking's unification ladder is the same story told in the companion editions: electromagnetism joins the weak force in the electroweak theory (Glashow, Weinberg, Salam; W and Z found in 1983); a grand unified step would pull in the strong force; gravity is last and hardest. Partial theories succeed when they make risky predictions. Strings earn their place in the lecture because they naturally include a graviton mode, not because experiment has crowned them.
- Electroweak confirmation: W and Z bosons, 1983
- Planck energy: about 1019 GeV
- Observable-universe particle count in the inflation story: about 1080
- Lecture's extra dimensions: ten or twenty-six (later: 10 for superstrings, 11 for M-theory)
Knowing the mind of God
Seventy years earlier, Eddington supposedly claimed only two people understood general relativity; now tens of thousands do. A complete theory should become understandable in broad principle by everyone. If the no-boundary proposal is right, God had no freedom to choose initial conditions. But "what is it that breathes fire into the equations?" If we find the answer to why we and the universe exist, "it would be the ultimate triumph of human reason, for then we would know the mind of God."
- "Ten or twenty-six" dimensions is dated: superstrings need ten, M-theory eleven (after 1995).
- Hawking himself changed his mind: in a 2002 lecture, "Gödel and the End of Physics," he suggested a complete final theory may be impossible.
- The Eddington anecdote is probably apocryphal.
- The Higgs boson (2012, Nobel 2013) completed the Standard Model; no LHC supersymmetry in the multi-TeV window reported so far.
- Proton decay unseen (Super-Kamiokande limits); Hyper-Kamiokande ramp-up continues.
- String theory / swampland: still no confirmed unique prediction. Estimates of string vacua remain enormous; swampland conjectures (de Sitter, distance, weak gravity and others) actively constrain cosmology but are not theorems. A 2026 analysis argues perturbative string theory lacks de Sitter × closed-manifold solutions under a Gibbons-Hawking entropy assumption.
Deeper notes from the lecture
Partial theories are the working method because a full unification is too hard at once. Einstein failed partly for lack of nuclear data. Born's 1928 "six months" boast after Dirac's electron equation is Hawking's cautionary tale. Gravity's spin-2 graviton resists the renormalization that tames other quantum fields; supergravity's hoped-for cancellations were too hard to verify.
Scherk and Schwarz (1974): strings can carry gravity. Histories as tubes; joining strings like trouser legs. Heterotic and related versions aim to cancel infinities. Extra dimensions (ten or twenty-six in the lecture) curl up small. Anthropic filter: fewer than three large space dimensions seems too cramped for complex chemistry and observers; more than three makes orbits unstable. Many compactifications, few sharp predictions.
Planck energy ~10¹⁹ GeV: above it a particle's energy looks like a black hole, possibly ending the infinite regress of deeper boxes. Three possibilities structure the close. Eddington's "two people understand GR" story (likely false) contrasts with tens of thousands today. Final cadence: equations need something that "breathes fire" into them; knowing why we exist would be to "know the mind of God."
Arguments in full: partial theories to mind of God
False dawns
Unification proceeds by partial theories that neglect or freeze other effects (chemistry without nuclear structure). Einstein's late unified search failed: nuclear forces unknown; he refused quantum uncertainty. Early 1900s continuous-matter hopes died with atoms and the uncertainty principle. Max Born (1928) told Göttingen visitors physics would be over in six months after Dirac's electron equation; the neutron and nuclear forces ended that. Hawking still claims cautious optimism: we know more now.
Renormalization vs gravity
Partial quantum theories cancel infinities by renormalization, adjusting masses and couplings by infinite amounts. It works empirically but cannot predict those values from first principles. GR has only two adjustable quantities (G and Λ); that is not enough. Virtual pairs in empty space would carry infinite energy and curl the universe to a point if gravity is quantized naively.
Supergravity (1976): add spins 3/2, 1, 1/2, 0 so negative-energy virtual pairs cancel many infinities. Remaining checks needed years of computer time and looked error-prone; fashion shifted to strings.
Strings: trousers, tensions, dimensions
Basic objects are one-dimensional strings, histories are world-sheets (tubes). Joining looks like trouser legs; forces like H-shaped plumbing. Late 1960s: strong-force strings with ~ten tons tension. Scherk and Schwarz (1974): gravity if tension ~1039 tons, new physics below ~10−33 cm. Little attention; Scherk died; Schwarz nearly alone until 1984, when supergravity stalled and Green-Schwarz anomaly cancellation plus left-handed particles revived the field. Heterotic strings looked promising for real particle content.
Consistency seems to need 10 or 26 space-time dimensions. Extra ones curl to ~10−33 inch scales; we see 3+1 flat dimensions, like an orange looking smooth from afar. Bad news for sci-fi shortcuts. Why four large? Anthropic: 2D bodies cannot digest or circulate blood without falling apart; more than 3 space dimensions make orbits and atoms unstable (forces fall too fast with distance). Other regions or universes may differ; no observers there.
Open problems named in the lecture: prove all infinities cancel; match string waves to observed particles. Hawking hoped answers by century's end.
Three possibilities
- A complete unified theory exists and we can find it.
- An infinite sequence of better approximations (boxes within boxes).
- No predictive theory; pure randomness.
(3) is largely redefined away: science aims to predict up to the uncertainty limit. (2) matches history, but Planck energy ~1019 GeV may cap the ladder: above it a particle would form a micro hole. Lab energies ~GeV; bridging needs an accelerator larger than the solar system. The early universe is the natural high-energy lab. Hawking foresaw a complete theory by 2000 "presuming we don't blow ourselves up first."
Knowing the mind of God
A final theory would end a chapter and, once digested, could be taught in outline in schools, as relativity moved from "two people" (Eddington joke) to tens of thousands of graduates. Einstein: how much choice did God have? No-boundary: no freedom on initial conditions; maybe little freedom on the laws if few self-consistent theories allow observers. Still open: what breathes fire into the equations? Why does the universe bother to exist? Philosophers once owned such questions; Wittgenstein's retreat to language analysis is, for Hawking, "what a comedown." If we find why, "we would know the mind of God."
- Complete theory: finite search ends.
- Infinite tower: always another layer at higher energy.
- No theory: unpredictability as last word (mostly rejected once goals include the uncertainty bound).
Hawking's "by the end of the century" unity did not arrive. Strings remain a framework without unique low-energy proof; LHC found the Higgs but not supersymmetry in the early multi-TeV window. The lecture's logic about Planck-scale limits and early-universe tests still structures the field.
Unification hopes and limits (depth)
Hawking’s closing lecture asks whether a finite set of principles can unite gravity with quantum field theory. Particle physics’ Standard Model works staggeringly well below Planck energies; gravity resists naive quantisation. String theory, loop quantum gravity and other programmes were younger hopes in the lecture era; none is confirmed as the TOE. Partial unification (electroweak) is real; full TOE remains aspiration.
No experimental confirmation of strings, supersymmetry at colliders, or a complete quantum gravity. Precision tests (Eöt-Wash-style, GW, CMB) constrain large deviations. Keep the lecture’s ambition; drop any “by year 2000” calendar optimism.
“Theory of everything” is a research goal name, not a completed product. Selling certainty past the data repeats the acceptance sins earlier lectures mock.
Lecture 7 working notes. Effective field theory explains why the Standard Model can be superbly accurate without being final. Gravity’s coupling grows with energy toward the Planck scale. Dualities and holography changed what “fundamental” can mean since the lectures. Experimental silence on TeV supersymmetry and on obvious string signatures is data, not rudeness. Keep ambition; update calendars.
PARTIAL-STRING-THREE. Physics advances by partial theories; strings are the gravity candidate; three endgames (final theory, endless sequence, or randomness). Partial-string-three ends the series.
Write Hawking's three possibilities as tick boxes. Add one modern note under each: Higgs completed the Standard Model (partial success); estimates of string vacua still vast (sequence worry); quantum mechanics already injects probability (randomness already partly true). Pick which box you would bet on, and why.
"Know the mind of God" can be read as a promise that a final equation ends curiosity. Hawking later (2002) doubted a complete final theory may be possible. The shadow is treating Lecture 7's optimism as his last word, or treating a slogan as a research programme.
Physics advances by partial theories; gravity's infinities resist renormalization, and string theory, with curled-up dimensions, is the main hope. There may be a final theory, an endless sequence, or none. Finding it would reveal why the universe exists: the mind of God.
Synthesis
Main Points
- Neither Newton's nor Einstein's gravity allows a lasting static universe.
- Hubble's redshift-distance law shows the universe is expanding; earlier times crowd toward a dense state.
- Olbers' paradox already hinted that stars have not shone forever.
- The Hawking-Penrose theorems prove a singularity if classical general relativity holds and there is enough matter.
- Stars above the Chandrasekhar limit cannot rest on electron degeneracy; heavier corpses face collapse.
- An event horizon is where outgoing light cones tip so far that escape ends.
- Black holes have no hair: classically only mass and spin (and charge) remain.
- Horizon area never decreases, the geometric twin of the second law.
- Bekenstein read area as entropy; temperature then seemed required.
- Hawking radiation supplies that temperature via quantum pairs near the horizon.
- Small holes run away to a final burst; solar-mass holes are colder than the CMB.
- The hot big bang fits light elements and the microwave sky but leaves heat, uniformity, flatness and lumps unexplained.
- Inflation answers those four with a burst of exponential growth and quantum seeds for galaxies.
- Imaginary time and the no-boundary proposal offer a finite cosmos without an edge.
- The thermodynamic arrow (disorder grows) sets the psychological arrow (memory).
- The cosmological arrow matches them in the expanding phase via no-boundary plus anthropic selection.
- Hawking's first claim that arrows reverse in recollapse was wrong; he said so in print.
- Physics advances by partial theories; gravity resists ordinary renormalization.
- String theory is the lecture's unification candidate; extra dimensions must hide.
- Three endgames remain: a final theory, an endless sequence, or residual randomness.
- Knowing why the equations describe a living world would be, in Hawking's phrase, to know the mind of God.
- This 2002 book was disowned by Hawking; treat it as 1980s lectures, not his last word.
Frameworks
| Name | What it says | Use it when |
|---|---|---|
| Singularity theorems | Classical gravity forces a beginning or an end | Asking whether time began |
| No-hair theorem | Black holes keep only a few charges | Thinking about information loss |
| Black hole thermodynamics | Area is entropy; temperature follows | Linking gravity and heat |
| Inflation | Exponential early growth | Explaining uniformity and flatness |
| No-boundary proposal | Space-time finite, no edge | Origin questions |
| Three arrows of time | Thermo sets psycho; cosmo aligns by anthropic selection | Why past ≠ future |
| Partial theories | Unify step by step | Planning a research programme |
- Hawking disowned this 2002 publication; the material is from the 1980s and much appears in A Brief History of Time.
- Several numbers are dated (age range, 1.5 solar mass limit, "ten or twenty-six" dimensions).
- Hawking's own views later moved: he conceded the information paradox (2004) and doubted a final theory (2002 Gödel lecture).
- Acceleration of the expansion (1998+) and the Hubble tension (2020s) post-date the lectures.
Who's who
| Person | Role in the book |
|---|---|
| Aristotle, Ptolemy, Copernicus, Kepler, Galileo, Newton | Path from central Earth to universal gravitation |
| Olbers | Dark night sky as a dating argument |
| Hubble, Friedmann | Expansion observed and predicted |
| Einstein | Cosmological constant to force stasis |
| Bondi, Gold, Hoyle | Steady state theory |
| Penzias, Wilson; Dicke, Peebles, Gamow | Microwave background |
| Penrose | Singularity theorems; cosmic censorship |
| Chandrasekhar, Eddington | Mass limit, and its denier |
| Oppenheimer | Collapse and horizons |
| Israel, Carter, Robinson, Wheeler | No-hair results |
| Bekenstein; Zeldovich, Starobinsky | Entropy hint; rotating-hole emission |
| Guth, Linde | Inflation |
| Hartle | No-boundary proposal |
| Page, Laflamme | Corrected the arrow-reversal claim |
| Scherk, Schwarz | Strings as a theory of gravity |
Frameworks and mental models
| Name | What it says | Use it when |
|---|---|---|
| Friedmann trio | Closed / open / critical from isotropy + homogeneity | Sketch cosmic fate before dark energy |
| Area theorem | Horizon area never decreases | Thermodynamic analogies for holes |
| No hair | Outside: mass, spin (charge) only | Build simple models vs data |
| Inflation | Supercooled vacuum drives rapid stretch | Flatness, horizon, ripple problems |
| No boundary | Finite Euclidean space-time without edge | Quantum initial conditions |
| Three arrows | Thermo, psychological, cosmological | Why we remember the past |
| Partial → unified | Approximate theories nest toward one | Research strategy, not only physics |
Who's who (whole book)
| Person | Role |
|---|---|
| Aristotle / Ptolemy | Earth-centred crystal spheres |
| Newton | Infinite static cosmos; gravity puzzle |
| Einstein | GR; cosmological constant "mistake" |
| Friedmann / Hubble | Expanding universe predicted / observed |
| Penzias / Wilson | CMB |
| Chandrasekhar / Oppenheimer | Collapse limits / GR collapse |
| Penrose / Hawking | Singularities; area; radiation; no boundary |
| Bekenstein | Horizon entropy |
| Guth / Linde | Inflation |
| Hartle | No-boundary partner |
| Wheeler | Named black holes; "no hair" |
These are 1980s lectures issued as a 2002 book Hawking disowned as unauthorized. Dark energy, precision CMB, gravitational waves, and EHT images post-date the talks. Treat numbers and forecasts (steady recollapse odds; unity by 2000) as historical; treat mechanisms (horizons, area, Hawking radiation, inflationary logic, no-boundary proposal) as the enduring payload.
reading Hawking now
These lectures are historical documents with enduring mechanisms. Use TO REMEMBER boxes for the mechanisms that did not. Cross-domain takes belong only where causal structure matches: horizons as information boundaries, entropy arrows as irreversibility budgets, unification as “do not sell the roadmap as the city.”
Pick one lecture. Write three lines: (1) mechanism that still holds, (2) number that aged, (3) 2026 measurement that would move your odds.
Glossary
| Term | Meaning |
|---|---|
| Absolute zero | The lowest possible temperature, at which a substance has the least possible heat energy |
| Anthropic principle (weak) | We see the universe as it is because, if it were different, we would not be here to observe it; used in Lecture 6 to explain why we live in the expanding phase |
| Antiparticle | A partner of each kind of matter particle with opposite charge; particle and antiparticle annihilate into energy when they meet |
| Arrow of time | Anything that distinguishes past from future: thermodynamic, psychological and cosmological arrows |
| Big bang | The singularity at the beginning of the universe, in classical general relativity |
| Black hole | A region of space-time from which nothing, not even light, can escape, because gravity is too strong |
| Boundary condition | The state of a system at the edge of space or time from which the laws predict its evolution |
| Chandrasekhar limit | Maximum mass (about 1.4 Suns) of a cold star that can support itself against gravity by the exclusion principle |
| Term | Meaning |
|---|---|
| Cosmic censorship | The conjecture that singularities are always hidden behind event horizons |
| Cosmic microwave background | Radiation left over from the hot early universe, now cooled to about 2.7 degrees above absolute zero; discovered in 1965 |
| Cosmological constant | A term Einstein added to his equations to allow a static universe; he later called it his biggest mistake. It is now used to describe dark energy |
| CPT symmetry | The laws of physics are unchanged if particles are swapped for antiparticles (C), left and right are mirrored (P) and motion is reversed (T) together |
| Dark energy | The unknown cause of the accelerating expansion of the universe, first inferred in 1998 |
| Doppler effect | The shift in frequency of waves from a moving source; light from receding galaxies is shifted to the red |
| Electromagnetic force | The force between electrically charged particles; the second strongest of the four forces |
| Electroweak unification | The theory joining the electromagnetic and weak forces, confirmed by the discovery of the W and Z particles (1983) |
| Term | Meaning |
|---|---|
| Entropy | A measure of disorder; in an isolated system it never decreases (second law of thermodynamics) |
| Event horizon | The boundary of a black hole, from which light cannot escape |
| Exclusion principle | Two identical matter particles cannot share the same position and velocity (within the uncertainty principle); supports white dwarfs and neutron stars |
| Friedmann models | Solutions of general relativity for a uniform universe that expands from a big bang, and either recollapses or expands forever |
| General relativity | Einstein's theory of gravity as the curvature of space-time by mass and energy |
| Grand unified theory (GUT) | A theory unifying the electromagnetic, weak and strong forces at very high energy |
| Hawking radiation | Thermal radiation emitted by black holes through quantum effects near the horizon, so that black holes slowly evaporate |
| Imaginary time | Time measured with imaginary numbers, in which time behaves like a direction in space; used in the no-boundary proposal |
| Term | Meaning |
|---|---|
| Inflation | A brief period of extremely rapid, accelerating expansion in the very early universe |
| Light cone | The surface in space-time marking the possible paths of light rays through an event; it separates events that can be influenced from those that cannot |
| M-theory | The proposed framework linking the different string theories and supergravity (after these lectures) |
| Neutron star | A cold star supported by the exclusion principle acting between neutrons; observed as pulsars |
| No-boundary proposal | Hartle and Hawking's idea that space-time is finite but has no boundary or edge in imaginary time, so the beginning is a smooth point |
| Primordial black hole | A small black hole that may have formed in the very early universe; small ones would emit strong Hawking radiation |
| Quantum gravity | A theory, not yet complete, combining quantum mechanics with general relativity |
| Quantum mechanics | The theory in which energy comes in packets (quanta) and outcomes are given as probabilities, governed by the uncertainty principle |
| Term | Meaning |
|---|---|
| Red shift | The reddening of light from a receding source, caused by the Doppler effect or by the expansion of space |
| Second law of thermodynamics | Total entropy (disorder) of an isolated system always increases or stays the same |
| Singularity | A point in space-time where curvature and density become infinite and the known laws break down |
| Singularity theorems | Theorems (Penrose and Hawking) showing that, under general conditions, general relativity predicts singularities in black holes and at the beginning of the universe |
| Space-time | The four-dimensional union of three dimensions of space and one of time |
| Steady state theory | Bondi, Gold and Hoyle's rival to the big bang, in which new matter is continuously created; ruled out by the microwave background |
| String theory | A theory in which basic objects are tiny one-dimensional strings whose vibrations appear as particles |
| Strong nuclear force | The force holding quarks together in protons and neutrons, and protons and neutrons in nuclei |
| Term | Meaning |
|---|---|
| Sum over histories | Feynman's formulation of quantum theory: the probability of an outcome comes from adding waves for every possible history |
| Uncertainty principle | Heisenberg's principle that position and velocity cannot both be known precisely; the more precise one, the less precise the other |
| Weak nuclear force | The force responsible for radioactive decay; it acts on matter particles but not on force-carrying particles |
| White dwarf | A cold star supported by the exclusion principle acting between electrons |
| Term | Meaning |
|---|---|
| Analogue Hawking radiation | Laboratory systems (fluids, optics, BECs) that mimic horizon physics; evidence for the mechanism, not detection from real holes |
| Area theorem | Hawking 1970 result: event horizon area never decreases in classical GR |
| Chaotic inflation | Linde's 1983 version in which inflation can start from generic conditions |
| Cygnus X-1 | First strong stellar-mass black hole candidate; subject of the Hawking-Thorne bet |
| Heterotic string | A string theory construction Hawking cites as a hope for cancelling infinities |
| Horizon problem | Puzzle that distant regions share a temperature despite never being in causal contact in the hot big bang without inflation |
| Hubble tension | Persistent mismatch between early-universe and local measurements of H0 (still open as of Oct 2026) |
| Kerr solution | The unique rotating black hole geometry in the classical no-hair theorems |
| No hair | Slogan that a black hole's exterior remembers only mass, spin and charge |
| Page curve | Modern (c. 2019 to 2020) result indicating information escapes in Hawking radiation |
| Planck energy | About 10^19 GeV; scale where a particle's gravity becomes as strong as other forces |
| Primordial black hole | Hole possibly formed from early-universe overdensities; small ones would be hot today |
| Soft hair | 2016 proposal (Hawking, Perry, Strominger) that horizons may store subtle information |
| Swampland | Conjectured set of effective field theories that cannot arise from consistent quantum gravity |
| Virtual pair | Short-lived particle-antiparticle fluctuation required by the uncertainty principle |
About this book
The Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking, 2002. 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.
Insight Editions · rajeshrmahapatra.com/insight-editions