/reality

An unofficial visual companion

Reality is not what it seems

— Carlo Rovelli (2014)

The ideas in Rovelli's book, one at a time. From the first atoms of Democritus to the quanta of space. Each idea starts with an everyday example, then the physics, drawn to real scale wherever possible.

The journey, in the book's order10 ideas
  1. 01c. 450 BCEGrains of matterDemocritus, Lucretius
  2. 021687Space and time as a stageNewton
  3. 031831–1865FieldsFaraday, Maxwell
  4. 041905The extended presentEinstein
  5. 051915Spacetime is a fieldEinstein
  6. 061900–1927QuantaPlanck, Bohr, Heisenberg
  7. 071936–1967Spacetime is quantumBronstein, Wheeler, DeWitt
  8. 081988–Quanta of spaceRovelli, Smolin, Ashtekar
  9. 091997–Time is not fundamentalSpinfoams, thermal time
  10. 102001–Before the Big Bang, inside black holesLoop cosmology, Planck stars
01c. 450 BCE · Atomism

Grains of matter

Leucippus and his student Democritus asked what happens if you keep cutting something in half. Their answer: you cannot go on forever. At some point you reach grains that cannot be cut, atoms. Everything is made of these grains, combined in different ways. The idea of a smallest grain returns at every step of Rovelli's story, all the way to space itself.

Everyday example

Letters make words

A few letters write every book. Change the shape, the order or the position of a letter and you get a different word. Democritus said atoms work the same way. The three examples on the right are Aristotle's own, from his account of the atomists. He also reported their line that a tragedy and a comedy are written with the same letters.

Fig. 1.1

Seeing atoms without seeing them

In 1827 Robert Brown saw tiny particles from pollen grains jiggling in water for no visible reason. In 1905 Einstein explained why: invisible molecules hit it from all sides, unevenly. From how far it wanders, he worked out how big atoms are. Perrin measured it in 1908, and the debate about atoms was over.

Hits per second, model
–
Wandered from start
–

A real particle a micrometre across is hit about 10¹⁹ times a second. On average its distance from the start grows with the square root of time. That pattern is the fingerprint of random hits.

Particle in waterMolecules drawn much larger than real

A smallest grain

Cutting cannot go on forever. There is a limit, and past it the thing you were cutting no longer exists.

Why

A sugar molecule's sweetness comes from how its atoms are arranged. Split the molecule and the arrangement is gone, and so is the sugar.

Few pieces, endless forms

About a hundred kinds of atoms make everything there is, the way a few letters make every book.

Why

Atoms bond in countless combinations and shapes. Carbon alone forms millions of different compounds, from sugar to DNA.

Finite, not infinite

Matter is not infinitely divisible. Rovelli returns to this again and again: nature puts a floor under things.

Why

If matter could be divided forever, every grain of sand would hold infinitely many parts and infinite detail. Experiments keep finding smallest units instead: atoms, then electrons and quarks.

Saved by a poem

Democritus's books are lost. His ideas survived in Lucretius's poem On the Nature of Things, found again in 1417.

Fig. 1.2

How many cuts to reach an atom

Start with a 1 cm sugar cube and cut it in half, again and again. Each bar is the number of cuts. It takes surprisingly few.

26 cuts

After 23 you hold one sugar molecule. Cut it again and it is no longer sugar. After 26 you reach single atoms.

021687 · Principia

Space and time as a stage

Newton built the world from three things. Space, a fixed container. Time, flowing the same everywhere. And particles moving inside, pulled by forces. One law of gravity explained both a falling apple and the Moon. It worked so well that for two centuries it seemed to be the world itself.

Everyday example

The Moon is falling, like an apple

Drop an apple and it falls 4.9 m in the first second. The Moon falls too: each second it drops 1.36 mm below the straight line it would otherwise follow. It also moves sideways 1 km each second, so it keeps missing the Earth.

4.9 m ÷ 3,600

The Moon is 60 Earth radii away, and gravity weakens with distance squared: 60 × 60 = 3,600. Newton checked exactly this.

Fig. 2.1

Newton's cannon

Newton's own thought experiment. Fire a cannonball sideways from high up. Faster shots land farther away. Fast enough, and the ground curves away as fast as the ball falls. It never lands. Computed with Newton's law, Earth to scale, air ignored.

Launch speed7.8 km/s
Result
–
Flight time
–
Distance flown
–
Earth to scaleLaunch 200 km up

Space is a container

Empty or full, it is always there, and it never changes. Things move in it; it does not react.

Why

Newton needed something fixed to say what is really moving and what is really at rest. Absolute space gave him that reference.

Time flows evenly

One time for the whole universe, ticking at the same rate for everyone, everywhere.

Why

Every law he wrote uses one shared t. Nothing in daily life contradicts it: the differences only show near light speed or with very precise clocks.

One law for sky and Earth

The pull that drops an apple holds the Moon. It weakens with the square of distance.

Why

Gravity spreads out over a sphere around the mass. A sphere's surface grows with distance squared, so the pull on each patch thins out the same way.

What it missed

Newton himself found a force acting across empty space absurd. The answer came two centuries later, with fields.

Why

In Newton's law, if the Sun moved, Earth would feel it instantly, with nothing carrying the news. Fields fix that: the change travels at light speed.

Fig. 2.2

Newton's picture of the world

A rigid grid of space that exists even when empty. Particles move through it in straight lines unless a force acts. One clock, outside everything, gives the time for all of it. Einstein will take each of these apart.

Absolute space · a fixed grid that never reactsParticles in straight lines
031831–1865 · Electromagnetism

Fields

Faraday imagined that the space around a magnet or a charge is filled with lines of force. Not empty space, but a real thing that bends, vibrates and carries influences from place to place: the field. Maxwell wrote its equations in 1865 and found waves in it that move at the speed of light. Light is a ripple of the electromagnetic field.

Everyday example

Iron filings around a magnet

Put a sheet of paper over a fridge magnet and sprinkle iron filings on it. They line up into curves from pole to pole. The pattern was there before the filings arrived. The filings only make it visible. Faraday's step was to take those lines seriously as a physical thing.

Bar magnet · computed field
Fig. 3.1

Shake a charge, make light

A charge moving up and down shakes the field around it. The disturbance spreads outward as a wave at 299,792 km/s. Bright and dark bands are the field pointing one way, then the other. Nothing travels straight above or below the charge. Radio antennas work exactly like this.

Shaking speedMedium

Shake faster and the waves get shorter. Radio, light and X-rays are the same wave at different speeds of shaking.

Oscillating chargeField strength, one slice

Fields are things

They fill space, carry energy, and exist even where there is no matter.

Why

Sunlight warms your skin after crossing 150 million km of empty space. Something had to carry that energy across. That something is the field.

Influence takes time

Shake a charge here and a charge over there feels it later, once the ripple arrives. No instant action at a distance.

Why

A field only changes by passing the change to its neighbour, point by point. So a disturbance has to spread, like a ripple across a pond.

Light is a field wave

Maxwell's equations predicted waves at about 300,000 km/s. That was the measured speed of light.

Why

The wave speed followed from two constants measured in lab experiments with electric charges and currents. It came out equal to light's speed, so light had to be electromagnetic.

Particles and fields

After 1865 the world has two kinds of things. By the end of Rovelli's story there is only one: quantum fields.

Why

Quantum theory showed that particles are small packets of energy in fields. An electron is one quantum of the electron field.

Fig. 3.2

One field, many waves

Length of a single wave of the electromagnetic field, on a log scale. Each grid step is ten times longer. Our eyes see one thin slice.

041905 · Special relativity

The extended present

In 1905 Einstein showed that there is no single "now" across the universe. Between your past and your future there is a stretch of events that are neither. For the Moon it lasts a few seconds. For a nearby star, years. Rovelli calls it the extended present.

Everyday example

The sky you see is old

Light takes time to arrive, so you always see things as they were. Ask "what is happening on Mars right now?" and there is no way to check, even in principle. Any answer would arrive minutes later. Einstein's point is stronger: the question itself has no single answer.

Fig. 4.1

Your now, and the space around it

Time runs up, distance runs right, light travels at 45°. Events inside the upper cone are your future. Inside the lower cone, your past. Everything in the shaded region is neither: the extended present. An observer moving past you draws "now" as a tilted line, and it lands somewhere else in that region. Both are right.

Extended present
–
Their now, over there
–
Time ↑ · distance → · light at 45°
Speed of a passing observer0.40 c

Speed changes time

A moving clock ticks slower than one at rest. The faster it goes, the slower it ticks.

Why REST MOVING

Light moves at the same speed for every observer. Picture a clock that ticks each time light bounces between two mirrors. Seen moving, the light must cover a longer diagonal path at that same speed, so each tick takes longer.

No common now

Observers moving differently disagree about which distant events happen at the same time. Neither is wrong.

Why

To check two distant flashes are simultaneous, see if their light meets at the midpoint. A moving observer's midpoint moves toward one flash. Light speed is the same for both, so they disagree.

The present has width

Between your past and your future lies a region that is neither. The farther away, the wider it gets.

Why

Nothing travels faster than light. An event on Mars less than 22 minutes before or after your now cannot send a signal to you in time, and you cannot reach it. So it is neither before nor after you.

Space and time join

Distances in space and in time mix into one four-dimensional spacetime. Minkowski drew it this way in 1908.

Why

Observers disagree about time and about length, but in a linked way. One combination of the two, the spacetime interval, is the same for everyone.

Fig. 4.2

Particles that live longer by moving fast

Cosmic rays create muons about 15 km up. A muon lives on average 2.2 µs. Even at 99.8% of light speed that is only 660 m of travel, so almost none should reach the ground. Many do, because their clocks run about 16 times slower. Measured by Rossi and Hall in 1941.

051915 · General relativity

Spacetime is a field

Newton's space was an empty stage. Faraday and Maxwell filled it with fields. Einstein joined the two ideas: the gravitational field is not something inside space. It is space. Rovelli, borrowing a metaphor from Einstein, says we are immersed in a gigantic, flexible mollusc that bends, stretches and ripples.

Everyday example

A clock on the table runs faster than one on the floor

The floor is closer to Earth's mass, so time there runs a little slower. The difference is real and measurable: in 2010, optical clocks at NIST detected it over a height of just 33 cm. It is just far too small to feel.

Why

Light climbing out of gravity loses a little energy, so its waves arrive stretched. A clock's ticks are like those waves: seen from the table, the floor clock's ticks arrive slightly stretched, so it runs slower.

Table gains per day
7.1 ps
Over 80 years
0.21 µs
Since you opened this
0.000 fs
True rate
Fig. 5.1

How a star curves the space around it

A flat slice through the star's middle, lifted into 3D so its shape shows. Near the star, distances are longer than flat geometry predicts. The funnel is that extra distance. Depth is drawn to true scale.

Surface clock vs far away
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Grazing light bends
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Escape speed
–
Compactness rs/R
–
Neutron star Grid 0.4 R · True scale Drag to turn

The star's matter Orbit, a free fall Light ray Light path without gravity

Matter curves spacetime

Mass and energy set the shape of the field. The more mass you pack into a small space, the deeper the curve.

Why

Einstein's equation (Fig. 5.3) sets the curvature at each point equal to the matter and energy there. More mass in less space, more curvature.

Falling is going straight

Nothing pulls the planets. They follow the straightest paths that curved spacetime allows, and those paths close into orbits.

Why

In free fall you feel no force at all: astronauts float. Einstein took this literally. If falling feels like no force, gravity must be the shape of the path.

Time is part of it

Near a mass, time itself runs slower. For planets and falling apples, this warp of time does most of the work.

Why

A falling apple travels 1 second through time but only a few metres through space. In spacetime, 1 second is worth 300,000 km, so a tiny warp of time bends its path most.

A field can move

Like any field, spacetime can ripple as gravitational waves, stretch as the universe expands, and close in on itself as a black hole.

Why

Einstein's equations, like Maxwell's, allow waves. Shake a mass, as two black holes orbiting each other do, and ripples spread out at light speed.

Fig. 5.2

Time runs faster higher up

How much more time a clock gains per day than an identical clock at sea level, from Earth's gravity alone. Log scale: each grid step is ten times more.

+2.4 ms

Over 80 years, someone living on the summit of Everest ages about 2.4 milliseconds more than their twin at sea level. There is no single time. Each place has its own.

Fig. 5.3

The whole theory in one line

Einstein's field equation. Rovelli calls general relativity the most beautiful of theories. The left side describes the shape of spacetime. The right side describes what is in it.

The constant 8πG/c⁴ is about 2.1 × 10⁻⁴³ in SI units. Spacetime is extremely stiff. It takes a whole planet to bend it a little, and a star to bend it a lot.

There are no fixed space and time underneath. The field gμν is both the geometry and the gravity, so the equation describes the stage and the actors at once.

Predicted, then measured

1915

Mercury's orbit turns

Its ellipse rotates 43 arcseconds per century more than Newton allows. Einstein's equations gave exactly that.

1919

Starlight bends

During a solar eclipse, stars beside the Sun appeared shifted by about 1.75 arcseconds, as predicted.

1959

Height changes time

Gamma rays sent up a 22.5 m tower at Harvard arrived shifted in frequency. Clocks higher up tick faster.

2015

Spacetime ripples

LIGO detected gravitational waves from two black holes that merged 1.3 billion years ago.

What the picture leaves out
  • The funnel is a 2D slice of 3D space. "Down" is not a real direction. It only shows that distances near the star are stretched.
  • Curved space is half the story. Curved time matters more for everyday gravity, and the full picture is 4D spacetime, which cannot be drawn directly.
  • Nothing rolls into the funnel. The usual rubber-sheet picture uses gravity to explain gravity. Here, the orbit and the light ray are computed from Einstein's equations, not from a ball on a sheet.
061900–1927 · Quantum mechanics

Quanta

From 1900, physicists found that nature at small scales is grainy and jumpy. Energy comes in packets. Outcomes come as odds, not certainties. Properties show up only when things interact. Rovelli sums it up in three words: granularity, indeterminism and relationality.

Everyday example

Stairs, not a ramp

On a ramp you can stop at any height. On stairs you can only stand on a step. The electron in a hydrogen atom lives on stairs. Its energy can take only certain values, and it jumps between them. The steps on the right are hydrogen's real ones, to scale.

You can see graininess yourself: a phone photo taken in near darkness looks speckled partly because light arrives in separate packets, photons, and there are too few of them.

Fig. 6.1

One particle at a time

Send light through two narrow slits, one photon at a time. Each one lands as a single dot, at a place nobody can predict. Yet after thousands, the dots build stripes: a wave pattern. Hitachi's team did this with single electrons in 1989.

Photons detected
0

Granularity

Energy, light and matter come in smallest packets. An atom's energy can only take certain values.

Why

An electron in an atom behaves like a wave trapped in a small space. Only whole numbers of waves fit, the way a guitar string only rings at certain notes.

Indeterminism

Nature does not say where the next dot will land. It gives only the odds, and the odds are exact.

Why

The theory has no ingredient that picks the outcome. Tests of Bell's inequality since the 1980s rule out hidden local details that would decide it in advance.

Relationality

An electron's properties show up only when it interacts with something else. Between interactions it has no definite place.

Why

This is Rovelli's own reading, relational quantum mechanics, from 1996. Properties are like speed: they only make sense relative to something else.

Never wrong so far

The theory predicts the electron's magnetism to about one part in a trillion, and matches the measurement.

Fig. 6.2

Hydrogen's fingerprint

Run electricity through hydrogen gas and it glows, but only in four visible colors. Each line is the electron jumping down the stairs to step 2, giving off one photon with exactly that energy. A ramp would give a smooth rainbow instead.

071936–1967 · Quantum gravity

Spacetime is quantum

If the gravitational field is space, and every field is quantum, then space itself must be quantum. In 1936 Matvei Bronstein saw what follows: there is a smallest length that can ever be probed, about 10⁻³⁵ m. In 1967 Wheeler and DeWitt wrote an equation for quantum space. It has no time variable in it.

Everyday example

You cannot read Braille in mittens

To feel small details you need a small probe. A fingertip resolves about 2 mm and reads the dots. A mitten smears them into one bump. Physics probes with waves, and smaller waves carry more energy. Push that far enough and the probe itself becomes the problem.

Same Braille, 6.2 mm per letter, drawn to scale
Fig. 7.1

Bronstein's limit

To see something of size λ you need a probe of energy about hc/λ. But energy curves spacetime, and enough of it in a small place makes a black hole. Move the slider toward smaller sizes. Where the two lines cross, the probe hides inside its own black hole. Nothing smaller can ever be seen.

Size you want to see–
Probe energy
–
Its black hole
–

Space must be quantum

Every field we know comes in quanta. If space is the gravitational field, it should too.

Why

A quantum particle can be in two places at once. A classical space would then have to curve in two ways at once, which makes no sense.

A smallest length

Below about 10⁻³⁵ m, the Planck length, distance stops making sense. It is not that our tools are weak.

Why

See Fig. 7.1. Looking smaller takes more energy, and below the Planck length that energy forms a black hole that hides the very region you aimed at.

An equation without time

The Wheeler–DeWitt equation describes quantum space with no t in it. Chapter 09 takes this seriously.

Why

In general relativity, time is part of the field, not an outside background. Make the field quantum and no outside clock is left to provide a t.

Far beyond experiments

The Planck length is about 10²⁰ times smaller than a proton. No collider will ever reach it directly.

Why

Probing it directly would take particles with about 10¹⁵ times the energy of the LHC's collisions.

Fig. 7.2

How small is the Planck length

Sizes on a log scale. Each grid step is 100,000 times smaller.

10,000 ly

A proton is about 10²⁰ times bigger than the Planck length. That is the same ratio as a distance of 10,000 light-years to a person.

081988– · Loop quantum gravity

Quanta of space

Loop quantum gravity, which Rovelli helped build from 1988, describes what those grains are. Space is a network. Nodes are grains of volume. Links between them are the surfaces where grains touch. Areas and volumes come only in fixed amounts. There is nothing between the grains, because the grains are space.

Everyday example

A metro map has no streets

A metro map shows stations and the lines between them, nothing else. Near and far are counted in stops, and on the map there is nowhere between two stations. Loop quantum gravity says space works like this. Grains of space are the stations, links are the tracks, and there is no street grid underneath.

Distance = links counted · nothing underneath
Fig. 8.1

Measuring an area by counting links

A spin network. Each link carries a spin j: ½, 1, 3/2 or 2. Draw a surface around some grains. Its area is set only by the links it cuts: each adds 8πγℓ² × √(j(j+1)), where ℓ is the Planck length. Drag or tap to move the surface.

Surface size–
Links cut
–
Grains inside
–
Σ √(j(j+1))
–
Area
–
Schematic · real networks are 3D

Grains of volume

Each node in the network is a tiny amount of space with a definite volume.

Why

Applying quantum rules to the geometry of space gives volume and area only certain values, just as quantum rules give an atom only certain energies.

Links are areas

Where two grains touch there is a surface. Its area is fixed by the link's spin number.

Why

An area is set by what crosses it. In the network, only links cross surfaces, so the links are what carry area.

Not in space

The network does not sit inside space. It is space. Distance only exists between grains.

Why

There is no background grid left underneath. Which grain is next to which is defined by the links. Here only means linked to.

Black hole entropy

Counting the ways links can cross a black hole's surface gives Bekenstein and Hawking's entropy, once one parameter is fixed.

Why

Entropy counts hidden arrangements. A black hole's surface can be pierced by links in an enormous number of ways, and that count matches its entropy.

Fig. 8.2

Area comes in steps

Allowed areas, in units of 8πγℓ². A ruler in our world can mark any value. A surface cut by one link can only take the values on the second ruler. With more links the steps crowd together, which is why space looks smooth to us.

≈ 10⁻⁶⁹ m²

The smallest area that exists, if the theory is right. A grain of space has a similarly tiny volume.

Where this stands
  • Loop quantum gravity is one candidate theory of quantum gravity. String theory is the best known alternative. Neither has been confirmed by experiment.
  • Rovelli is one of the founders of loop quantum gravity, so this part of the book argues for his own approach.
091997– · Spinfoams

Time is not fundamental

In the equations of quantum gravity there is no time variable. Things do not change in time; they change relative to one another. The network of grains does not sit in time either: its changes, called spinfoams, are the events. Time as we feel it appears at large scales, together with heat and our blurred view of many particles.

Everyday example

Play the film backwards

Film two billiard balls colliding and play it in reverse. It still looks normal. Film an ice cube melting and play it in reverse. Everyone can tell. The difference between past and future appears only when many particles and heat are involved. At the level of single collisions, it is not there.

Fig. 9.1

Change without a clock

Two real pendulums, 1.00 m and 0.56 m long. With a time axis, you see each swing against t. Turn the time axis off and plot one against the other. Every prediction is still there, as a curve relating A to B. A clock is just one more swinging thing. Physics can describe how things change relative to each other, with no t at all.

No time variable

The basic equations do not mention time. They relate quantities to each other.

Why

The Wheeler–DeWitt equation has the form HΨ = 0. There is no rate of change with t in it, only a rule for how quantities fit together.

Clocks are things

A clock is another physical system that changes. We compare changes; we never see time itself.

Why

Every time measurement compares one change with another: Earth turning, a pendulum swinging, a caesium atom vibrating. Nobody has ever read t directly.

Events, not objects

The world is a network of events. Spinfoams describe what the grains of space do, not where they are.

Time from heat

The flow of time appears when we describe many particles without following each one. Connes and Rovelli called this thermal time.

Why

There are vastly more messy arrangements of many particles than tidy ones, so things drift toward mess. That drift, entropy rising, is what separates past from future.

Fig. 9.2

A spinfoam

To make it drawable, space is shrunk to one line, so the network is a row of grains joined by links. Up the page goes from before to after. Each grain traces a line and each link sweeps out a face, like a soap film. At the event one grain becomes three, and two new links are born. The event is the basic unit of change, with no clock ticking behind it.

Schematic · space shown as a line
102001– · Quantum cosmology

Before the Big Bang, inside black holes

Remove infinity and old puzzles change. Run the universe backward and, in loop quantum cosmology, it does not crush to a point of infinite density. It bounces. The same may happen inside black holes. These are the newest and least tested ideas in the book, and Rovelli says so.

Everyday example

A ball does not vanish into the floor

Drop a ball. It squashes, pushes back, and bounces. It never shrinks to a point. The harder it lands, the more it squashes, but it always springs back. If space is made of grains, it cannot be squeezed without limit either. Squeeze the whole universe hard enough and it pushes back.

Fig. 10.1

The Big Bounce

The size and density of the universe around its smallest moment. Classical general relativity (dashed) shrinks it to zero size and infinite density. With quanta of space (solid), density reaches a maximum and the universe rebounds. Model: Ashtekar, Pawlowski and Singh, 2006.

Time around the bounce–
Density, quantum
–
Density, classical
–

For scale, water is 1,000 kg/m³ and an atomic nucleus about 2 × 10¹⁷ kg/m³.

No infinity

A smallest grain sets a maximum density. Nothing in nature becomes truly infinite.

Why

You cannot squeeze matter into less than one grain of space, so density has a ceiling, roughly 10⁹⁶ kg/m³.

A bounce, not a beginning

The Big Bang may have been the rebound of an earlier universe that contracted.

Why

In loop cosmology, near maximum density the grains of space push back: gravity effectively becomes repulsive and turns contraction into expansion.

Planck stars

A star collapsing inside a black hole may bounce too, and eventually come back out.

Why

The same quantum pressure that bounces the universe would stop a collapsing star before it reaches zero size.

Information

Rovelli ends with information: physics as a description of what systems can know about each other.

Fig. 10.2

Two clocks at a black hole

Inside, the collapsing star reaches maximum density and bounces almost at once. Outside, near the black hole time runs so slowly that the same bounce takes enormously long to show. Proposed by Rovelli and Vidotto, and by Haggard and Rovelli, in 2014.

Schematic · not to scale
Where this stands
  • The bounce and Planck stars are calculations in a theory that has not been tested. They could be wrong.
  • Possible signals exist in principle, such as traces in the cosmic microwave background or bursts from exploding primordial black holes. None has been seen yet.
  • Rovelli closes the book with doubt as a virtue: science is the search for the best current picture, ready to change.