Introduction
You live in a world that feels solid, stable, and anchored by familiar concepts of space and time. Physics reveals that these everyday assumptions are illusions built on deeper layers of reality. You might wonder what the universe is truly made of once you strip away familiar objects, rigid geometry, and absolute clocks.
Physics reveals that reality is not made of independent objects in space and time, but of a relational network of covariant quantum fields.
Carlo Rovelli takes you on a journey through the evolution of scientific thought from ancient Greece to modern quantum gravity. You will explore how thinkers dismantled the notion of absolute substances to reveal a relational cosmos.
- What are space and time made of at the deepest level?
- Why does quantum mechanics show that nature is granular rather than continuous?
- How does loop quantum gravity eliminate space and time as fundamental entities?
1. Roots of Atomism
Scientific thought originated in Miletus when thinkers began seeking natural, rational answers rather than relying on mythological explanations. In the 6th century BCE, Milesian thinkers abandoned elaborate stories of deities. They instead used observation, reason, and critical debate to understand natural phenomena.
Hecataeus visited Cape Tenaro, determined that there was no subterranean passage to Hades, and judged the myth to be false.
The Milesian Revolution
Democritus and Leucippus founded ancient atomism by proposing that the universe consists entirely of a boundless void and indivisible atoms whose combinations create all matter. Atoms possess no qualities such as color, taste, or weight, but differ only in shape and arrangement. All substances, life forms, thoughts, and objects are merely accidental combinations of these elementary grains.
Democritus compared the combination of atoms to the letters of the alphabet, which can be rearranged to form everything from ridiculous stories to epic poems. Around 450 BCE, Leucippus embarked from Miletus to Abdera.
Democritean Atomism
Democritus argued that matter cannot be infinitely divisible because infinitely small points without extension could never form extended matter. Using philosophical reasoning reported by Aristotle, he established that matter must comprise a finite number of discrete, indivisible pieces. Zeno of Elea formulated paradoxes, such as the Achilles and the tortoise fable, to challenge the reliability of sensory experience and the concept of motion. Zeno argued that because a runner must cross an infinite number of ever-decreasing distances, ordinary motion is absurd and illusory.
The tortoise challenged Achilles to a race with a 10-meter advantage, and Achilles supposedly could never catch up because he must endlessly cross the remaining fractions of distance.
The Rediscovery of Lucretius
Albert Einstein provided definitive proof for the atomic hypothesis in 1905 by calculating atom dimensions through the observation of Brownian motion. At the age of 25, while working in the Berne patent office, he showed that the random zigzagging of tiny particles suspended in a fluid is caused by random collisions from discrete molecules.
Robert Brown described in detail the trembling of small particles suspended in still air or liquid.
The Roman poet Lucretius preserved the core philosophy of ancient atomism in his poem "De Rerum Natura", saving it from total intellectual loss during the Middle Ages. Lucretius channeled the ideas of Epicurus and Democritus into luminous verse, promoting a naturalistic worldview devoid of capricious gods and fear.
Lucretius used the visible dancing of tiny dust particles in sunbeams inside a building as living proof of the hidden collisions of underlying atoms.
The rediscovery of Lucretius's lost manuscript by Poggio Bracciolini during the Renaissance fueled the revival of materialist and modern scientific thinking. This discovery transformed European intellectual culture by reintroducing an articulate alternative to the medieval hierarchical cosmos, inspiring figures from Galileo to Darwin.
Poggio Bracciolini discovered the manuscript in January 1417 in the library of a German monastery, and his friend Niccolò Niccoli made the complete copy known as the Codex Laurenziano 35.30. During the period of 390-391, Emperor Theodosius declared Christianity the sole obligatory religion of the empire, leading to the destruction of pagan texts. Later, the Florentine Synod prohibited reading Lucretius in schools in December 1516, and the Council of Trent banned his work in 1551.
2. Foundations of Modern Physics
Galileo, Newton, Faraday, and Maxwell transformed physics by using mathematics and introducing fields to describe motion and forces.
From Aristotle to Galileo
Aristotle created the first systematic physics, which served as a sound approximation for bodies immersed in a fluid under gravity and friction. He distinguished between the heavens made of crystalline circles and Earth characterized by forced and natural motions, where each substance sought its natural place.
Pythagoras and Plato established the foundational premise of Western science that mathematics is the ideal language for describing the world. Plato famously had the phrase "Let no one enter here who is ignorant of geometry" carved on the door of his school.
Galileo founded modern experimental science by using the telescope to observe celestial bodies and by discovering the mathematical law of falling bodies on Earth. Through experiments, he discovered that falling objects accelerate at a constant rate.
Galileo pointed the newly invented telescope toward the sky and observed rings around Saturn, mountains on the moon, phases of Venus, and moons of Jupiter.
Newtonian Mechanics
Newton unified celestial and terrestrial mechanics by demonstrating that the same universal force of gravity causes objects to fall on Earth and keeps the moon in orbit.
By calculating the centripetal acceleration of an imaginary little moon skimming just above mountain peaks, Newton found it matched the 9.8 meters per second per second acceleration of falling bodies on Earth. Newton calculated that a hypothetical little moon orbiting Earth at a minimal distance would complete an orbit every hour and a half.
Electromagnetism and Fields
Michael Faraday revolutionized physics by introducing the concept of the field, proposing that forces between distant objects are transmitted through invisible lines of force filling space. Faraday explored electrical and magnetic attraction using bobbins, needles, knives, and iron cages in his London laboratory.
James Clerk Maxwell translated Faraday's field intuitions into rigorous equations, revealing that light, color, and electromagnetic waves are vibrations of Faraday's lines of force. Heinrich Hertz revealed electromagnetic waves predicted by Maxwell, and Guglielmo Marconi subsequently built the first radio.
3. Relativity and Spacetime
Einstein proved that space and time form a flexible, dynamic spacetime manifold rather than a rigid background.
Special Relativity
Special relativity reveals that absolute simultaneity is an illusion and that an intermediate zone called the extended present exists between past and future. Because the speed of light is finite, events separated in space cannot be deemed to happen strictly now. The duration of this extended present depends on distance, lasting nanoseconds nearby, fractions of a second across oceans, and a quarter of an hour on Mars.
Conversations with Mars require an inevitable quarter-hour delay that cannot be reduced, proving that an absolute universal now does not exist.
Energy and mass are not independently conserved principles but are two facets of the same entity described by the formula E=mc^2. Einstein realized that mass and energy fuse together similarly to space and time. Transforming a tiny amount of mass yields an enormous amount of energy due to the speed of light squared.
The energy obtained from transforming one gram of mass is enough to illuminate a city and power a country's industries for months, or to destroy hundreds of thousands of human beings in a city like Hiroshima.
General Relativity
Einstein's general relativity establishes that Newton's rigid space and the gravitational field are actually the exact same thing. Space is the gravitational field itself, serving as a dynamical, flexible entity that undulates and bends rather than an invisible rigid scaffolding.
Planets circle the sun and objects fall not because of a mysterious distant force, but because they move along straight trajectories in the curved spacetime around heavy masses.
Einstein utilized Bernhard Riemann's mathematical curvature to write an equation showing that spacetime curves proportionally to the energy of matter. This explained tiny discrepancies in planetary orbits that Newton's equations could not account for.
Einstein computed the movement of Mercury and found that its closest point to the sun moves every year 0.43 seconds of arc more than Newton predicted, perfectly matching observations.
Time is not universal and fixed; gravity distorts spacetime, causing time to pass more slowly closer to massive bodies like Earth. A clock placed on the floor registers less passing of time than one placed on a table, meaning twins living at different altitudes will age at different rates.
Two twins living respectively at sea level and in the mountains will find that the twin in the mountains has aged more when they meet again.
General relativity successfully predicted extreme astrophysical phenomena including black holes, gravitational waves, and an expanding universe. When massive stars collapse under their own weight, they curve space so intensely that it forms a black hole. Additionally, the theory predicts space ripples and that the universe emerged from a hot cosmic explosion.
Gravitational waves produced by two black holes falling into each other were directly observed by an antenna on Earth in late 2015.
Cosmology
Einstein proposed that the universe can be finite yet have no boundary by adopting the topology of a three-dimensional sphere, or 3-sphere. Just as the two-dimensional surface of Earth is finite but has no edge, a three-dimensional space can curve such that a traveler moving continually in a straight line would eventually return to the starting point.
American mathematician Mark Peterson noticed in 1979 that Dante Alighieri's descriptions in the Paradiso of spheres that surround and are surrounded by each other constitute an exact medieval description of a 3-sphere.
Although Einstein initially resisted his equations because he believed the universe was static, observations proved the universe is expanding. Because everything attracts, a finite universe must either expand or collapse, much like a ball thrown upward. Einstein added a cosmological constant term to prevent expansion, but later abandoned it when galaxies were observed moving away.
In 1964, American radio-astronomers Arno Penzias and Robert Wilson discovered background radiation diffused throughout the universe, proving it originated from the immense heat of an early cosmic explosion.
4. The Quantum Revolution
Quantum mechanics revealed that nature is granular, indeterminate, and relational at its microscopic core.
In 1900, Max Planck computed electromagnetic waves in a hot box by assuming energy is distributed in small packets whose size depends on frequency. He introduced the first formula of quantum mechanics:
- $E = h \nu$, where $h$ is the Planck constant fixing the scale of quantum phenomena.
Albert Einstein proved that light is granular by explaining the photoelectric effect using Planck's packets of energy in 1905. He argued that light is composed of particles called photons, and the photoelectric effect occurs only if the frequency of light is high enough for individual grains to dislodge electrons.
Einstein compared light to a hail shower, noting that car damage depends on the size of individual hailstones rather than the total amount of falling hail.
Niels Bohr explained atomic spectra by hypothesizing that electrons inside atoms possess quantized energy and occupy specific orbits. He proposed that electrons exist only at certain special distances from the nucleus determined by Planck's constant and can execute quantum leaps between permitted orbits.
Bohr built an atomic model that successfully computed the spectra of sodium, mercury, lithium, and hydrogen. This model saw a centenary commemoration in 2013.
The Mechanics of Relations
Werner Heisenberg formulated the equations of quantum mechanics by realizing that electrons exist and have positions only when they interact. At the age of 25 in 1925, Heisenberg understood that electrons do not follow continuous trajectories between observations, but literally vanish and reappear during collisions with other objects.
Heisenberg got his intuition during a walk in a dark park in Copenhagen while observing a man passing beneath dimly lit street lamps.
Paul Dirac constructed the rigorous mathematical scaffolding of quantum mechanics, introducing probability and universal relationality. Dirac formulated a theory where every object is defined by an abstract space, and its variables acquire reality only during an interaction. The theory replaces deterministic predictions with probabilistic calculations of the spectrum of variables.
Quantum mechanics reveals three fundamental aspects of reality:
- granularity, which limits the information and possible states within a system;
- indeterminism, meaning the future is genuinely unpredictable and subject to continuous microscopic fluctuations;
- relationality, establishing that physical properties exist only in relations and interactions between systems.
Richard Feynman developed the sum over paths method in the 1950s, showing that an electron behaves as if passing through all possible trajectories to move from point A to B.
Dirac applied quantum mechanics to fields, showing that fields are made of quanta and particles are quanta of an underlying field. The Standard Model of elementary particles successfully categorizes approximately fifteen fields and their corresponding elementary particles, completing by the 1970s. The Higgs particle was observed with precisely the properties predicted by the Standard Model, causing a sensation in 2013.
5. Quantum Gravity and Space
Physical space is not a continuous background but a discrete, granular structure composed of elementary quanta of space woven by a network of nodes and links.
Loop quantum gravity describes space as a discrete network of elementary quanta and eliminates fundamental time.
By combining quantum theory with general relativity, Faraday's gravitational field lines become discrete threads. The nodes where these lines intersect represent discrete packets of volume, while the links connecting them represent quanta of area and proximity relations between adjacent regions of space.
Measuring the volume of a room or the area of a page is fundamentally equivalent to counting the discrete grains of space or the links of the web traversing it. More than one hundred digits of grains of space are contained in a room, while approximately seventy digits of quanta traverse a page of a book.
Quanta of Space
Quantum states of space are described by spin networks, and their dynamic evolution over spacetime is represented by spinfoams. A spin network is a graph where nodes represent elementary grains of volume and links carry half-integer spins representing area. Spinfoams represent the history of these spin networks as they combine, separate, and evolve through probabilistic interactions.
The spinfoam technique used to compute probabilities in quantum gravity simultaneously functions as a Feynman diagram representing particle interactions and as a lattice approximation of continuous spacetime.
Time Does Not Exist
At the fundamental microscopic scale, time does not exist as a universal flowing variable, and instead change is relational and localized. The fundamental equations of quantum gravity lack the time variable t. The experience of time is an emergent macroscopic approximation resulting from coarse-grained perceptions of quantum interactions among elementary processes.
Clocks run at different speeds depending on their proximity to Earth because time is a localized phenomenon determined by the local gravitational field. Everything in the physical world is made of covariant quantum fields that generate their own spacetime. Particles, light, energy, space, and time are manifestations of covariant quantum fields acting as fields on fields without needing an external background substratum.
Beyond the Big Bang
In 1927, the Belgian priest Georges Lemaitre understood the expansion of the universe. On November 22, 1951, Pope Pius XII publicly declared the Big Bang confirmed Genesis. Fourteen billion years ago, the universe was in an extremely hot, compact state.
Henrietta Leavitt's distance-measuring technique and Edwin Hubble's telescope observations confirmed that distant galaxies are moving away at speeds proportional to their distance. Lemaitre championed the expansion of the universe against initial skepticism from Einstein and theological co-opting by Pope Pius XII. In loop quantum gravity, quantum repulsion prevents infinite collapse, causing a contracting universe to rebound into expansion.
6. Information and Thermal Time
Verifiable quantitative predictions are instruments to validate hypotheses, while the true objective of science is to understand how the world functions. Theories like general relativity and quantum mechanics earned credibility gradually as their bizarre predictions were confirmed.
Physical reality consists of relational information and thermodynamic correlations rather than absolute substances.
Lemaître defended the expanding universe against Einstein's disbelief, and observations proved Einstein wrong. The discovery of the Higgs boson at CERN, Planck satellite measurements, and the detection of gravitational waves all confirmed general relativity, quantum mechanics, and the Standard Model. The Large Hadron Collider at CERN did not find anticipated supersymmetric particles, disappointing many string theorists.
Empirical Confirmations
Abhay Ashtekar, Ivan Agullo, and William Nelson calculated that the statistical distribution of cosmic radiation fluctuations should reflect the effect of the initial bounce. Stephen Hawking deduced that black holes emit heat and evaporate. Loop theory explains that this heat comes from the individual quanta of space vibrating on the black hole surface. Eugenio Bianchi completed a calculation showing how to derive Hawking's black hole heat formula using loop quantum gravity equations.
Quantum Black Holes
Quantum gravity places a lower limit on the divisibility of space and cures the pathological infinities and singularities of classical theories. Because space has a discrete granular structure and cannot be smaller than the Planck length, these infinities disappear. Dirac was deeply unhappy with infinities and divergences in quantum field theory despite it successfully reproducing experimental measurements. Theoretical physics has discovered three fundamental limitations concerning velocity, information, and length, defined by universal constants:
- $c$ establishes a maximum velocity for all systems via the speed of light.
- $h$ establishes a maximum of information or action via Planck's constant.
- $L_P$ establishes a minimum length via the Planck length.
Information and Reality
Claude Shannon worked for a telephone company and defined information while measuring telephone line capacity. In the physical world, atoms and systems are interconnected through a network of correlations where the arrangement of one set of atoms provides information about another. Ludwig Boltzmann committed suicide at age fifty-six in Duino, but today his formula is engraved on his tomb. Time is not a fundamental constituent of the universe but emerges as an approximate macroscopic effect arising from averages of microscopic variables.
Reality is fundamentally a relational network of reciprocal information and correlations between physical systems rather than an amorphous collection of independent objects. Knowledge is intrinsically relational, depending on the object and subject. Objects like ocean waves or mountains are conventional ways you slice up the variable flux of the world to organize information. Democritus defined man as what we all know, emphasizing that human nature resides within a network of personal, familial, and social interactions.
10 Key Ideas
- Democritus and Leucippus founded ancient atomism by proposing that the universe consists entirely of a boundless void and indivisible atoms whose combinations create all matter.
- Galileo, Newton, Faraday, and Maxwell transformed physics by using mathematics and introducing fields to describe motion and forces.
- Einstein proved that space and time form a flexible, dynamic spacetime manifold rather than a rigid background.
- General relativity establishes that Newton's rigid space and the gravitational field are actually the exact same thing.
- Quantum mechanics revealed that nature is granular, indeterminate, and relational at its microscopic core.
- Loop quantum gravity describes space as a discrete network of elementary quanta and eliminates fundamental time.
- Quantum states of space are described by spin networks, and their dynamic evolution over spacetime is represented by spinfoams.
- At the fundamental microscopic scale, time does not exist as a universal flowing variable, and instead change is relational and localized.
- Quantum gravity places a lower limit on the divisibility of space and cures the pathological infinities and singularities of classical theories.
- Physical reality consists of relational information and thermodynamic correlations rather than absolute substances.