Chapter 1
In Miletus, in the 6th century BC, the dawn of scientific thought took place. Critical thought replaced myth and fantasy. Anaximander (610 - 546 BC) knows that the Earth floats in the sky and that man evolved from other animals (because human infants are too helpless to have survived originally). This last is amazing. Democritus (460-370 BC) posited that all matter was made of atoms, which exist in a boundless space. There is no cosmic purpose, just randomness. Democritus was a humanist, a rationalist, a materialist.
Through Democritus, Rovelli introduces the idea that the world is not as it appears, that what we perceive results from movement and combinations of atoms, which lack qualities. Secondary qualities are not in the world — they arise from interaction.
Chapter 2
The first systematic physics we know of is Aristotle's, and it is not bad at all. It was for centuries the best available model for understanding motion. Plato is perhaps even more important to scientific history, for he understood that the way forward in science was to follow Pythagoras, ie develop mathematics. Plato divested Pythagorism of its cumbersome and useless mystical baggage. He absorbed and distilled its message: that mathematics is the language best adapted to understand and describe the world. Plato asked whether his followers could find the mathematical laws followed by celestial bodies. We know of the successes of Aristarchus and Hipparchus because of a single book by Ptolemy (100-170 AD) The Almagest. At this time, science was in decline and about to disappear altogether because of the collapse of the Hellenistic world and suffocation by the Christianisation of the empire. Even today, it is possible to use Ptolemy's techniques to calculate the position of Mars 1900 years after the book was written. The realisation that this magic is possible is the basis of modern science and owes not a little to Pythagoras and Plato.
After the collapse of ancient science, the knowledge travelled to India and then returned to Europe via Persian and Arab scientists, who were able to understand and preserve it. But astronomy didn't make any very significant step forward for over a thousand years. Copernicus (1473-1543) places the sun at the centre. He hoped the calculations will work better than Ptolemy's - they actually work less well. Then Kepler (1571-1630) showed that Copernicus' system can be made to work better than Ptolemy's.
Science really takes off with Galileo (1564-1642). He decides the Earth is a planet like all the others and sets out to study how objects move on Earth when they are set free. For the first time in human history, an experiment is made. He works out that objects accelerate when they fall.
Then came Newton (1643-1727), the greatest scientist of all time. He combined celestial with earthly motion, united by the same gravity. He invented calculus and made seminal contributions to optics. His list of discoveries and inventions is staggering. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science. It now seemed that the fundamental laws had all been discovered.
However, Newton knew that his equations did not describe all the forces of nature. It turns out that almost all the phenomena we see are governed by a single force, and it is not gravity. Electromagnetism holds matter together in solid bodies, holds together atoms in molecules and electrons in atoms. It also makes matter "solid". Without it, you'd fall through your chair, as an atom is 99.999% empty space.
Michael Faraday (1791-1867) had no formal education and knew little mathematics but he was a scientific visionary. James Clerk Maxwell (1831-1879) is his complement, one of the greatest mathematicians of the century. Together, combining two kinds of genius, they open the way to modern physics. Faraday intuitively understood that distant objects do not attract or repel each other directly but only via the medium interposed between them. This solved the puzzle that had stymied Newton: how can distant objects affect each other?
Maxwell translated Faraday's intuitions into mathematics. Maxwell's equations are used every day to describe all electric and magnetic phenomena. Almost everything that we witness, apart from gravity, is well described by Maxwell's equations. Moreover, the equations tell us what light is - an electromagnetic wave. Our entire current technology is based on electromagnetic fields. This was not discovered empirically. It was predicted by Maxwell, simply by searching for the mathematical description accounting for the intuition Faraday got from bobbins and needles. This is the outstanding power of theoretical physics. Remarkably, Special Relativity is implicitly built into Maxwell's equations.
Chapter 3
The two most important streams in twentieth-century physics are general relativity and quantum mechanics. Both demand a daring re-evaluation of our conventional ideas about the world: space and time in relativity, matter and energy in quantum theory.
The annus mirabilis papers of 1905 are four papers that Albert Einstein published in the scientific journal Annalen der Physik (Annals of Physics). They revolutionized science's understanding of the fundamental concepts of space, time, mass, and energy. The first paper explained the photoelectric effect, which established the energy of the light quanta. The second paper explained Brownian motion, which compelled physicists to accept the existence of atoms. The third paper introduced Einstein's special theory of relativity, which proclaims the constancy of the speed of light and derives the Lorentz transformations. The Lorentz transformation is a set of mathematical formulas that relate the position and time of an event measured by one observer to the position and time of the same event measured by another observer who is moving at a constant speed relative to the first. An important consequence of Relativity is that simultaneity is relative. The fourth paper, a consequence of special relativity, developed the principle of mass–energy equivalence, expressed in the equation E = mc^2 and which led to the discovery and use of nuclear power decades later. Any of the four papers was worthy of a Nobel prize. Einstein got it for the photoelectric effect.
These four papers, together with quantum mechanics and Einstein's later general theory of relativity, are the foundation of modern physics.
Einstein makes a startling discovery, that the present has extension, ie duration, which depends on distance. This extended present amounts to a few seconds in the case of the moon and between 3 and 22 minutes for us with regard to Mars, depending on relative positions around the sun. It is because of the velocity of light. Space and time fuse into spacetime. Space does not exist independently of time. There isn't always a 'before' and 'after' between two events in the universe. It's not that the present has duration for you, but only that it has duration with regard to another observer at a distance from you.
Consider a flash of light in the middle of a moving train carriage. To a passenger on the train, the light will reach the front and back of the carriage at the same time - those events are simultaneous. To an observer on the platform, the back of the carriage is rushing forward to meet the light, and the front of the carriage is rushing away from the light. The result is that it arrives at the back before it arrives at the front because it has a shorter distance to travel to the back. Hence those events are not simultaneous according to an observer on the platform.
The crucial idea at the heart of General Relativity is that space itself is nothing but the gravitational field. Rovelli describes this as "one of the greatest flights in the history of human thinking". The world is made up of particles and fields, and nothing else. There is no need to add space as an extra ingredient. Space is akin to the magnetic field. It is a real entity which undulates, fluctuates, bends and contorts. Planets circle around the sun and things fall because the space around them is curved. Actually, what curves is not space but spacetime. The curvature of spacetime is proportional to the energy of matter. Einstein predicted that the Sun causes light to curve around it. This was confirmed in 1919. Einstein predicted that time passes more quickly at altitude. This too was verified. Time is not universal and fixed, it is something that expands and shrinks, according to the vicinity of masses. If one twin spends his life at sea level while his twin lives at altitude then when they meet the twin who lived high up will be older. However, the difference would only be a fraction of a second. This is the gravitational dilation of time.
Einstein had a unique capacity to imagine how the world might be constructed. The equations came afterwards, they were the language with which to make concrete his vision of reality.
Einstein sees the universe as finite but unbounded, for three-dimensional space is curved - like the surface of a sphere which is finite but unbounded. He saw the universe as a 3-sphere, a four-dimensional analogue of a sphere in our familiar 3 dimensions. It has the same property as the earth - if you move in a straight line then you will eventually end up where you started. Einstein's spacetime is not curved in the sense that it curves in an external space. It is curved in the sense that its intrinsic geometry is not the geometry of a flat space.
Einstein shows that spacetime is a field; the world is only made up of fields and particles.
Chapter 4
The two pillars of 20th century physics - general relativity and quantum mechanics - could not be more different from each other. General relativity is a compact jewel conceived by a single mind. It is a simple and coherent vision of gravity, space and time. Quantum mechanics arose through the work of many scientists over a quarter of a century. It achieved unparalleled experimental success but, more than a century after its birth, its meaning remains obscure.
The three aspects of reality unveiled by quantum physics are granularity, indeterminism and relationality.
In 1900, Planck finds that in order to explain experimental results, it is necessary to break up energy into quanta. However, he sees this as just a trick of calculation. He finds that the energy of light is proportional to its frequency. It is Einstein in 1905, who shows that Planck's quanta are real by investigating the photoelectric effect. Bohr realises that just as the energy of light is granular, so is the energy of electrons in the atom, which themselves give rise to light. Bohr posits that only certain orbits are allowed for electrons in an atom. Using this assumption, he is able to explain why atoms have the spectra that they do, something which was a mystery until then.
Heisenberg takes the next step. He suggests that in between being detected, an electron could be nowhere. This explained the mystery of quantum leaps between one orbit and another. This is what Rovelli calls relationality: electrons don't always exist; they exist when they interact. An electron is a combination of leaps from one interaction to another. Heisenberg writes the equations of quantum mechanics. These equations never fail. Dirac then creates the coherent theory that has endured till today. He also predicted anti-matter before it was discovered. Heisenberg had seen that the position of a subatomic particle is undefined, now, according to Dirac, no variable of the object is defined in between one interaction and the next. Only constants like mass are always defined. A new development is that Dirac's theory is fundamentally probabilistic. It does away with Newtonian determinism. Chance operates at the atomic level. Newton's physics allows for the prediction of the future with exactitude; quantum mechanics only allows us to predict the probability of an event. This absence of determinism is intrinsic to nature. The apparent determinism of the macroscopic world is due only to the fact that microscopic randomness cancels out on average.
An example of the amazing efficacy of quantum mechanics is that it exactly explains the structure of Mendeleev's periodic table. The solutions to the equation that determines the orbitals of an electron correspond exactly to the known elements. Rovelli, "The infinite complexity of chemistry, captured by the solutions of a single equation!"
After completing the general formulation of quantum mechanics, Dirac applied it to electromagnetic fields and made it consistent with special relativity. Making it consistent with general relativity proved much harder. It is a work in progress and the main subject of Rovelli's book. In addition, Dirac merges the notions of particle and field. For instance, a photon or electron can behave like a particle or a wave, depending on the experimental apparatus. Particles are quanta of a field, just as photons are quanta of light. All fields display a granular structure in their interactions.
By 1970 the Standard Model is completed and its last remaining particle is detected, with exactly the properties that were predicted. This was the Higgs boson, first sighted in 2013. The Standard Model is a far-reaching theory that answers two fundamental questions: What is matter and how does it interact?
Quantum mechanics offers a spectacularly effective description of nature. The world is not made up of fields and particles, but of a single type of entity: the quantum field, whose elementary events happen in spacetime.
The world is a sequence of granular quantum events. At the quantum scale, everything is constantly vibrating, a microscopic swarming of fleeting micro-events.
To compute the probability that an electron starting at A will reappear at position B, Feynman conceived of summing over all possible paths from A to B. It is as though the electron unfurled into a cloud in order to converge mysteriously on point B, where it collides with something else. Left alone, the electron dissolves into a cloud of probability.
Perhaps the most counter-intuitive aspect of quantum mechanics is that the theory does not describe things as they are, but only how they interact with each other. It doesn't describe where there is a particle but how the particle shows itself to others. Reality is reduced to interaction. All variable aspects of an object exist only in relation to other objects. It isn't that things enter into relations, but rather that relations ground the notion of 'thing'. The world of quantum mechanics is not a world of objects; it is a world of events. This is what Rovelli means by relationality.
Feynman, perhaps the leading physicist of the second half of the 20th century, said, "I think I can state that nobody really understands quantum mechanics". What is the real meaning of this theory? Some scientists have tried to modify it in order to make it more in keeping with our intuition. Rovelli thinks that its dramatic empirical success should compel us to take it seriously, and to ask ourselves not what there is to change in the theory, but rather what is limited about our intuition that makes it so strange to us.
Chapter 5
Both general relativity and quantum mechanics have survived every test. Yet it seems that the two theories are founded on assumptions that contradict each other. In most situations, we can ignore one theory or the other. The Moon is too large to be sensitive to quantum granularity, the atom is too light to bend space appreciably. However, there are situations where both the quantum granularity and the curvature of space matter. One example is the interior of black holes, another is what happened during the Big Bang. Scientists are labouring to resolve the schizophrenia between quanta and gravity.
Historically, great advances have occurred when seemingly contradictory theories were synthesised into something greater. Newton discovered universal gravity by combining Galileo's terrestrial physics with Kepler's heavenly mechanics. Maxwell and Faraday found the equations of electromagnetism by combining what was known about magnetism and electricity. Einstein created special relativity by resolving the apparent conflict between Newtonian mechanics and Maxwell's electromagnetism. Later, he created general relativity in order to resolve the conflict between Newtonian mechanics and special relativity. A conflict of this type is an extraordinary opportunity.
The first scientist to take a significant step was Matvei Bronstejn in 1937. He discovered that the gravitational field at a point is not well defined, when quanta are taken into account. According to Heisenberg's uncertainty principle, if a particle is confined to an extremely small space then its energy becomes enormous. Now energy makes space curve. A lot of energy will make space curve a great deal. If it is confined to a miniscule volume then it will create a black hole, meaning that the particle disappears.
This means that it is not possible to measure arbitrarily small regions of space. This argument can be made mathematically precise. The conclusion is that there is a limit to the divisibility of space. Nothing exists below a certain scale. The minimum length can be calculated to be 10^-35 metres, called the Planck length. To visualize this, if a proton were expanded to the size of the observable universe, the Planck length would only be about the size of a tree. Quantum gravity manifests itself at this extremely minute scale. It is theorized to be the scale at which the fabric of spacetime becomes "pixelated" or discrete, rather than smooth.
In 1967, Wheeler and DeWitt devised an equation for a wave function of space. It was the result of applying the general equations of quantum mechanics written by Dirac to Einstein's gravitational field. To find solutions of this equation it seemed necessary to use closed lines in space, ie loops. The theory of loop quantum gravity was born. This is a work in progress as at 2026.
Chapter 6 (Warning: this chapter is tough!)
Fields are the true basic entities of reality. A field is something that exists everywhere in space. There is an electron field everywhere. What we call an “electron” is a localized excitation (a ripple) in that field.
The lines of the quantum gravitational field are the threads of which space is woven. In quantum theory everything is discrete. We are not speaking of fields immersed in space but of the very structure of space itself. Space itself is discrete — made of “atoms of space”. Continuity is an approximation at large scales.
The theory of loop quantum gravity combines general relativity with quantum mechanics in a conservative way, because it does not employ any other hypothesis. General relativity tells us space is something dynamic like the electromagnetic field; it stretches and bends. This is because moving masses cause space to warp dynamically. Quantum mechanics tells us that a field is made of quanta, ie that it has a fine granular structure. So physical space is made up of quanta. This gives a new solution to Zeno's paradox of Achilles and the tortoise. Because space is not infinitely divisible, when Achilles is a Planck length away from the tortoise, he reaches it in a single quantum leap.
The quanta of gravity constitute space itself. Space is not a continuum, it is formed from atoms of space.
Quantum gravity sees reality as a spin network. This is a graph containing nodes and links, where links carry quantum numbers (spins). Nodes represent chunks of volume, ie atoms of space. Links describe adjacency and connectivity. The volume of space resides in the nodes of the graph, not the lines linking them. The lines link the nodes together, essentially determining which bits of space are contiguous. The quantum numbers of the links are used to calculate area.
Spin networks are not static. They evolve into spin foams. This describes the quantum evolution of spacetime itself. Spin networks evolve in a random way. Spin networks are not entities; they describe the effect of space upon things. Just as an electron is in no place but diffused in a cloud of probability in all places, space is not actually formed by a single spin network but rather by a cloud of probabilities over the whole range of all possible spin networks. Space is a fluctuating swarm of quanta of gravity which act upon each other.
To sum up: space is composed of discrete “atoms” whose areas and volumes take quantized values, and whose structure is described by spin networks—relational graphs that replace the idea of a continuous spacetime.
[I confess that Rovelli has lost me here. Even after multiple readings, I am confused as to what he means. I asked ChatGPT to explain, but this did not help much.]
Chapter 7
We know from general relativity that time is a localised phenomenon. Every object in the universe has its own time running, at a pace determined by the local gravitational field and motion. Rovelli makes the bold statement that time does not exist, but what he really means is that at the micro level there is no distinguished, universal time variable - only physical variables that can be used as clocks relative to one another.
There is no fundamental, universal variable called “time” in the basic equations of quantum gravity. When you write the fundamental equations (Wheeler–DeWitt–type equations) there is no time variable at all. The equations describe relations between physical quantities, but not how they evolve in time. Variables change with respect to other variables, not with respect to time.
The analogy with our heartbeat and the pendulum as timing devices is instructive. Neither the heartbeat nor the pendulum allows us to observe time itself, but only how they are synchronised with regard to each other. In quantum gravity, instead of “X evolves over time” we have “X changes with respect to Y”, as in the heart-pendulum analogy, where we compare heartbeats to pendulum swings. Instead of the universe evolving in time, the universe is a set of correlated events. Time is a way we organise those correlations at the macroscopic level. At the micro level things change only in relation to one another. At a fundamental level, there is no time as we understand it.
In general relativity time is part of the geometry of spacetime. In quantum gravity, geometry itself is quantized and fluctuating, so you cannot have a fixed external clock. There is no background time to evolve in. Time becomes just another physical variable at the macro level, not something fundamental. The universe is a network of events, not things evolving in time. Instead of the Universe evolving in time, the Universe is a web of interacting processes and time is a way we organise these processes at our macro level.
Time and space are no longer a backdrop or framework and classic particles have also disappeared. So what is the world made of? Particles are quanta of quantum fields, space is nothing more than a field, which is also made of quanta; and time emerges from the processes of this same field, ie from gravity. In other words, the world is made entirely from quantum fields. These fields do not live in spacetime, they live one on top of the other, fields on fields. The space and time we perceive at our large scale are our blurred and approximate image of the gravitational field.
Note
Although Rovelli is the founder of loop quantum gravity, he is not arrogant. He admits that quantum gravity is a work in progress, as well as that there are other, competing programmes within fundamental physics. These include supersymmetry, string theory and asymptotic safety.