Reality Is Not What It Seems: The Journey to Quantum Gravity

by Carlo Rovelli

This strange new world is slowly emerging today from the study of the main open question posed in fundamental physics: quantum gravity. It’s the problem of coherently synthesizing what we have learned about the world with the two major discoveries of twentieth-century physics: general relativity and quantum theory.

Then, at Miletus, at the beginning of the fifth century before our era, Thales, his pupil Anaximander, Hecataeus and their school find a different way of looking for answers. This immense revolution in thought inaugurates a new mode of knowledge and understanding, and signals the first dawn of scientific thought. The Milesians understand that by shrewdly using observation and reason, rather than searching for answers in fantasy, ancient myths or religion – and, above all, by using critical thought in a discriminating way – it is possible to repeatedly correct our world view, and to discover new aspects of reality which are hidden to the common view. It is possible to discover the new. Perhaps the decisive discovery is that of a different style of thinking, where the disciple is no longer obliged to respect and share the ideas of the master but is free to build on those ideas without being afraid to discard or criticize the part that can be improved.

Situated at a point of conjunction between the emergent Greek civilization and the ancient empires of Mesopotamia and Egypt, nourished by their knowledge but immersed in the liberty and the political fluidity which is typically Greek; in a social space without imperial palaces, or powerful priestly castes, where individual citizens discuss their destinies in open agoras, Miletus is the place where, for the first time, men decide collectively their own laws; where the first parliament in the history of the world gathers – the Panionium, meeting-place of the delegates of the Ionian League – and where for the first time men doubt that only the gods are capable of accounting for the mysteries of the world. Through discussion, it is possible to reach the best decisions for the community; through discussion, it is possible to understand the world. This is the immense legacy of Miletus, cradle of philosophy, of the natural sciences, and of geographical and historical studies. It is no exaggeration to say that the entire scientific and philosophical tradition, Mediterranean and then modern, has a crucial root in the speculations of the thinkers of Miletus in the sixth century BCE.

When atoms aggregate, the only thing that matters, the only thing that exists at the elementary level, is their shape, their arrangement, and the order in which they combine. Just as by combining the letters of the alphabet in different ways we may obtain comedies or tragedies, ridiculous stories or epic poems, so elementary atoms combine to produce the world in its endless variety. The metaphor is Democritus’s own.

The ethical ideal of Democritus is that of a serenity of mind reached through moderation and balance, by trusting in reason and not allowing oneself to be overwhelmed by passions. Plato and Aristotle were familiar with Democritus’s ideas, and fought against them. They did so on behalf of other ideas, some of which were later, for centuries, to create obstacles to the growth of knowledge. Both insisted on rejecting Democritus’s naturalistic explanations, in favour of trying to understand the world in finalistic terms – believing, that is, that everything that happens has a purpose; a way of thinking that would reveal itself to be very misleading for understanding the ways of nature – or in terms of good and evil, confusing human issues with matters which do not relate to us.

Richard Feynman, wrote at the beginning of his wonderful introductory lessons on physics: If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis, or the atomic fact, or whatever you wish to call it, that all things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied.

We have been left with all of Aristotle, by way of which Western thought reconstructed itself, and nothing by Democritus. Perhaps, if all of the works of Democritus had survived, and nothing of Aristotle’s, the intellectual history of our civilization would have been better … But centuries dominated by monotheism have not permitted the survival of Democritus’s naturalism. The closure of the ancient schools such as those of Athens and Alexandria and the destruction of all the texts not in accordance with Christian ideas were vast and systematic, at the time of the brutal anti-pagan repression following from the edicts of Emperor Theodosius, which, in 390–1 declared that Christianity was to be the only and obligatory religion of the empire. Plato and Aristotle, pagans who believed in the immortality of the soul or in the existence of a Prime Mover, could be tolerated by a triumphant Christianity. Not Democritus.

The book is the proof that the intuition of Pythagoras was correct. Mathematics allows the world to be described and the future to be predicted: the apparently wandering and disorderly movements of the planets can be precisely predicted by using mathematical formulae that Ptolemy, summarizing the results of centuries of work by Greek astronomers, presents in a systematic and masterly way. Even today, with a little studying, it is possible to open Ptolemy’s book, learn its techniques and calculate, for example, the position which Mars will have in a future sky. Today: two thousand years, that is, after the book was written. The realization that working this magic is really possible is the basis of modern science and owes not a little to Pythagoras and Plato.

Confident of the rationality of nature and of the Pythagorean-Platonic vision that nature is understandable through mathematics, Galileo decides to study how objects move on Earth when they are set free – that is, when they fall. Convinced that a relevant mathematical law must exist, he sets out to search for it, by trial and error. For the first time in the history of mankind, an experiment is made. Experimental science begins with Galileo. His experiment is simple: he lets objects fall; that is, he lets them follow what for Aristotle was their natural movement and seeks to measure precisely their falling speed.

Newton makes the simple calculation, and the result is … 9.8 metres per second per second! The same acceleration as in Galileo’s experiments for falling bodies on Earth. Coincidence? It can’t be, reasons Newton. If the effect is the same – a downwards acceleration of 9.8 metres per second per second – the cause must be the same. And so: the force which causes the little moon to turn around its orbit must be the same as that which causes objects to fall to the ground on Earth. We call the force causing objects to fall gravity.

A simple calculation with the little moon allows Newton to deduce how the force of gravity changes with distance and to determine its strength,* given by what we call today Newton’s constant, indicated by the letter ‘G’ for ‘gravity’. On Earth, this force causes things to fall; in the heavens it holds planets and satellites on their orbits. The force is the same.

It is characteristic of genius to be aware of the limitations of its own findings, even in the case of such momentous outcomes as Newton’s discovery of the laws of mechanics and universal gravity. Newton’s theory worked so well, it turned out to be so useful, that for two centuries no one bothered any longer to question it – until Faraday, the ‘reader’ to whom Newton had bequeathed the unanswered question, found the key to understanding how bodies can attract and repel each other at a distance in a reasonable manner. Einstein will later apply Faraday’s brilliant solution to Newton’s own theory of gravity.

We see the world around us in colour. What is colour? Put simply, it is the frequency (the speed of oscillation) of the electromagnetic wave that light is. If the wave vibrates more rapidly, the light is bluer. If it vibrates a little more slowly, the light is redder. Colour, as we perceive it, is the psychophysical reaction of the nerve signal generated by the receptors of our eyes, which distinguish electromagnetic waves of different frequencies.

Maxwell recognizes that the equations foresee that Faraday’s lines can also vibrate at much lower frequencies, that is to say, more slowly than light. Therefore, there must be other waves which nobody had yet seen, produced by the movement of electrical charges, which in turn move electrical charges. It must be possible to shake an electric charge here, and to produce a wave which will drive an electric current there. Only a few years later, these waves, anticipated theoretically by Maxwell, will be revealed by the German physicist Heinrich Hertz; and just a few years later still, Guglielmo Marconi builds the first radio.

All modern communications technology – radio, television, telephones, computers, satellites, wi-fi, the internet, etc. – is an application of Maxwell’s prediction; the Maxwell equations are the basis for all calculations made by telecommunications engineers.

Our entire current technology is founded on the use of a physical thing – electromagnetic waves – which 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.

At a distance of a few metres from your nose, dear reader, the duration of what for you is the intermediate zone, neither past nor future, is no more than a few nanoseconds: next to nothing (the number of nanoseconds in a second is the same as the number of seconds in thirty years). This is much less than we could possibly notice. On the other side of the ocean, the duration of this intermediate zone is a thousandth of a second, still well below the threshold of our perception of time – the minimum amount of time we perceive with our senses – which is somewhere in the order of a tenth of a second. But on the Moon the duration of the expanded present is a few seconds, and on Mars it is a quarter of an hour. This means we can say that, on Mars, there are events that in this precise moment have already happened, events that are yet to happen, but also a quarter of an hour during which things occur that are neither in our past nor in our future.

This implies that it makes no sense to say of an event on Mars that it is taking place ‘just now’, because ‘just now’ does not exist (figure 3.3).fn11 In technical terms, we say that Einstein has understood that ‘absolute simultaneity’ does not exist: there is no collection of events in the universe which exist ‘now’. The collection of all the events in the universe cannot be described as a succession of ‘now’s, of presents, one following the other; it has a more complex structure, illustrated in figure 3.2. The figure describes that which in physics is called spacetime: the set of all past and future events, but also those that are ‘neither-past-nor-future’; these do not form a single instant: they have themselves a duration.

A rapid calculation teaches Einstein how much energy is obtained by transforming one gram of mass. The result is the celebrated formula E = mc². Since the speed of light c is a very large number, and c² an even greater number, the energy obtained from transforming one gram of mass is enormous; it is the energy of millions of bombs exploding at the same time – enough energy to illuminate a city and power the industries of a country for months or, conversely, capable of destroying in a second hundreds of thousands of human beings, in a city such as Hiroshima.

And it’s here that Einstein’s extraordinary stroke of genius occurs, one of the greatest flights in the history of human thinking: what if the gravitational field turned out actually to be Newton’s mysterious space? What if Newton’s space was nothing more than the gravitational field? This extremely simple, beautiful, brilliant idea is the theory of general relativity.

Space is no longer different from matter. It is one of the ‘material’ components of the world, akin to the electromagnetic field. It is a real entity which undulates, fluctuates, bends and contorts.

With a great deal of effort, seeking help from friends better versed in mathematics than himself, Einstein learns Riemann’s maths – and writes an equation where R is proportional to the energy of matter. In words: spacetime curves more where there is matter. That is it. The equation is the analogue of the Maxwell equations, but for gravity rather than electricity. The equation fits into half a line, and there is nothing more. A vision – that space curves – becomes an equation. But within this equation there is a teeming universe. And here the magical richness of the theory opens up into a phantasmagorical succession of predictions that resemble the delirious ravings of a madman but which have all turned out to be true. Even up to the beginning of the 1980s, almost nobody took the majority of these fantastical predictions entirely seriously. And yet, one after another, they have all been verified by experience. Let’s consider a few of them.

This rich and complex range of phenomena – bending of rays of light, modification of Newton’s force, slowing down of clocks, black holes, gravitational waves, expansion of the universe, the Big Bang – follow from understanding that space is not a dull, fixed container but possesses its own dynamic, its own ‘physics’, just like the matter and the other fields it contains. Democritus himself would have smiled with pleasure, had he been able to see that his idea of space would turn out to have such an impressive future. It is true that he termed it non-being, but what he meant by being (δέν) was matter; and he wrote that his non-being, the void, nevertheless ‘has a certain physics (ϕύσιν) and a substantiality of its own’.fn14 How right he was.

Our culture is foolish to keep science and poetry separated: they are two tools to open our eyes to the complexity and beauty of the world. Dante’s 3-sphere is only an intuition within a dream. Einstein’s 3-sphere has mathematical form and follows from the theory’s equations. The effect of each is different. Dante moves us deeply, touching the sources of our emotions. Einstein opens a road towards the unsolved mysteries of our universe. But both count among the most beautiful and significant flights that the mind can achieve.

A few years later Einstein is forced to give up: it is his theory that is right, not his reservations about it. Astronomers realize that all galaxies are indeed moving away from us. The universe is expanding, exactly as the equations predicted. Fourteen billion years ago, the universe was concentrated almost to a single, furiously hot point. From there it expanded in a colossal ‘cosmic’ explosion – and here the term ‘cosmic’ is not used in any rhetorical sense: it is, literally, a cosmic explosion. This is the ‘Big Bang’.

Ever since we discovered that the Earth is round and turns like a mad spinning-top, we have understood that reality is not what it seems: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen. But the leap made by Einstein is unparalleled: spacetime is a field; the world is made only of fields and particles; space and time are not something else, something different from the rest of nature: they are just a field among the others

To comprehend how light may be simultaneously an electromagnetic wave and a swarm of photons will require the entire construction of quantum mechanics. But the first building block of this theory has been established: there exists a fundamental granularity in all things, including light.

What if these were the mysterious quantum leaps which appeared to underlie the structure of the atomic spectra? What if, between one interaction with something, and another with something else, the electron could literally be nowhere.

Heisenberg returns home gripped by feverish emotion, and plunges into calculations. He emerges, some time later, with a disconcerting theory: a fundamental description of the movement of particles, in which they are described not by their position at every moment but only by their position at particular instants: the instants in which they interact with something else. This is the second cornerstone of quantum mechanics, its hardest key: the relational aspect of things. Electrons don’t always exist. They exist when they interact. They materialize in a place when they collide with something else. The quantum leaps from one orbit to another constitute their way of being real: an electron is a combination of leaps from one interaction to another. When nothing disturbs it, an electron does not exist in any place. Instead of writing the position and velocity of the electron, Heisenberg writes tables of numbers (matrices).

Dirac’s quantum mechanics is the mathematical theory used today by any engineer, chemist or molecular biologist. In it, every object is defined by an abstract spacefn20 and has no property in itself, apart from those that are unchanging, such as mass. Its position and velocity, its angular momentum and its electrical potential, and so on, acquire reality only when it collides – ‘interacts’– with another object. It is not just its position which is undefined, as Heisenberg had recognized: no variable of the object is defined between one interaction and the next. The relational aspect of the theory becomes universal.

Quantum mechanics brings probability to the heart of the evolution of things. This indeterminacy is the third cornerstone of quantum mechanics: the discovery that chance operates at the atomic level. While Newton’s physics allows for the prediction of the future with exactitude, if we have sufficient information about the initial data and if we can make the calculations, quantum mechanics allows us to calculate only the probability of an event. This absence of determinism at a small scale is intrinsic to nature. An electron is not obliged by nature to move towards the right or the left; it does so by chance. The apparent determinism of the macroscopic world is due only to the fact that the microscopic randomness cancels out on average, leaving only fluctuations too minute for us to perceive in everyday life.

The electromagnetic waves are vibrations of Faraday’s lines, but also, at a small scale, swarms of photons. When they interact with something else, as in the photoelectric effect, they manifest themselves as particles: to our eye, light rains in separate droplets, in single photons. Photons are the quanta of the electromagnetic field.

bodies. If we look at a stone, it stays still. But if we could see its atoms, we would observe them constantly spread here and there, and in ceaseless vibration. Quantum mechanics reveals to us that, the more we look at the detail of the world, the less constant it is. The world is not made up of tiny pebbles. It is a world of vibrations, a continuous fluctuation, a microscopic swarming of fleeting micro-events.

The theory does not describe things as they are: it describes how things occur and how they interact with each other. It doesn’t describe where there is a particle but how the particle shows itself to others. The world of existent things is reduced to a realm of possible interactions. Reality is reduced to interaction. Reality is reduced to relation.

Galileo understood that this is the reason why the Earth can move with respect to the Sun without us feeling the movement. Speed is not a property of an object on its own: it is the property of the motion of an object with respect to another object. Einstein extended the notion of relativity to time: we can say that two events are simultaneous only relatively to a given motion (see here). Quantum mechanics extends this relativity in a radical way: all variable aspects of an object exist only in relation to other objects. It is only in interactions that nature draws the world.

To summarize, quantum mechanics is the discovery of three features of the world: Granularity (figure 4.8). The information in the state of a system is finite, and limited by Plank’s constant. Indeterminacy. The future is not determined unequivocally by the past. Even the more rigid regularities we see are, ultimately, statistical. Relationality. The events of nature are always interactions. All events of a system occur in relation to another system.

Ultimately, Einstein accepts that the theory represents a gigantic leap forward in our understanding of the world, and that it is coherent. But he remains convinced that things could not be as strange as this theory proposed – and that, ‘behind’ it, there must be a further, more reasonable explanation. A century has passed, and we are at the same point. Richard Feynman, who more than anyone has known how to juggle with the theory, has written, ‘I think I can state that nobody really understands quantum mechanics.’ The equations of the theory and their consequences are used daily in a wide variety of fields: by physicists, engineers, chemists and biologists. But they remain mysterious: they do not describe physical systems but only how physical systems interact with and affect one another. What does this mean?

What, then, is quantum space? What is quantum time? This is the problem we call quantum gravity. A band of theoretical physicists scattered across five continents is laboriously seeking to solve the problem. Their objective is to find a theory, that is to say, a set of equations – but, above all, a coherent vision of the world – with which to resolve the current schizophrenia between quanta and gravity.

The central prediction of loop theory is therefore that space is not a continuum, it is not divisible ad infinitum, it is formed of ‘atoms of space’. A billion billion times smaller than the smallest of atomic nuclei. Loop theory describes this atomic and granular quantum structure of space in a precise mathematical form. It is obtained by applying the general equations of quantum mechanics written by Dirac to Einstein’s gravitational field. In particular, loop theory specifies that volume (for example, the volume of a given cube) cannot be arbitrarily small. A minimum volume exists. No space smaller than this minimum volume exists. There is a minimum quantum of volume: an elementary atom of space.

The crucial difference between photons (the quanta of the electromagnetic field) and the nodes of the graph (the quanta of gravity) is that photons exist in space, whereas the quanta of gravity constitute space themselves. Photons are characterized by ‘where they are’.fn37 Quanta of space have no place to be in, because they are themselves that place.

Space as an amorphous container of things disappears from physics with quantum gravity. Things (the quanta) do not inhabit space, they dwell one over the other, and space is the fabric of their neighbouring relations. As we abandon the idea of space as an inert container, similarly, we must abandon the idea of time as an inert flow along which reality unfurls.

We must not think of time as if there were a great cosmic clock that marks the life of the universe. We have known for more than a century that we must think of time instead as a localized phenomenon: every object in the universe has its own time running, at a pace determined by the local gravitational field.

The backdrop of space has disappeared, time has disappeared, classic particles have disappeared, along with the classic fields. So what is the world made of? The answer now is simple: the particles are quanta of quantum fields; light is formed by quanta of a field; space is nothing more than a field, which is also made of quanta; and time emerges from the processes of this same field. In other words, the world is made entirely from quantum fields (figure 7.8). These fields do not live in spacetime; they live, so to speak, one on top of the other: fields on fields. The space and time that we perceive in large scale are our blurred and approximate image of one of these quantum fields: the gravitational field.

Covariant quantum fields have become today the best description that we have of the ἄπειρον, the apeiron, the primal substance of which everything is formed hypothesized by the man that could perhaps be called the first scientist and the first philosopher, Anaximander.fn45 The separation between the curved and continuous space of Einstein’s general relativity and the discrete quanta of quantum mechanics which dwell in a flat and uniform space has dissolved. The apparent contradiction is no longer there. Between the spacetime continuum and quanta of space, there is the same relationship as between electromagnetic waves and photons. The waves give an approximate large-scale vision of photons. Photons are the way in which waves interact. Continuous space and time are an approximate large-scale vision of the dynamic of quanta of gravity. The quanta of gravity are the way in which space and time interact.

But it is the young Belgian priest who understands, already in 1927, the crucial consequence: if we see a stone flying up, it means that the stone was previously lower down and something has thrown it upwards. If we see the galaxies moving away and the universe expanding, it means that the galaxies were previously much closer and the universe was smaller: and something caused it to start expanding. The young Belgian priest suggests that the universe was originally extremely small and compressed, and started its expansion in a gigantic explosion. He calls this initial state the primordial atom. Today it is known as the Big Bang. His name was Georges Lemaître. In French, this name sounds like le maître meaning ‘the master’, and few names are more appropriate for the man who first understood the existence of the Big Bang.

We can reconstruct in detail the history of the universe, starting with its initial hot, compressed state. We know how atoms, elements, galaxies and stars formed and how the universe as we see it today developed. Recent extended observations of the radiation that fills the universe carried out mainly by the Planck satellite once again confirmed in full the theory of the Big Bang. We know with a reasonable degree of certainty what happened on a large scale to our universe in the last 14 billion years, from the time when it was a ball of fire.

But what happened before this initial hot and compressed state? Regressing in time, temperature increases, as does the density of matter and energy. There is a point at which they reach the Planck scale: 14 billion years ago. At that point, the equations of general relativity are no longer valid, because it is no longer possible to ignore quantum mechanics. We enter into the realm of quantum gravity.

When Lemaître defends the idea that the universe is expanding, and Einstein does not believe it, one of the two is wrong; the other right. All of Einstein’s results, his fame, his influence on the scientific world, his immense authority, count for nothing. The observations prove him wrong, and it’s game over. An obscure Belgian priest is right. It is for this reason that scientific thinking has power.

What Copernicus, Newton, Einstein and many others did was to build upon pre-existing theories which synthesized empirical knowledge across vast fields of nature, and to find a way of combining and rethinking them to improve the general picture.

Black holes populate our universe in great number. They are regions in which space is so curved as to collapse in on itself, and where time comes to a standstill. As mentioned, they form, for instance, when a star has burned up all of the available hydrogen and collapses. Frequently, the collapsed star formed part of a pair of neighbouring stars and, in this case, the black hole and the surviving counterpart circle one around the other; the black hole sucks matter from the other star continuously