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

by Carlo Rovelli

The human race is like a growing child who discovers with amazement that the world consists not just of his bedroom and playground, but that it is vast, and that there are a thousand things to discover, and innumerable ideas quite different from those with which he began.

An elementary structure of the world is emerging, generated by a swarm of quantum events, where time and space do not exist. Quantum fields draw together space, time, matter, and light, exchanging information between one event and another. Reality is a network of granular events; the dynamic that connects them is probabilistic; between one event and another, space, time, matter, and energy melt into a cloud of probability.

Science is a continual exploration of ways of thinking. Its strength is its visionary capacity to demolish preconceived ideas, to reveal new regions of reality, and to construct new and more effective images of the world. This adventure rests upon the entirety of past knowledge, but at its heart is change.

The incompleteness and the uncertainty of our knowledge, our precariousness, suspended over the abyss of the immensity of what we don’t know, does not render life meaningless: it makes it interesting and precious.

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 worldview and to discover new aspects of reality that are hidden to the common view. It is possible to discover the new.

key to the subsequent development of philosophical and scientific thinking: from this moment onward, knowledge begins to grow at a vertiginous pace, nourished by past knowledge but at the same time by the possibility of criticism, and therefore improving knowledge and understanding.

The idea of Democritus’s system is extremely simple: the entire universe is made up of a boundless space in which innumerable atoms run. Space is without limits; has neither an above nor a below; is without a center or a boundary. Atoms have no qualities at all, apart from their shape. They have no weight, no color, no taste. “Sweetness is opinion, bitterness is opinion; heat, cold and color are opinion: in reality only atoms, and vacuum.”

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.

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.

Could small particles of extended dimension remain? No, because if this were the case, the piece of matter would not yet be broken up to infinity. Therefore, only points without extension would remain. But now let us try to put together the piece of matter starting from these points: by putting together two points without extension, you cannot obtain a thing with extension, nor can you with three, or even with four. No matter how many you put together, in fact, you never have extension, because points have no extension. Therefore we cannot think that matter is made of points without extension, because no matter how many of these we manage to put together, we never obtain something with an extended dimension. The only possibility, Democritus concludes, is that any piece of matter is made up of a finite number of discrete pieces that are indivisible, each one having finite size: the atoms.

And there is a serene acceptance of the inevitability of death, which cancels every evil, and about which there is nothing to fear. For Lucretius, religion is ignorance: reason is the torch that enlightens.

There is a feeling of deep universalism, in the wake of the splendid words of Democritus: “To a wise man, the whole earth is open, because the true country of a virtuous soul is the entire universe.”25

And he did think and work. After all, this is what he had done since his early youth: he would read Euclid’s Elements and Kant’s Critique of Pure Reason instead of attending to what he was being taught at school. You don’t get to new places by following established tracks.

“Democritus postulated the full and the empty, calling one ‘Being,’ and the other ‘Non-Being,’” says Simplicius.1 Atoms are Being. Space is “Non-Being.” A “Non-Being” that, nevertheless, exists. It is difficult to be more obscure than this.

But it is not only space that curves: time does too. Einstein predicts that time on Earth passes more quickly at higher altitude, and more slowly at lower altitude.

Without the notion of fields introduced by Faraday, without the spectacular power of mathematics, without the geometry of Gauss and Riemann, this “certain physics” would have remained incomprehensible. Empowered by new conceptual tools and by mathematics, Einstein writes the equations that describe Democritus’s void and finds for its “certain physics” a colorful and amazing world where universes explode, space collapses into bottomless holes, time slows down in the vicinity of a planet, and the boundless expanses of interstellar space ripple and sway like the surface of the sea. . . .

Rab – ½ Rgab + Λgab = 8πG Tab In 1915, the equation was simpler still, because the term “+ Λgab,” which Einstein added two years later (and which I discuss in the next section) did not yet exist.* Rab depends on Riemann’s curvature, and together with ½ Rgab, represents the curvature of spacetime; Tab stands for the energy of matter; G is the same constant that Newton had found, the constant that determines the strength of the force of gravity.

For Einstein, the theory of general relativity is not a collection of equations: it is a mental image of the world arduously translated into equations.

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.

Dirac’s quantum mechanics thus allows us to do two things. First, to calculate which values a physical variable may assume. This is called “calculation of the spectrum of a variable”; it captures the granular nature of things. When an object (atom, electromagnetic field, molecule, pendulum, stone, star, and the like) interacts with something else, the values computed are those that its variables can assume in the interaction (relationism). The second thing that Dirac’s quantum mechanics allows us to do is to compute the probability that this or that value of a variable appears at next interaction. This is called “calculation of an amplitude of transition.” Probability expresses the third feature of the theory: indeterminacy, the fact that it does not give unique predictions, only probabilistic ones.

The world is not made up of tiny pebbles. It is a world of vibrations, a continuous fluctuation, a microscopic swarming of fleeting microevents.

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.

The world of quantum mechanics is not a world of objects: it is a world of events.

Quantum mechanics does not describe objects: it describes processes and events that are junction points between processes.

Quantum mechanics teaches us not to think about the world in terms of “things” that are in this or that state but in terms of “processes” instead. A process is the passage from one interaction to another. The properties of “things” manifest themselves in a granular manner only in the moment of interaction—that is to say, at the edges of the processes—and are such only in relation to other things. They cannot be predicted in an unequivocal way, but only in a probabilistic one.

This argument can be made more precise with a little mathematics. The result is general: quantum mechanics and general relativity, taken together, imply that there is a limit to the divisibility of space. Below a certain scale, nothing more is accessible. More precisely, nothing exists there.

For, as Petrarch sings: “The wound does not heal for the weakening of the bow.”

Imagine that you are looking at the sea from a great height: you perceive a vast expanse of it, a flat cerulean table. Now you descend and look at it more closely. You begin to make out the great waves swollen by the wind. You descend farther, and you see that the waves break up, and that the surface of the sea is a turbulent frothing. This is what space is like, as imagined by Wheeler.* On our scale space is smooth. If we move down to smaller and smaller regions of space, we reach a minute scale, called the “Planck scale,” where space shatters and foams.

To summarize, the theory of loop quantum gravity, or “loop theory,” combines general relativity with quantum mechanics in a rather conservative way, because it does not employ any other hypotheses apart from those of the two theories themselves, suitably rewritten to render them compatible. But the consequences are radical.

And there is the fact that what matters is not how things are, but rather how they interact. Spin networks are not entities; they describe the effect of space upon things. Just as an electron is in no place—is diffused in a cloud of probability in all places—space is not actually formed by a single specific spin network, but rather by a cloud of probabilities over the whole range of all possible spin networks.

It must not be claimed that anyone can sense time by itself apart from the movement of things. LUCRETIUS, De rerum natura1

Thus, the world described by the theory is far from the one we are familiar with. There is no longer space that “contains” the world, and no longer time “during the course of which” events occur. There are elementary processes in which the quanta of space and matter continuously interact with one another. Just as a calm and clear Alpine lake is made up of a rapid dance of a myriad of minuscule water molecules, the illusion of being surrounded by continuous space and time is the product of a farsighted vision of a dense swarming of elementary processes.

Quantum mechanics assumes that between the initial boundary, where the two balls enter, and the final boundary, where they exit, there is no definite spacetime or definite trajectory of the balls. There is a quantum “cloud” in which all the possible spacetimes and all possible trajectories exist together. The probability of seeing the balls going out in one way or another can be computed by summing all possible spacetimes.

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

But if we take quantum mechanics into account, the universe cannot be indefinitely squashed. A quantum repulsion makes it rebound. A contracting universe does not collapse down to a point: it bounces back and begins to expand, as if it were emerging from a cosmic explosion (figure 8.3). The past of our universe, therefore, may well be the result of just such a rebound. A gigantic rebound known as a Big Bounce instead of Big Bang.

The sociology of science has shed light on the complexity of the process of scientific understanding; like any other human endeavor, this process is beset by irrationality, intersects with the game of power, and is affected by every sort of social and cultural influence. Nevertheless, despite all this, and in opposition to the exaggerations of a few postmodernists, cultural relativists, and the like, none of this diminishes the practical and theoretical efficacy of scientific thinking. Because in the end, in the majority of cases, it is possible to establish with clarity who is right and who is wrong. And even the great Einstein could go on to say (and he did so): “Ah . . . I made a mistake!” Science is the best strategy if we value reliability.

The objective of scientific research is not just to arrive at predictions: it is to understand how the world functions. To construct and develop an image of the world, a conceptual structure to enable us to think about it. Before being technical, science is visionary.

It is in this data and in these theories that we must try to uncover what we have been unable yet to imagine. This is how Copernicus, Newton, Maxwell, and Einstein proceeded. They never tried to “guess” a new theory; unlike, in my opinion, the way in which too many theoretical physicists are trying to do today.

When we take quantum gravity into account, the infinite compression of the universe into a single infinitely small point, predicted by general relativity at the Big Bang, disappears. Quantum gravity is the discovery that no infinitely small point exists. There is a lower limit to the divisibility of space. The universe cannot be smaller than the Planck scale, because nothing exists that is smaller than the Planck scale.

The point at stake here is not the presumption of knowing everything. It is the opposite: an awareness that yesterday’s ignorance may have light shed on it today; and that today’s might be illuminated tomorrow.

information is the measure of the number of possible alternatives for something.

It is always heat and only heat that distinguishes the past from the future.

Hence time is not a fundamental constituent of the world, but it appears because the world is immense, and we are small systems within the world, interacting only with macroscopic variables that average among innumerable small, microscopic variables. We, in our everyday lives, never see a single elementary particle, or a single quantum of space. We see stones, mountains, the faces of our friends—and each of these things we see is formed by myriads of elementary components. We are always correlated with averages. Averages behave like averages: they disperse heat and, intrinsically, generate time.

Democritus gave a strange definition of “man”: “man is what we all know.”2 At first sight this seems rather silly and empty, but it is not so. Solomon Luria, the major scholar of Democritus, observes that it is not a banality that Democritus is giving us. The nature of a man is not his internal structure but the network of personal, familial, and social interactions within which he exists. It is these that “make” us, these that guard us. As humans, we are that which others know of us, that which we know of ourselves, and that which others know about our knowledge. We are complex nodes in a rich web of reciprocal information.

This acute awareness of our ignorance is the heart of scientific thinking. It is thanks to this awareness of the limits of our knowledge that we have learned so much. We are not certain of all that we suspect, just as Socrates was not sure of the spherical nature of Earth. We are exploring at the borders of our knowledge.

The answers given by science, then, are not reliable because they are definitive. They are reliable because they are not definitive. They are reliable because they are the best available today. And they are the best we have because we don’t consider them to be definitive, but see them as open to improvement. It’s the awareness of our ignorance that gives science its reliability.

This means not giving credence to those who say they are in possession of the truth. For this reason, science and religion frequently find themselves on a collision course. Not because science pretends to know ultimate answers, but precisely for the opposite reason: because the scientific spirit distrusts whoever claims to be the one having ultimate answers or privileged access to Truth. This distrust is found to be disturbing in some religious quarters. It is not science that is disturbed by religion: there are certain religions that are disturbed by scientific thinking.

To seek to look further, to go further, seems to me to be one of the splendid things that give sense to life. Like loving, or looking at the sky. The curiosity to learn, to discover, to look over the next hill, the desire to taste the apple: these are the things that make us human. As Dante’s Ulysses reminds his companions, we are not made “to live like brutes, but to seek virtue and knowledge.”