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

by Carlo Rovelli

The cloud of probability which accompanies electrons between one interaction and another does resemble a field. Faraday and Maxwell’s fields, in turn, are made up of grains: photons. Not only are the particles in a certain sense diffused in space like fields but the fields interact like particles. The notions of fields and particles, separated by Faraday and Maxwell, end up merging in quantum mechanics.

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.

The general form of quantum theory compatible with special relativity is thus called quantum field theory, and it forms the basis of today’s particle physics. Particles are quanta of a field, just as photons are quanta of light. All fields display a granular structure in their interactions.

The world is not made up of fields and particles but of a single type of entity: the quantum field. There are no longer particles which move in space with the passage of time, but quantum fields whose elementary events happen in spacetime. The world is strange, but simple

quantum mechanics has revealed three aspects of the nature of things: granularity, indeterminacy and the relational structure of the world.

Instead, quantum mechanics tells us that between five and six centimetres there is a finite number of possible values of the amplitude, hence our missing information about the pendulum is finite.

Therefore, the first meaning of quantum mechanics is the existence of a limit to the information that can exist within a system: a limit to the number of distinguishable states in which a system can be.

The future is genuinely unpredictable. This is the second fundamental lesson learned with quantum mechanics.

Due to this indeterminacy, in the world described by quantum mechanics, things are constantly subject to random change. All the variables ‘fluctuate’ continually, as if, at the smallest scale, everything is constantly vibrating.

Vibrating

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.

interesting

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.

wow

Nelson Goodman wrote in the 1950s, in a beautiful phrase, ‘An object is a monotonous process.’ A stone is a vibration of quanta that maintains its structure for a while, just as a marine wave maintains its identity for a while before melting again into the sea. What is a wave, which moves on water without carrying with it any drop of water? A wave is not an object, in the sense that it is not made of matter that travels with it. The atoms of our body, as well, flow in and away from us. We, like waves and like all objects, are a flux of events; we are processes, for a brief time monotonous …

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.

Einstein did not want to relent on what for him was the key point: the notion that there is an objective reality, independent of whatever interacted with what. He refused to accept the relational aspect of the theory, the fact that things manifest themselves only through interactions. Bohr did not want to concede on the validity of the profoundly new way in which the real was conceptualized by the theory. 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.

When Einstein died, his greatest rival, Bohr, found for him words of moving admiration. When, a few years later, Bohr in turn died, someone took a photograph of the blackboard in his study. There’s a drawing on it. It represents the ‘box of light’ of Einstein’s thought experiment. To the very last, the desire to debate, to understand more. To the very last, doubt.

Bohr, Heisenberg and Dirac understood that physical fields have a quantum character: granular, probabilistic, manifesting through interactions. It follows that space and time must also be quantum entities possessing these strange properties. What, then, is quantum space? What is quantum time? This is the problem we call quantum gravity.

If the particle escapes at great speed, it has a great deal of energy. Now let us take Einstein’s theory into account. Energy makes space curve. A lot of energy means that space will curve a great deal. A lot of energy in a small region results in curving space so much that it collapses into a black hole, like a collapsing star. But if a particle plummets into a black hole, I can no longer see it. I can no longer use it as a reference point for a region of space. I can’t manage to measure arbitrarily small regions of space, because if I try to do this these regions disappear inside a black hole.

The length LP, determined in this fashion, is called the Planck length. It should be called the Bronštejn length, but such is the way of the world. In numerical terms, it is equivalent to approximately one millionth of a billionth of a billionth of a billionth of a centimetre (10-33 centimetres). So, that is to say … small. It is at this extremely minute scale that quantum gravity manifests itself. To give an idea of the smallness of the scale we are discussing: if we enlarged a walnut shell until it had become as big as the whole observable universe, we would still not see the Planck length. Even after having been enormously magnified thus, it would still be a million times smaller than the actual walnut shell was before magnification. At this scale, space and time change their nature. They become something different; they become ‘quantum space and time’, and understanding what this means is the problem.

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 further, 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.fn30 On our scale, immensely larger than the Planck length, space is smooth. If we move down to the Planck scale, it shatters and foams.

But two new ingredients are now added to Faraday’s ideas. The first is that we are dealing with quantum theory. In quantum theory, everything is discrete. This implies that the infinitely fine, continuous spiderweb of Faraday’s lines now becomes similar to a real spiderweb: it has a finite number of distinct threads. Every single line determining a solution of the Wheeler–DeWitt equation describes one of the threads of this web. The second new aspect, the crucial one, is that we are speaking of gravity and, therefore, as Einstein understood, we are not speaking of fields immersed in space but of the very structure of space itself. Faraday’s lines of the quantum gravitational field are the threads of which space is woven.

it became clear that the key to understanding the physics of these solutions lies in the points where these lines intersect. These points are called nodes, and the lines between nodes are called links. A set of intersecting lines forms what is called a graph, that is to say, a combination of nodes connected by links, as in figure 6.3

A calculation, in fact, demonstrates that, without nodes, physical space has no volume. In other words, it is in the nodes of the graph, not in the lines, that the volume of space ‘resides’. The lines ‘link together’ individual volumes sitting at the nodes.

Volume is a geometrical quantity which depends on the geometry of space, but the geometry of space – as Einstein understood, and as I recounted in Chapter 3 – is the gravitational field. Volume is therefore a property of the gravitational field, expressing how much gravitational field there is between the walls of the room. But the gravitational field is a physical quantity and, like all physical quantities, is subject to the laws of quantum mechanics. In particular, like all physical quantities, volume may not assume arbitrary values but only certain particular ones, as I described in Chapter 4. The list of all possible values is called, if you remember, the spectrum. Hence there should exist a ‘spectrum of the volume’ (figure 6.2

The nodes are the elementary quanta of which physical space is made. Every node of the graph is a ‘quantum particle of space’.

Now we can understand what it represents: if you imagine two nodes as two small ‘regions of space’, these two regions will be separated by a small surface. The size of this surface is its area. The second quantity, after the volume, which characterizes the quantum webs of space, is the area associated with each line.fn35

General relativity taught us that space is something dynamic, like the electromagnetic field: an immense, mobile mollusc in which we are immersed, which stretches and bends. Quantum mechanics teaches us that every field of this sort is made of quanta, that is to say, it has a fine, granular structure. It follows that physical space, being a field, is made of quanta as well. The same granular structure characterizing the other quantum fields also characterizes the quantum gravitational field, and therefore space. We expect space to be granular. We expect quanta of gravity, just as there are quanta of light, quanta of the electromagnetic field, and as particles are quanta of quantum fields.

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. They have only one piece of information which characterizes them spatially: information about which other quanta of space they are adjacent to, which one is next to which other. This information is expressed by the links in the graph. Two nodes connected by a link are two nodes in proximity. They are two grains of space in contact with each other: this ‘touching’ constructs the structure of space.

The quanta of gravity, that is, are not in space, they are themselves space. The spin networks which describe the quantum structure of the gravitational field are not immersed in space; they do not inhabit a space. The location of single quanta of space is not defined with regard to something else but only by the links and the relation these express.

π is the Greek pi which we studied at school: the constant which gives the relation between the circumference and the diameter of any circle, and which appears everywhere in physics, I don’t know why.

8πL2p is simply a ‘small’ area: the area of a minuscule square with a side which is about a millionth of a billionth of a billionth of a billionth of a centimetre (10-66 cm²).

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. Just as the idea of the space continuum containing things disappears, so, too, does the idea of a flowing continuum ‘time’ during the course of which phenomena happen.

the quanta of gravity do not evolve in time. Time just counts their interactions. As evidenced with the Wheeler–De Witt equation, the fundamental equations no longer contain the time variable. Time emerges, like space, from the quantum gravitational field.

The moment we take quantum mechanics into account, we recognize that time, too, must have those aspects of probabilistic indeterminacy, granularity and relationality which are common to all of reality. It becomes a ‘time’ markedly different from all that we have hitherto meant by the word.

The closer you get to the Earth, where gravityfn39 is more intense, the slower time passes.

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. But even this notion of a localized time no longer works when we take the quantum nature of the gravitational field into account. Quantum events are no longer ordered by the passage of time at the Planck scale. Time, in a sense, ceases to exist.

First, the absence of the variable time from the fundamental equations does not imply that everything is immobile and that change does not happen. On the contrary, it means that change is ubiquitous. Only: elementary processes cannot be ordered along a common succession of instants. At the extremely small scale of the quanta of space, the dance of nature does not develop to the rhythm kept by the baton of a single orchestral conductor: every process dances independently with its neighbours, following its own rhythm. The passing of time is intrinsic to the world, it is born of the world itself, out of the relations between quantum events which are the world and which themselves generate their own time.

It’s a fine story but, on reflection, it leaves us perplexed – and this perplexity goes to the heart of the problem of time. How could Galileo know that his own individual pulse-beats all lasted for the same amount of time?fn41 Not many years after Galileo, doctors began to measure their patients’ pulses by using a watch – which is nothing, after all, but a pendulum. So we use the beats to assure ourselves that the pendulum is regular, and then the pendulum to ascertain the regularity of the pulse-beats. Is this not somewhat circular? What does it mean? It means that we, in reality, never measure time itself; we always measure the physical variables A, B, C … (oscillations, beats, and many other things) and compare one variable with another, that is to say, we measure the functions A(B), B(C), C(A), and so on. We can count how many beats for each oscillation; how many oscillations for every tick of my stopwatch; how many ticks of my stopwatch between intervals of the clock on the bell-tower …

Having clarified this, we can return to quantum gravity and the meaning of the statement that ‘time does not exist’. It simply means that the Newtonian schema no longer works when we are dealing with small things. It was a good one, but only for large things.

What we must do is simply to enumerate the variables A, B, C … which we actually observe, and write equations expressing relations between these variables, and nothing else: that is, equations for the relations A(B), B(C), C(A) … which we observe, and not for the functions A(t), B(t), C(t) … which we do not observe.

We must not, in other words, describe only the two balls, but also all that is around them: the table and any other material objects – and the space in which they are immersed during the time that elapses between the start of the shot and the end of the process. Space and time are the gravitational field, Einstein’s ‘mollusc’: we are also including the gravitational field, that is to say, a piece of the mollusc, in the process. Everything is immersed in Einstein’s great mollusc: here, imagine that you are slicing a small, finite portion of it, like a piece of sushi, which encompasses the collision and what surrounds it.

The key to understanding how quantum gravity works lies in considering not solely the physical process given by the two balls but rather the entire process defined by the whole box with all that it entails, including the gravitational field.

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.

Fields that live on themselves, without the need of a spacetime to serve as a substratum, as a support, and which are capable by themselves of generating spacetime, are called ‘covariant quantum fields’. The substance of which the world is made has been radically simplified in recent years. The world, particles, light, energy, space and time – all of...

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.

Interesting

Lemaître was convinced that it was foolish to mix science and religion in this way: the Bible knows nothing about physics, and physics knows nothing about God.2 Pius XII allowed himself to be persuaded, and the Catholic church never again made public allusion to the subject.

Quantum mechanics prevents a real electron from falling into a nucleus. A quantum repulsion pushes away the electron when it gets too close to the centre. Thus, thanks to quantum mechanics, matter is stable. Without it, electrons would fall into nuclei, there would be no atoms and we would not exist.

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).

Interesting

The word ‘universe’ becomes ambiguous. If, by ‘universe’, we mean ‘all that there is’, then, by definition, there cannot be a second universe. But the word ‘universe’ has assumed another meaning in cosmology: it refers to the spacetime continuum that we see directly around us, filled with galaxies the geometry and history of which we observe. There is no reason to be certain that, in this sense, this universe is the only one in existence.

Which new data were available to Copernicus? None. He had the same data as Ptolemy. Which new data did Newton have? Almost none. His real ingredients were Kepler’s laws and Galileo’s results. What new data did Einstein have to discover general relativity? None. His ingredients were special relativity and Newton’s theory. It simply isn’t true that physics advances only when it is afforded new data.