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

by Carlo Rovelli

Does it really make sense to talk of a billionth of a billionth of a billionth of a millimeter, and then to think of dividing it again, a further innumerable number of times? The calculation of the quantum spectra of geometric quantities indicates that the answer is negative: arbitrarily small chunks of space do not exist.

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 itself.

If I step from grain to grain along the links, until completing a circuit returning to the grain from which I started, I will have made a “loop.” These are the original loops of the “loop” theory.

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.

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 neighboring relations.

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.

In the same sense, time no longer exists in the fundamental theory: the quanta of gravity do not evolve in time. Time just counts their interactions.

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.

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.

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.

The passing of time is intrinsic to the world; it is born of the world itself, out of the relations between quantum events that are the world, and that themselves generate their own time.

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.

In other words, the existence of the variable time is a useful assumption, not the result of an observation.

The idea of a time t that flows by itself, and in relation to which all things evolve, is no longer a useful one. The world is not described by equations of evolution in time t. What we must do is simply enumerate the variables A, B, C . . . that 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) . . . that we observe, and not for the functions A(t), B(t), C(t) . . . , which we do not observe.

What we obtain from this is a spacetime box (as in figure 7.1): a finite portion of spacetime a few cubic meters in dimension by a few seconds of time. This process does not occur “in” time. The box is not in spacetime; it includes spacetime. It isn’t a process in time, in the same way in which grains of space are not in space.

Space is a spin network whose nodes represent its elementary grains, and whose links describe their proximity relations. Spacetime is generated by processes in which these spin networks transform into one another, and these processes are described by sums over spinfoams. A spinfoam represents a history of a spin network, hence a granular spacetime where the nodes of the graph combine and separate.

This microscopic swarming of quanta, which generates space and time, underlies the calm appearance of the macroscopic reality surrounding us. Every cubic centimeter of space, and every second that passes, is the result of this dancing foam of extremely small quanta.

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 ἂπειρον, the apeiron, the primal substance of which everything is formed, hypothesized by the man who could perhaps be called the first scientist and the first philosopher, Anaximander.

The conceptual price paid is the relinquishing of the idea of space, and of time, as general structures within which to frame the world. Space and time are approximations that emerge at a large scale.

The main reward of this kind of physics is that, as we shall see in the next chapter, infinity disappears. The infinitely small no longer exists. The infinities that plague conventional quantum field theory, predicated on the notion of a continuous space, now vanish, because they were generated precisely by the assumption, physically incorrect, of the continuity of space. The singularities that render Einstein’s equations absurd when the gravitational field becomes too strong also disappear: they are only the result of neglecting the quantization of the field. Little by little, the pieces of the puzzle find their place. In the final sections of this book, I describe some of the physical consequences of this theory.

fourteen billion years ago the universe was a compressed 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, fourteen 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.

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. This is what seems to emerge from the equations of loop quantum gravity, when they are applied to the expansion of the universe.

Our universe could thus be the result of the collapse of a previous contracting universe passing across a quantum phase, where space and time are dissolved into probabilities.

The most studied alternative to the research direction recounted in this book is string theory.

supersymmetric particles. String theory needs these particles to be consistent: that is why the string theorists eagerly expected them to be found. Loop quantum gravity, on the other hand, is well defined, even without supersymmetric particles.

The supersymmetric particles were not observed, to the great disappointment of many. The fanfare that greeted the discovery of the Higgs boson in 2013 also masked this disappointment.

There have been three major experimental results in fundamental physics in recent years. The first is the revelation of the Higgs boson at CERN in Geneva (figure 9.1). The second is the Planck satellite (figure 9.2) measurements, the data of which were also made public in 2013, confirming the standard cosmological model. The third is the first detection of gravitational waves announced in the first months of 2016. These are the three signals that nature has recently given us.

The discovery of the Higgs boson is a rock-hard confirmation of the validity of the ideas behind the Standard Model of elementary particles, based on quantum mechanics.

The Planck measurements are a solid confirmation of the standard cosmological model, based on general relativity with the cosmological constant.

detection of gravitational waves is a spectacular confirmation of general relativity, a theo...

What enters a black hole does not come out again, at least if we neglect quantum theory. The surface of a black hole is like the present: it can be crossed in only one direction. From the future, there is no return. For a black hole, the past is the outside, the future is the inside.

Thus, traveling to the past is difficult, but traveling to the future is easy: we need only to get close to a black hole with a spaceship, keep within its vicinity for a while, and then move away.

there are two mysteries of black holes that do require quantum mechanics to be unraveled, and for each of these, loop theory offers a possible solution.

The first application of quantum gravity to black holes concerns a curious fact discovered by Stephen Hawking. Early in the 1970s, he theoretically deduced that black holes are “hot.” They behave like hot bodies: they emit heat. In doing so, they lose energy and hence mass (since energy and mass are the same thing), becoming progressively smaller. They “evaporate.” This “evaporation of black holes” is the most important discovery made by Hawking.

What are the elementary “atoms” that vibrate, making a black hole hot? Hawking left this problem unanswered. Loop theory provides a possible answer. The elementary “atoms” of a black hole that vibrate, responsible for its temperature, are the individual quanta of space on its surface.

the heat is the result of the microscopic “vibrations” of the individual atoms of space. These vibrate because in the world of quantum mechanics, everything vibrates; nothing stays still.

There is another way of understanding the origin of the heat of black holes. The quantum fluctuations generate a correlation between the interior and the exterior of a hole.

The second application of loop quantum gravity to black hole physics is more spectacular. Once collapsed, a star vanishes from external view: it is inside the black hole. But inside the hole, what happens to it? What would you see if you let yourself fall into the hole?

General relativity predicts that everything is squashed at the center into an infinitely small point of infinite density. But this is, once again, if we ignore quantum theory.

If we take quantum gravity into account, this prediction is no longer correct—there is quantum repulsion, the same repulsion that makes the universe bounce at the Big Bang. What we expect is that, on getting closer to the center, the falling matter is slowed down by this quantum pressure, up to a very high but finite density.

The bounce of a collapsing star can be very fast, if watched from down there. But—remember—time passes much slower there than outside. Seen from the outside, the process of the bounce can take billions of years.

Thus, quantum gravity might imply that black holes are not eternally stable objects, as classical general relativity predicted, after all. They are ultimately unstable.

Quantum gravity is the discovery that no infinitely small point exists.

The universe cannot be smaller than the Planck scale, because nothing exists that is smaller than the Planck scale.

The pathological situations predicted by general relativity, where the theory gives infinite quantities, are called “singularities.” Quantum gravity places a limit to infinity and “cures” t...

Putting a limit to infinity is a recurrent theme in modern physics. Special relativity may be summarized as the discovery that there exists a maximum velocity for all physical systems. Quantum mechanics can be summarized as the discovery that there exists a maximum of information for each physical system. The minimum length is the Planck length LP, the maximum velocity is the speed of light c, and the total information is determined by the Planck constant h.

We can fix the value 1 for the velocity c and write, for example, v = ½, for a body that is moving at half the speed of light. In the same way, we can posit LP = 1 by definition and measure length in multiples of Planck’s length. And we can posit h = 1 and measure actions in multiples of Planck’s constant. In this way, we have a natural system of fundamental unities from which the others follow. The unity of time is the time that light takes to cover the Planck length, and so on. The “natural unities” are commonly used in research on quantum gravity.