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

by Carlo Rovelli

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.”5 Atoms are indivisible; they are the elementary grains of reality, which cannot be further subdivided, and everything is made of them. They move freely in space, colliding with one another; they hook on to and push and pull one another. Similar atoms attract one another and join.

There is no finality, no purpose, in this endless dance of atoms. We, just like the rest of the natural world, are one of the many products of this infinite dance—the product, that is, of an accidental combination. Nature continues to experiment with forms and structures; and we, like the animals, are the products of a selection that is random and accidental, over the course of eons of time.

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 favor 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 that 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.

Imagine, says Democritus, that matter is infinitely divisible, that is to say, that it may be broken down an infinite number of times. Imagine then that you break up a piece of matter ad infinitum. What would be left? 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.

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.

The universe is granular, not continuous.

Say I am on Mars and you are here; I ask you a question and you reply as soon as you’ve heard what I said; your reply reaches me a quarter of an hour after I had posed the question. This quarter of an hour is time that is neither past nor future to the moment you’ve replied to me. The key fact that Einstein understood is that this quarter of an hour is inevitable: there is no way of reducing it. It is woven into the texture of the events of space and of time: we cannot abbreviate it, any more than we can send a letter to the past.

In technical terms, we say that Einstein has understood that “absolute simultaneity” does not exist: there is no collection of events in the universe that exist “now.” The collection of all the events in the universe cannot be described as a succession of “nows,” 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 a duration.

spacetime curves more where there is matter. That is it.

Ever since we discovered that 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.

The two pillars of twentieth-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, based on combining previous theories, it is a simple and coherent vision of gravity, space, and time. Quantum mechanics, or quantum theory, on the other hand, emerges from experiments in the course of a long gestation over a quarter of a century, to which many have contributed; achieves unequaled experimental success; and leads to applications that have transformed our everyday lives (the computer on which I write, for instance); but more than a century after its birth, it remains shrouded in obscurity and incomprehensibility.

three aspects of reality it has unveiled: granularity, indeterminism, and relationality.

The idea that energy could be made up of finite packets is at odds with everything that was known at the time: energy was considered something that could vary in a continuous manner, and there was no reason to treat it as if it were made up of grains.

Today we call these packets of energy “photons,” from the Greek word for light: ϕώς. Photons are the grains of light, its quanta.

To comprehend how light may be simultaneously an electromagnetic wave and a swarm of photons will require the entire construction of quantum mechanics.

there exists a fundamental granularity in all things, including light.

a fundamental description of the movement of particles, in which they are not described by their position at every moment, but only by their position at a particular instant—the instants in which they interact with something else. This is a 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.

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 space,* 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 only acquire reality when it collides—interacts—with another object. It is not just its position that 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.

We do not know with certainty where the electron will appear, but we can compute the probability that it will appear here or there. This is a radical change from Newton’s theory, where it is possible, in principle, to predict the future with certainty. Quantum mechanics brings probability to the heart of the evolution of things. This indeterminacy is the third cornerstone of quantum mechanics:

Dirac discovers an ulterior, profound simplification of our description of nature: the convergence between the notion of particles used by Newton, and the notion of fields introduced by Faraday. The cloud of probability that accompanies electrons between one interaction and another does resemble a field. Faraday’s 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 small scale, swarms of photons. When they interact with something else, as in the photoelectric effect, they manifest themselves as particles: on our eyes, 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 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.

There are approximately fifteen fields, whose quanta are the elementary particles (electrons, quarks, muons, neutrinos, Higgs, and little else), plus a few fields similar to the electromagnetic one, which describe electromagnetic force and the other forces operating at a nuclear scale, whose quanta are similar to the photons.

The world is not made up of fields and particles but of a single type of entity: the quantum field.

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

The first is the existence of a fundamental granularity in nature. The granularity of matter and light is at the heart of quantum theory. It isn’t the same granularity intuited by Democritus, however.

quantum mechanics tells us that between five and six centimeters 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.

Quantum mechanics introduces an elementary indeterminacy to the heart of the world. 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 was constantly vibrating.

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

It is as if the electron, in order to go from A to B, passed “through all possible trajectories,” or, in other words, unfurled into a cloud in order to then converge mysteriously on point B, where it collides again with something else (

The third discovery about the world articulated by quantum mechanics is the most profound and difficult—and one that was not anticipated by the atomism of antiquity. The theory does not describe things as they “are”: it describes how things “occur,” and how they “interact with each other.”

What is quantum theory, a century after its birth? An extraordinary dive deep into the nature of reality? A blunder that works, by chance? Part of an incomplete puzzle? Or a clue to something profound regarding the structure of the world, which we have yet to fully decipher?

In my opinion, 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 seem so strange to us.

they appear to contradict each other. The gravitational field is described without taking quantum mechanics into account, without accounting for the fact that fields are quantum fields—and quantum mechanics is formulated without taking into account the fact that spacetime curves and is described by Einstein’s equations.

the morning, the world is a curved spacetime where everything is continuous; in the afternoon, the world is a flat one where discrete quanta of energy leap and interact.

The paradox resides in the fact that both theories work remarkably well.

In most situations, we can neglect quantum mechanics or general relativity (or both). The moon is too large to be sensitive to minute quantum granularity; so we can forget the quanta when describing its movements. On the other hand, an atom is too light to curve space to a significant degree, and when we describe it we can forget the curvature of space. But there are situations where both curvature of space and quantum granularity matter, and for these we do not yet have an established physical theory that works. An example is the interior of black holes. Another is what happened to the universe during the Big Bang.

In more general terms, we do not know how time and space behave at very small scale.

Einstein understood that space and time are manifestations of a physical field: the gravitational field. Bohr, Heisenberg, and Dirac understood that physical fields have 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.”

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.

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 centimeter (10-33 centimeters). So that is to say . . . small.

It is at this extremely minute scale that quantum gravity manifests itself.

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.

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.

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.

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.