The Order of Time

by Carlo Rovelli

Reality is often very different from what it seems. The Earth appears to be flat but is in fact spherical. The sun seems to revolve in the sky when it is really we who are spinning. Neither is the structure of time what it seems to be: it is different from this uniform, universal flowing. I discovered this, to my utter astonishment, in the physics books I read as a university student: time works quite differently from the way it seems to.

The nature of time is perhaps the greatest remaining mystery. Curious threads connect it to those other great open mysteries: the nature of mind, the origin of the universe, the fate of black holes, the very functioning of life on Earth.

This is what it means to think about time. What exactly is this flowing? Where is it nestled in the grammar of the world? What distinguishes the past, its having been, from the future, its not having been yet, in the folds of the mechanism of the world? Why, to us, is the past so different from the future? Nineteenth- and twentieth-century physics engaged with these questions and ran into something unexpected and disconcerting—much more so than the relatively marginal fact that time passes at different speeds in different places. The difference between past and future, between cause and effect, between memory and hope, between regret and intention . . . in the elementary laws that describe the mechanisms of the world, there is no such difference.

Perhaps poetry is another of science’s deepest roots: the capacity to see beyond the visible.

If nothing else around it changes, heat cannot pass from a cold body to a hot one. The crucial point here is the difference from what happens with falling bodies: a ball may fall, but it can also come back up, by rebounding, for instance. Heat cannot. This is the only basic law of physics that distinguishes the past from the future.

In the elementary equations of the world,13 the arrow of time appears only where there is heat.* The link between time and heat is therefore fundamental: every time a difference is manifested between the past and the future, heat is involved. In every sequence of events that becomes absurd if projected backward, there is something that is heating up.

If I watch a film that shows a ball rolling, I cannot tell if the film is being projected correctly or in reverse. But if the ball stops, I know that it is being run properly; run backward, it would show an implausible event: a ball starting to move by itself. The ball’s slowing down and coming to rest are due to friction, and friction produces heat. Only where there is heat is there a distinction between past and future. Thoughts, for instance, unfold from the past to the future, not vice versa—and, in fact, thinking produces heat in our heads. . . .

Clausius introduces a quantity that measures this irreversible progress of heat in only one direction and, since he was a cultivated German, he gives it a name taken from ancient Greek—entropy: I prefer to take the names of important scientific quantities from ancient languages, so that they may be the same in all the living languages. I therefore propose to call entropy the quantity (S) of a body, from the Greek word for transformation: ἡ τροπὴ.14 The page of the article by Clausius in which he introduces for the first time the concept and the word “entropy.” The equation provides the m...

It is the only equation of fundamental physics that knows any difference between past and future. The only one that speaks of the flowing of time. Behind this unusual equation, an entire world lies hidden.

If I observe the microscopic state of things, then the difference between past and future vanishes. The future of the world, for instance, is determined by its present state—though neither more nor less than is the past.19 We often say that causes precede effects and yet, in the elementary grammar of things, there is no distinction between “cause” and “effect.”

This is the disconcerting conclusion that emerges from Boltzmann’s work: the difference between the past and the future refers only to our own blurred vision of the world. It’s a conclusion that leaves us flabbergasted: Is it really possible that a perception so vivid, basic, existential—my perception of the passage of time—depends on the fact that I cannot apprehend the world in all of its minute detail? On a kind of distortion that’s produced by myopia? Is it true that, if I could see exactly and take into consideration the actual dance of millions of molecules, then the future would be “just like” the past? Is it possible that I have as much knowledge of the past—or ignorance of it—as I do of the future? Even allowing for the fact that our perceptions of the world are frequently wrong, can the world really be so profoundly different from our perception of it as this?

Physicists call “fields” the substances that, to the best of our knowledge, constitute the weave of the physical reality of the world. Sometimes they may be given exotic names: the fields “of Dirac” are the fabric of which tables and stars are made. The “electromagnetic” field is the weave of which light is made, as well as the origin of the forces that make electric motors turn and the needle of a compass point north. But—here is the key point—there is also a “gravitational” field: it is the origin of the force of gravity, but it is also the texture that forms Newton’s space and time, the fabric on which the rest of the world is drawn. Clocks are mechanisms that measure its extension. The meters used for measuring length are portions of matter that measure another aspect of its extension. Spacetime is the gravitational field—and vice versa. It is something that exists by itself, as Newton intuited, even without matter. But it is not an entity that is different from the other things in the world—as Newton believed—it is a field like the others. More than a drawing on a canvas, the world is like a superimposition of canvases, of strata, where the gravitational field is only one among others. Just like the others, it is neither absolute nor uniform, nor is it fixed: it flexes, stretches, and jostles with the others, pushing and pulling against them. Equations describe the reciprocal influences that all the fields have on each other, and spacetime is one of these fields.*

Time thus becomes part of a complicated geometry woven together with the geometry of space.

All this is perfectly coherent, and Einstein’s equations describing the distortions of the gravitational field and its effects on clocks and meters have been repeatedly verified for more than a century.

The “quantization” of time implies that almost all values of time t do not exist. If we could measure the duration of an interval with the most precise clock imaginable, we should find that the time measured takes only certain discrete, special values. It is not possible to think of duration as continuous. We must think of it as discontinuous: not as something that flows uniformly but as something that in a certain sense jumps, kangaroo-like, from one value to another. In other words, a minimum interval of time exists. Below this, the notion of time does not exist—even in its most basic meaning.

Granularity is ubiquitous in nature: light is made of photons, the particles of light. The energy of electrons in atoms can acquire only certain values and not others. The purest air is granular, and so, too, is the densest matter. Once it is understood that Newton’s space and time are physical entities like all others, it is natural to suppose that they are also granular.

The idea that time could be granular, that there could be minimal intervals of time, is not new. It was defended in the seventh century by Isidore of Seville in his Etymologiae, and in the following century by the Venerable Bede in a work suggestively entitled De Divisionibus Temporum (“On the Divisions of Time”). In the thirteenth century, the great philosopher Maimonides writes: “Time is composed of atoms, that is to say of many parts that cannot be further subdivided, on account of their short duration.”53

The spatial sister of Planck time is Planck length: the minimum limit below which the notion of length becomes meaningless. Planck length is around 10-33 centimeters: a millionth of a billionth of a billionth of a billionth of a millimeter.

Even the distinction between present, past, and future thus becomes fluctuating, indeterminate.

“Fluctuation” does not mean that what happens is never determined. It means that it is determined only at certain moments, and in an unpredictable way. Indeterminacy is resolved when a quantity interacts with something else.* In the interaction, an electron materializes at a certain point. For example, it collides with a screen, is captured by a particle detector, or collides with a photon—thus acquiring a concrete position. But there is a strange aspect to this materialization of the electron: the electron is concrete only in relation to the other physical objects it is interacting with.56 With regard to all the others, the effect of the interaction is only to spread the contagion of indeterminacy. Concreteness occurs only in relation to a physical system: this, I believe, is the most radical discovery made by quantum mechanics.*

Time has loosened into a network of relations that no longer holds together as a coherent canvas. The picture of spacetimes (in the plural) fluctuating, superimposed one above the other, materializing at certain times with respect to particular objects, provides us with a very vague vision. But it is the best that we have for the fine granularity of the world. We are peering into the world of quantum gravity.

Let me reprise the long dive into the depths made in the first part of this book. There is no single time: there is a different duration for every trajectory; and time passes at different rhythms according to place and according to speed. It is not directional: the difference between past and future does not exist in the elementary equations of the world; its orientation is merely a contingent aspect that appears when we look at things and neglect the details. In this blurred view, the past of the universe was in a curiously “particular” state. The notion of the “present” does not work: in the vast universe there is nothing that we can reasonably call “present.” The substratum that determines the duration of time is not an independent entity, different from the others that make up the world; it is an aspect of a dynamic field. It jumps, fluctuates, materializes only by interacting, and is not to be found beneath a minimum scale. . . .

Time, as Aristotle suggested, is the measure of change; different variables can be chosen to measure that change, and none of these has all the characteristics of time as we experience it. But this does not alter the fact that the world is in a ceaseless process of change. The entire evolution of science would suggest that the best grammar for thinking about the world is that of change, not of permanence. Not of being, but of becoming.

We can think of the world as made up of things. Of substances. Of entities. Of something that is. Or we can think of it as made up of events. Of happenings. Of processes. Of something that occurs. Something that does not last, and that undergoes continual transformation, that is not permanent in time. The destruction of the notion of time in fundamental physics is the crumbling of the first of these two perspectives, not of the second. It is the realization of the ubiquity of impermanence, not of stasis in a motionless time. Thinking of the world as a collection of events, of processes, is the way that allows us to better grasp, comprehend, and describe it. It is the only way that is compatible with relativity. The world is not a collection of things, it is a collection of events.

The difference between things and events is that things persist in time; events have a limited duration. A stone is a prototypical “thing”: we can ask ourselves where it will be tomorrow. Conversely, a kiss is an “event.” It makes no sense to ask where the kiss will be tomorrow. The world is made up of networks of kisses, not of stones. The basic units in terms of which we comprehend the world are not located in some specific point in space. They ar...

What works instead is thinking about the world as a network of events. Simple events, and more complex events that can be disassembled into combinations of simpler ones. A few examples: A war is not a thing, it’s a sequence of events. A storm is not a thing, it’s a collection of occurrences. A cloud above a mountain is not a thing, it is the condensation of humidity in the air that the wind blows over the mountain. A wave is not a thing, it is a movement of water, and the water that forms it is always different. A family is not a thing, it is a collection of relations, occurrences, feelings. And a human being? Of course it’s not a thing; like the cloud above the mountain, it’s a complex process, where food, information, light, words, and so on enter and exit. . . . A knot of knots in a network of social relations, in a network of chemical processes, in a network of emotions exchanged with its own kind. For a long time, we have tried to understand the world in terms of some primary substance. Perhaps physics, more than any other discipline, has pursued this primary substance. But the more we have studied it, the less the world seems comprehensible in terms of something that is. It seems to be a lot more intelligible in terms of relations between events.

The words of Anaximander quoted in the first chapter of this book invited us to think of the world “according to the order of time.” If we do not assume a priori that we know what the order of time is—if we do not, that is, presuppose that it is the linear and universal order that we are accustomed to—Anaximander’s exhortation remains valid: we understand the world by studying change, not by studying things.

The physics and astronomy that will work, from Ptolemy to Galileo, from Newton to Schrödinger, will be mathematical descriptions of precisely how things change, not of how they are. They will be about events, not things.

We therefore describe the world as it happens, not as it is. Newton’s mechanics, Maxwell’s equations, quantum mechanics, and so on, tell us how events happen, not how things are. We understand biology by studying how living beings evolve and live. We understand psychology (a little, not much) by studying how we interact with each other, how we think. . . . We understand the world in its becoming, not in its being. “Things” in themselves are only events that for a while are monotonous.58

The absence of time does not mean, therefore, that everything is frozen and unmoving. It means that the incessant happening that wearies the world is not ordered along a time line, is not measured by a gigantic ticktocking. It does not even form a four-dimensional geometry. It is a boundless and disorderly network of quantum events.

In 1967, an equation accounting for quantum gravity was written for the first time without any time variable. This equation was discovered by two American physicists—Bryce DeWitt and John Wheeler—and today it’s known as the Wheeler–DeWitt equation.69 At first no one could understand the significance of an equation without a time variable, perhaps not even Wheeler and DeWitt themselves. (Wheeler: “Explain time? Not without explaining existence! Explain existence? Not without explaining time! To uncover the deep and hidden connection between time and existence . . . is a task for the future.”70) The issue was discussed at great length; there were conferences, debates; rivers of ink flowed.71 I think that the dust has now settled and things have become much clearer. There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists. The theory does not describe how things evolve in time. The theory describes how things change one in respect to the others,72 how things happen in the world in relation to each other. That’s all there is to it.

Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions. In a theory of this kind, time and space are no longer containers or general forms of the world. They are approximations of a quantum dynamic that in itself knows neither space nor time. There are only events and relations. It is the world without time of elementary physics.

And it is this thermal and quantum time, I believe,88 that is the variable that we call “time” in our real universe, where a time variable does not exist at the fundamental level. The intrinsic quantum indeterminacy of things produces a blurring, like Boltzmann’s blurring, which ensures—contrary to what classic physics seemed to indicate—that the unpredictability of the world is maintained even if it were possible to measure everything that is measurable. Both the sources of blurring—quantum indeterminacy, and the fact that physical systems are composed of zillions of molecules—are at the heart of time. Temporality is profoundly linked to blurring. The blurring is due to the fact that we are ignorant of the microscopic details of the world. The time of physics is, ultimately, the expression of our ignorance of the world. Time is ignorance.

The entire difference between past and future may be attributed solely to the fact that the entropy of the world was low in the past.

Entropy is not an arbitrary quantity, nor a subjective one. It is a relative one, like speed.

In other words, if in the universe there is something like this—and it seems natural to me that there could be—then we belong to that something. Here, “we” refers to that collection of physical variables to which we commonly have access and by means of which we describe the universe. Perhaps, therefore, the flow of time is not a characteristic of the universe: like the rotation of the heavens, it is due to the particular perspective that we have from our corner of it. But why should we belong to one of these special systems? For the same reason that apples grow in northern Europe, where people drink cider, and grapes grow in the south, where people drink wine; or that I was born where people happen to speak my native language; or that the sun which warms us is at the right distance from us—not too close and not too far away. In all these cases, the “strange” coincidence arises from confusing the causal relations: it isn’t that apples grow where people drink cider, it is that people drink cider where apples grow. Put this way, there is no longer anything strange about it.

In order to understand our experience of space, it is not enough to think of Newtonian space. We must remember that we see this space from inside it, that we are localized. In order to understand time, it is not enough to think of it from outside: it is necessary to understand that we, in every moment of our experience, are situated within time.

We observe the universe from within it, interacting with a minuscule portion of the innumerable variables of the cosmos. What we see is a blurred image. This blurring suggests that the dynamic of the universe with which we interact is governed by entropy, which measures the amount of blurring. It measures something that relates to us more than to the cosmos.

Energy (be it mechanical, chemical, electrical, or potential) transforms itself into thermal energy, that is to say, into heat: it goes into cold things, and there is no free way of getting it back from there to reuse it to make a plant grow, or to power a motor. In this process, the energy remains the same but the entropy increases, and it is this which cannot be turned back. The second law of thermodynamics demands it.

Over the course of this irregular trajectory, large or small portions of the universe remain isolated in relatively stable situations for periods that can be very prolonged.

Even the most banal phenomena are governed by the second law of thermodynamics. A stone falls to the ground. Why? One often reads that it’s because the stone places itself “in a state of lower energy” that it ends up lower down. But why does the stone put itself into a state of lower energy? Why should it lose energy if energy is conserved? The answer is that when the stone hits the Earth, it warms it: its mechanical energy is transformed into heat. And there is no way back from there. If the second law of thermodynamics did not exist, if heat did not exist, if there existed no microscopic swarming, the stone would rebound perpetually; it would never land and be still. It is entropy, not energy, that keeps stones on the ground and the world turning.

What causes events to happen in the world, what writes its history, is the irresistible mixing of all things, going from the few ordered configurations to the countless disordered ones. The entire universe is like a mountain that collapses in slow motion. Like a structure that very gradually crumbles. From the most minute events to the more complex ones, it is this dance of ever-increasing entropy, nourished by the initial low entropy of the universe, that is the real dance of Shiva, the destroyer.

Traces of the past exist, and not traces of the future, only because entropy was low in the past. There can be no other reason, since the only source of the difference between past and future is the low entropy of the past. In order to leave a trace, it is necessary for something to become arrested, to stop moving, and this can happen only in an irreversible process—that is to say, by degrading energy into heat. In this way, computers heat up, the brain heats up, the meteors that fall into the moon heat it; even the goose quill of a medieval scribe in a Benedictine abbey heats a little the page on which he writes. In a world without heat, everything would rebound elastically, leaving no trace.100

It is the presence of abundant traces of the past that produces the familiar sensation that the past is determined. The absence of any analogous traces of the future produces the sensation that the future is open. The existence of traces serves to make it possible for our brain to dispose of extensive maps of past events. There is nothing analogous to this for future ones. This fact is at the origin of our sensation of being able to act freely in the world: choosing between different futures, even though we are unable to act upon the past.

It is memory that solders together the processes, scattered across time, of which we are made. In this sense we exist in time. It is for this reason that I am the same person today as I was yesterday. To understand ourselves means to reflect on time. But to understand time we need to reflect on ourselves. A recent book by Dean Buonomano devoted to research on the functioning of the brain is entitled Your Brain Is a Time Machine.111 It discusses the many ways in which the brain interacts with the passage of time and establishes bridges between past, present, and future. To a large extent, the brain is a mechanism for collecting memories of the past in order to use them continually to predict the future. This happens across a wide spectrum of time scales, from the very short to the very long. If someone throws something at us to catch, our hand moves skillfully to the place where the object will be in a few instants: the brain, using past impressions, has very rapidly calculated the future position of the object that is flying toward us. Further along the scale, we plant seed so that corn will grow. Or invest in scientific research so that tomorrow it might result in knowledge and new technology. The possibility of predicting something in the future obviously improves our chances of survival and, consequently, evolution has selected the neural structures that allow it. We are the result of this selection. This being between past and future events is central to our mental str...

There are elementary structures in the wiring of our nervous system that immediately register movement: an object that appears in one place and then immediately afterward in another does not generate two distinct signals that travel separately toward the brain, but a single signal correlated with the fact that we are looking at something that is moving. In other words, what we perceive is not the present, which in any case makes no sense for a system that functions on a scale of finite time, but rather something that happens and extends in time. It is in our brains that an extension in time becomes condensed into a perception of duration.

When we listen to a hymn, the meaning of a sound is given by the ones that come before and after it. Music can occur only in time, but if we are always in the present moment, how is it possible to hear it? It is possible, Augustine observes, because our consciousness is based on memory and on anticipation. A hymn, a song, is in some way present in our minds in a unified form, held together by something—by that which we take time to be. And hence this is what time is: it is entirely in the present, in our minds, as memory and as anticipation.

This is the flow of time familiar from our experience: it is inside there that it nestles, inside of us, in the utterly crucial presence of traces of the past in our neurons.

We are stories, contained within the twenty complicated centimeters behind our eyes, lines drawn by traces left by the (re)mingling together of things in the world, and oriented toward predicting events in the future, toward the direction of increasing entropy, in a rather particular corner of this immense, chaotic universe.

The Buddha summed this up in a few maxims that millions of human beings have adopted as the foundations of their lives: birth is suffering, decline is suffering, illness is suffering, death is suffering, union with that which we hate is suffering, separation from that which we love is suffering, failure to obtain what we desire is suffering.124 It’s suffering because we must lose what we have and are attached to. Because everything that begins must end. What causes us to suffer is not in the past or the future: it is here, now, in our memory, in our expectations. We long for timelessness, we endure the passing of time: we suffer time. Time is suffering.