The Order of Time

by Carlo Rovelli

One after another, the characteristic features of time have proved to be approximations, mistakes determined by our perspective, just like the flatness of the Earth or the revolving of the sun.

The physics on which I work—quantum gravity—is an attempt to understand and lend coherent meaning to this extreme and beautiful landscape. To the world without time.

If things fall, it is due to this slowing down of time. Where time passes uniformly, in interplanetary space, things do not fall. They float, without falling. Here on the surface of our planet, on the other hand, the movement of things inclines naturally toward where time passes more slowly, as when we run down the beach into the sea and the resistance of the water on our legs makes us fall headfirst into the waves. Things fall downward because, down there, time is slowed by the Earth.5

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.

Thermal agitation is like a continual shuffling of a pack of cards: if the cards are in order, the shuffling disorders them. In this way, heat passes from hot to cold, and not vice versa: by shuffling, by the natural disordering of everything. The growth of entropy is nothing other than the ubiquitous and familiar natural increase of disorder. This is what Boltzmann understood. The difference between past and future does not lie in the elementary laws of motion; it does not reside in the deep grammar of nature. It is the natural disordering that leads to gradually less particular, less special situations. It was a brilliant intuition, and a correct one. But does it clarify the difference between past and future? It does not. It just shifts the question. The question now becomes: Why, in one of the two directions of time—the one we call past—were things more ordered? Why was the great pack of cards of the universe in order in the past? Why, in the past, was entropy lower?

This is what Boltzmann understood. The difference between past and future does not lie in the elementary laws of motion; it does not reside in the deep grammar of nature. It is the natural disordering that leads to gradually less particular, less special situations.

It follows that the notion of certain configurations being more particular than others (twenty-six red cards followed by twenty-six black, for example) makes sense only if I limit myself to noticing only certain aspects of the cards (in this case, the colors). If I distinguish between all the cards, the configurations are all equivalent: none of them is more or less particular than others.18 The notion of “particularity” is born only at the moment we begin to see the universe in a blurred and approximate way. Boltzmann has shown that entropy exists because we describe the world in a blurred fashion. He has demonstrated that entropy is precisely the quantity that counts how many are the different configurations that our blurred vision does not distinguish between. Heat, entropy, and the lower entropy of the past are notions that belong to an approximate, statistical description of nature.

The difference between past and future is deeply linked to this blurring. . . . So if I could take into account all the details of the exact, microscopic state of the world, would the characteristic aspects of the flowing of time disappear? Yes. If I observe the microscopic state of things, then the difference between past and future vanishes.

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.

Later on, I will delve into the mystery of this blurring, to see how it is tied to the strange initial improbability of the universe. For now, I will end with the mind-boggling fact that entropy, as Boltzmann fully understood, is nothing other than the number of microscopic states that our blurred vision of the world fails to distinguish.

The notion of “the present” refers to things that are close to us, not to anything that is far away. Our “present” does not extend throughout the universe. It is like a bubble around us.

Special relativity is the discovery that the temporal structure of the universe is like the one established by filiation: it defines an order between the events of the universe that is partial, not complete. The expanded present is the set of events that are neither past nor future: it exists, just as there are human beings who are neither our descendants nor our forebears.

If, my dear cultivated reader, the existence of this Newtonian concept of time which is independent of things seems to you simple and natural, it’s because you encountered it at school.

The difference between Aristotle and Newton is glaring. For Newton, between two things there may also be “empty space.” For Aristotle, it is absurd to speak of “empty” space, because space is only the spatial order of things. If there are no things—their extension, their contacts—there is no space. Newton imagines that things are situated in a “space” that continues to exist, empty, even when divested of things. For Aristotle, this “empty space” is nonsensical, because if two things do not touch it means that there is something else between them, and if there is something, then this something is a thing, and therefore a thing that is there. It cannot be that there is “nothing.” For my part, I find it curious that both these ways of thinking about space originate from our everyday experience. The difference between them exists due to a quirky accident of the world in which we live: the lightness of air, the presence of which we only barely perceive. We can say: I see a table, a chair, a pen, the ceiling—and that between myself and the table there is nothing. Or we can say that between one and another of these things there is air. Sometimes we speak of air as if it were something, sometimes as if it were nothing. Sometimes as if it were there, sometimes as if it were not there. We are used to saying “This glass is empty” in order to say that it is full of air. We can consequently think of the world around us as “almost empty,” with just a few objects here and there, or alter...

Even the distinction between present, past, and future thus becomes fluctuating, indeterminate. Just as a particle may be diffused in space, so, too, the differences between past and future may fluctuate: an event may be both before and after another one.

RELATIONS “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.* When an electron collides with an object—the screen of an old television set with a cathode ray tube, for example—the cloud of probability with which we conceived of it “collapses” and the electron materializes at a point on the screen, producing one of the luminous dots that goes into the making of a TV image. But it is only in relation to the screen that this happens. In relation to another object, the electron and screen are now together in a superposition of configurations, and it is only at the moment of further interaction with a third object that their shared cloud of probability “collapses” and materializes in a particular confi...

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.

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.

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.

When an interaction renders the position of a molecule concrete, the state of the molecule is altered. The same applies for its speed. If what materializes first is the speed and then the position, the state of the molecule changes in a different way than if the order of the two events were reversed. The order matters. If I measure the position of an electron first and then its speed, its state changes differently than if I were to measure its velocity first and then its position. This is called the “noncommutativity” of the quantum variables, because position and speed “do not commute,” that is to say, they cannot exchange order with impunity. This noncommutativity is one of the characteristic phenomena of quantum mechanics. Noncommutativity determines an order and, consequently, a germ of temporality in the determination of two physical variables. To determine a physical variable is not an isolated act; it involves interaction. The effect of such interactions depends on their order, and this order is a primitive form of the temporal order.

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.

Between ourselves and the rest of the world there are physical interactions. Obviously, not all the variables of the world interact with us, or with the segment of the world to which we belong. Only a very minute fraction of these variables does so; most of them do not react with us at all. They do not register us, and we do not register them. This is why distinct configurations of the world seem equivalent to us. The physical interaction between myself and a glass of water—two pieces of the world—is independent of the motion of the single molecules of water. In the same way, the physical interaction between myself and a distant galaxy—two pieces of the world—ignores what happens in detail out there. Therefore, our vision of the world is blurred because the physical interactions between the part of the world to which we belong and the rest are blind to many variables. This blurring is at the heart of Boltzmann’s theory.93 From this blurring, the concepts of heat and entropy are born—and these are linked to the phenomena that characterize the flow of time. The entropy of a system depends explicitly on blurring. It depends on what I do not register, because it depends on the number of indistinguishable configurations. The same microscopic configuration may be of high entropy with regard to one blurring and of low in relation to another. This does not mean that blurring is a mental construct; it depends on actual, existing physical interactions.94 Entropy is not an arbitrary ...

The entropy of A with regard to B counts the number of configurations of A that the physical interactions between A and B do not distinguish.

Let me summarize the hard ground covered in the last two chapters, in the hope that I have not already lost all my readers. At the fundamental level, the world is a collection of events not ordered in time. These events manifest relations between physical variables that are, a priori, on the same level. Each part of the world interacts with a small part of all the variables, the value of which determines “the state of the world with regard to that particular subsystem.” A small system S does not distinguish the details of the rest of the universe because it interacts only with a few among the variables of the rest of the universe. The entropy of the universe with respect to S counts the (micro)states of the universe undistinguishable by S. The universe appears in a high-entropy configuration with respect to S, because (by definition) there are more microstates in high-entropy configurations, therefore it is more likely to happen to be in one of these microstates. As explained above, there is a flow associated with high-entropy configurations, and the parameter of this flow is thermal time. For a generic small system S, entropy remains generally high along the entire flow of thermal time, perhaps just fluctuating up and down, because, after all, we are dealing here with probabilities, not fixed rules. But among the innumerable small systems S that exist in this extraordinarily vast universe where we happen to live, there will be a few special ones for which the fluctuations...

What makes the world go round are not sources of energy but sources of low entropy. Without low entropy, energy would dilute into uniform heat and the world would go to sleep in a state of thermal equilibrium—there would no longer be any distinction between past and future, and nothing would happen. Near to the Earth we have a rich source of low entropy: the sun. The sun sends us hot photons. Then the Earth radiates heat toward the black sky, emitting colder photons. The energy that enters is more or less equal to the energy that exits; consequently, we do not generally gain energy in the exchange. (Gaining energy in the exchange is disastrous for us: it is global warming.) But for every hot photon that arrives, the Earth emits ten cold ones, since a hot photon from the sun has the same energy as ten cold photons emitted by the Earth. The hot photon has less entropy than the ten cold photons, because the number of configurations of a single (hot) photon is lower than the number of configurations of ten (cold) photons. Therefore, the sun is a continual rich source of low entropy for us. We have at our disposal an abundance of low entropy, and it is this that allows plants and animals to grow, enables us to build motors and cities—and to think and to write books such as this one. Where does the low entropy of the sun come from? From the fact that, in turn, the sun is born out of an entropic configuration that was even lower: the primordial cloud from which the solar system w...

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

In our experience, the notion of cause is thus asymmetrical in time: cause precedes effect. When we recognize in particular that two events “have the same cause,” we find this common cause102 in the past, not in the future. If two waves of a tsunami arrive together at two neighboring islands, we think that there has been an event in the past that has caused both. We do not look for it in the future. But this does not happen because there is a magical force of “causality” going from the past to the future. It happens because the improbability of a correlation between two events requires something improbable, and it is only the low entropy of the past that provides such improbability. What else could? In other words, the existence of common causes in the past is nothing but a manifestation of low entropy in the past. In a state of thermal equilibrium, or in a purely mechanical system, there isn’t a direction to time identified by causality.

What (little) we are beginning to understand of this functioning is that our entire brain operates on the basis of a collection of traces of the past left in the synapses that connect neurons. Synapses are continually formed in their thousands and then erased—especially during sleep, leaving behind a blurry reflection of that which has acted on our nervous system in the past. A blurred image, no doubt—think of how many millions of details our eyes see every moment that do not stay in our memory—but one which contains worlds.

Many parts of this story are solid, others plausible, others still are guesses hazarded in an attempt at understanding the whole. Practically all the things recounted in the first part of the book have been ascertained from innumerable experiments: the slowing down of time according to altitude and speed; the nonexistence of the present; the relation between time and the gravitational field; the fact that the relations between different times are dynamic, that elementary equations do not recognize the direction of time; the relation between entropy and blurring. All this has been well ascertained.127 That the gravitational field has quantum properties is a shared conviction, albeit one currently supported only by theoretical arguments rather than by experimental evidence. The absence of the time variable from the fundamental equations, as discussed in Part Two, is plausible—but on the form of these equations debate still rages. The origin of time pertaining to quantum noncommutativity, of thermal time, and the fact that the increase in entropy which we observe depends on our interaction with the universe are ideas that I find fascinating but are far from being confirmed or widely accepted.

We may gesture clumsily toward an immediate sense of time beyond what we can articulate (“Fine, but why does it ‘pass’?”), but I believe that at this point we are merely confusing matters, attempting illegitimately to transform approximate words into things. When we cannot formulate a problem with precision, it is often not because the problem is profound: it’s because the problem is false.

“The ‘Past Hypothesis’: Not Even False,”

95. A contemporary philosopher who has shed light on these aspects of the perspectival nature of the world is Jenann T. Ismael, The Situated Self (New York: Oxford University Press, 2007). Ismael has also written an excellent book on free will: How Physics Makes Us Free (New York: Oxford University Press, 2016).

Carlo Rovelli, Meaning = Information + Evolution, 2016, https://arxiv.org/abs/1611.02420.