The Order of Time

by Carlo Rovelli

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 p...

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.

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. . .

The growth of entropy is nothing other than the ubiquitous and familiar natural increase of disorder.

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 chara...

Yes. If I observe the microscopic state of things, then the difference between p...

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 cann...

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?

But just as with the movement of the Earth, the evidence is overwhelming: all the phenomena that characterize the flowing of time are reduced to a “particular” state in the world’s past, the “particularity” of which may be attributed to the blurring of our perspective.

entropy, as Boltzmann fully understood, is nothing other than the number of microscopic states that our blurred vision of the world fails to distinguish.

“Proper time” depends not only on where you are and your degree of proximity to masses; it depends also on the speed at which you move.

Our “present” does not extend throughout the universe. It is like a bubble around us.

The relation of “temporal precedence” is a partial order made of cones.31 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 we want to represent all the events in the universe and their temporal relations, we can no longer do so with a single, universal distinction between past, present, and future, like this: We must do so instead by placing above and below every event the cones of its future and past events: (Physicists have the habit in such diagrams, I don’t know why, of placing the future above and the past below—the opposite of how it is done in genealogical trees.) Every event has its past, its future, and a part of the universe that is neither past nor future, just as every person has forebears, descendants, and others who are neither forebears nor descendants. Light travels along the oblique lines that delimit these cones. This is why we call them “light cones.” It is customary, as in the previous diagram, to draw these lines at an angle of forty-five degrees, but it would be more realistic to make them more horizontal, like this: The reason for this is that, at the scale to which we are accustomed, the expanded present separating our past from our future is extremely brief (a matter of nanoseconds) and almost imperceptible, as a result of which it is “squashed” into a thin horizontal ban...

“How long is forever?” asks Alice. “Sometimes, just one second,” replies the White Rabbit.

Time is elastic in our personal experience of it.

Hours fly by like minutes, and minutes are oppressively slow, as if they were centuries.

For centuries, we have divided time into days. The word “time” derives from an Indo-European root—di or dai—meaning “to divide.”

The good Lord has not drawn the world with continuous lines: with a light hand, he has sketched it in dots, like the painter Georges Seurat.

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.

Concreteness occurs only in relation to a physical system: this, I believe, is the most radical discovery made by quantum mechanics.*

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 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.

we understand the world by studying change, not by studying things. Those who have neglected this good advice have paid a heavy price for it. Two of the greats who fell into this error were Plato and Kepler, both curiously seduced by the same mathematics. In the Timaeus, Plato has the excellent idea of attempting to translate into mathematics the physics insights gained by atomists such as Democritus. But he goes about it the wrong way: he tries to write the mathematics of the shape of atoms, rather than the mathematics of their movements. He allows himself to be fascinated by a mathematical theorem which establishes that there are five—and only five—regular polyhedra, these ones: And he attempts to advance the audacious hypothesis that these are the actual shapes of the atoms of the five elementary substances that in antiquity were thought to form everything: earth, water, air, fire, and the quintessence of which the heavens are made. A beautiful idea. But completely mistaken. The error lies in seeking to understand the world in terms of things rather than events. It lies in ignoring change. 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. The shapes of atoms will be eventually understood only with solutions to Schrödinger’s equations describing how the electrons in atoms move. Events again, not things.

People like us who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.61

To describe the world, the time variable is not required. What is required are variables that actually describe it: quantities that we can perceive, observe, and eventually measure. The length of a road, the height of a tree, the temperature of a forehead, the weight of a piece of bread, the color of the sky, the number of stars in the celestial vault, the elasticity of a piece of bamboo, the speed of a train, the pressure of a hand on a shoulder, the pain of a loss, the position of the hands on a clock, the height of the sun in the sky . . . These are the terms in which we describe the world. Quantities and properties that we see continuously changing. In these changes there are regularities: a stone falls faster than a feather. Sun and moon circle after each other in the sky, passing by each other once a month. . . . Among these quantities there are some that we see changing regularly with respect to others: the number of days, the phases of the moon, the height of the sun on the horizon, the position of the hands of a clock. It is useful to employ these as points of reference: let’s meet three days after the next full moon, when the sun is at its highest in the sky. I’ll see you tomorrow, when the clock shows 4:35. If we find a sufficient number of variables that remain synchronized enough in relation to each other, it is convenient to use them in order to speak of when. There is no need in any of this to choose a privileged variable and call it “time.” What we need, if...

Wheeler–DeWitt equation.

There is a time to be born and a time to die, a time to weep and a time to dance, a time to kill and a time to heal. A time to destroy and a time to build.77 Up to this point, it has been a time to destroy time. Now it is time to rebuild the time that we experience: to look for its sources, to understand where it comes from.

In the frenzy of thermal molecular mingling, all the variables that can possibly vary do so continuously. One, however, does not vary: the total amount of energy in any isolated system.

Between energy and time there is a close bond. They form one of those characteristic couples of quantities that physicists call “conjugate,” such as position and momentum, or orientation and angular momentum. The two terms of these couples are tied to each other.

On the one hand, knowing what the energy of a system may be78—how it is linked to the other variables—is the same as knowing how time flows, because the equations of evolution in time follow from the form of its energy.79 On the other, energy is conserved in time, hence it cannot vary, even when everything else varies. In its thermal agitation, a system80 passes through all the configurations that have the same energy, but only these. The set of these configurations—which o...

That is, to observe that a macroscopic state, which is to say a blurred vision of the world, may be interpreted as a mingling that preserves an energy, and this in its turn generates a time. That is: macroscopic state → energy → time

I’ll repeat this point, because it is a key one: a macroscopic state (which ignores the details) chooses a particular variable that has some of the characteristics of time.

In other words, a time becomes determined simply as an effect of blurring.

Boltzmann understood that the behavior of heat involves blurring, from the fact that inside a glass of water there is a myriad of microscopic variables that we do not see. The number of possible microscopic configurations for water is its entropy. But something further ...

In fundamental relativistic physics, where no variable plays a priori the role of time, we can reverse the relation between macroscopic state and evolution of time: it is not the evolution of time that determines the state, it is the state—the blurring—that determines a time. Time that is determined in this way by a macroscopic state is called “thermal time.” In what sense may it be said to be a time? From a microscopic point of view, there is nothing special about it—it is a variable like any other. But from a macroscopic one, it has a crucial characteristic: among so many variables all at the same level, thermal time is the one with behavior that most closely resembles the variable we usually call “time,” because its relations with the macroscopic states are exactly those that we know from thermodynamics. But it is not a universal time. It is determined by a macroscopic ...

Roger Penrose is among the most lucid of those scientists who have focused on space and time.83 He reached the conclusion that the physics of relativity is not incompatible with our experience of the flowing of time but that it does not seem sufficient to account for it. He has suggested that what’s missing might be what happens in a quantum interaction.84 Alain Connes, the great French mathematician, has pointed out the deep role of quantum interaction at the root of time.

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 interact...

Perhaps it is the very fact that the effect of these interactions depends on the order in which they take place that is at the root of the temporal order of the world. This is the fascinating idea suggested by Connes: the first germ of temporality in elementary quantum transitions lies in the fact that these interactions are naturally (partially) ordered. Connes has provided a refined mathematical version of this idea: he has shown that a kind of temporal flow is implicitly defined by the noncommutativity of the physical variables. Due to this noncommutativity, the set of physical variables in a system defines a mathematical structure called “noncommutative von Neumann algebra,” and Connes has shown that these structures have within themselves an implicitly defined flow.85 Surprisingly, there is an extremely close relation between Alain Connes’s flow for quantum systems and the thermal time that I have discussed above. Connes has shown that, in a quantum system, the thermal flows determined by different macroscopic states are equivalent, up to certain internal symmetries,86 and that, together, they form precisely the Connes flow.87 Put more simply: the time d...

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...