For this intermediate phase, where time is wholly indeterminate, we still have equations that tell us what happens. Equations without time.
This is the world described by loop theory.
Am I certain that this is the correct description of the world? I am not, but it is today the only coherent and complete way that I know of to think about the structure of spacetime without neglecting its quantum properties. 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.
PART III THE SOURCES OF TIME
9 TIME IS IGNORANCE
Do not ask
about the outcome of my days, or of yours,
Leuconoe—
it’s a secret, beyond us.
And don’t attempt abstruse calculations. (I, 11)
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.
If, in the elementary dynamic of the world, all the variables are equivalent, what is this thing that we humans call “time”? What is it that my watch measures? What is it that always runs forward, and never backward—and why? It may not be part of the elementary grammar of the world, but what is it?
There are so many things that are not part of the elementary grammar of the world and that simply “emerge” in some way. For example:
A cat is not part of the elementary ingredients of the universe. It is something complex that emerges, and repeats itself, in various parts of our planet.
A group of boys on a field decide to have a match. They form teams. This is how we used to do it: the two most enterprising would take turns choosing the players they wanted, having tossed a coin to see who would have first pick. At the end of this solemn procedure, there were two teams. Where were the teams before they were chosen? Nowhere. They emerged from the procedure.
Where do “high” and “low” come from—terms that are so familiar and yet are not in the elementary equations of the world? From the Earth that is so close to us and that attracts. “High” and “low” emerge in certain circumstances in the universe, as when there is a large mass nearby.
In the mountains, we see a valley covered by a sea of white clouds. The surface of the clouds gleams, immaculate. We start to walk toward the valley. The air becomes more humid, then less clear; the sky is no longer blue. We find ourselves in a fog. Where did the well-defined surface of the clouds go? It vanished. Its disappearance is gradual; there is no surface that separates the fog from the sparse air of the heights. Was it an illusion? No, it was a view from afar. Come to think of it, it’s like this with all surfaces. This dense marble table would look like a fog if I were shrunk to a small enough, atomic scale. Everything in the world becomes blurred when seen close up. Where exactly does the mountain end and where do the plains begin? Where does the savannah begin and the desert end? We cut the world into large slices. We think of it in terms of concepts that are meaningful for us, that emerge at a certain scale.
We see the sky turning around us every day, but we are the ones who are turning. Is the daily spectacle of a revolving universe “illusory”? No, it is real, but it doesn’t involve the cosmos alone. It involves our relation with the sun and the stars. We understand it by asking ourselves how we move. Cosmic movement emerges from the relation between the cosmos and ourselves.
In these examples, something that is real—a cat, a football team, high and low, the surface of clouds, the rotation of the cosmos—emerges from a world that at a much simpler level has no cats, teams, up or down, no surfaces of clouds, no revolving cosmos. . . . Time emerges from a world without time, in a way that has something in common with each of these examples.
The reconstruction of time begins here, in two little chapters—this one and the next—that are brief and technical. If you find them heavy going, skip them and go directly to chapter 11. From there, step by step, we will gradually reach more human things.
THERMAL TIME
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 our blurred macroscopic vision does not distinguish—is the “(macroscopic) state of equilibrium”: a placid glass of hot water.
The usual way of interpreting the relation between time and state of equilibrium is to think that time is something absolute and objective; energy governs the time-evolution of a system; and the system in equilibrium mixes all configurations of equal energy. The conventional logic for interpreting this relation is therefore:
time → energy → macroscopic state81
That is: to define the macroscopic state, we first need to know the energy, and to define energy we first need to know what is time. In this logic, time comes first and is independent from the rest.
But there is another way of thinking about this same relationship: by reading it in reverse. 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 → time82
This observation opens up a new perspective: in an elementary physical system without any privileged variable that acts like “time”—where, in effect, all the variables are on the same level but we can have only a blurred vision of them described by macroscopic states. A generic macroscopic state determines a 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 is also true: the blurring itself determines a particular variable—time.