But it isn’t absence that causes sorrow. It is affection and love. Without affection, without love, such absences would cause us no pain. For this reason, even the pain caused by absence is, in the end, something good and even beautiful, because it feeds on that which gives meaning to life.
Bryce, I met in London, on the first occasion that I went to seek out a group working on quantum gravity. I was a young novice, fascinated by this arcane subject that no one in Italy was working on; he was its grand guru. I had gone to Imperial College to meet up with Chris Isham, and when I arrived I was told that he was on the top-floor terrace. Sitting together at a small table up there, I found Chris Isham, Karel Kuchar, and Bryce DeWitt—the three main authors whose ideas I had been studying in recent years. I remember vividly the intense impression I had on seeing them there through the glass, calmly discussing among themselves. I did not dare to interrupt. They seemed to me like three great Zen masters exchanging unfathomable truths between enigmatic smiles.
They were probably only deciding where to go for dinner. Revisiting and reflecting on the episode, I realize that at the time they were younger than I am now. This, too, is time: a strange shifting of perspective. Shortly before he died, Bryce gave a long interview in Italy, subsequently published in a small book.73 And it was only then I became aware that he’d followed my work much more closely, and with more sympathy, than I had ever suspected from our conversations together, in which he was more prone to express criticism than encouragement.
John and Bryce were my spiritual fathers. Thirsting, I found in their ideas fresh, clear water to drink. So, thank you, John; thanks, Bryce. As human beings, we live by emotions and thoughts. We exchange them when we are in the same place at the same time, talking to each other, looking into each other’s eyes, brushing against each other’s skin. We are nourished by this network of encounters and exchanges. But, in reality, we do not need to be in the same place and time to have such exchanges. Thoughts and emotions that create bonds of attachment between us have no difficulty in crossing seas and decades, sometimes even centuries, tied to thin sheets of paper or dancing between the microchips of a computer. We are part of a network that goes far beyond the few days of our lives and the few square meters that we tread. This book is also a part of that weave. . . .
But I have digressed and lost my thread. Nostalgia for John and Bryce has caused me to deviate from my path. All I had intended to say in this chapter is that they had discovered the extremely simple structure of the equation that describes the dynamics of the world. It describes possible events and the correlations between them, and nothing else.
It’s the elementary form of the mechanics of the world, and it does not need to mention “time.” The world without a time variable is not a complicated one. It’s a net of interconnected events, where the variables in play adhere to probabilistic rules that, incredibly, we know for a good part how to write. And it’s a clear world, windswept and full of beauty as the crests of mountains; aridly beautiful as the cracked lips of the adolescent you loved.
ELEMENTARY QUANTUM EVENTS AND SPIN NETWORKS
The equations of loop quantum gravity74 on which I work are a modern version of the theory of Wheeler and DeWitt. There is no time variable in these equations.
The variables of the theory describe the fields that form matter, photons, electrons, other components of atoms and the gravitational field—all on the same level. Loop theory is not a “unified theory of everything.” It doesn’t even begin to claim that it’s the ultimate theory of science. It’s a theory made up of coherent but distinct parts. It seeks to be “only” a coherent description of the world as we understand it so far.
The fields manifest themselves in granular form: elementary particles, photons, and quanta of gravity—or rather “quanta of space.” These elementary grains do not exist immersed in space; rather, they themselves form that space. The spatiality of the world consists of the web of their interactions. They do not dwell in time: they interact incessantly with each other, and indeed exist only in terms of these incessant interactions. And this interaction is the happening of the world: it is the minimum elementary form of time that is neither directional nor linear. Nor does it have the curved and smooth geometry studied by Einstein. It is a reciprocal interaction in which quanta manifest themselves in the interaction, in relation to what they interact with.
The dynamic of these interactions is probabilistic. The probabilities that something will happen—given the occurrence of something else—can in principle be calculated with the equations of the theory.
We cannot draw a complete map, a complete geometry, of everything that happens in the world, because such happenings—including among them the passage of time—are always triggered only by an interaction with, and with respect to, a physical system involved in the interaction. The world is like a collection of interrelated points of view. To speak of the world “seen from outside” makes no sense, because there is no “outside” to the world.
Representation of the web of elementary grains of space (or spin network).
The elementary quanta of the gravitational field exist at the Planck scale. They are the elementary grains that weave the mobile fabric with which Einstein reinterpreted Newton’s absolute space and time. It is these, and their interactions, that determine the extension of space and the duration of time.
The relations of spatial adjacency tie the grains of space into webs. We call these “spin networks.” The name “spin” comes from the mathematics that describe the grains of space.75 A ring in the spin network is called a “loop,” and these are the loops that give “loop theory” its name.
The webs, in turn, transform into each other in discrete leaps, described in the theory as structures called “spinfoam.”76
The occurrence of these leaps draws the patterns that on a large scale appear to us like the smooth structure of spacetime. On a small scale, the theory describes a “quantum spacetime” that is fluctuating, probabilistic, and discrete. At this scale, there is only the frenzied swarming of quanta that appear and vanish.
Representation of spinfoam.
This is the world with which I seek daily to come to terms. An unusual world, but not a meaningless one.
In my research group in Marseille, for example, we are attempting to calculate the time needed for a black hole to explode when it passes through a quantum phase.
During the course of this phase, inside the black hole and within its immediate vicinity there is no longer a single and determinate spacetime. There is a quantum superposition of spin webs. Just as an electron can unfurl into a cloud of probabilities between the moment it is emitted and the moment it arrives on a screen, passing through more than one place, so the spacetime of the quantum collapse of a black hole passes through a phase in which time fluctuates violently, there is a quantum superposition of different times, and then, later, a return to a determined state after the explosion.