The Order of Time

1 LOSS OF UNITY

Dances of love intertwine

such graceful girls

lit by the moon

on these clear nights. (I, 4)

THE SLOWING DOWN OF TIME

Let’s begin with a simple fact: time passes faster in the mountains than it does at sea level.

The difference is small but can be measured with precision timepieces that can be bought today on the internet for a few thousand dollars. With practice, anyone can witness the slowing down of time. With the timepieces of specialized laboratories, this slowing down of time can be detected between levels just a few centimeters apart: a clock placed on the floor runs a little more slowly than one on a table.

It is not just the clocks that slow down: lower down, all processes are slower. Two friends separate, with one of them living in the plains and the other going to live in the mountains. They meet up again years later: the one who has stayed down has lived less, aged less, the mechanism of his cuckoo clock has oscillated fewer times. He has had less time to do things, his plants have grown less, his thoughts have had less time to unfold. . . . Lower down, there is simply less time than at altitude.

Is this surprising? Perhaps it is. But this is how the world works. Time passes more slowly in some places, more rapidly in others.

The surprising thing, perhaps, is that someone understood this slowing down of time a century before we had clocks precise enough to measure it. His name, of course, was Albert Einstein.

The ability to understand something before it’s observed is at the heart of scientific thinking. In antiquity, Anaximander understood that the sky continues beneath our feet long before ships had circumnavigated the Earth. At the beginning of the modern era, Copernicus understood that the Earth turns long before astronauts had seen it do so from the moon. In a similar way, Einstein understood that time does not pass uniformly everywhere before the development of clocks accurate enough to measure the different speeds at which it passes.

In the course of making such strides, we learn that the things that seemed self-evident to us were really no more than prejudices. It seemed obvious that the sky was above us and not below; otherwise, the Earth would fall down. It seemed self-evident that the Earth did not move; otherwise, it would cause everything to crash. That time passed at the same speed everywhere seemed equally obvious to us. . . . Children grow up and discover that the world is not as it seemed from within the four walls of their homes. Humankind as a whole does the same.

Einstein asked himself a question that has perhaps puzzled many of us when studying the force of gravity: how can the sun and the Earth “attract” each other without touching and without utilizing anything between them?

He looked for a plausible explanation and found one by imagining that the sun and the Earth do not attract each other directly but that each of the two gradually acts on that which is between them. And since what lies between them is only space and time, he imagined that the sun and the Earth each modified the space and time that surrounded them, just as a body immersed in water displaces the water around it. This modification of the structure of time influences in turn the movement of bodies, causing them to “fall” toward each other.⁴

What does it mean, this “modification of the structure of time”? It means precisely the slowing down of time described above: a mass slows down time around itself. The Earth is a large mass and slows down time in its vicinity. It does so more in the plains and less in the mountains, because the plains are closer to it. This is why the friend who stays at sea level ages more slowly.

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

Hence, even though we cannot easily observe it, the slowing down of time nevertheless has crucial effects: things fall because of it, and it allows us to keep our feet firmly on the ground. If our feet adhere to the pavement, it is because our whole body inclines naturally to where time runs more slowly—and time passes more slowly for your feet than it does for your head.

Does this seem strange? It is like when, watching the sun going down gloriously at sunset, disappearing slowly behind distant clouds, we suddenly remember that it’s not the sun that’s moving but the Earth that’s spinning, and we see with the unhinged eye of the mind our entire planet—and ourselves with it—rotating backward, away from the sun. We are seeing with “mad” eyes, like those of Paul McCartney’s Fool on the Hill: the crazed vision that sometimes sees further than our bleary, customary eyesight.

TEN THOUSAND DANCING SHIVAS

I have an enduring passion for Anaximander, the Greek philosopher who lived twenty-six centuries ago and understood that the Earth floats in space, supported by nothing.⁶ We know of Anaximander’s thought from other writers. Only one small original fragment of his writings has survived—just one:

Things are transformed one into another according to necessity,

and render justice to one another

according to the order of time.

“According to the order of time” (κατὰ τὴν τοῦ χρόνου τάξιν). From one of the crucial, initial moments of natural science there remains nothing but these obscure, arcanely resonant words, this appeal to the “order of time.”

Astronomy and physics have since developed by following this seminal lead given by Anaximander: by understanding how phenomena occur according to the order of time. In antiquity, astronomy described the movements of stars in time. The equations of physics describe how things change in time. From the equations of Newton, which establish the foundations of mechanics, to those of Maxwell for electromagnetic phenomena; from Schrödinger’s equation describing how quantum phenomena evolve, to those of quantum field theory for the dynamics of subatomic particles: the whole of our physics, and science in general, is about how things develop “according to the order of time.”

It has long been the convention to indicate this time in equations with the letter t (the word for “time” begins with t in Italian, French, and Spanish, but not in German, Arabic, Russian, or Mandarin). What does this t stand for? It stands for the number measured by a clock. The equations tell us how things change as the time measured by a clock passes.

But if different clocks mark different times, as we have seen above, what does t indicate? When the two friends meet up again after one has lived in the mountains and the other at sea level, the watches on their wrists will show different times. Which of the two is t? In a physics laboratory, a clock on a table and another on the ground run at different speeds. Which of the two tells the time? How do we describe the difference between them? Should we say that the clock on the ground has slowed relative to the real time recorded on the table? Or that the clock on the table runs faster than the real time measured on the ground?

The question is meaningless. We might just as well ask what is most real—the value of sterling in dollars or the value of dollars in sterling. There is no “truer” value; they are two currencies that have value relative to each other. There is no “truer” time; there are two times and they change relative to each other. Neither is truer than the other.

But there are not just two times. Times are legion: a different one for every point in space. There is not one single time; there is a vast multitude of them.

The time indicated by a particular clock measuring a particular phenomenon is called “proper time” in physics. Every clock has its proper time. Every phenomenon that occurs has its proper time, its own rhythm.

Einstein has given us the equations that describe how proper times develop relative to each other. He has shown us how to calculate the difference between two times.⁷

The single quantity “time” melts into a spiderweb of times. We do not describe how the world evolves in time: we describe how things evolve in local time, and how local times evolve relative to each other. The world is not like a platoon advancing at the pace of a single commander. It’s a network of events affecting each other.

This is how time is depicted in Einstein’s general theory of relativity. His equations do not have a single “time”; they have innumerable times. Between two events, just as between the two clocks that are separated and then brought together again, the duration is not a single one.⁸ Physics does not describe how things evolve “in time” but how things evolve in their own times, and how “times” evolve relative to each other.*

Time has lost its first aspect or layer: its unity. It has a different rhythm in every different place and passes here differently from there. The things of this world interweave dances made to different rhythms. If the world is upheld by the dancing Shiva, there must be ten thousand such dancing Shivas, like the dancing figures painted by Matisse. . . .