The Order of Time

4 LOSS OF INDEPENDENCE

And on that wave

we will all have to navigate,

all who are nourished

by the fruits of the Earth. (II, 14)

WHAT HAPPENS WHEN NOTHING HAPPENS?

It only takes a few micrograms of LSD to expand our experience of time onto an epic and magical scale.³⁵ “How long is forever?” asks Alice. “Sometimes, just one second,” replies the White Rabbit. There are dreams lasting an instant in which everything seems frozen for an eternity.³⁶ Time is elastic in our personal experience of it. Hours fly by like minutes, and minutes are oppressively slow, as if they were centuries. On the one hand, time is structured by the liturgical calendar: Easter follows Lent, and Lent follows Christmas; Ramadan opens with Hilal and closes with Eid al-Fitr. On the other, every mystical experience, such as the sacred moment in which the host is consecrated, throws the faithful outside of time, putting them in touch with eternity. Before Einstein told us that it wasn’t true, how the devil did we get it into our heads that time passes everywhere at the same speed? It was certainly not our direct experience of the passage of time that gave us the idea that time elapses at the same rate, always and everywhere. So where did we get it from?

For centuries, we have divided time into days. The word “time” derives from an Indo-European root—di or dai—meaning “to divide.” For centuries, we have divided the days into hours.³⁷ But for most of those centuries, however, hours were longer in the summer and shorter in the winter, because the twelve hours divided the time between dawn and sunset: the first hour was dawn, and the twelfth was sunset, regardless of the season, as we read in the parable of the winegrower in the Gospel according to Matthew.³⁸ Since, as we say nowadays, during summer “more time” passes between dawn and sunset than during the winter, in the summer the hours were longer, and the hours were shorter in wintertime.

Sundials, hourglasses, and water clocks already existed in the ancient world, in the Mediterranean region and in China—but they did not play the cruel role that clocks do today in the organization of our lives. It is only in the fourteenth century in Europe that people’s lives start to be regulated by mechanical clocks. Cities and villages build their churches, erect bell towers next to them, and place a clock on the bell tower to mark the rhythm of collective activities. The era of clock-regulated time begins.

Gradually, time slips from the hands of the angels and into those of the mathematicians—as is graphically illustrated by Strasbourg Cathedral, where two sundials are surmounted, respectively, by an angel (one inspired by earlier sundials from 1200) and by a mathematician (on the sundial put there in 1400).

The usefulness of clocks supposedly resides in the fact that they tell the same time. And yet this idea is also more modern than we might imagine. For centuries, as long as travel was on horseback, on foot, or in carriages, there was no reason to synchronize clocks between one place and another. There was good reason for not doing so. Midday is, by definition, when the sun is at its highest. Every city and village had a sundial that registered the moment the sun was at its midpoint, allowing the clock on the bell tower to be regulated with it, for all to see. But the sun does not reach midday at the same moment in Lecce as it does in Venice, or in Florence, or in Turin, because the sun moves from east to west. Midday arrives first in Venice, and significantly later in Turin, and for centuries the clocks in Venice were a good half hour ahead of those in Turin. Every small village had its own peculiar “hour.” A train station in Paris kept its own hour, a little behind the rest of the city, as a kind of courtesy toward travelers running late.³⁹

In the nineteenth century, the telegraph arrives, trains become commonplace and fast, and the problem arises of properly synchronizing clocks between one city and another. It is awkward to organize train timetables if each station marks time differently. It is in the United States that the first attempt is made to standardize time. Initially, it is proposed to fix a universal hour for the entire world. To call, for instance, “twelve o’clock” the moment at which it is midday in London, so that midday would fall at 12 noon in London and around 6 p.m. in New York. The proposal is not well received, because people are attached to local time. In 1883, a compromise is reached with the idea of dividing the world into time zones, thereby standardizing time only within each zone. In this way, the discrepancy between twelve on the clock and local midday is limited to a maximum of about thirty minutes. The proposal is gradually accepted by the rest of the world and clocks begin to be synchronized between different cities.⁴⁰

It can hardly be pure coincidence that, before gaining a university position, the young Einstein worked in the Swiss patent office, dealing specifically with patents relating to the synchronization of clocks at railway stations. It was probably there that it dawned on him: the problem of synchronizing clocks was, ultimately, an insoluble one.

In other words, only a few years passed between the moment at which we agreed to synchronize clocks and the moment at which Einstein realized that it was impossible to do so exactly.

For millennia before clocks, our only regular way of measuring time had been the alternation of day and night. The rhythm of day followed by night also regulates the lives of plants and animals. Diurnal rhythms are ubiquitous in the natural world. They are essential to life, and it seems to me probable that they played a key role in the very origin of life on Earth, since an oscillation is required to set a mechanism in motion. Living organisms are full of clocks of various kinds—molecular, neuronal, chemical, hormonal—each of them more or less in tune with the others.⁴¹ There are chemical mechanisms that keep to a twenty-four-hour rhythm even in the biochemistry of single cells.

The diurnal rhythm is an elementary source of our idea of time: night follows day; day follows night. We count the beats of this great clock: we count the days. In the ancient consciousness of humanity, time is, above all, this counting of days.

As well as the days, we then count the years and the seasons, the cycles of the moon, the swings of a pendulum, the number of times that an hourglass is turned. This is the way in which we have traditionally conceived of time: counting the ways in which things change.

Aristotle is the first we are aware of to have asked himself the question “What is time?,” and he came to the following conclusion: time is the measurement of change. Things change continually. We call “time” the measurement, the counting of this change.

Aristotle’s idea is sound: time is what we refer to when we ask “when?” “After how much time will you return?” means “When will you return?” The answer to the question “when?” refers to something that happens. “I’ll return in three days’ time” means that between departure and return the sun will have completed three circuits in the sky. It’s as simple as that.

So if nothing changes, if nothing moves, does time therefore cease to pass?

Aristotle believed that it did. If nothing changes, time does not pass—because time is our way of situating ourselves in relation to the changing of things: the placing of ourselves in relation to the counting of days. Time is the measure of change:⁴² if nothing changes, there is no time.

But what is then the time that I hear coursing in the silence? “If it is dark and our bodily experience is nil,” Aristotle writes in his Physics, “but some change is happening within the mind, we immediately suppose that some time has passed as well.”⁴³ In other words, even the time that we perceive flowing within us is the measure of a movement: a movement that is internal. . . . If nothing moves, there is no time, because time is nothing but the registering of movement.

Newton, instead, assumes the exact opposite. In his magnum opus, the Principia, he writes:

I do not define Time, Space, Place and Motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into Absolute and Relative, True and Apparent, Mathematical and Common.⁴⁴

In other words, Newton recognizes that a kind of “time” exists that measures days and movements: the one treated by Aristotle (relative, apparent, and common). But he also contends that, in addition to this, another time must exist: “true” time that passes regardless, independently of things and of their changes. If all things remained motionless and even the movements of our souls were to be frozen, this time would continue to pass, according to Newton, unaffected and equal to itself: “true” time. It’s the exact opposite of what Aristotle writes.

“True” time, says Newton, is not directly accessible—only indirectly, through calculation. It is not the same as that given by days, because “the natural days are truly unequal, though they are commonly consider’d as equal, and used for a measure of time: Astronomers correct this inequality that they may measure the celestial motions by a more accurate time.”⁴⁵

So, who is right: Aristotle or Newton? Two of the most acute and profound investigators of nature that the world has ever seen are proposing two opposite ways of thinking about time. Two giants are pulling us in opposite directions.⁴⁶

Time is only a way of measuring how things change, as Aristotle would have it—or should we be thinking that an absolute time exists that flows by itself, independently of things? The question we should really be asking is this: which of these two ways of thinking about time helps us to understand the world better? Which of the two conceptual schemes is more efficient?

Aristotle: Time is nothing other than the measurement of change.

For a few centuries, reason seemed to come down on the side of Newton. Newton’s model, based on the idea of a time independent of things, has enabled the construction of modern physics—a physics that works incredibly well. And it assumes that time exists as an entity that runs in a way which is uniform and imperturbable. Newton writes equations containing the letter t for time that describe how things move in time.⁴⁷ What does this letter mean? Does t indicate time shaped by the longer hours of summer and the shorter ones of winter? Obviously not. It indicates time that is “absolute, true, and mathematical,” assumed by Newton to run independently of things that change or things that move.

Newton: There is a time that passes even when nothing changes.

Clocks, for Newton, are devices that seek, albeit in a manner that is always imprecise, to follow this equal and uniform flowing of time. Newton writes that this “absolute, true, and mathematical” time is not perceptible. It must be deduced, through calculation and observation, from the regularity of phenomena. Newton’s time is not the evidence given to us by our senses: it is an elegant intellectual construction. 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. Because it has gradually become the way in which we all think about time. It has filtered through school textbooks throughout the world and ended up becoming our common way of understanding time. We have turned it into our common sense. But the existence of a time that is uniform, independent of things and of their movement that today seems so natural to us is not an ancient intuition that is natural to humanity itself. It’s an idea of Newton’s.

The majority of philosophers have in fact responded negatively to this idea. In a still celebrated, furious counterblast, Leibniz defended the traditional thesis according to which time is only the order of events, arguing that there is no such thing as an autonomous time. Legend has it that Leibniz, whose name is still occasionally spelled with a “t” (Leibnitz), had deliberately dropped the letter from his name in accordance with his belief in the nonexistence of the absolute Newtonian time t.⁴⁸

Before Newton, time for humanity was the way of counting how things changed. Before him, no one had thought it possible that a time independent of things could exist. Don’t take your intuitions and ideas to be “natural”: they are often the products of the ideas of audacious thinkers who came before us.

But of these two giants, Aristotle and Newton, was it really Newton who was right? What exactly is this “time” that he introduced, managing to convince the entire world that it exists, one that works so brilliantly well in his equations and yet is not the time that we perceive?

To get out from between these two giants, and in a strange way to reconcile them, a third was needed. Before getting to him, however, a brief digression on space is in order.

WHAT IS THERE, WHERE THERE IS NOTHING?

The two interpretations of time (the measure of “when” with regard to events, as Aristotle wanted; the entity that runs even when nothing happens, according to Newton) can be repeated for space. Time is what we speak of when we ask “when?” Space is what we speak of when we ask “where?” If I ask “Where is the Coliseum?” one possible answer is: “It’s in Rome.” If I ask “Where are you?” a possible answer might be: “At home.” To reply to the question “Where is something?” means to indicate something else that is around that thing. If I say “In the Sahara,” you will visualize me surrounded by sand dunes.

Aristotle was the first to discuss in depth and with acuity the meaning of “space,” or “place,” and to arrive at a precise definition: the place of a thing is what surrounds that thing.⁴⁹

As in the case of time, Newton suggests that we should think differently. The space defined by Aristotle, the enumeration of what surrounds each thing, is called “relative, apparent, and common” by Newton. He calls “absolute, true, and mathematical” space in itself, which exists even where there is nothing.

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 alternatively as “completely full” of air. In the end, Aristotle and Newton do not engage in profound metaphysics: they are only using these two different intuitive and ingenious ways of seeing the world around us—taking or not taking air into account—and transforming them into definitions of space.

Aristotle, always top of the class, wants to be precise: he does not say that the glass is empty; he says that it is full of air. And he remarks that, in our experience, there is never a place where “there is nothing, not even air.” Newton, looking not so much for accuracy as for efficiency of the conceptual paradigm that needs to be constructed in order to describe the movement of things, thinks not about air but about objects. Air, after all, seems to have little effect on a falling stone. We can imagine that it is not even there.

As in the case of time, Newton’s “container space” may seem natural to us, but it is a recent idea that has spread due to the enormous influence of his thought. That which seems intuitive to us now is the result of scientific and philosophical elaborations in the past.

The Newtonian idea of “empty space” seems to be confirmed when Torricelli demonstrates that it is possible to remove the air from a bottle. It soon becomes clear, however, that inside the bottle many physical entities remain: electric and magnetic fields, and a constant swarming of quantum particles. The existence of a complete void, without any physical entity except amorphous space, “absolute, true, and mathematical,” remains a brilliant theoretical idea introduced by Newton to found his physics on, for there is no scientific, experimental evidence to support its existence. An ingenious hypothesis, perhaps the most profound insight achieved by one of the greatest scientists—but is it one that actually corresponds to the reality of things? Does Newton’s space really exist? If it exists, is it really amorphous? Can a place exist where nothing exists?

The question is identical to the analogous one regarding time: does Newton’s “absolute, true, and mathematical” time exist, flowing when nothing happens? If it exists, is it something altogether different from the things of this world? Is it so very independent from them?

The answer to all these questions lies in an unexpected synthesis of the apparently contradictory ideas held by these two giants. And to accomplish this, it was necessary for a third giant to enter the dance.*

THE DANCE OF THE THREE GIANTS

The synthesis between Aristotle’s time and Newton’s is the most valuable achievement made by Einstein. It is the crowning jewel of his thought.

The answer is that the time and space Newton had intuited the existence of, beyond tangible matter, do effectively exist. They are real. Time and space are real phenomena. But they are in no way absolute; they are not at all independent from what happens; they are not as different from the other substances of the world, as Newton had imagined them to be. We can think of a great Newtonian canvas on which the story of the world is drawn. But this canvas is made of the same stuff that everything else in the world is made of, the same substance that constitutes stone, light, and air: it is made of fields.

Physicists call “fields” the substances that, to the best of our knowledge, constitute the weave of the physical reality of the world. Sometimes they may be given exotic names: the fields “of Dirac” are the fabric of which tables and stars are made. The “electromagnetic” field is the weave of which light is made, as well as the origin of the forces that make electric motors turn and the needle of a compass point north. But—here is the key point—there is also a “gravitational” field: it is the origin of the force of gravity, but it is also the texture that forms Newton’s space and time, the fabric on which the rest of the world is drawn. Clocks are mechanisms that measure its extension. The meters used for measuring length are portions of matter that measure another aspect of its extension.

Spacetime is the gravitational field—and vice versa. It is something that exists by itself, as Newton intuited, even without matter. But it is not an entity that is different from the other things in the world—as Newton believed—it is a field like the others. More than a drawing on a canvas, the world is like a superimposition of canvases, of strata, where the gravitational field is only one among others. Just like the others, it is neither absolute nor uniform, nor is it fixed: it flexes, stretches, and jostles with the others, pushing and pulling against them. Equations describe the reciprocal influences that all the fields have on each other, and spacetime is one of these fields.*

The gravitational field can also be smooth and flat, like a straight surface, and this is the version that Newton described. If we measure it in meters, we discover that the Euclidian geometry that we learned at school applies. But the field can also undulate, in what we call “gravitational waves.” It can contract and expand.

Remember the clocks in chapter 1 that slow down in the vicinity of a mass? They slow down because there is, in a precise sense, “less” gravitational field there. There is less time there.

The canvas formed by the gravitational field is like a vast elastic sheet that can be pulled and stretched. Its stretching and bending is the origin of the force of gravity, of things falling, and provides a better explanation of this than the old Newtonian theory of gravity.

Look again at the figure here which illustrates how more time passes above than below, but imagine now that the piece of paper on which the diagram is drawn is elastic; imagine stretching it so that the time in the mountains actually becomes elongated. You will obtain something like the image below, which represents space (the height, on the vertical axis) and time (on the horizontal)—but, now, the “longer” time in the mountains effectively corresponds to a greater length of time.

The image above illustrates what physicists call “curved” spacetime. “Curved” because it is distorted: distances are stretched and contracted, just like the elastic sheet when it is pulled. This is why the light cones were inclined in the diagrams in chapter 3.

Time thus becomes part of a complicated geometry woven together with the geometry of space. This is the synthesis that Einstein found between Aristotle’s conception of time and Newton’s. With a tremendous beat of his wings, Einstein understands that Aristotle and Newton are both right. Newton is right in intuiting that something else exists in addition to the simple things that we see moving and changing. True and mathematical Newtonian time exists; it is a real entity; it is the gravitational field, the elastic sheet, the curved spacetime in the diagram. But Newton is wrong in assuming that this time is independent from things—and that it passes regularly, imperturbably, separately, from everything else.

For his part, Aristotle is right to say that “when” and “where” are always located in relation to something. But this something can also be just the field, the spatiotemporal entity of Einstein. Because this is a dynamic and concrete entity, like all those in reference to which, as Aristotle rightly observed, we are capable of locating ourselves.

All this is perfectly coherent, and Einstein’s equations describing the distortions of the gravitational field and its effects on clocks and meters have been repeatedly verified for more than a century. But our idea of time has lost another of its constituent parts: its supposed independence from the rest of the world.

The three-handed dance of these intellectual giants—Aristotle, Newton, and Einstein—has guided us to a deeper understanding of time and of space. There is a structure of reality that is the gravitational field; it is not separate from the rest of physics, nor is it the stage across which the world passes. It is a dynamic component of the great dance of the world, similar to all the others, interacting with the others, determining the rhythm of those things that we call meters and clocks and the rhythm of all physical phenomena.

Success, as ever, is destined to be short-lived—even great success. Einstein writes the equations of the gravitational field in 1915, and barely a year later it is Einstein himself who observes that this cannot be the last word on the nature of time and space, because of the existence of quantum mechanics. The gravitational field, like all physical things, must necessarily have quantum properties.