The Matter of Time

                               by George Musser

If any subject deserves an interdisciplinary treatment, it is time. Our experience of time is so fundamental and so mysterious that it takes all areas of human endeavor to come to grips with it. Historically, scientific and artistic ideas of time have played off one another, and I think that remains true today. In this short talk, I’ll focus on the scientific ideas, but as I’ll mention toward the end of my remarks, those ideas have evolved in parallel with social and cultural attitudes toward time.

Almost all the major questions of modern physics boil down to an inability to understand time and its conjoined twin, space. Many of these conundrums arise from the particular way of conceptualizing time that physicists have adopted, so let me begin with it. This conception of time has been extremely useful in making physics the most precise of all sciences. Yet it has its limits and those limits have become increasingly pressing.

Physicists conceptually divide nature into two elements: (a) the state of the world, and (b) the laws of physics. The state of the world is defined in space. In classical mechanics, such as the rules that govern a pool table, the state consists of the positions and velocities of objects. The laws of physics operate in time. They take one state to the next. These laws work both ways: we can run the laws in reverse to reconstruct what the world used to be like.

This division of labor leads us to a picture known as the spacetime diagram

Figure 1- A spacetime diagram represents time spatially. A tilted line represents the path of moving object. A 45-degree line represents the path of a light beam. People moving at different speeds slice spacetime into space and time differently.

For these purposes, we’re not worried about all the spatial relationships that objects can have, so we can represent all the spatial dimensions with a single dimension, the horizontal axis of this diagram. The state of the world is defined along this direction. By applying the laws of physics, you can take the state and predict the state at any time in the future. Over time, objects trace out an entire line. A car moving at a steady speed, for example, corresponds to a straight, tilted line. So you can lay out time like a spatial dimension.

This geometric idea of time as a gridline underpins everything I’ll say about time today. Spatializing time seems so commonsensical that even many non-physicists forget how remarkable it is. We do not perceive time as anything remotely resembling a spatial dimension. We routinely draw the path of a baseball thrown into the air as an arc, but we do not directly see it that way. Rather, we see the world unfold from one moment to the next.

What gives this spatialized view of time more than metaphorical significance is that how you divvy up space and time can change. Spacetime gets sliced differently into space and time differently depending on your velocity. To the driver of the car, it looks like he’s stationary and the rest of the world shoots by. The speed of a car looks like zero if you’re driving, 55 mph if you’re on the ground, or 110 mph in a head-on collision. The moving car becomes, to the driver, a fixed reference point, and he divides up space differently than the observer on the ground. This is the principle of relativity first articulated by Galileo.

Einstein showed that even time looks different depending on your velocity. The reason is that the speed of light, unlike the speed of a car, looks the same to every observer. For the speed of light to remain the same, you can’t simply determine relative speed by adding or subtracting, because then you could exceed the speed of light; instead you need a more complicated relative-velocity formula that mixes space and time. Loosely speaking, for the speed of light to remain the same as you speed up, the passage of time must slow down for you. On a spacetime diagram, the faster you go, the more the line representing your velocity gets tilted, approaching the diagonal line that represents the speed of light. Each of us moves into the future at his or her own pace.

You have to take care with spatializing time. People often talk of time as the fourth dimension, but that doesn’t mean space and time are the same; the two may be related, but they’re still distinct. Time plays a special role in nature. This distinctiveness is the heart of many of the deep problems in modern physics.

Maybe the most important is what physicists refer to as causality: the principle that there is an objective distinction between cause and effect. More precisely, if we have two events ‘A’ and ‘B’, event ‘A’ can help cause event ‘B’ if it (a) precedes it in time, and (b) is close enough to exert an influence on ‘B’. If these two conditions are true for one observer, they’re true for all observers, no matter how fast those observers are moving.

Figure 2 - Time is structured to ensure that cause-effect relations are objective. If one person sees an event ‘A’ cause, or help to cause, an event ‘B’, so will other people, even when they’re moving at different speeds. The time interval between ‘A’ and ‘B’ might differ, but one will always precede the other.

For example, in pool, if the cue ball hits the 4-ball and the 4-ball knocks the 8-ball into a pocket, this sequence will be the same for everyone looking on. Nobody will see the reverse sequence in which the 8-ball jumps out of the pocket and hits the 4.

The reason causality holds is that there’s a limit to how much space and time mix. The space axis always remains below the line representing the speed of light, and the time axis always remains above it. Otherwise, you might get a case where space and time switch places, such that events that occur sequentially to a slow observer occur simultaneously to a faster one and in reverse order to an even faster one. If such reversals happened, you could set up time loops in which it wouldn’t be clear what is cause and what is effect. And that might allow for paradoxes—the same kinds of paradoxes that can arise in time travel, such as events that cause themselves or, conversely, prevent themselves from happening. It would give a whole new twist to the chicken-and-egg problem if a chicken could lay the egg that she hatched from.

So time looks almost but not quite like a spatial dimension. In space, you have freedom to move around and you can see a whole landscape spread out before you. That’s obviously not true in time. Our experience of time is different from that of space in several ways.

First, we experience that time is unidirectional—the so-called arrow of time. The past is different from the future, even though the laws of physics are bidirectional. The classic example is an egg breaking. We see eggs crack and then break open, but never the opposite, an egg spontaneously healing its cracks. How do you reconcile the unidirectionality we see with the bidirectionality of the laws of physics?

The thinking, going back to the 19th century, is that time itself has no directionality and that the arrow is an emergent property of nature: something that’s not present at the foundations, but arises in the aggregate. The arrow characterizes the motion not of individual molecules, but of a mass of molecules. After all, there’s no such thing as an egg, broken or otherwise, in the basic laws. The difference between eggs in various states of repair, and therefore the directionality of the process, has to do with how the molecules are organized. The fresh egg is the most highly organized, the broken egg slightly less so, the shattered egg even less.

What I mean by the word “organized” is that there are more ways for the egg to be a little broken than pristine, and even more ways to be completely broken. So just by the laws of probability, the egg is more likely to be broken than not, and if you start with a pristine egg, practically anything the molecules do is likely to lead to breakage. The real question, then, is why you ever had a pristine egg to begin with. The probabilistic progression implies that whatever came before was even less probable, and before that, even less probable, all the way to the origin of the universe. The universe was originally in a very particular state.

Over time, the universe approaches the most probable, most generic state possible, a condition of complete dissipation known as heat death. Living things resist this overall trend toward degeneration; we carve out little pockets of order in an increasingly disorderly world. But in bucking the trend, we actually contribute to the overall degeneration. The act of living literally kills the universe.

And you know what makes it even more tragic? It’s forgetting that causes the most damage. Because the laws of physics are reversible, whenever we forget, the world must take on the burden of remembering for us. Forgetting—erasing—is essential to the process of creation. Art is tragic in many ways, but surely this is the worst.

The second way that time differs from space is that not only do we perceive a directionality to time, we perceive a “flow” to time: the sense that only the present moment is real. Yet physics and philosophical logic hold that time is laid out in its entirety—that the past and future exist equally. Otherwise, how could different observers slice up time differently? Whose “flow” would be right? Most scientists would argue that past, present, and future all exist, and we move among them like a car driving down the road. Some, to be sure, think it’s the physicists’ notion of time that should give.

The flow of time raises two questions. Why do we perceive it? That is, why don’t we see time as spatialized? Presumably that, too, has something to do with what it means to be alive. An even deeper question is: If the world is laid out and everything is preordained, does time matter at all? The state of the world at one time determines it at all times. The past and future exist in the present, as T.S. Eliot wrote:

Time present and time past

Are both perhaps present in time future,

And time future contained in time past.

If all time is eternally present

All time is unredeemable.

Third and finally, there’s a specific technical sense in which time doesn’t seem to matter at all. This is something that comes out of Einstein’s general theory of relativity. In this theory, not only do space and time unite, but they can distort,

Figure 3 - Spacetime not only can be divided up differently, it can distort, producing what we perceive as the force of gravity. The fact that time can distort is one of the reasons physicists suspect that it is not truly fundamental to nature.

They’re malleable. We become aware of this as the force of gravity. The problem comes when you try to describe the distortion of space as a process occurring in time. You find that the shapes space takes are mathematically different, but physically equivalent. So nothing truly changes. The world according to physics is frozen in place, incapable of true change, which flies in the face of what we see. This is one of the biggest reasons why it has been hard to unite general relativity with other theories of physics.

Lecturers on physics often mention the malleability of space without explaining what it means, so let me digress for just a moment to flesh it out a little bit. The idea is that our Earth, for example, bends both space and time. At the surface of our planet, the fractional distortion is about one part in a billion. The temporal distortion is a distortion to how fast clocks tick. The closer you are to the center of the Earth, the slower a clock will tick; clocks on the ground tick more slowly than they do in orbit. Space also gets distorted, altering the distance between objects, but most of the things we deal with, like baseballs, move so slowly that they don’t probe much of space. Their path through spacetime is mostly a path through time.

Figure 4a - In the conventional view, time is fundamental and defines the motion and oscillation of objects: a gear turns, a pendulum swings, and a heart beats once per second. In the relational view, time is derivative. Objects bear certain relationships to one another—a gear turns once per swing of a pendulum or beat of a heart—and we introduce the abstraction of time to make it easier to describe this web of relationships, much as we introduce money to simplify economic transactions.

What physicists do is define a notion of spacetime distance that includes both spatial distance and time duration. The baseball naturally follows a path that maximizes its spacetime distance; this is the spacetime counterpart to a straight line in space. Now, because the spacetime distance for a baseball is mostly just the time distance, this means that the baseball wants to maximize the duration of its flight, as measured by its own internal clock. And that means it wants to spend as much time far from the Earth’s center as it can. When it’s far out, its internal clock ticks faster, so the baseball maximizes its flight time out there. The ball wants to move slowly at the top of its arc and faster at the bottom, so it can linger as long as possible at the top. Thus it decelerates as it moves up, or conversely accelerates as it moves down.

In relativity theory, that’s why things accelerate toward the center of the Earth. If you throw a baseball, the curved arc is typically about a quadrillionth of a second longer than sitting on the ground. The baseball doesn’t want to go too crazy and fly off into deep space, though, or otherwise spatial distance would become a factor and the increases in duration would be offset by spatial distance. This balance is what determines the precise shape of the arc it follows.

I’m glossing over the details here, and I want to get back from this digression to my regularly scheduled program, but I just wanted to connect this concept of spacetime distortion that you may have heard about to something you can actually see and think about the text time you throw a ball up into the air.

In short, physicists face the problem that their concept of time doesn’t match our everyday experience of time. Ironically, their reaction is to go even farther away from everyday notions of time. The leading idea is that time is not fundamental. How could it be, if it can bend? Just as substances emerge from atoms, and we emerge from substances, time might emerge, too. The seemingly contradictory properties of time might emerge with it. So we can treat time (and space) much as we treat matter, bringing me back to the title of this talk.

Figure 4b

Just as you see structure such as atoms as you zoom in on matter, if you zoom in on the spacetime continuum, we may seem some kind of filigree structure. There might be a smallest meaningful time duration—an “atom” of time. These “atoms” of time would be governed by quantum theory, with its own rules. For instance, there would be no single unique arrangement of atoms. The spacetime we see would be a composite of all possible arrangements.

Even these atoms may not be truly fundamental. Space and time might emerge from still more fundamental ingredients. This is hard to get your head around. How do you describe emergence if it is something that occurs within time? Here’s one way that some physicists try. Earlier, I mentioned the role that time plays in ordering the world. You can flip this role on its head and say that the world has an order and time describes it. We usually assume time precedes and defines processes, but you could relate processes to one another without introducing time. Time provides a convenient but unnecessary medium of exchange, like money.

In that case, time is meaningful because processes in nature have a particular structure to their relationships. You can imagine a set of relationships that is too complicated to describe by a time parameter. So, the world, at root, may have no concept of duration. That concept, and the rest of structure of time, may have developed in the aggregate as the relationships organized themselves. Time does not impose order on the world, but rather the opposite.

As you can see, physicists have conflicted attitudes toward time. Let me close by noting this is also true of our culture. On the one hand, we’re hyperscheduled and obsessed with punctuality, especially here in New York. We have come to regard ageing as something to be resisted. On the other hand, we tell ourselves we need to relax about time, to spend quality time with people, to goof off online.

Our attitudes toward space are conflicted, too. Airline travel and telecommunications have made distance matter a lot less to us than it did to our grandparents. The modern world is defined by mobility, both geographical and social. At the same time, there’s an countervailing attitude that our individuality and independence are important to us—that we want to keep our distance from other people. And we obsess about the tradeoffs this involves. We bemoan that we feel disconnected from one another.

This conflict defines modern society, and physicists are discovering that it defines the physical universe as well. On the one hand, time may not matter at a fundamental level. It emerges. On the other hand, it has to emerge if we are to exist. Life is meaningless without time. We fight the ravages of time, but time gives us dynamism and purpose. On the one hand, distance, too, may be a construct. When two people are far apart, they might actually be right next to one another, considered in some broader sense. On the other hand, our existence requires the emergence of a concept of distance. The very concept of a “thing” requires it. If space and time had never emerged, the world would have remained a structureless mush.

Art thrives on tension, so this should give artists some rich ideas to explore, and physicists, for their part, can learn from artists that tension is not something to be explained away, but to be embraced.

George Musser is an editor at Scientific American magazine and the author of The Complete Idiot’s Guide to String Theory. He was a co-recipient of the National Magazine Award for editorial excellence for the magazine’s special issue “A Matter of Time” in September 2002.