From Eternity to Here (3 page)

The real universe is not an avant-garde film. We experience a degree of continuity through time—if the cat is on your lap now, there might be some danger that she will stalk off, but there is little worry that she will simply dematerialize into nothingness one moment later. This continuity is not absolute, at the microscopic level; particles can appear and disappear, or at least transform under the right conditions into different kinds of particles. But there is not a wholesale rearrangement of reality from moment to moment.

This phenomenon of persistence allows us to think about “the world” in a different way. Instead of a collection of things distributed through space that keep changing into different configurations, we can think of the entire
history
of the world, or any particular thing in it, in one fell swoop. Rather than thinking of Miss Kitty as a particular arrangement of cells and fluids, we can think of her entire life stretching through time, from birth to death. The history of an object (a cat, a planet, an electron) through time defines its
world line
—the trajectory the object takes through space as time passes.
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The world line of an object is just the complete set of positions the object has in the world, labeled by the particular time it was in each position.

Figure 1:
The world, ordered into different moments of time. Objects (including people and cats) persist from moment to moment, defining world lines that stretch through time.

Finding ourselves

Thinking of the entire history of the universe all at once, rather than thinking of the universe as a set of things that are constantly moving around, is the first step toward thinking of time as “kind of like space,” which we will examine further in the chapters to come. We use both time and space to help us pinpoint things that happen in the universe. When you want to meet someone for coffee, or see a certain showing of a movie, or show up for work along with everyone else, you need to specify a time: “Let’s meet at the coffee shop at 6:00 P.M. this Thursday.”

If you want to meet someone, of course, it’s not sufficient just to specify a time; you also need to specify a place. (Which coffee shop are we talking about here?) Physicists say that space is “three-dimensional.” What that means is that we require three numbers to uniquely pick out a particular location. If the location is near the Earth, a physicist might give the latitude, longitude, and height above ground. If the location is somewhere far away, astronomically speaking, we might give its direction in the sky (two numbers, analogous to latitude and longitude), plus the distance from Earth. It doesn’t matter how we choose to specify those three numbers; the crucial point is that you will always need exactly three. Those three numbers are the
coordinates
of that location in space. We can think of a little label attached to each point, telling us precisely what the coordinates of that point are.

Figure 2:
Coordinates attached to each point in space.

In everyday life, we can often shortcut the need to specify all three coordinates of space. If you say “the coffee shop at Eighth and Main Street,” you’re implicitly giving two coordinates—“Eighth” and “Main Street”—and you’re assuming that we all agree the coffee shop is likely to be at ground level, rather than in the air or underground. That’s a convenience granted to us by the fact that much of the space we use to locate things in our daily lives is effectively two-dimensional, confined near the surface of the Earth. But in principle, all three coordinates are needed to specify a point in space.

Each point in space occurs once at each moment of time. If we specify a certain location in space at one definite moment in time, physicists call that an
event
. (This is not meant to imply that it’s an especially exciting event; any random point in empty space at any particular moment of time would qualify, so long as it’s uniquely specified.) What we call the “universe” is just the set of all events—every point in space, at every moment of time. So we need four numbers—three coordinates of space, and one of time—to uniquely pick out an event. That’s why we say that the universe is four-dimensional. This is such a useful concept that we will often treat the whole collection, every point in space at every moment of time, as a single entity called
spacetime
.

This is a big conceptual leap, so it’s worth pausing to take it in. It’s natural to think of the world as a three-dimensional conglomeration that keeps changing (“happening over and over again, slightly differently each time”). We’re now suggesting that we can think of the whole shebang, the entire history of the world, as a single four-dimensional thing, where the additional dimension is time. In this sense, time serves to slice up the four-dimensional universe into copies of space at each moment in time—the whole universe at 10:00 A.M. on January 20, 2010; the whole universe at 10:01 A.M. on January 20, 2010; and so on. There are an infinite number of such slices, together making up the universe.

2. Time measures the duration elapsed between events

The second aspect of time is that it measures the duration elapsed between events. That sounds pretty similar to the “labels moments in the universe” aspect already discussed, but there is a difference. Time not only labels and orders different moments; it also measures the distance between them.

When taking up the mantle of philosopher or scientist and trying to make sense of a subtle concept, it’s helpful to look at things operationally—how do we actually use this idea in our experience? When we use time, we refer to the measurements that we get by reading clocks. If you watch a TV show that is supposed to last one hour, the reading on your clock at the end of the show will be one hour later than what it read when the show began. That’s what it
means
to say that one hour elapsed during the broadcast of that show: Your clock read an hour later when it ended than when it began.

But what makes a good clock? The primary criterion is that it should be consistent—it wouldn’t do any good to have a clock that ticked really fast sometimes and really slowly at others. Fast or slow compared to what? The answer is: other clocks. As a matter of empirical fact (rather than logical necessity), there are some objects in the universe that are consistently periodic—they do the same thing over and over again, and when we put them next to one another we find them repeating in predictable patterns.

Think of planets in the Solar System. The Earth orbits around the Sun, returning to the same position relative to the distant stars once every year. By itself, that’s not so meaningful—it’s just the definition of a “year.” But Mars, as it turns out, returns to the same position once every 1.88 years. That kind of statement is extremely meaningful—without recourse to the concept of a “year,” we can say that Earth moves around the Sun 1.88 times every time Mars orbits just once.
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Likewise, Venus moves around the Sun 1.63 times every time Earth orbits just once.

The key to measuring time is
synchronized repetition
—a wide variety of processes occur over and over again, and the number of times that one process repeats itself while another process returns to its original state is reliably predictable. The Earth spins on its axis, and it’s going to do so 365.25 times every time the Earth moves around the Sun. The tiny crystal in a quartz watch vibrates 2,831,155,200 times every time the Earth spins on its axis. (That’s 32,768 vibrations per second, 3,600 seconds in an hour, 24 hours in a day.
⁵
) The reason why quartz watches are reliable is that quartz crystal has extremely regular vibrations; even as the temperature or pressure changes, the crystal will vibrate the same number of times for every one rotation of the Earth.

So when we say that something is a good clock, we mean that it repeats itself in a predictable way relative to other good clocks. It is a fact about the universe that such clocks exist, and thank goodness. In particular, at the microscopic level where all that matters are the rules of quantum mechanics and the properties (masses, electric charges) of individual elementary particles, we find atoms and molecules that vibrate with absolutely predictable frequencies, forming a widespread array of excellent clocks marching in cheerful synchrony. A universe without good clocks—in which no processes repeated themselves a predictable number of times relative to other repeating processes—would be a scary universe indeed.
⁶

Still, good clocks are not easy to come by. Traditional methods of timekeeping often referred to celestial objects—the positions of the Sun or stars in the sky—because things down here on Earth tend to be messy and unpredictable. In 1581, a young Galileo Galilei reportedly made a breakthrough discovery while he sat bored during a church service in Pisa. The chandelier overhead would swing gently back and forth, but it seemed to move more quickly when it was swinging widely (after a gust of wind, for example) and more slowly when wasn’t moving as far. Intrigued, Galileo decided to measure how much time it took for each swing, using the only approximately periodic event to which he had ready access: the beating of his own pulse. He found something interesting: The number of heartbeats between swings of the chandelier was roughly the same, regardless of whether the swings were wide or narrow. The size of the oscillations—how far the pendulum swung back and forth—didn’t affect the frequency of those oscillations. That’s not unique to chandeliers in Pisan churches; it’s a robust property of the kind of pendulum physicists call a “simple harmonic oscillator.” And that’s why pendulums form the centerpiece of grandfather clocks and other timekeeping devices: Their oscillations are extremely reliable. The craft of clock making involves the search for ever-more-reliable forms of oscillations, from vibrations in quartz to atomic resonances.

Our interest here is not really in the intricacies of clock construction, but in the meaning of time. We live in a world that contains all sorts of periodic processes, which repeat a predictable number of times in comparison to certain other periodic processes. And that’s how we measure duration: by the number of repetitions of such a process. When we say that our TV program lasts one hour, we mean that the quartz crystal in our watch will oscillate 117,964,800 times between the start and end of the show (32,768 oscillations per second, 3,600 seconds in an hour).

Notice that, by being careful about defining time, we seem to have eradicated the concept entirely. That’s just what any decent definition should do—you don’t want to define something in terms of itself. The passage of time can be completely recast in terms of certain things happening together, in synchrony. “The program lasts one hour” is equivalent to “there will be 117,964,800 oscillations of the quartz crystal in my watch between the beginning and end of the program” (give or take a few commercials). If you really wanted to, you could reinvent the entire superstructure of physics in a way that completely eliminated the concept of “time,” by replacing it with elaborate specifications of how certain things happen in coincidence with certain other things.
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But why would we want to? Thinking in terms of time is convenient, and more than that, it reflects a simple underlying order in the way the universe works.

Figure 3:
Good clocks exhibit synchronized repetition. Every time one day passes, the Earth rotates once about its axis, a pendulum with a period of 1 second oscillates 86,400 times, and a quartz watch crystal vibrates 2,831,155,200 times.

Slowing, stopping, bending time

Armed with this finely honed understanding of what we mean by the passage of time, at least one big question can be answered: What would happen if time were to slow down throughout the universe? The answer is: That’s not a sensible question to ask. Slow down relative to what? If time is what clocks measure, and every clock were to “slow down” by the same amount, it would have absolutely no effect at all. Telling time is about synchronized repetition, and as long as the rate of one oscillation is the same relative to some other oscillation, all is well.