From Eternity to Here (4 page)

As human beings we
feel
the passage of time. That’s because there are periodic processes occurring within our own metabolism—breaths, heartbeats, electrical pulses, digestion, rhythms of the central nervous system. We are a complicated, interconnected collection of clocks. Our internal rhythms are not as reliable as a pendulum or a quartz crystal; they can be affected by external conditions or our emotional states, leading to the impression that time is passing more quickly or more slowly. But the truly reliable clocks ticking away inside our bodies—vibrating molecules, individual chemical reactions—aren’t moving any faster or slower than usual.
⁸

What could happen, on the other hand, is that certain physical processes that we thought were “good clocks” would somehow go out of synchronization—one clock slows down, or speeds up, compared to all the rest. A sensible response in that case would be to blame that particular clock, rather than casting aspersions on time itself. But if we stretch a bit, we can imagine a particular collection of clocks (including molecular vibrations and other periodic processes) that all change in concert with one another, but apart from the rest of the world. Then we would have to ask whether it was appropriate to say that the rate at which time passes had really changed within that collection.

Consider an extreme example. Nicholson Baker’s novel
The Fermata
tells the story of a man, Arno Strine, with the ability to “stop time.” (Mostly he uses this miraculous power to go around undressing women.) It wouldn’t mean anything if time stopped everywhere; the point is that Arno keeps moving through time, while everything around him stops. We all know this is unrealistic, but it’s instructive to reflect upon the way in which it flouts the laws of physics. What this approach to stopping time entails is that every kind of motion and rhythm in Arno’s body continues as usual, while every kind of motion and rhythm in the outside world freezes absolutely still. Of course we have to imagine that time continues for all of the air and fluids within Arno, otherwise he would instantly die. But if the air in the rest of the room has truly stopped experiencing time, each molecule must remain suspended precisely in its location; consequently, Arno would be unable to move, trapped in a prison of rigidly stationary air molecules. Okay, let’s be generous and assume that time would proceed normally for any air molecules that came sufficiently close to Arno’s skin. (The book alludes to something of the sort.) But everything outside, by assumption, is not changing in any way. In particular, no sound or light would be able to travel to him from the outside world; Arno would be completely deaf and blind. It turns out not to be a promising environment for a Peeping Tom.
⁹

What if, despite all the physical and narrative obstacles, something like this really could happen? Even if we can’t stop time around us, presumably we can imagine speeding up the motion of some local clocks. If we truly measure time by synchronized repetition, and we arranged an ensemble of clocks that were all running fast compared to the outside world while they remained in synchrony with one another, wouldn’t that be something like “time running faster” within that arrangement?

It depends. We’ve wandered far afield from what might actually happen in the real world, so let’s establish some rules. We’re fortunate enough to live in a universe that features very reliable clocks. Without such clocks, we can’t use time to measure the duration between events. In the world of
The Fermata
, we could say that time slowed down for the universe outside Arno Strine—or, equivalently and perhaps more usefully, that time for him sped up, while the rest of the world went on as usual. But just as well, we could say that “time” was completely unaffected, and what changed were the laws of particle physics (masses, charges on different particles) within Arno’s sphere of influence. Concepts like “time” are not handed to us unambiguously by the outside world but are invented by human beings trying to make sense of the universe. If the universe were very different, we might have to make sense of it in a different way.

Meanwhile, there is a very real way for one collection of clocks to measure time differently than another: have them move along different paths through spacetime. That’s completely compatible with our claim that “good clocks” should measure time in the same way, because we can’t readily compare clocks unless they’re next to one another in space. The total amount of time elapsed on two different trajectories can be different without leading to any inconsistencies. But it does lead to something important—the theory of relativity.

Twisty paths through spacetime

Through the miracle of synchronized repetition, time doesn’t simply put different moments in the history of the universe into order; it also tells us “how far apart” they are (in time). We can say more than “1776 happened before 2010”; we can say “1776 happened 234 years before 2010.”

I should emphasize a crucial distinction between “dividing the universe into different moments” and “measuring the elapsed time between events,” a distinction that will become enormously important when we get to relativity. Let’s imagine you are an ambitious temporal
¹⁰
engineer, and you’re not satisfied to just have your wristwatch keep accurate time; you want to be able to know what time it is at every other event in spacetime as well. You might be tempted to wonder: Couldn’t we (hypothetically) construct a time coordinate all throughout the universe, just by building an infinite number of clocks, synchronizing them to the same time, and scattering them throughout space? Then, wherever we went in spacetime, there would be a clock sitting at each point telling us what time it was, once and for all.

The real world, as we will see, doesn’t let us construct an absolute universal time coordinate. For a long time people thought it did, under no less an authority than that of Sir Isaac Newton. In Newton’s view of the universe, there was one particular right way to slice up the universe into slices of “space at a particular moment of time.” And we could indeed, at least in a thought-experiment kind of way, send clocks all throughout the universe to set up a time coordinate that would uniquely specify when a certain event was taking place.

But in 1905, along comes Einstein with his special theory of relativity.
¹¹
The central conceptual breakthrough of special relativity is that our two aspects of time, “time labels different moments” and “time is what clocks measure,” are
not
equivalent, or even interchangeable. In particular, the scheme of setting up a time coordinate by sending clocks throughout the universe
would not work
: two clocks, leaving the same event and arriving at the same event but taking different paths to get there, will generally experience different durations along the journey, slipping out of synchronization. That’s not because we haven’t been careful enough to pick “good clocks,” as defined above. It’s because
the duration elapsed along two trajectories connecting two events in spacetime need not be the same
.

This idea isn’t surprising, once we start thinking that “time is kind of like space.” Consider an analogous statement, but for space instead of time: The distance traveled along two paths connecting two points in space need not be the same. Doesn’t sound so surprising at all, does it? Of course we can connect two points in space by paths with different lengths; one could be straight and one could be curved, and we would always find that the distance along the curved path was greater. But the difference in
coordinates
between the same two points is always the same, regardless of how we get from one point to another. That’s because, to drive home the obvious, the distance you travel is not the same as your change in coordinates. Consider a running back in football who zips back and forth while evading tacklers, and ends up advancing from the 30-yard line to the 80-yard line. (It should really be “the opponent’s 20-yard line,” but the point is clearer this way.) The change in coordinates is 50 yards, no matter how long or short was the total distance he ran.

Figure 4:
Yard lines serve as coordinates on a football field. A running back who advances the ball from the 30-yard line to the 80-yard line has changed coordinates by 50 yards, even though the distance traveled may have been much greater.

The centerpiece of special relativity is the realization that
time is like that
. Our second definition, time is duration as measured by clocks, is analogous to the total length of a path through space; the clock itself is analogous to an odometer or some other instrument that measures the total distance traveled. This definition is simply not the same as the concept of a coordinate labeling different slices of spacetime (analogous to the yard lines on a football field). And this is not some kind of technical problem that we can “fix” by building better clocks or making better choices about how we travel through spacetime; it’s a feature of how the universe works, and we need to learn to live with it.

As fascinating and profound as it is that time works in many ways similar to space, it will come as no surprise that there are crucial differences as well. Two of them are central elements of the theory of relativity. First, while there are three dimensions of space, there is only one of time; that brute fact has important consequences for physics, as you might guess. And second, while a straight line between two points in space describes the shortest distance, a straight trajectory between two events in spacetime describes the
longest
elapsed duration.

But the most obvious, blatant, unmistakable difference between time and space is that time has a direction, and space doesn’t. Time points from the past toward the future, while (out there in space, far away from local disturbances like the Earth) all directions of space are created equal. We can invert directions in space without doing damage to how physics works, but all sorts of real processes can happen in one direction of time but not the other. It’s to this crucial difference that we now turn.

3. Time is a medium through which we move

The sociology experiment suggested at the beginning of this chapter, in which you ask strangers how they would define “time,” also serves as a useful tool for distinguishing physicists from non-physicists. Nine times out of ten, a physicist will say something related to one of the first two notions above—time is a coordinate, or time is a measure of duration. Equally often, a non-physicist will say something related to the third aspect we mentioned—time is something that flows from past to future. Time whooshes along, from “back then” to “now” and on toward “later.”

Or, conversely, someone might say that we move through time, as if time were a substance through which we could pass. In the Afterword to his classic
Zen and the Art of Motorcycle Maintenance
, Robert Pirsig relates a particular twist on this metaphor. The ancient Greeks, according to Pirsig, “saw the future as something that came upon them from behind their backs, with the past receding away before their eyes.”
¹²
When you think about it, that seems a bit more honest than the conventional view that we march toward the future and away from the past. We know something about the past, from experience, while the future is more conjectural.

Common to these perspectives is the idea that time is a
thing
, and it’s a thing that can
change
—flow around us, or pass by as we move through it. But conceptualizing time as some sort of substance with its own dynamics, perhaps even the ability to change at different rates depending on circumstances, raises one crucially important question.

What in the world is that supposed to
mean
?

Consider something that actually does flow, such as a river. We can think about the river from a passive or an active perspective: Either we are standing still as the water rushes by, or perhaps we are on a boat moving along with the river as the banks on either side move relative to us.

The river flows, no doubt about that. And what that means is that the location of some particular drop of river water
changes with time
—here it is at some moment, there it is just a bit later. And we can talk sensibly about the
rate
at which the river flows, which is just the velocity of the water—in other words, the distance that the water travels in a given amount of time. We could measure it in miles per hour, or meters per second, or whatever units of “distance traveled per interval of time” you prefer. The velocity may very well change from place to place or moment to moment—sometimes the river flows faster; sometimes it flows more slowly. When we are talking about the real flow of actual rivers, all this language makes perfect sense.