The Fabric of the Cosmos: Space, Time, and the Texture of Reality (18 page)

Similarly, there are things about our future, such as who will win the U.S. presidential election in the year 2100, that seem completely open: more than likely, the candidates for that election haven't even been born, much less decided to run for office. But if Chewie gets up from his chair and walks toward earth at about 6.4 miles per hour, his now-slice—his conception of what exists, his conception of what has happened
—will
include the selection of the first president of the twenty-second century. Something that seems completely undecided to us is something that, for him, has already happened. Again, Chewie won't know the outcome of the election for billions of years, since that's how long it will take our television signals to reach him. But when word of the election results reaches Chewie's descendants and they use it to update Chewie's flip-card book of history, his collection of past now-lists, they will find that the election results belong on the same now-list in which Chewie got up and started walking toward earth—a now-list, Chewie's descendants note, that occurs just a moment after one that contains you, in the early years of earth's twenty-first century, finishing this paragraph.

This example highlights two important points. First, although we are used to the idea that relativistic effects become apparent at speeds near that of light, even at low velocities relativistic effects can be greatly amplified when considered over large distances in space. Second, the example gives insight into the issue of whether spacetime (the loaf) is really an entity or just an abstract concept, an abstract union of space right
now
together with its history and purported future.

You see, Chewie's conception of reality, his freeze-frame mental image, his conception of what exists
now,
is every bit as real for him as our conception of reality is for us. So, in assessing what constitutes reality, it would be stunningly narrow-minded if we didn't also include his perspective. For Newton, such an egalitarian approach wouldn't make the slightest difference, because, in a universe with absolute space and absolute time, everyone's now-slice coincides. But in a relativistic universe, our universe, it makes a big difference. Whereas our familiar conception of what exists right now amounts to a single now-slice—we usually view the past as gone and the future as yet to be—we must augment this image with Chewie's now-slice, a now-slice that, as the discussion revealed, can differ substantially from our own. Furthermore, since Chewie's initial location and the speed with which he moves are arbitrary, we should include the now-slices associated with all possibilities. These now-slices, as in our discussion above, would be centered on Chewie's—or some other real or hypothetical observer's—initial location in space and would be rotated at an angle that depends on the velocity chosen. (The only restriction comes from the speed limit set by light and, as explained in the notes, in the graphic depiction we are using this translates into a limit on the rotation angle of 45 degrees, either clockwise or counterclockwise.) As you can see, in Figure 5.5, the collection of all these now-slices fills out a substantial region of the spacetime loaf. In fact, if space is infinite—if now-slices extended infinitely far—then the rotated now-slices can be centered arbitrarily far away, and hence their union sweeps through
every
point in the spacetime loaf.
⁹

So:
if you buy the notion that reality consists of the things in your
freeze-frame mental image right now, and if you agree that your
now
is no
more valid than the
now
of someone located far away in space who can
move freely, then reality encompasses all of the events in spacetime.
The total loaf exists. Just as we envision all of space as
really
being out there, as
really
existing, we should also envision all of time as
really
being out there, as
really
existing, too. Past, present, and future certainly appear to be distinct entities. But, as Einstein once said, "For we convinced physicists, the distinction between past, present, and future is only an illusion, however persistent."
⁵
The only thing that's real is the whole of spacetime.

Figure 5.5 A sample of now-slices for a variety of observers (real or hypothetical) situated at a variety of distances from earth, moving with a variety of velocities.

In this way of thinking, events, regardless of when they happen from any particular perspective, just
are.
They all exist. They eternally occupy their particular point in spacetime. There is no flow. If you were having a great time at the stroke of midnight on New Year's Eve, 1999, you still are, since that is just one immutable location in spacetime. It is tough to accept this description, since our worldview so forcefully distinguishes between past, present, and future. But if we stare intently at this familiar temporal scheme and confront it with the cold hard facts of modern physics, its only place of refuge seems to lie within the human mind.

Undeniably, our conscious experience seems to sweep through the slices. It is as though our minds provide the projector light referred to earlier, so that moments of time come to life when they are illuminated by the power of consciousness. The flowing sensation from one moment to the next arises from our conscious recognition of change in our thoughts, feelings, and perceptions. And the sequence of change seems to have a continuous motion; it seems to unfold into a coherent story. But—without any pretense of psychological or neurobiological precision—we can envision how we might experience a flow of time even though, in actuality, there may be no such thing. To see what I mean, imagine playing
Gone with the Wind
through a faulty DVD player that randomly jumps forward and backward: one still frame flashes momentarily on the screen and is followed immediately by another from a completely different part of the film. When you watch this jumbled version, it will be hard for you to make sense of what's going on. But Scarlett and Rhett have no problem. In each frame, they do what they've always done in that frame. Were you able to stop the DVD on some particular frame and ask them about their thoughts and memories, they'd respond with the same answers they would have given had you played the DVD in a properly functioning player. If you asked them whether it was confusing to romp through the Civil War out of order, they'd look at you quizzically and figure you'd tossed back one too many mint juleps. In any given frame, they'd have the thoughts and memories they've always had in that frame—and, in particular, those thoughts and memories would give them the sensation that time is smoothly and coherently flowing forward, as usual.

Similarly, each moment in spacetime—each time slice—is like one of the still frames in a film. It exists whether or not some light illuminates it. As for Scarlett and Rhett, to the you who is in any such moment, it
is
the
now,
it
is
the moment you experience at
that
moment. And it always will be. Moreover, within each individual slice, your thoughts and memories are sufficiently rich to yield a sense that time has continuously flowed to that moment. This feeling, this sensation that time is flowing, doesn't require previous moments—previous frames—to be "sequentially illuminated."
⁶

And if you think about it for one more moment, you'll realize that's a very good thing, because the notion of a projector light sequentially bringing moments to life is highly problematic for another, even more basic reason. If the projector light properly did its job and illuminated a given moment—say, the stroke of midnight, New Year's Eve, 1999—what would it mean for that moment to then go dark? If the moment were lit, then being illuminated would be a feature of the moment, a feature as everlasting and unchanging as everything else happening at that moment. To experience illumination—to be "alive," to be the present, to be
the
now—
and to then experience darkness—to be "dormant," to be the past, to be what was—is to experience change.
But the concept of change has no
meaning with respect to a single moment in time.
The change would have to occur through time, the change would mark the passing of time, but what notion of time could that possibly be? By definition, moments
don't
include the passing of time—at least, not the time we're aware of— because moments just are, they are the raw material of time, they
don't
change. A particular moment can no more change in time than a particular location can move in space: if the location were to move, it would be a different location in space; if a moment in time were to change, it would be a different moment in time. The intuitive image of a projector light that brings each new
now
to life just doesn't hold up to careful examination. Instead, every moment is illuminated, and every moment remains illuminated. Every moment
is.
Under close scrutiny, the flowing river of time more closely resembles a giant block of ice with every moment forever frozen into place.
⁷

This conception of time is significantly different from the one most of us have internalized. Even though it emerged from his own insights, Einstein was not hardened to the difficulty of fully absorbing such a profound change in perspective. Rudolf Carnap
⁸
recounts a wonderful conversation he had with Einstein on this subject: "Einstein said that the problem of the now worried him seriously. He explained that the experience of the now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation."

This resignation leaves open a pivotal question: Is science unable to grasp a fundamental quality of time that the human mind embraces as readily as the lungs take in air, or does the human mind impose on time a quality of its own making, one that is artificial and that hence does not show up in the laws of physics? If you were to ask me this question during the working day, I'd side with the latter perspective, but by nightfall, when critical thought eases into the ordinary routines of life, it's hard to maintain full resistance to the former viewpoint. Time is a subtle subject and we are far from understanding it fully. It is possible that some insightful person will one day devise a new way of looking at time and reveal a bona fide physical foundation for a time that flows. Then again, the discussion above, based on logic and relativity, may turn out to be the full story. Certainly, though, the feeling that time flows is deeply ingrained in our experience and thoroughly pervades our thinking and language. So much so, that we have lapsed, and will continue to lapse, into habitual, colloquial descriptions that refer to a flowing time. But don't confuse language with reality. Human language is far better at capturing human experience than at expressing deep physical laws.

A thousand times a day, our experiences reveal a distinction between things unfolding one way in time and the reverse. A piping hot pizza cools down en route from Domino's, but we never find a pizza arriving hotter than when it was removed from the oven. Cream stirred into coffee forms a uniformly tan liquid, but we never see a cup of light coffee unstir and separate into white cream and black coffee. Eggs fall, cracking and splattering, but we never see splattered eggs and eggshells gather together and coalesce into uncracked eggs. The compressed carbon dioxide gas in a bottle of Coke rushes outward when we twist off the cap, but we never find spread-out carbon dioxide gas gathering together and swooshing back into the bottle. Ice cubes put into a glass of room-temperature water melt, but we never see globules in a room-temperature glass of water coalesce into solid cubes of ice. These common sequences of events, as well as countless others, happen in only one temporal order. They never happen in reverse, and so they provide a notion of before and after—they give us a consistent and seemingly universal conception of past and future. These observations convince us that were we to examine all of spacetime from the outside (as in Figure 5.1), we would see significant asymmetry along the time axis. Splattered eggs the world over would lie to one side—the side we conventionally call the future—of their whole, unsplattered counterparts.

Perhaps the most pointed example of all is that our minds seem to have access to a collection of events that we call the past—our memories—but none of us seems able to remember the collection of events we call the future. So it seems obvious that there is a big difference between the past and the future. There seems to be a manifest orientation to how an enormous variety of things unfold in time. There seems to be a manifest distinction between the things we can remember (the past) and the things we cannot (the future). This is what we mean by time's having an orientation, a direction, or an arrow.
¹

Physics, and science more generally, is founded on regularities. Scientists study nature, find patterns, and codify these patterns in natural laws. You would think, therefore, that the enormous wealth of regularity leading us to perceive an apparent arrow of time would be evidence of a fundamental law of nature. A silly way to formulate such a law would be to introduce the Law of Spilled Milk, stating that glasses of milk spill but don't unspill, or the Law of Splattered Eggs, stating that eggs break and splatter but never unsplatter and unbreak. But that kind of law buys us nothing: it is merely descriptive, and offers no explanation beyond a simple observation of what happens. Yet we expect that somewhere in the depths of physics there must be a less silly law describing the motion and properties of the particles that make up pizza, milk, eggs, coffee, people, and stars—the fundamental ingredients of everything—that shows why things evolve through one sequence of steps but never the reverse. Such a law would give a fundamental explanation to the observed arrow of time.

The perplexing thing is that no one has discovered any such law. What's more, the laws of physics that have been articulated from Newton through Maxwell and Einstein, and up until today, show a
complete symmetry
between past and future.
¹⁰
Nowhere in any of these laws do we find a stipulation that they apply one way in time but not in the other. Nowhere is there any distinction between how the laws look or behave when applied in either direction in time. The laws treat what we call past and future on a completely equal footing. Even though experience reveals over and over again that there is an arrow of how events unfold in time, this arrow seems not to be found in the fundamental laws of physics.

How can this be? Do the laws of physics provide no underpinning that distinguishes past from future? How can there be no law of physics explaining that events unfold in
this
order but never in reverse?

The situation is even more puzzling. The known laws of physics actually declare—contrary to our lifetime of experiences—that light coffee can separate into black coffee and white cream; a splattered yolk and a collection of smashed shell pieces can gather themselves together and form a perfectly smooth unbroken egg; the melted ice in a glass of room-temperature water can fuse back together into cubes of ice; the gas released when you open your soda can rush back into the bottle. All the physical laws that we hold dear fully support what is known as
time-reversalsymmetry.
This is the statement that if some sequence of events can unfold in one temporal order (cream and coffee mix, eggs break, gas rushes outward) then these events can also unfold in reverse (cream and coffee unmix, eggs unbreak, gas rushes inward). I'll elaborate on this shortly, but the one-sentence summary is that not only do known laws fail to tell us why we see events unfold in only one order, they also tell us that, in theory, events can unfold in reverse order.
¹¹

The burning question is
Why don't we ever see such things?
I think it's a safe bet that no one has ever actually witnessed a splattered egg unsplattering. But if the laws of physics allow it, and if, moreover, those laws treat splattering and unsplattering equally, why does one never happen while the other does?

As a first step toward resolving this puzzle, we need to understand in more concrete terms what it means for the known laws of physics to be time-reversal symmetric. To this end, imagine it's the twenty-fifth century and you're playing tennis in the new interplanetary league with your partner, Coolstroke Williams. Somewhat unused to the reduced gravity on Venus, Coolstroke hits a gargantuan backhand that launches the ball into the deep, isolated darkness of space. A passing space shuttle films the ball as it goes by and sends the footage to CNN (Celestial News Network) for broadcast. Here's the question: If the technicians at CNN were to make a mistake and run the film of the tennis ball in reverse, would there be any way to tell? Well, if you knew the heading and orientation of the camera during the filming you might be able to recognize their error. But could you figure it out solely by looking at the footage itself, with no additional information? The answer is no. If in the correct (forward) time direction the footage showed the ball floating by from left to right, then in reverse it would show the ball floating by from right to left. And certainly, the laws of classical physics allow tennis balls to move either left or right. So the motion you see when the film is run in either the forward time direction or the reverse time direction is perfectly consistent with the laws of physics.

We've so far imagined that no forces were acting on the tennis ball, so that it moved with constant velocity. Let's now consider the more general situation by including forces. According to Newton, the effect of a force is to change the velocity of an object: forces impart accelerations. Imagine, then, that after floating awhile through space, the ball is captured by Jupiter's gravitational pull, causing it to move with increasing speed in a downward, rightward-sweeping arc toward Jupiter's surface, as in Figures 6.1a and 6.1b. If you play a film of this motion in reverse, the tennis ball will appear to move in an arc that sweeps upward and toward the left, away from Jupiter, as in Figure 6.1c. Here's the new question: is the motion depicted by the film when played backward—the time-reversed motion of what was actually filmed—allowed by the classical laws of physics? Is it motion that could happen in the real world? At first, the answer seems obviously to be yes: tennis balls can move in downward arcs to the right or upward arcs to the left, or, for that matter, in innumerable other trajectories. So what's the difficulty? Well, although the answer is indeed yes, this reasoning is too glib and misses the real intent of the question.

Figure 6.1 (a) A tennis ball flying from Venus to Jupiter together with (b) a close-up. (c) Tennis ball's motion if its velocity is reversed just before it hits Jupiter.

When you run the film in reverse, you see the tennis ball leap from Jupiter's surface, moving upward and toward the left, with exactly the same speed (but in exactly the opposite direction) from when it hit the planet. This initial part of the film is certainly consistent with the laws of physics: we can imagine, for example, someone launching the tennis ball from Jupiter's surface with precisely this velocity. The essential question is whether the
rest
of the reverse run is also consistent with the laws of physics. Would a ball launched with this initial velocity—and subject to Jupiter's downward-pulling gravity—actually move along the trajectory depicted in the rest of the reverse run film? Would it exactly retrace its original downward trajectory, but in reverse?

The answer to this more refined question
is
yes. To avoid any confusion, let's spell this out. In Figure 6.1a, before Jupiter's gravity had any significant effect, the ball was heading purely to the right. Then, in Figure 6.1b, Jupiter's powerful gravitational force caught hold of the ball and pulled it toward the planet's center—a pull that's mostly downward but, as you can see in the figure, is also partially to the right. This means that as the ball closed in on Jupiter's surface, its rightward speed had increased somewhat, but its downward speed had increased dramatically. In the reverse run film, therefore, the ball's launch from Jupiter's surface would be headed somewhat
leftward
but predominantly
upward,
as in Figure 6.1c. With this starting velocity, Jupiter's gravity would have had its greatest impact on the ball's upward speed, causing it to go slower and slower, while also decreasing the ball's leftward speed, but less dramatically. And with the ball's upward speed rapidly diminishing, its motion would become dominated by its speed in the leftward direction, causing it to follow an upward-arcing trajectory toward the left. Near the end of this arc, gravity would have sapped all the upward motion as well as the additional rightward velocity Jupiter's gravity imparted to the ball on its way down, leaving the ball moving purely to the left with exactly the same speed it had on its initial approach.

All this can be made quantitative, but the point to notice is that this trajectory is exactly the reverse of the ball's original motion. Simply by reversing the ball's velocity, as in Figure 6.1c—by setting it off with the same speed but in the opposite direction—one can make it fully retrace its original trajectory, but in reverse. Bringing the film back into the discussion, we see that the upward-arcing trajectory to the left—the trajectory we just figured out with reasoning based on Newton's laws of motion—is exactly what we would see upon running the film in reverse. So the ball's time-reversed motion, as depicted in the reverse-run film, conforms to the laws of physics just as surely as its forward-time motion. The motion we'd see upon running the film in reverse is motion that could
really
happen in the real world.

Although there are a few subtleties I've relegated to the endnotes, this conclusion is general.
²
All the known and accepted laws relating to motion—from Newton's mechanics just discussed, to Maxwell's electromagnetic theory, to Einstein's special and general theories of relativity (remember, we are putting off quantum mechanics until the next chapter)—embody time-reversal symmetry: motion that can occur in the usual forward-time direction can equally well occur in reverse. As the terminology can be a bit confusing, let me reemphasize that we are not reversing time. Time is doing what it always does. Instead, our conclusion is that
we
can make an object trace its trajectory in reverse by the simple procedure of
reversing its velocity at any point along its path.
Equivalently, the same procedure—reversing the object's velocity at some point along its path— would make the object execute the motion we'd see in a reverse-run film.