by Brian Greene
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.
6 - Chance and the Arrow
DOES TIME HAVE A DIRECTION?
Even if time doesn't flow, it still makes sense to ask whether it has an arrow—whether there is a direction to the way things unfold in time that can be discerned in the laws of physics. It is the question of whether there is some intrinsic order in how events are sprinkled along spacetime and whether there is an essential scientific difference between one ordering of events and the reverse ordering. As everyone already knows, there certainly appears to be a huge distinction of this sort; it's what gives life promise and makes experience poignant. Yet, as we'll see, explaining the distinction between past and future is harder than you'd think. Rather remarkably, the answer we'll settle upon is intimately bound up with the precise conditions at the origin of the universe.
The Puzzle
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.
Past, Future, and 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?
Time-Reversal Symmetry
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.
Tennis Balls and Splattering Eggs
Watching a tennis ball shoot between Venus and Jupiter—in either direction—is not particularly interesting. But as the conclusion we've reached is widely applicable, let's now go someplace more exciting: your kitchen. Place an egg on your kitchen counter, roll it toward the edge, and let it fall to the ground and splatter. To be sure, there is a lot of motion in this sequence of events. The egg falls. The shell cracks apart. Yolk splatters this way and that. The floorboards vibrate. Eddies form in the surrounding air. Friction generates heat, causing the atoms and molecules of the egg, floor, and air to jitter a little more quickly. But just as the laws of physics show us how we can make the tennis ball trace its precise path in reverse, the same laws show how we can make every piece of eggshell, every drop of yolk, every section of flooring, and every pocket of air exactly trace its motion in reverse, too. "All" we need do is reverse the velocity of each and every constituent of the splatter. More precisely, the reasoning used with the tennis ball implies that if, hypothetically, we were able to simultaneously reverse the velocity of every atom and molecule involved directly or indirectly with the splattering egg, all the splattering motion would proceed in reverse.
Again, just as with the tennis ball, if we succeeded in reversing all these velocities, what we'd see would look like a reverse-run film. But, unlike the tennis ball's, the egg-splattering's reversal of motion would be extremely impressive. A wave of jostling air molecules and tiny floor vibrations would converge on the collision site from all parts of the kitchen, causing every bit of shell and drop of yolk to head back toward the impact location. Each ingredient would move with exactly the same speed it had in the original splattering process, but each would now move in the opposite direction. The drops of yolk would fly back into a globule just as scores of little shell pieces arrived on the outskirts, perfectly aligned to fuse together into a smooth ovoid container. The air and floor vibrations would precisely conspire with the motion of the myriad coalescing yolk drops and shell pieces to give the newly re-formed egg just the right kick to jump off the floor in one piece, rise up to the kitchen counter, and land gently on the edge with just enough rotational motion to roll a few inches and gracefully come to rest. This is what would happen if we could perform the task of total and exact velocity reversal of everything involved. 3
