by Brian Greene
Coming of Age in Space and Time
When I turned the last page of The Myth of Sisyphus many years ago, I was surprised by the text's having achieved an overarching feeling of optimism. After all, a man condemned to pushing a rock up a hill with full knowledge that it will roll back down, requiring him to start pushing anew, is not the sort of story that you'd expect to have a happy ending. Yet Camus found much hope in the ability of Sisyphus to exert free will, to press on against insurmountable obstacles, and to assert his choice to survive even when condemned to an absurd task within an indifferent universe. By relinquishing everything beyond immediate experience, and ceasing to search for any kind of deeper understanding or deeper meaning, Sisyphus, Camus argued, triumphs.
I was struck by Camus' ability to discern hope where most others would see only despair. But as a teenager, and only more so in the decades since, I found that I couldn't embrace Camus' assertion that a deeper understanding of the universe would fail to make life more rich or worthwhile. Whereas Sisyphus was Camus' hero, the greatest of scientists— Newton, Einstein, Niels Bohr, and Richard Feynman—became mine. And when I read Feynman's description of a rose—in which he explained how he could experience the fragrance and beauty of the flower as fully as anyone, but how his knowledge of physics enriched the experience enormously because he could also take in the wonder and magnificence of the underlying molecular, atomic, and subatomic processes—I was hooked for good. I wanted what Feynman described: to assess life and to experience the universe on all possible levels, not just those that happened to be accessible to our frail human senses. The search for the deepest understanding of the cosmos became my lifeblood.
As a professional physicist, I have long since realized that there was much naïveté in my high school infatuation with physics. Physicists generally do not spend their working days contemplating flowers in a state of cosmic awe. Instead, we devote much of our time to grappling with complex mathematical equations scrawled across well-scored chalkboards. Progress can be slow. Promising ideas, more often than not, lead nowhere. That's the nature of scientific research. Yet, even during periods of minimal progress, I've found that the effort spent puzzling and calculating has only made me feel a closer connection to the cosmos. I've found that you can come to know the universe not only by resolving its mysteries, but also by immersing yourself within them. Answers are great. Answers confirmed by experiment are greater still. But even answers that are ultimately proven wrong represent the result of a deep engagement with the cosmos—an engagement that sheds intense illumination on the questions, and hence on the universe itself. Even when the rock associated with a particular scientific exploration happens to roll back to square one, we nevertheless learn something and our experience of the cosmos is enriched.
Of course, the history of science reveals that the rock of our collective scientific inquiry—with contributions from innumerable scientists across the continents and through the centuries—does not roll down the mountain. Unlike Sisyphus, we don't begin from scratch. Each generation takes over from the previous, pays homage to its predecessors' hard work, insight, and creativity, and pushes up a little further. New theories and more refined measurements are the mark of scientific progress, and such progress builds on what came before, almost never wiping the slate clean. Because this is the case, our task is far from absurd or pointless. In pushing the rock up the mountain, we undertake the most exquisite and noble of tasks: to unveil this place we call home, to revel in the wonders we discover, and to hand off our knowledge to those who follow.
For a species that, by cosmic time scales, has only just learned to walk upright, the challenges are staggering. Yet, over the last three hundred years, as we've progressed from classical to relativistic and then to quantum reality, and have now moved on to explorations of unified reality, our minds and instruments have swept across the grand expanse of space and time, bringing us closer than ever to a world that has proved a deft master of disguise. And as we've continued to slowly unmask the cosmos, we've gained the intimacy that comes only from closing in on the clarity of truth. The explorations have far to go, but to many it feels as though our species is finally reaching childhood's end.
To be sure, our coming of age here on the outskirts of the Milky Way 6 has been a long time in the making. In one way or another, we've been exploring our world and contemplating the cosmos for thousands of years. But for most of that time we made only brief forays into the unknown, each time returning home somewhat wiser but largely unchanged. It took the brashness of a Newton to plant the flag of modern scientific inquiry and never turn back. We've been heading higher ever since. And all our travels began with a simple question.
What is space?
2 - The Universe and the Bucket
IS SPACE A HUMAN ABSTRACTION OR A PHYSICAL ENTITY?
It's not often that a bucket of water is the central character in a three-hundred-year-long debate. But a bucket that belonged to Sir Isaac Newton is no ordinary bucket, and a little experiment he described in 1689 has deeply influenced some of the world's greatest physicists ever since. The experiment is this: Take a bucket filled with water, hang it by a rope, twist the rope tightly so that it's ready to unwind, and let it go. At first, the bucket starts to spin but the water inside remains fairly stationary; the surface of the stationary water stays nice and flat. As the bucket picks up speed, little by little its motion is communicated to the water by friction, and the water starts to spin too. As it does, the water's surface takes on a concave shape, higher at the rim and lower in the center, as in Figure 2.1.
That's the experiment—not quite something that gets the heart racing. But a little thought will show that this bucket of spinning water is extremely puzzling. And coming to grips with it, as we have not yet done in over three centuries, ranks among the most important steps toward grasping the structure of the universe. Understanding why will take some background, but it is well worth the effort.
Figure 2.1 The surface of the water starts out flat and remains so as the bucket starts to spin. Subsequently, as the water also starts to spin, its surface becomes concave, and it remains concave while the water spins, even as the bucket slows and stops.
Relativity Before Einstein
"Relativity" is a word we associate with Einstein, but the concept goes much further back. Galileo, Newton, and many others were well aware that velocity— the speed and direction of an object's motion—is relative. In modern terms, from the batter's point of view, a well-pitched fastball might be approaching at 100 miles per hour. From the baseball's point of view, it's the batter who is approaching at 100 miles per hour. Both descriptions are accurate; it's just a matter of perspective. Motion has meaning only in a relational sense: An object's velocity can be specified only in relation to that of another object. You've probably experienced this. When the train you are on is next to another and you see relative motion, you can't immediately tell which train is actually moving on the tracks. Galileo described this effect using the transport of his day, boats. Drop a coin on a smoothly sailing ship, Galileo said, and it will hit your foot just as it would on dry land. From your perspective, you are justified in declaring that you are stationary and it's the water that is rushing by the ship's hull. And since from this point of view you are not moving, the coin's motion relative to your foot will be exactly what it would have been before you embarked.
Of course, there are circumstances under which your motion seems intrinsic, when you can feel it and you seem able to declare, without recourse to external comparisons, that you are definitely moving. This is the case with accelerated motion, motion in which your speed and/or your direction changes. If the boat you are on suddenly lurches one way or another, or slows down or speeds up, or changes direction by rounding a bend, or gets caught in a whirlpool and spins around and around, you know that you are moving. And you realize this without looking out and comparing your motion with some chosen point of reference. Even if your eyes are closed, you know y
ou're moving, because you feel it. Thus, while you can't feel motion with constant speed that heads in an unchanging straight-line trajectory —constant velocity motion, it's called—you can feel changes to your velocity.
But if you think about it for a moment, there is something odd about this. What is it about changes in velocity that allows them to stand alone, to have intrinsic meaning? If velocity is something that makes sense only by comparisons—by saying that this is moving with respect to that— how is it that changes in velocity are somehow different, and don't also require comparisons to give them meaning? In fact, could it be that they actually do require a comparison to be made? Could it be that there is some implicit or hidden comparison that is actually at work every time we refer to or experience accelerated motion? This is a central question we're heading toward because, perhaps surprisingly, it touches on the deepest issues surrounding the meaning of space and time.
Galileo's insights about motion, most notably his assertion that the earth itself moves, brought upon him the wrath of the Inquisition. A more cautious Descartes, in his Principia Philosophiae, sought to avoid a similar fate and couched his understanding of motion in an equivocating framework that could not stand up to the close scrutiny Newton gave it some thirty years later. Descartes spoke about objects' having a resistance to changes to their state of motion: something that is motionless will stay motionless unless someone or something forces it to move; something that is moving in a straight line at constant speed will maintain that motion until someone or something forces it to change. But what, Newton asked, do these notions of "motionless" or "straight line at constant speed" really mean? Motionless or constant speed with respect to what? Motionless or constant speed from whose viewpoint? If velocity is not constant, with respect to what or from whose viewpoint is it not constant? Descartes correctly teased out aspects of motion's meaning, but Newton realized that he left key questions unanswered.
Newton—a man so driven by the pursuit of truth that he once shoved a blunt needle between his eye and the socket bone to study ocular anatomy and, later in life as Master of the Mint, meted out the harshest of punishments to counterfeiters, sending more than a hundred to the gallows—had no tolerance for false or incomplete reasoning. So he decided to set the record straight. This led him to introduce the bucket. 1
The Bucket
When we left the bucket, both it and the water within were spinning, with the water's surface forming a concave shape. The issue Newton raised is, Why does the water's surface take this shape? Well, because it's spinning, you say, and just as we feel pressed against the side of a car when it takes a sharp turn, the water gets pressed against the side of the bucket as it spins. And the only place for the pressed water to go is upward. This reasoning is sound, as far as it goes, but it misses the real intent of Newton's question. He wanted to know what it means to say that the water is spinning: spinning with respect to what? Newton was grappling with the very foundation of motion and was far from ready to accept that accelerated motion such as spinning—is somehow beyond the need for external comparisons. 1
A natural suggestion is to use the bucket itself as the object of reference. As Newton argued, however, this fails. You see, at first when we let the bucket start to spin, there is definitely relative motion between the bucket and the water, because the water does not immediately move. Even so, the surface of the water stays flat. Then, a little later, when the water is spinning and there isn't relative motion between the bucket and the water, the surface of the water is concave. So, with the bucket as our object of reference, we get exactly the opposite of what we expect: when there is relative motion, the water's surface is flat; and when there is no relative motion, the surface is concave.
In fact, we can take Newton's bucket experiment one small step further. As the bucket continues to spin, the rope will twist again (in the other direction), causing the bucket to slow down and momentarily come to rest, while the water inside continues to spin. At this point, the relative motion between the water and the bucket is the same as it was near the very beginning of the experiment (except for the inconsequential difference of clockwise vs. counterclockwise motion), but the shape of the water's surface is different (previously being flat, now being concave); this shows conclusively that the relative motion cannot explain the surface's shape.
Having ruled out the bucket as a relevant reference for the motion of the water, Newton boldly took the next step. Imagine, he suggested, another version of the spinning bucket experiment carried out in deep, cold, completely empty space. We can't run exactly the same experiment, since the shape of the water's surface depended in part on the pull of earth's gravity, and in this version the earth is absent. So, to create a more workable example, let's imagine we have a huge bucket—one as large as any amusement park ride—that is floating in the darkness of empty space, and imagine that a fearless astronaut, Homer, is strapped to the bucket's interior wall. (Newton didn't actually use this example; he suggested using two rocks tied together by a rope, but the point is the same.) The telltale sign that the bucket is spinning, the analog of the water being pushed outward yielding a concave surface, is that Homer will feel pressed against the inside of the bucket, his facial skin pulling taut, his stomach slightly compressing, and his hair (both strands) straining back toward the bucket wall. Here is the question: in totally empty space—no sun, no earth, no air, no doughnuts, no anything—what could possibly serve as the "something" with respect to which the bucket is spinning? At first, since we are imagining space is completely empty except for the bucket and its contents, it looks as if there simply isn't anything else to serve as the something. Newton disagreed.
He answered by fixing on the ultimate container as the relevant frame of reference: space itself. He proposed that the transparent, empty arena in which we are all immersed and within which all motion takes place exists as a real, physical entity, which he called absolute space. 2 We can't grab or clutch absolute space, we can't taste or smell or hear absolute space, but nevertheless Newton declared that absolute space is a something. It's the something, he proposed, that provides the truest reference for describing motion. An object is truly at rest when it is at rest with respect to absolute space. An object is truly moving when it is moving with respect to absolute space. And, most important, Newton concluded, an object is truly accelerating when it is accelerating with respect to absolute space.
Newton used this proposal to explain the terrestrial bucket experiment in the following way. At the beginning of the experiment, the bucket is spinning with respect to absolute space, but the water is stationary with respect to absolute space. That's why the water's surface is flat. As the water catches up with the bucket, it is now spinning with respect to absolute space, and that's why its surface becomes concave. As the bucket slows because of the tightening rope, the water continues to spin—spinning with respect to absolute space—and that's why its surface continues to be concave. And so, whereas relative motion between the water and the bucket cannot account for the observations, relative motion between the water and absolute space can. Space itself provides the true frame of reference for defining motion.
The bucket is but an example; the reasoning is of course far more general. According to Newton's perspective, when you round the bend in a car, you feel the change in your velocity because you are accelerating with respect to absolute space. When the plane you are on is gearing up for takeoff, you feel pressed back in your seat because you are accelerating with respect to absolute space. When you spin around on ice skates, you feel your arms being flung outward because you are accelerating with respect to absolute space. By contrast, if someone were able to spin the entire ice arena while you stood still (assuming the idealized situation of frictionless skates)—giving rise to the same relative motion between you and the ice—you would not feel your arms flung outward, because you would not be accelerating with respect to absolute space. And, just to make sure you don't get sidetracked by the irrelevant deta
ils of examples that use the human body, when Newton's two rocks tied together by a rope twirl around in empty space, the rope pulls taut because the rocks are accelerating with respect to absolute space. Absolute space has the final word on what it means to move.
But what is absolute space, really? In dealing with this question, Newton responded with a bit of fancy footwork and the force of fiat. He first wrote in the Principia "I do not define time, space, place, and motion, as [they] are well known to all," 3 sidestepping any attempt to describe these concepts with rigor or precision. His next words have become famous: "Absolute space, in its own nature, without reference to anything external, remains always similar and unmovable." That is, absolute space just is, and is forever. Period. But there are glimmers that Newton was not completely comfortable with simply declaring the existence and importance of something that you can't directly see, measure, or affect. He wrote,
It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent, because the parts of that immovable space in which those motions are performed do by no means come under the observations of our senses. 4
So Newton leaves us in a somewhat awkward position. He puts absolute space front and center in the description of the most basic and essential element of physics—motion—but he leaves its definition vague and acknowledges his own discomfort about placing such an important egg in such an elusive basket. Many others have shared this discomfort.
