Zoom: From Atoms and Galaxies to Blizzards and Bees: How Everything Moves (17 page)

In his heretical publication The Starry Messenger, Galileo didn’t make much ado about nothingness only because it was the least of his revelations. He also boldly claimed that Aristotle was wrong when he said that massive objects fall faster than skimpy ones. After all, Galileo’s biggest metal balls rolled no faster than his lighter models. Instead, he proclaimed, it was merely air resistance that slowed down spread-out objects, such as feathers. (We got to see Galileo’s breakthrough notions come true on the moon when astronaut David Scott simultaneously dropped a hammer and feather and both plummeted in perfect sync. He did this near the end of the Apollo 15 mission in 1971.)

And now we come, inevitably and predictably, to Isaac Newton. Who, by the way, indeed told at least four people that he got his inspiration about gravity from watching a falling apple. The only false aspect of his popularized, American Idol–like bio is the business about a Golden Delicious bonking him on the head.

Pondering the way the moon and apples behave, Newton realized that Galileo had been onto something. Both objects move the same way. Abandoning the Greeks’ longstanding linear-versus-circular reasoning, he unified the heavens and the earth by coining a new word: gravity. He created it from gravitas, the Latin word for “heaviness.” What exactly it was he could not say. But how it acted—ah, this he could quantify perfectly.

Actually, his contemporaries, including Robert Hooke and Edmond Halley, also assumed that some mysterious force pulled objects toward the center of the earth. Halley even presumed it grew less powerful with distance and, in a now-forgotten experiment, carried a pendulum to the top of a 2,500-foot hill, where, he claimed, he watched it swing a bit more slowly there. These natural philosophers, as scientists were then called, not only believed the planets were yanked by the sun but also correctly said that this force grew proportionally weaker with the square of their distance. Meaning an object that’s three times farther away from the sun than you are experiences three times three, or nine, times less of a pull.5

So Newton hardly came up with the idea of the force, even though he named it and introduced it to the Western world. Rather, he accurately described how it behaved.

Isaac Newton was born in 1643, in Lincolnshire, England, one year after Galileo died. He studied at Trinity College in Cambridge and later became professor of mathematics there. In a paper published in 1687 that soon became widely known as the Principia, Newton mathematically proved that the sun’s gravity should make planets travel in elliptical paths, thus effectively awarding Kepler a posthumous 1600 SAT score. It was here that he offered his famous three laws of motion, although in fairness Galileo had already pretty much stated the first two:

Every body continues in a state of rest, or of uniform motion in a straight line, unless it is impelled to change that state by forces impressed upon it.

The change of motion is proportional to the force impressed, and it is made in the direction of the straight line in which that force acts.

To every action there is an equal and opposite reaction.

In plain language, a moving body tends to keep moving. And a stationary body likes to remain at rest. Both of these tendencies are called inertia. Newton also introduced the concept of momentum. Momentum involves exactly two things: the mass of an object (what one perceives as its weight) multiplied by its speed. A slow-moving truck may move at the same speed as a bicycle, but the truck has more mass and hence more momentum. It’s harder to stop.

Newton was also the first to state the obvious—that the strength of a force is determined by how it influences a body’s motion. He also spoke of acceleration as a change in movement, whether of speed or of direction.

Newton regarded gravity as a force simply because it changes the way objects move. It pulls them ever faster. Here on Earth, we know that gravity yanks things toward Earth’s center at the rate of twenty-two miles per hour faster every second. Newton’s brilliance was in understanding that a falling apple behaves exactly the same way as the moon orbiting around us does.6

Newton’s third law expressed something totally new: the notion of equal and opposite reactions. This means that any object exerting a force also feels it acting on itself. If you push a stalled car, you feel that same force upon your hands, pushing back at you.

The exploding charge propelling a bullet forward also creates a recoil in the rifle. Because the bullet weighs less than the rifle, one object enjoys more forward speed while the heavier one moves backward with less oomph. This inequality business goes off the scale when it comes to events that involve our planet. If you jump up, you are simultaneously pushing Earth backward in the opposite direction. However, since Earth weighs an octillion times more than you, it moves an octillion times less than you do when you jump.

That equal-but-opposite law showed why a rocket sending a stream of high-speed gas out its bottom end, even in the vacuum of space, moves the opposite way—upward. There’s no need for those gases to push against anything.

Using Newton’s figures and just a tiny bit of math we can figure out how fast a bar of bullion would fall if tossed exuberantly from the Fort Knox roof by a gold-standard extremist. Or how fast a midlife-crisis bungee jumper falls when leaping from a twenty-story bridge. Grab a one-dollar calculator. Don’t be afraid. It’s time for the “fun with math” segment.

Multiply the jumper’s altitude (in feet) by 64.4, then hit the square root button. That’s his final speed in feet per second. If you prefer miles per hour, multiply this by 0.68.

Let’s consider one example. Our bungee jumper leaps from two hundred feet, so this figure times 64.4 is 12,880. The square root of this is 113. And that’s his final speed: 113 feet per second. Multiplying that by 0.68 yields seventy-seven miles per hour. Not so difficult.

The greatest speed you’d reach if you jumped from the highest possible perch—by falling toward Earth from even beyond the moon, say—would be 25,031 miles an hour, ignoring air resistance. It’s exactly the same speed needed to escape from Earth with a single upward blast, as though you were a circus performer fired from a cannon. So the velocity needed to escape any celestial body is also the velocity at which you’d land if you fell there from a great height.

This up-speed-equals-down-speed business is pretty cool. Toss an orange up and let it land back in your hand. Interestingly, the exact speed at which you chose to toss it up is the same speed at which it’s coming down when you catch it.

Each celestial body has its own impact speed, or escape speed, predetermined by its mass and its diameter. For the moon that’s 5,368 miles an hour. For the sun it’s more than a million miles an hour, or 384 miles per second. That’s how fast a drifting, out-of-fuel spacecraft piloted by incompetent aliens would be pulled into the sun by its gravity.

On Earth, air resistance slows things down. In skydiving class they make you practice spreading your arms and legs to let your body present its maximum surface area to the wind. If you do that you won’t gain any additional speed beyond 120 miles an hour. This is the famous “terminal velocity.”7

It’s reached pretty quickly, after jumping from a height of just five hundred feet, or fifty stories. So, perhaps surprisingly, you’ll not go any faster if you jump from the 110th floor than you would if you jump from the fiftieth floor. Daredevils who bypass the fiftieth floor in favor of leaping from the roof much higher up merely want to buy themselves extra air time for their parachutes to open—an excellent idea.8

But we still haven’t explained why all this happens. So let’s fast-forward to Albert Einstein, born in 1879.

In his 1905 and, especially, his 1915 relativity theories, Albert Einstein did not just tweak Newtonian mechanics. He tossed it out, replacing it with concepts so bizarre that even now, a century later, they remain mind-twisting. It was a brand-new way of thinking about movement in the universe.

Einstein would not have invented a better mousetrap if the old one worked just fine. But the behavior of celestial bodies contained a few slight but inexplicable wrinkles when examined through the lens of the old, simple, Newtonian calculations of force and mass and acceleration.9

Einstein decided that gravity wasn’t a force at all. In a leap of inspiration unequaled before or since, except perhaps among the quantum gang of Heisenberg and company, Einstein said that an unseen matrix he called spacetime pervades every cosmic nook and cranny. An amalgam of time and space, its configuration dictates how any object must move through it. An object’s very presence, its mass, distorts the surrounding spacetime. Anything moving through this region has its trajectory of motion, as well as its passage of time, change in a predictable way.

By this thinking, the sun doesn’t pull on our world. Instead, Earth merely falls in the straightest, laziest, most direct path through the local curved spacetime. Our nearby sun’s enormous mass depresses spacetime like a heavy ball resting on a rubber sheet and making it sag. Earth rolls along this warped rubber membrane and curvingly arcs back to its starting point after a year.

Nor is spacetime limited to faraway places. It’s also right here in the room. We stand on Earth’s surface and feel the ground pushing up against our soles and heels. That’s because we experience Earth’s motion and ours through the local spacetime, which has been distorted by Earth’s mass.

So Einstein replaced gravity with geometry. Every object’s path is dictated by the configuration of the local spacetime. As a close-up example of how it works, consider two batters stepping to the plate. The first hits a pop-up that travels skyward a great distance and stays aloft a long time before it’s caught by the shortstop. The next batter hits a line drive. It takes a more linear path before being snagged by the same shortstop and gets there much faster.

To our minds, which regard time and space separately, these two hit balls take very different trajectories. They appear to be dissimilar events. But plotted in the single matrix of spacetime, they took identical paths. Indeed, whenever objects are released to travel on their own (as long as they leave from and arrive at the same two points) they must follow identical geodesics (paths through spacetime). Only to our human perceptions does each consume a different amount of time and a dissimilar route through space. In truth, the two are so linked that should you alter the time path of an object (e.g., make the ball stay longer in the air) it automatically changes the space path.

Unfortunately, Einstein’s field equations for the way spacetime is warped and the way objects move through it are incredibly complex.10 They’re so labor intensive that even NASA doesn’t use them when they calculate spacecraft travel routes to the planets. They prefer to stick with Newton’s simpler math, which yields results that are good enough and far easier to manage.

Today’s schoolchildren are still usually taught the older, Newtonian viewpoint, that Earth circles the sun because of solar gravity. Few science curricula provide children with the superior Einstein concept, that our planet merely falls along a straight path (geodesic) through the curved spacetime produced by the nearby massive sun.

We could end the story of dropped keys and whizzing planets right here, except for one problem. Whether we call it distorted spacetime or gravity, the phenomenon of objects being pulled toward others remains mysterious. After all, spacetime is a mathematical model, not an actual entity such as Swiss cheese. Time has no independent existence on its own except as a way we humans perceive change. Space, too, is not a real commodity. We cannot bring it to a lab and analyze it as we would a piece of quartz. Spacetime is an accurate mathematical way to describe and predict motion; it is not an ultimate explanation. Many physicists still prefer to speak of gravity as if Einstein never existed.

We may someday find out why objects pull toward other objects. If gravity is a force, there ought to be a force-carrying particle that brings it from one place to another. After all, photons (bits of light) are the force-carrying particles that transport electromagnetism. Einstein postulated “gravitons” as gravity’s butlers. So far, however, they have not been detected. (Although if gravity is nothing but a kind of geometry, a distortion of spacetime, then perhaps force carriers may not be needed.11)

Does gravity’s power depend on the rest of the universe? Does it somehow involve hypothetical strings? Does the gravitational “constant” change as the universe expands? Will Earth’s gravity grow weaker over time? Can gravity be some sort of influence from another dimension?

Gravity’s enigmas, like autumn’s falling apples, Newton’s original inspiration, still plop all around us.

CHAPTER 11: Rush Hour for Every Body

Revelations Gained by Looking Within

And the heart must pause to breathe…

—LORD BYRON, “SO WE’LL GO NO MORE A ROVING” (1830)

Sorry, I’m busy right now,” you tell a friend.

That’s so true. Your body is as busy as the galaxy.

Even when we’re resting and daydreaming, internal activity is nonstop. Some of it is obvious. We can feel our pulse, our heartbeat, our heaving chest. Maybe our stomach gurgles for a moment. Not much else. This limited awareness of a mere handful of internal motions is a good thing. Nature has spared us from being overwhelmed by its myriad under-the-skin dramas.

But let’s be aware now. If only to appreciate the exquisite, epic complexity involved when a teenager applies eyeliner.

We might start by thinking about thinking. The brain, of course, is the crown jewel of our nervous system. (Or is the brain just blowing its own horn at this moment by making me write this?) It has eighty-five billion neuron cells and, even more impressive, boasts 150 trillion synapses. These are its electrical connections, its possibilities. This figure is nearly a thousand times greater than the number of stars in the Milky Way galaxy.

The number of brain neurons is staggering. To count them at the rate of one per second would require 3,200 years. But the number of brain synapses, or electrical connections, is beyond belief. Those 150 trillion could be counted only in three million years. And that’s still not the end of the matter. What’s relevant is how many ways each cell can connect with the others. For this we must use factorials. They’re very cool. Let’s say we want to know how many ways we can arrange four books on a shelf. It’s easy: you find the possibilities by multiplying 4 × 3 × 2, which is pronounced “four factorial” and written as 4!—i.e., twenty-four. But what if you have ten books? Easy again: it’s 10!, or 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2, which is—ready?—3,628,800 different ways. Imagine: going from four items to ten increases the possible arrangements from twenty-four to 3.6 million!