Zero (25 page)

When an equation has an infinity in it, physicists usually assume that there is something wrong; the infinity has no physical meaning. The zero-point energy is no different; most scientists ignore it completely. They simply pretend that the zero-point energy is zero, even though they know it is infinite. It's a convenient fiction, and it usually doesn't matter. However, sometimes it does. In 1948 two Dutch physicists, Hendrick B. G. Casimir and Dik Polder, first realized that the zero-point energy can't always be ignored. The two scientists were studying the forces between atoms when they realized that their measurements didn't match the forces that had been predicted. In a search for an explanation, Casimir realized that he had felt the force of nothing.

The secret to the Casimir force lies with the nature of waves. In ancient Greece, Pythagoras saw the peculiar behavior of waves that traveled up and down a plucked string—how certain notes were allowed and others were forbidden. When Pythagoras strummed a string, the string sounded a clear note, the tone known as the fundamental. When he gently placed his finger in the middle of the string and plucked again, he got another nice, clear note, this time one octave above the fundamental. One-third of the way down yielded another nice tone. But Pythagoras realized that not all notes are allowed. When he placed his finger randomly on the string, he seldom got a clear note. Only certain notes can be played on the string; most are excluded (Figure 48).

Matter waves are not so different from string waves. Just as a guitar string of a given size is not capable of playing every possible note—some waves are “forbidden” from appearing on the string—some particle waves are forbidden from being inside a box. Put two metal plates close together, for instance, and you can't fit every sort of particle inside. Only those whose waves match the size of the box are allowed in (Figure 49).

Figure 48: Forbidden notes on a guitar string

Casimir realized that the forbidden particle waves would affect the zero-point energy of the vacuum, since particles are everywhere winking in and out of existence. If you put two metal plates close together and some of those particles aren't allowed between the plates, then there are more particles on the outside of the plates than on the inside. The undiminished zoo of particles presses on the outside of the plates, and without the full complement on the inside, the plates are crushed together, even in the deepest vacuum. This is the force of the vacuum, a force produced by nothing at all. This is the Casimir effect.

Figure 49: The Casimir effect

Though the Casimir force—a mysterious, phantom force exerted by nothing at all—seems like science fiction, it exists. It is a tiny force and very difficult to measure, but in 1995 the physicist Steven Lamoreaux measured the Casimir effect directly. By putting two gold-covered plates on a sensitive twist-measuring device, he determined how much force it took to counteract the Casimir force between them. The answer—about the weight of one slice of an ant that's been chopped into 30,000 pieces—agreed with Casimir's theory. Lamoreaux had measured the force exerted by empty space.

Zero in quantum mechanics invests the vacuum with infinite energy. A zero in the other great modern theory—relativity—creates another paradox: the infinite nothing of the black hole.

Like quantum mechanics, the theory of relativity was born in light; this time it was the speed of light that caused the trouble. Most objects in the universe don't have a speed that every observer can agree on. For instance, imagine a small boy who is throwing stones in all directions. For an observer approaching the boy, the stones seem to be going faster than for an observer who is running away; the velocity of the stones seems to depend on your direction and speed. In the same way, the speed of light should depend on whether you are running toward or running away from the lightbulb that's shining on you. In 1887 the American physicists Albert Michelson and Edward Morley tried to measure this effect. They were baffled when they found no difference; the speed of light was the same in every direction. How could this be?

Again, it was the young Einstein who had the answer in 1905. And again, very simple assumptions would have enormous consequences.

The first assumption Einstein made seems fairly obvious. Einstein stated that if a number of people watch the same phenomenon—say, the flight of a raven toward a tree, the laws of physics are the same for each observer. If you compare the notes of a person on the ground and a person on a train moving parallel to the raven, they would disagree about the speed of the raven and the tree. But the eventual outcome of the flight is the same: after a few seconds, the raven arrives at the tree. Both observers agree on the final result, though they might disagree about some of the details. This is the principle of relativity. (In the special theory of relativity, which we are discussing here, there are restrictions on the kind of motion that is allowed. Each observer must be moving with constant velocity in a straight line. In other words, they can't feel an acceleration. With the general theory of relativity, the restrictions are removed.)

The second assumption is a little more troubling, especially since it seems to contradict the principle of relativity. Einstein assumed that everybody—no matter at what speed they are traveling—agrees about the speed of light in a vacuum: about 300 million meters per second, a constant denoted by the letter
c.
If someone shines a flashlight at you, the light rushes at you at a speed of
c.
It doesn't matter whether the person holding the flashlight is standing still, running toward you, or running away; the beam of light always travels at a speed of
c
from your point of view—and everybody else's.

This assumption challenged everything physicists had assumed about the motion of objects. If the raven were acting like a photon, then an observer on the train and the person standing still would have to agree on the value for the raven's speed. That would mean that the two observers would disagree about
when
the raven meets the tree (Figure 50). Einstein realized that there is one way around this: the flow of time changes, depending on an observer's speed. The clock on the train must tick more slowly than the stationary clock. Ten seconds for the observer on the ground might seem like only five seconds for somebody on the train. It's the same thing for a person who zooms away at great speed. Every tick of his stopwatch takes more than a second from a stationary observer's point of view. If an astronaut took a 20-year journey (according to his pocket watch) at nine-tenths of the speed of light, he would come back to Earth having aged 20 years, as expected. But everyone who stayed behind would have aged 46 years.

Figure 50: The raven's constant speed means that time must be relative.

Not only does time change with speed, so do length and mass. As objects speed up, they get shorter and heavier. At nine-tenths of the speed of light, for instance, a yardstick would only be 0.44 yards long, and a one-pound bag of sugar would weigh nearly 2.3 pounds—from a stationary observer's point of view. (Of course, this doesn't mean that you would be able to bake more cookies with the same bag of sugar. From the bag's point of view, its weight stays the same.)

This variability in the flow of time might be hard to believe, but it has been observed. When a subatomic particle travels very fast, it survives longer than expected before it decays, because its clock is slow. Also, a very precise clock has been observed to slow down ever so slightly when flown in an airplane at great speed. Einstein's theory works. There was a potential problem though: zero.

When a spaceship approaches the speed of light, time slows down more and more and more. If the ship were to travel at the speed of light, every tick of the clock on board would equal infinite seconds on the ground. In less than a fraction of a second, billions and billions of years would pass; the universe would have already met its ultimate fate and burned itself out. For an astronaut aboard the spaceship, time stops. The flow of time is multiplied by zero.

Luckily, it is not so easy to stop time. As the spaceship goes ever faster, time slows down more and more, but at the same time, the spaceship's mass gets greater and greater. It is like pushing a baby carriage where the baby grows and grows. Pretty soon you are pushing a sumo wrestler—not so easy. If you manage to push the carriage even faster, the baby becomes as massive as a car…and then a battleship…and then a planet…and then a star…and then a galaxy. As the baby gets more massive, your push has less and less effect. In the same way, you can take a spaceship and accelerate it, getting it closer and closer to the speed of light. But after a while, it gets too massive to push any longer. The spaceship—or for that matter any other object with mass—never quite reaches the speed of light. The speed of light is the ultimate speed limit; you cannot reach it, much less exceed it. Nature has defended itself from an unruly zero.

However, zero is too powerful even for nature. When Einstein extended the theory of relativity to include gravity, he did not suspect that his new equations—the general theory of relativity—would describe the ultimate zero and the worst infinity of them all: the black hole.

Einstein's equations treat time and space as different aspects of the same thing. We are already used to the idea that if you accelerate, you change the way you move through space; you can speed up or slow down. What Einstein's equations showed was that just as acceleration changes the way you move through space, it changes the way you move through time. It can speed up the way time flows or slow it down. Thus, when you accelerate an object—when you subject it to any force, be it gravity or be it the push of a gigantic cosmic elephant—you change its motion through space and through time: through
space-time.

It's a difficult concept to grasp, but the easiest way to approach space-time is through an analogy: space and time are like a gigantic rubber sheet. Planets, stars, and everything else sit on that sheet, distorting it slightly. That distortion—the curvature caused by objects sitting on the sheet—is gravity. The more massive the object that is sitting on the sheet, the more the sheet gets distorted, and the larger the dimple around that object. The pull of gravity is just like the tendency of objects to roll into the dimple.