Zero (26 page)

The curvature of the rubber sheet is not only a curvature of space, but a curvature of time as well. Just as space gets distorted close to a massive object, time does, too. It gets slower and slower as the curvature gets greater and greater. The same thing happens with mass. As you get into greatly curved regions of space, bodies' masses effectively increase, a phenomenon known as
mass inflation.

This analogy explains the orbits of the planets; Earth is simply rolling around in the dimple that the sun makes in the rubber sheet. Light doesn't go in a straight line, but in a curved path around stars—an effect that the British astronomer Sir Arthur Eddington went on an expedition in 1919 to observe. Eddington measured the position of a star during a solar eclipse and spotted the curvature that Einstein had predicted (Figure 51).

Einstein's equations also predicted something much more sinister: the black hole, a star so dense that nothing can escape its grasp, not even light.

Figure 51: Gravity bends light around the sun.

A black hole begins, like all stars, as a big ball of hot gas—mostly hydrogen. If left to its own devices, a sufficiently large ball of gas would collapse under the weight of its own gravity; it would crush itself into a tiny lump. Luckily for us, stars don't collapse because there is another force at work: nuclear fusion. As a cloud of gas collapses, it gets hotter and denser, and hydrogen atoms slam into one another with increasing force. Eventually, the star gets so hot and dense that the hydrogen atoms stick to one another and fuse, creating helium and releasing large quantities of energy. This energy shoots out from the center of the star, causing it to expand a little bit. During most of its life, a star is in an uneasy equilibrium: the propensity to collapse under its own gravity is balanced by the energy that comes from the fusing hydrogen in its center.

This equilibrium cannot last forever; the star has only a limited amount of hydrogen fuel to burn. After a while, the fusion reaction dims, and the equilibrium is upset. (How long this process takes depends on how big the star is. Ironically, the bigger the star—the more hydrogen it has—the shorter its life, because it burns much more violently. The sun has about five billion years of fuel left, but don't let that make you complacent. The sun's temperature will increase gradually before that, boiling off the oceans and turning Earth into an uninhabitable desert like Venus. We should count ourselves lucky if we have a mere billion years left of life on Earth.) After a drawn-out series of death throes—the precise sequence of events depends, again, on the mass of the star—the star's fusion engine fails, and the star begins to collapse under its own gravity.

A quantum-mechanical law called the Pauli exclusion principle keeps matter from squishing itself into a point. Discovered in the mid-1920s by German physicist Wolfgang Pauli, the exclusion principle states, roughly, that no two things can be in the same place at the same time. In particular, no two electrons of the same quantum state can be forced into the same spot. In 1933, the Indian physicist Subrahmanyan Chandrasekhar realized that the Pauli exclusion principle had only a limited ability to fight against the squeeze of gravity.

As pressure in the star increases, the exclusion principle states that electrons inside must move faster and faster to avoid one another. But there's a speed limit: electrons cannot move faster than the speed of light, so if you put enough pressure on a lump of matter, electrons cannot move fast enough to stop the matter from collapsing. Chandrasekhar showed that a collapsing star that has about 1.4 times the mass of our sun will have enough gravity to overwhelm the Pauli exclusion principle. Above this
Chandrasekhar limit
a star's gravity will pull on itself so strongly that electrons can't stop its collapse. The force of gravity is so great that the star's electrons give up their struggle once and for all; the electrons smash into the star's protons, creating neutrons. The massive star winds up being a gigantic ball of neutrons: a neutron star.

Further calculations showed that when collapsing stars are a little more massive than the Chandrasekhar limit, the pressure of the resulting neutrons—similar to the pressure of electrons—can stave off collapse for a little while; this is what happens in a neutron star. At this point, the star is so dense that every teaspoon weighs hundreds of millions of tons. There is a limit, though, to even the pressure that neutrons can bear. Some astrophysicists believe that a little more squeezing makes the neutrons break down into their component quarks, creating a quark star. But that is the last stronghold. After that, all hell breaks loose.

When an extremely massive star collapses, it disappears. The gravitational attraction is so great that physicists know of no force in the universe that can stop its collapse—not the repulsion of its electrons, not the pressure of neutron against neutron or quark against quark—nothing. The dying star gets smaller and smaller and smaller. Then…zero. The star crams itself into zero space. This is a black hole, an object so paradoxical that some scientists believe that black holes can be used to travel faster than light—and backward in time.

The key to a black hole's strange properties is the way it curves space-time. A black hole takes up no space at all, but it still has mass. Since the black hole has mass, it causes space-time to curve. Normally, this would not cause a problem. As you approach a heavy star, the curvature gets greater and greater, but once you have passed the outer edge of the star itself, the curvature decreases again, bottoming out at the center of the star. In contrast, a black hole is a point. It takes up zero space, so there is no outer edge, no place where space begins to flatten out again. The curvature of space gets greater and greater as you approach a black hole, and it never bottoms out. The curvature goes off to infinity because the black hole takes up zero space; the star has torn a hole in space-time (Figure 52). The zero of a black hole is a singularity, an open wound in the fabric of the universe.

This is a very troublesome concept. The smooth, continuous fabric of space-time might have tears in it, and nobody knows quite what happens in the region of those tears. Einstein was so disturbed by the idea of singularities that he denied the existence of black holes. He was wrong; black holes do exist. However, the singularity of a black hole is so ugly, so dangerous, that nature tries to shield it, preventing anyone from seeing the zero at the center of a black hole and returning to tell the tale. Nature has a “cosmic censor.”

Figure 52: Unlike other stars, a black hole tears a hole in space-time.

The censor is gravity itself. If you toss a rock upward, it will curve back down, pulled back by the earth's gravity. But if you throw a rock fast enough, it won't curve back down to earth; it will zoom out of the earth's atmosphere and escape the earth's gravitational pull. This is roughly what NASA does when it sends a spacecraft to Mars. The minimum speed you need to throw the rock to enable it to escape is called, naturally enough, the
escape velocity.
Black holes are so dense that if you get too close—past the so-called event horizon—the escape velocity is faster than the speed of light. Past the event horizon the pull of a black hole's gravity is so strong—and space is so curved—that nothing can escape, not even light.

Even though a black hole is a star, none of the light it shines ever escapes past the event horizon; that's why it's black. The only way to view a black hole's singularity is to go beyond the event horizon and see for yourself. However, even if you had an impossibly strong spacesuit that kept you from being stretched into a piece of astronaut spaghetti, you could never tell anybody about what you saw. Once you pass the event horizon, signals you broadcast can't escape the black hole's pull—neither can you. Traveling beyond the edge of the event horizon is like stepping off the edge of the universe. You will never return. This is the power of the cosmic censor.

Even though nature tries to shield the singularities of black holes, scientists know that black holes exist. In the direction of the constellation Sagittarius, at the very center of our galaxy, sits a supermassive black hole that weighs as much as two-and-a-half million suns. Astronomers have watched stars dance around an invisible partner; the stars' motions reveal the presence of the black hole even if the black hole is not visible. However, though scientists can detect black holes, they still haven't spotted the zeros at their centers, since the ugly singularities are shielded by the event horizon.

This is a good thing. If there were no event horizon, no cosmic censor that shields the singularity from the rest of the universe, very strange things might happen. In theory, a
naked singularity
with no event horizon might allow you to travel faster than light or backward in time. This could be done with a structure known as a
wormhole.

Back in the rubber-sheet analogy, a singularity is a point of infinite curvature; it is a hole in the fabric of space and time. Under certain circumstances that hole can be stretched out. For instance, if a black hole is spinning or has an electric charge, mathematicians have calculated that the singularity is not a point—a pinpoint hole in space-time—but a ring. Physicists have speculated that two of these stretched-out singularities might be linked with a tunnel: a wormhole (Figure 53). A person who travels through a wormhole will emerge at another point in space—and perhaps in time. Just as worm-holes can, in theory, send you halfway across the universe in the blink of an eye, they can send you backward and forward in time (see appendix E). You might even be able to track down your mother and kill her before she meets your father, preventing you from being born and causing a terrible paradox.

A wormhole is a paradox caused by a zero in the equations of general relativity. Nobody truly knows whether or not wormholes exist—but NASA is hoping that they do.

Figure 53: A wormhole

NASA hopes that zero might hold the secret to traveling to distant stars. In 1998, NASA held a symposium entitled Physics for the Third Millennium, where scientists debated the merits of wormholes, warp drives, vacuum-energy engines, and other far-out ideas.

The problem with space travel is that there is nothing to push against. When you swim through a pool, you push against the water, forcing it backward and pushing you forward. When you walk on the ground, your feet are pushing against the floor, providing the force to drive you forward. In space, there is nothing to push backward; you can paddle all you want, but you'll get nowhere.