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
Something for Nothing?
There’s no such thing as a free lunch.
—“THE SECOND LAW OF THERMODYNAMICS”
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.
Rockets bring their own supply of stuff to push against. Rocket fuel burns in the engine and is sent out the back of the rocket, driving the spaceship forward, just as the rush of air out of a balloon sends it flying around the room. But tossing away fuel is an expensive and cumbersome way to go places, and even modern improvements on the chemical engine, such as engines that use electricity to throw stuff out the back of a rocket, are unable to provide the fuel efficiency to send probes to distant stars in a reasonable amount of time. To get even to the nearest star, you would need an enormous amount of fuel to jettison out the back of the rocket—a tremendous waste.
Physicist Marc Millis heads NASA’s Breakthrough Propulsion Project and hopes to overcome this problem with the physics of zero. Unfortunately, the zeros of black holes—singularities—look like unlikely candidates in the short term. Not only is it extremely difficult to create a naked singularity that a wormhole needs, but it also appears that even a naked singularity will tear space travelers to shreds. In 1998 two physicists from the Hebrew University in Jerusalem showed that even a spinning or charged black hole—with a nice, ring-shaped singularity—will kill an astronaut, thanks to mass inflation. As you fall toward the singularity, the black hole’s mass appears to grow and grow to infinity. The gravitational tug is so strong that you’d be torn apart in a fraction of a second. Wormholes would be hazardous to your health.
Even if the zeros at the center of black holes don’t provide an easy way to travel through space, the zero of quantum mechanics p
rovides an alternative: the zero-point energy might be the ultimate fuel. It is here that the mainstream of physics ends and the fringe begins.
According to Millis, astronauts might harness the energy in the vacuum to push a spaceship, just as mariners harnessed the wind to drive a frigate. “I’m making an analogy to the Casimir effect, where you can push plates together with a noticeable radiation pressure from the vacuum,” he says. “If there were any way to get asymmetric forces out of that, where you get force in one direction and not the other, you’d get a propulsive force.” Unfortunately, so far the Casimir effect seems to be symmetric; both plates collapse and pull each other together. The action of one has an equal and opposite reaction on the other. But if there were some sort of quantum sail, a one-way mirror that reflected virtual particles on one side but let them pass unhindered through the other, the vacuum energy would push the whole object toward the unreflective half of the sail. Millis admits that nobody has any clue how to do this. “There are no theories how to engineer the device,” he says sadly.
The problem is that the laws of physics say you can’t get something for nothing; just as the frigate lowers the speed of the wind, the quantum sail would have to lower the energy of the vacuum. How can you modify nothing?
Harold Puthoff, the director of the Institute for Advanced Studies in Austin, Texas, believes that a quantum sail would simply alter the properties of the vacuum. (Puthoff is best known for his 1974 paper in Nature that purported to prove that Uri Geller and other psychics could view objects remotely—without their eyes. This conclusion was not in the mainstream of science.) “The vacuum decays to a slightly lower state,” says Puthoff. If so, then quantum sails are just the beginning; it would be possible to make engines that run solely on zero-point energy. Their only drawback would be that the fabric of the universe would fall apart. Slowly. “We’d never make a dent. It’s like scooping up cupfuls of water from the ocean,” says Puthoff.
It might also destroy the universe.
There is no question that the vacuum has energy; the Casimir force is witness to that fact. But is it possible that the energy of the vacuum is truly the lowest possible energy? If not, danger might be lurking in the vacuum. In 1983 two scientists suggested in Nature that tinkering with the energy of the vacuum might cause the universe to self-destruct. The paper argued that our vacuum might be a “false” vacuum in an unnaturally energetic state—like a ball perched precariously on the side of a hill. If we give the vacuum a big enough nudge, it might start rolling down the hill—settling into a lower energy state—and we would not be able to stop it. We would release a huge bubble of energy that expands at the speed of light, leaving a vast trail of destruction in its wake. It might be so bad that every one of our atoms would be torn apart during the apocalypse.
Luckily, this is an extremely unlikely scenario. Our universe has lasted billions of years, and it’s improbable that we are living in such a precarious state; cosmic-ray collisions would probably already have “sparked” the vacuum with enough energy to cause such a disaster were it possible. This hasn’t stopped some believers—physicists included—from picketing high-energy laboratories like Fermilab; they believe that a high-energy collision could cause a spontaneous collapse of the vacuum. Even if those concerns were valid, it seems all but impossible to propel a spaceship with zero-point energy. However, Puthoff believes he has a way to extract energy from the void.
In theory, scientists can get energy from the Casimir effect even at absolute zero in the bleakest part of the vacuum of space. Two plates generate heat when they smack together—heat that can be converted to electricity. Alas, the plates have to be pried apart again, which requires more energy than was initially produced; most scientists believe that this fact kills the idea of making a perpetual-motion machine that runs on vacuum energy. But Puthoff thinks he sees several ways around this dilemma. One is to use plasmas instead of plates.
A plasma, a gas of charged particles, is just like a metal plate as far as the Casimir effect is concerned. A conducting, cylinder-shaped gas would be compressed by the zero-point fluctuations just as plates are forced together. The collapse would heat the plasma, releasing energy. Unlike metal plates, plasmas could be made easily with a bolt of electricity, according to Puthoff, and instead of having to pry the plates apart again, the plasma “ash” is discarded. Puthoff gingerly claims to have gotten out 30 times more energy with this method than was put in. “There’s some evidence; we’ve even got a patent,” he says. However, Puthoff’s device is one in a long line of “free energy” machines—none of which, in the past, have withstood scientific scrutiny. It is unlikely that his device to harness the zero-point energy will be any different.
According to quantum mechanics and general relativity, the power of zero is infinite, so it’s no surprise that people are hoping to tap its potential. But for the time being, it appears that nothing will come of nothing.
Chapter 8
Zero Hour at Ground Zero
[ZERO AT THE EDGE OF SPACE AND TIME]
Alien they seemed to be:
No mortal eye could see
The intimate welding of their later history…
—THOMAS HARDY, “THE CONVERGENCE OF THE TWAIN”
Modern physics is a struggle of two titans. General relativity holds sway in the realm of the very, very big: the most massive objects in the universe, such as stars, solar systems, and galaxies. Quantum mechanics rules the domain of the very, very small: atoms and electrons and subatomic particles. It would seem that these two theories could live in harmony together, each dictating the rules of physics for different aspects of the universe.
Unfortunately, there are objects that lie in both realms. Black holes are very, very massive, so they are subject to the laws of relativity; at the same time, black holes are very, very tiny, so they are in the domain of quantum mechanics. And far from agreeing, the two sets of laws clash at the center of a black hole.
Zero dwells at the juxtaposition of quantum mechanics and relativity; zero lives where the two theories meet, and zero causes the two theories to clash. A black hole is a zero in the equations of general relativity; the energy of the vacuum is a zero in the mathematics of quantum theory. The big bang, the most puzzling event in the history of the universe, is a zero in both theories. The universe came from nothing—and both theories break down when they try to explain the origin of the cosmos.
To understand the big bang, physicists must marry quantum theory with relativity. In the past few years they have begun to succeed, creating a monster theory that explains the quantum-mechanical nature of gravity, allowing them to peer at the very creation of our universe. All they had to do was banish zero.
The Theory of Everything is, in truth, a theory of nothing.
Zero Banished: String Theory
The problem is, when we try to calculate all the way down to zero distance, the equation blows up in our face and gives us meaningless answers—things like infinity. This caused a lot of trouble when the theory of quantum electrodynamics first came out. People were getting infinity for every problem they tried to calculate!
—RICHARD FEYNMAN
General relativity and quantum mechanics were bound to be incompatible. The universe of general relativity is a smooth rubber sheet. It is continuous and flowing, never sharp, never pointy. Quantum mechanics, on the other hand, describes a jerky and discontinuous universe. What the two theories have in common—and what they clash over—is zero.
The infinite zero of a black hole—mass crammed into zero space, curving space infinitely—punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.
Quantum mechanics has a similar problem, a problem related to the zero-point energy. The laws of quantum mechanics treat particles such as the electron as points; that is, they take up no space at all. The electron is a zero-dimensional object, and its very zerolike nat
ure ensures that scientists don’t even know the electron’s mass or charge.
This seems like a silly statement. It has been nearly a century since scientists measured the electron’s mass and charge. How could physicists not know something that has been measured? The answer lies with zero.
The electron that scientists see in the laboratory—the electron that physicists, chemists, and engineers have known and loved for decades—is an impostor. It is not the true electron. The true electron is hidden in a shroud of particles, made up of the zero-point fluctuations, those particles that constantly pop in and out of existence. As an electron sits in the vacuum, it occasionally absorbs or spits out one of these particles, such as a photon. The swarm of particles makes it difficult to get a measurement of the electron’s mass and charge, because the particles interfere with the measurement, masking the electron’s true properties. The “true” electron is a bit heavier and carries a greater charge than the electron that physicists observe.
Scientists might get a better idea of the true mass and charge of the electron if they could get a little closer; if they could invent a tiny device that could get a short distance inside the cloud of particles, they would be able to see more clearly. According to quantum theory, as the measuring device gets past the first few virtual particles on the rim of the cloud, scientists would see the mass and charge of the electron go up, and as the probe gets closer and closer to the electron, it would pass more and more virtual particles, so the observed mass and charge go up and up. As the probe approaches zero distance from the electron, the number of particles it passes goes up to infinity—so the probe’s measurements of the mass and charge of the electron also go to infinity. According to the rules of quantum mechanics, the zero-dimensional electron has infinite mass and infinite charge.
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