by Michio Kaku
Physicists have discovered that there are at least two types of black holes. The first type is the remnant of a giant star as described above. The second type of black hole is found at the center of galaxies. These galactic black holes can be millions or even billions of times more massive than our sun. Many astronomers believe that black holes lie in the center of every galaxy.
In the last few decades, astronomers have identified hundreds of possible black holes in space. At the center of our own Milky Way lies a monster black hole whose mass is two to four million times that of our sun. It is located in the constellation Sagittarius. (Unfortunately, dust clouds obscure the area, so we cannot see it. But if the dust clouds were to part, then every night, a magnificent, blazing fireball of stars, with the black hole at its center, would light up the night sky, perhaps outshining the moon. It would truly be a spectacular sight.)
The latest excitement concerning black holes came about when the quantum theory was applied to gravity. These calculations unleashed a wellspring of unexpected phenomena that test the limits of our imagination. As it turns out, our guide through this uncharted territory was totally paralyzed.
As a graduate student at Cambridge University, Stephen Hawking was an ordinary youth, without much direction or purpose. He went through the motions of being a physicist, but his heart was not there. It was obvious that he was brilliant, but he seemed unfocused. But one day, he was diagnosed with amyotrophic lateral sclerosis (ALS) and told he would die within two years. Although his mind would be intact, his body would rapidly waste away, losing all ability to function, until he died. Depressed and shaken to the core, he realized that his life up to that point had been wasted.
He decided to dedicate the few remaining years of his life to doing something useful. To him, this meant solving one of the biggest problems in physics: the application of the quantum theory to gravity. Fortunately, his disease progressed much more slowly than his doctors predicted, so he was able to continue pathbreaking research in this new area even as he was confined to a wheelchair and lost control of his limbs and even vocal cords. I once was invited by Hawking to give a talk at a conference he was organizing. I had the pleasure of visiting his house and was surprised by the different gadgets that allowed him to continue his research. One device was a page turner. You could put a journal into this contraption, and it would automatically turn the pages. I was impressed by the degree to which he was determined not to allow his illness to detract from his life’s goal.
Back then, most theoretical physicists were working on the quantum theory, but a small handful of renegades and diehards were trying to find more solutions to Einstein’s equation. Hawking asked himself a different but profound question: What happens when you combine these two systems and apply quantum mechanics to a black hole?
He realized that the problem of calculating quantum corrections to gravity was much too difficult to solve. So he chose a simpler task: calculating quantum corrections just to the atoms inside a black hole, ignoring the more complex quantum corrections of the gravitons.
The more he read about black holes, the more he realized that something was wrong. He began to suspect that the traditional thinking—that nothing can escape a black hole—violated the quantum theory. In quantum mechanics, everything is uncertain. A black hole looks perfectly black because it absorbs absolutely everything. But perfect blackness violated the uncertainty principle. Even blackness had to be uncertain.
He came to the revolutionary conclusion that black holes must necessarily emit a very faint glow of quantum radiation.
Hawking then showed that the radiation emitted by a black hole was actually a form of blackbody radiation. He calculated this by realizing that the vacuum was not just the state of nothingness but was actually bubbling with quantum activity. In the quantum theory, even nothingness is in a state of constant, churning uncertainty, where electrons and anti-electrons could suddenly jump out of the vacuum, then collide and disappear back into the vacuum. So nothingness was actually frothing with quantum activity. He then realized that if the gravitational field was intense enough, then electron and anti-electron pairs could be created out of the vacuum, creating what are called virtual particles. If one member falls into the black hole, while the other particles escapes, it would create what is now called Hawking radiation. The energy to create this pair of particles comes from the energy contained in the black hole’s gravity field. Because the second particle leaves the black hole forever, it means that the net matter and energy content of the black hole and its gravity field has decreased.
This is called black hole evaporation and describes the ultimate fate of all black holes: they will gently radiate Hawking radiation for trillions of years, until they exhaust all their radiation and die in a fiery explosion. So even black holes have a finite lifetime.
Trillions upon trillions of years from now, the stars of the universe will have exhausted all their nuclear fuel and become dark. Only black holes will survive in this bleak era. But even black holes must eventually evaporate, leaving nothing but a drifting sea of subatomic particles. Hawking asked himself another question: What happens if you throw a book into a black hole? Is the information in that book lost forever?
According to quantum mechanics, information is never lost. Even if you burn a book, by tediously analyzing the molecules of the burned paper, it’s possible to reconstruct the entire book.
But Hawking stirred up a hornet’s nest of controversy by saying that information thrown inside a black hole is indeed lost forever, and that quantum mechanics therefore breaks down in a black hole.
As previously mentioned, Einstein once said that “God does not play dice with the world”—that is, you cannot reduce everything to chance and uncertainty. Hawking added, “Sometimes God throws the die where you cannot find them,” meaning that the dice may land inside a black hole, where the laws of the quantum may not hold. So the laws of uncertainty fail when you go past the event horizon.
Since then, other physicists have come to the defense of quantum mechanics, showing that advanced theories like string theory, which we will discuss in the next chapter, can preserve information even in the presence of black holes. Eventually, Hawking conceded that perhaps he was wrong. But he proposed his own novel solution. Perhaps when you throw a book into a black hole, the information is not lost forever, as he previously thought, but it comes back out, in the form of Hawking radiation. Encoded within the faint Hawking radiation is all the information necessary to re-create the original book. So perhaps Hawking was incorrect, but the correct solution lies in the radiation that he had found previously.
In conclusion, whether information is lost in a black hole is still an ongoing question, fiercely debated among physicists. But ultimately we may have to wait until we have the final quantum theory of gravity that includes graviton quantum corrections. In the meantime, Hawking turned to the next puzzling question involving combining the quantum theory and general relativity.
Through the Wormhole
If black holes eat up everything, then where does all that stuff go?
The short answer is, we don’t know. The answer may ultimately be solved by unifying the quantum theory with general relativity.
Only when we finally find a quantum theory of gravity (and not just matter) can we answer this question: What lies on the other side of a black hole?
But if we blindly accept Einstein’s theory, then we get into trouble, since his equations predict that the gravitational force at the very center of a black hole or the beginning of time is infinite, which makes no sense.
But in 1963, mathematician Roy Kerr found an entirely new solution to Einstein’s equations for a rotating black hole. Previously, in Schwarzschild’s work, black holes collapsed into a stationary, tiny dot, called a singularity, where gravitational fields became infinite and everything was crushed into a single poi
nt. But if you analyze Einstein’s equations for a spinning black hole, Kerr found that strange things happen.
First, the black hole does not collapse into a dot. Instead, it collapses into a rapidly spinning ring. (Centrifugal forces on the spinning ring are strong enough to prevent the ring from collapsing under its own gravity.)
Second, if you fall through the ring, it’s possible you may not be crushed to death at all but may pass through the ring. The gravity inside the ring is actually finite.
Third, the mathematics indicates that as you pass through the ring, you could enter a parallel universe. You literally leave our universe and enter into another sister universe. Think of two sheets of paper, stacked one on top of the other. And then stick a straw through both of them. By passing through the straw, you leave one universe and enter a parallel universe. This straw is called a wormhole.
Fourth, as you reenter the ring, you could proceed to another universe. Like taking an elevator in an apartment building, you pass from one floor to the next, from one universe to another. Each time you reenter the wormhole, you could enter an entirely new universe. So this introduced a startling new picture of a black hole. At the very center of a spinning black hole, we find something resembling the looking glass of Alice. On one side, we have the tranquil countryside of Oxford, England. But if you stuck your hand through the looking glass, you would wind up somewhere else entirely.
Fifth, if you succeed in passing through the ring, there is also the chance that you will wind up in a distant region of your same universe. So the wormhole could be like a subway system, taking an invisible shortcut through space and time. Calculations show that you might be able to go faster than the speed of light, or even go backward in time, perhaps without violating known physical laws.
These bizarre conclusions, no matter how outrageous, cannot be easily dismissed, since they are solutions to Einstein’s equation, and they describe spinning black holes, which we now believe are by far the most common kind.
Wormholes were actually first introduced by Einstein himself in 1935, in a paper with Nathan Rosen. They imagined two black holes joined together, which resemble two funnels in space-time. If you fell into one funnel, you would be thrust out the end of the other funnel without being crushed to death.
Figure 10. In principle, one might hypothetically be able to reach the stars or even the past by going through the wormhole.
There is this famous line in T. H. White’s novel The Once and Future King: “Everything not forbidden is compulsory.” Physicists actually take this statement seriously. Unless there is a physical law against a phenomenon, perhaps it exists somewhere in the universe.
For example, even though wormholes are notoriously hard to create, some physicists have speculated that wormholes may have existed at the beginning of time and then expanded after the Big Bang. Maybe they exist naturally. One day, our telescopes may actually see a wormhole in space. Although wormholes have fired up the imagination of science fiction writers, actually creating one in a laboratory poses daunting problems.
First, you need to assemble vast amount of positive energy, comparable to a black hole, to open the gateway through space-time. This alone would require the technology of a very advanced civilization. So we don’t expect amateur inventors to be able to create a wormhole in their basement laboratories any time soon.
Second, such a wormhole is going to be unstable and will close by itself, unless one adds a new, exotic ingredient, called negative matter or negative energy, which is entirely different from antimatter. Negative matter and energy are repulsive, which can keep the wormhole from collapsing.
Physicists have never seen negative matter. In fact, it would obey anti-gravity, so it would fall up, rather than down. If negative matter were on the Earth billions of years ago, it would have been repelled by the gravity of the Earth and flung into outer space. So we don’t expect to find negative matter on the Earth.
Negative energy, in contrast to negative matter, does in fact exist, but only in minuscule amounts, too small to be of practical value. Only a very advanced civilization, perhaps millennia more advanced than us, would be able to harness enough positive and negative energy to create a wormhole and then keep it from collapsing.
Third, radiation from gravity itself (called graviton radiation) might be enough to cause the wormhole to explode.
Ultimately the final answer to the question of what happens when you fall into a black hole must await a true theory of everything, in which both matter and gravity are quantized.
Some physicists have seriously proposed the controversial idea that when stars fall into a black hole, they are not crushed into a singularity but instead are blown out the other side of a wormhole, creating a white hole. A white hole obeys precisely the same equations as a black hole, except the arrow of time is reversed, so matter spews out of a white hole. Physicists have looked for white holes in space, but so far have turned up empty-handed. The point of mentioning white holes is that perhaps the Big Bang was originally a white hole, and all the stars and planets we see in the heavens were flung out of a black hole—about fourteen billion years ago.
The point is that only a theory of everything can tell us what lies on the other side of a black hole. Only by calculating quantum corrections to gravity can we answer the deepest questions raised by wormholes.
But if wormholes might one day take us instantly across the galaxy, can they also take us to the past?
Time Travel
Time travel is a staple of science fiction, ever since H. G. Wells’s The Time Machine. We can move freely in three dimensions (forward, sideways, and upward), so perhaps there was a way to move in the fourth dimension, time. Wells envisioned entering a time machine, spinning a dial, and then soaring hundreds of thousands of years into the future to the year 802,701 CE.
Since then, scientists have studied the possibility of time travel. When Einstein first proposed his theory of gravity in 1915, he was worried that his equations might allow one to twist time so that one could enter the past, which he believed would indicate a flaw in his theory. But this nagging problem became a real possibility in 1949, when his neighbor at Princeton’s famed Institute for Advanced Study, the great mathematician Kurt Gödel, found that if the universe rotated, and one could travel around the spinning universe fast enough, then one could enter the past—that is, you could return before you left. Einstein was stunned by this unorthodox solution. Einstein, in his memoirs, finally concluded that even though time travel was possible in Gödel’s universe, it could be dismissed “on physical grounds,” meaning that the universe expanded and did not rotate.
Now, although physicists are still not convinced about the possibility of time travel, they are taking the question very seriously. A variety of solutions to Einstein’s equations have been discovered that allow for time travel.
To Newton, time was like an arrow. Once fired, it would unerringly proceed with uniform speed throughout the universe. One second on the Earth was one second everywhere in space. Clocks could be synchronized anywhere in the universe. To Einstein, however, time was more like a river. It could speed up or slow down as it meandered its way across stars and galaxies. Time could tick at different rates across the universe. The new picture, however, states that the river of time could have whirlpools that might sweep you to the past (physicists call them CTCs, or closed timelike curves). Or perhaps the river of time might fork into two rivers, so the time line splits, creating two parallel universes.
Hawking was so fascinated by time travel that he issued a challenge to other physicists. He believed there must be a hidden law of physics, not yet found, that he called the chronology protection conjecture, which ruled out time travel once and for all. But try as he might, he could never prove this hypothesis. This means that time travel might still be consistent with the laws of physics, with nothin
g to prevent the existence of time machines.
Also, tongue in cheek, he said that time travel was not possible, because “where are the tourists from the future?” At every major historical event, there should be hordes of tourists with their cameras elbowing one another, frantically trying to get the best picture of the event to show their friends in the future.
For the moment, think of the mischief you could create if you had a time machine. Going back in time, you could make bets on the stock market and become a billionaire. You could change the course of past events. History could never be written down. Historians would be out of a job.
Time travel, of course, has serious problems. There are a host of logical paradoxes associated with time travel, such as:
Making the present impossible: If you go back in time to meet your grandfather as a child and kill him, then how can you even exist?
Time machine from nowhere: Someone from the future gives you the secret of time travel. Years later, you go back in time and give the secret of time travel to your younger self. Then where did the secret of time travel come from?
Becoming your own mother: Science fiction writer Robert Heinlein wrote about becoming your own family tree. Assume that an orphan girl grows up, but changes into a man. The man then goes back in time, meets herself, and has a baby girl with her. The man then takes the baby girl further back in time, and drops the baby off at the same orphanage, and then repeats the cycle. In this way, she becomes her own mother, daughter, grandmother, granddaughter, etc.
