If You Threw a Book Into a Black Hole, Would It Ever Come
Out Again?

In 2019, newspapers and websites across the planet splashed sensational news on the front page: astronomers had just taken the first photograph of a black hole. Billions of people saw the stark image, a red ball of hot fiery gas with a black, round silhouette in the middle. This mysterious object captured the public’s imagination and dominated the news. Not only have black holes intrigued and fascinated physicists, but they have also entered into the public’s consciousness, being featured in numerous science specials and a plethora of movies.

The black hole that was photographed by the Event Horizon Telescope lies inside the galaxy M87, 53 million light-years from Earth. The black hole is truly a monster, weighing in at a staggering five billion times the mass of the sun. Our entire solar system, even past Pluto, could easily fit inside the black silhouette in the photograph.

To accomplish this stunning achievement, astronomers created a super telescope. Normally, a radio telescope is not large enough to take in enough faint radio signals to create an image of an object so distant. But astronomers were able to photograph this black hole by lashing together the signals from five individual ones scattered around the world. By using supercomputers to carefully combine these diverse signals, they effectively created a single giant radio telescope the size of planet Earth itself. This composite was so powerful that it could, in principle, detect an orange sitting on the surface of moon from the Earth.

A host of new, remarkable astronomical discoveries like this have rejuvenated interest in Einstein’s theory of gravity. Sadly, for the past 50 years, research in Einstein’s general relativity was relatively stagnant. The equations were fiendishly difficult, often involving hundreds of variables; and experiments on gravity were simply too expensive, involving detectors that were miles across.

The irony is that, although Einstein had reservations about the quantum theory, the current renaissance in relativity research has been fueled by the merger of the two, by the application of the quantum theory to general relativity. As we mentioned, a complete understanding of the graviton and how to eliminate its quantum corrections is considered too difficult, but a more modest application of the quantum theory to stars (neglecting graviton corrections) has opened the heavens to a wave of startling scientific breakthroughs.

*

The basic idea of a black hole actually can be traced back to Newton’s discovery of the laws of gravity. His Principia gave us a simple picture: if you fire a cannonball with enough energy, it will completely circle the Earth, then return to its original point.

But what happens if you aim the cannonball straight up? Newton realized that the cannonball will eventually reach a maximum height and then fall back to Earth. But with enough energy, the cannonball would reach escape velocity, that is, the speed necessary to escape the Earth’s gravity and soar into space, never to return.

It is a simple exercise, using Newton’s laws to calculate the escape velocity of the Earth, which turns out to be 25,000 miles per hour. This is the velocity that our astronauts had to attain to reach the moon in 1969. If you do not reach escape velocity, then you will either enter orbit or fall back to Earth.

In 1783, an astronomer named John Michell asked himself a deceptively simple question: What happens if the escape velocity is the speed of light? If a light beam is emitted from a giant star so massive that its escape velocity is the speed of light, then perhaps even its light cannot escape. All light emitted from this star will eventually fall back into the star. Michell called these dark stars, celestial bodies that appeared black because light could not escape their immense gravity. Back in the 1700s, scientists knew little about the physics of stars and did not know the correct value for the speed of light, and hence this idea languished for several centuries.

In 1916 during World War I, German physicist Karl Schwarzschild was stationed on the Russian front as an artilleryman. While fighting in the middle of a bloody war, he found time to read and digest Einstein’s famous 1915 paper introducing general relativity. In a brilliant stroke of mathematical insight, Schwarzschild somehow found an exact solution of Einstein’s equations. Instead of solving the equations for a galaxy or the universe, which was too difficult, he started with the simplest of all possible objects, a tiny point particle. This object, in turn, would approximate the gravity field of a spherical star as seen from a distance. One could then compare Einstein’s theory with experiment.

Einstein’s reaction to Schwarzshild’s paper was ecstatic. Einstein realized that this solution of his equations would allow him to make more precise calculations with his theory, such as the bending of starlight around the sun and the wobbling of the planet Mercury. So instead of making crude approximations to his equations, he could calculate exact results from his theory. This was a monumental breakthrough that would prove important for understanding black holes. (Schwarzschild died shortly after his remarkable discovery. Saddened, Einstein wrote a moving eulogy for him.)

But despite the enormous impact of Schwarzschild’s solution, it also raised some bewildering questions. From the start, his solution had weird properties that pushed the boundaries of our understanding of space and time. Surrounding a supermassive star was an imaginary sphere (which he called the magic sphere and today is called the event horizon). Far outside this sphere, the gravity field resembled an ordinary Newtonian star’s, so Schwarzschild’s solution could be used to approximate its gravity. But if you were unfortunate enough to approach the star and pass through the event horizon, you would be trapped forever and would be crushed to death. The event horizon is the point of no return: anything that falls in never comes out.

But as you approached the event horizon, even more bizarre things would begin to happen. For example, you would encounter light beams that had been trapped for perhaps billions of years and are still orbiting the star. The gravity pulling on your feet would be greater than the gravity pulling on your head, so you would be stretched like spaghetti. In fact, this spaghettification becomes so severe that even the atoms of your body get pulled apart and eventually disintegrate.

To someone watching this remarkable event from a great distance, it would appear as if time inside the rocket ship on the edge of the event horizon had gradually slowed down. In fact, to an outsider, it appears as if time has stopped as the ship hits the event horizon. What is remarkable is that, to the astronauts in the ship, everything seems to be normal as they pass through the event horizon—normal, that is, until they are torn apart.

This concept was so bizarre that, for many decades, it was considered science fiction, a strange by-product of Einstein’s equations that didn’t exist in the real world. Astronomer Arthur Eddington once wrote that “there should be a law of Nature to prevent a star from behaving in this absurd way!”

Einstein even wrote a paper arguing that, under normal conditions, black holes could never form. In 1939, he showed that a whirling ball of gas could never be compressed by gravity to within the event horizon.

Ironically, that very same year, Robert Oppenheimer and his student Hartland Snyder showed that black holes could indeed form from natural processes that Einstein did not foresee. If you start with a giant star ten to fifty times more massive than our sun, when it uses up its nuclear fuel, it can eventually explode as a supernova. If the remnant of the explosion is a star that is compressed by gravity to its event horizon, then it can collapse into a black hole. (Our sun is not massive enough to undergo a supernova explosion, and its event horizon is about two miles across. No known natural process can squeeze our sun down to two miles, and hence our sun will not become a black hole.)

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 schlerosis (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, it 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 blackhole 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,” that is, 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 recreate 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.

__________________________________

From the book The God Equation: The Quest for a Theory of Everything by Michio Kaku published by Doubleday, an imprint of The Knopf Doubleday Publishing Group, a division of Penguin Random House LLC. Copyright © 2021 Michio Kaku.