Gravity and Early Predictions of Black Holes

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Chapter 1
Gravity and Early Predictions of Black Holes

Just about everyone has heard of black holes. But many nonscientists are not exactly sure what these bizarre objects are and what they are capable of doing. This is partly because their name can be somewhat misleading. A black hole is not simply an empty hole, or void, in space, but instead a cosmic entity having very substantial mass. (Mass is the measurable quantity of matter possessed by physical objects.) A black hole does have a hole, or tunnel, as part of its structure; but unlike a void, it possesses a number of physical properties as well, some of which can be measured by human instruments.

For example, a black hole's large mass generates an equally large gravitational field, which scientists can detect. Gravity is a force or property of all matter that attracts one object to another. In small objects such as molecules, pebbles, people, houses, and so forth, gravitational attractions are very slight and neither noticeable to the human senses nor measurable by instruments; only on planetary and larger scales do these attractions become obvious and easily measurable. Thus, Earth's gravity holds the Moon in orbit around the planet, and the gravity of the Sun, the star at the center of our solar system, keeps Earth and the other planets in orbit around it. Likewise, a black hole exerts a gravitational attraction on any objects that happen to stray too close to it. "In fact," writes astronomer Thomas T. Arny,

the gravitational field generated by a black hole is no different from that generated by any other body of the same mass. For example, if the sun were suddenly to become a black hole with the same mass it has now [something that could not actually happen], the Earth would continue to orbit it just as it does now.6

"Creatures of Gravity"

Not only do black holes exert large gravitational pulls, they also form through a process in which gravity crushes an enormous amount of material into a very small amount of space. This makes a black hole an extremely dense, or compact, object. So dense and massive is such an object that its gravity is far stronger than that of ordinary planets and stars, which have much less mass. Indeed, a black

hole's gravity is so intense that it can even imprison light, which moves at nature's highest possible speed. This is why a black hole appears black—no light escapes it to reveal its presence to human eyes and telescopes.

Considering this close relationship between black holes and gravity, black holes might be said to be "creatures of gravity." It is not possible, therefore, to discuss black holes without understanding how gravity works, especially under extreme conditions. In fact, it was during the years immediately following the discovery of how gravity works that scientists first predicted the existence of black holes, although at the time they were not called black holes and not a shred of evidence for them yet existed.

The Discovery of Universal Gravitation

The first major theory of gravity came in 1666. Before this date, scientists assumed that the force that keeps people, houses, trees, and mountains firmly in place on Earth and the force that keeps the Earth in orbit around the Sun were separate and distinct attractions. Then a brilliant young Englishman named Isaac Newton showed that this was not the case; at the same time, he demonstrated how gravity actually works.

According to Newton, he got his first major clue to gravity's identity when he witnessed an apple falling from a tree. He was not surprised that the apple fell and struck the ground, of course, since it had long been common knowledge that some mysterious power drew all objects toward the center of the Earth. What suddenly piqued Newton's interest was the concept of distance as it related to the mystery force. It occurred to him that if he stood at the top of the tallest mountain in the world and tossed out an apple, the apple would fall to the ground just as surely as it did from the branch of the tree. This meant that the mystery force was strong enough to pull on objects over distances of tens of thousands of feet. Perhaps, then, that force might pull on objects lying much farther away.

This naturally led Newton to think about the Moon, which was clearly hundreds of thousands of miles away from Earth. Maybe, he reasoned, the same force that caused the apple to fall was pulling on the Moon. In that case, the Moon was "falling" toward Earth and the only reason the two objects did not collide was that the Moon's rapid motion outward, into space, cancelled out, or balanced, the attraction of the mystery force. From this logical (and as it turned out, correct) realization, it was not a great leap to suppose that the very same force kept Earth and the other planets in orbit around the Sun. Newton concluded that the mystery force, which he called gravity, existed throughout the universe, and was therefore universal. And appropriately, he dubbed his new theory the law of universal gravitation.

Through an elegant mathematical formula, Newton demonstrated that the gravitational pull exerted between two objects depends on two factors—the mass of the objects and the distance separating them. A small object with very little mass, he showed, exerts very little attraction on another object; a very large and massive object, such as a planet, exerts a measurable gravitational pull on another object. At the same time, distance comes into play. The farther apart two objects are, Newton showed, the less their gravities attract each other. And the reverse is also true—the closer the two objects are, the stronger they attract each other. This explains why the Sun easily maintains its hold on Earth, which lies relatively near the star, while the Sun's gravity has no measurable effect on other stars, which exist at distances thousands of times greater than that between the Sun and Earth.

Newton's theory of universal gravitation revolutionized the physical sciences, especially the disciplines of physics and astronomy. As noted science writer John Gribbin states it:

Newton really had explained the fall of an apple and the motion of the Moon with one set of laws. In doing so, he removed the mystery from the behavior of heavenly bodies, and opened the eyes of scientists to the fact that the behavior of the stars and planets—the behavior of the whole universe—might be explained using the same laws of physics that are derived from studies carried out in laboratories on Earth.7

Escape Velocity and Invisible Stars

One of the many implications of Newton's gravitational theory almost inevitably led to the basic concept of what are today called black holes. While studying gravitational attraction, some of his immediate scientific successors considered what requirements would be needed to overcome that attraction. Newton's formula showed why Earth remains in orbit around the Sun and does not fall onto the star; namely, the planet moves away from the Sun at just the right speed to match and balance its great gravitational pull. But what if Earth could suddenly move faster, some scientists wondered? Logically, it would then be able to overcome the Sun's gravity and escape from the star's grip.

The speed at which an object must move in order to escape the gravity of another object became known as its escape velocity. Earth's escape velocity, for instance, is about seven miles per second, which means that a rocket or space shuttle must achieve that speed to escape the pull of Earth's gravity. In contrast, a rocket blasting off from Jupiter at seven miles per second would not be able to escape that planet. This is because Jupiter is a good deal more massive than Earth and therefore has much stronger gravity. "The escape velocity is different for different worlds," renowned science writer Isaac Asimov explains.

A world that is less massive than Earth … has a lower escape velocity from its surface…. On the other hand, worlds that are more massive than Earth have higher escape velocities than it has. It is not surprising that the giant of the planetary system, Jupiter, has the highest escape velocity…. From Jupiter's surface, the escape velocity is … 5.4 times that from Earth's surface.8

During the 1700s, a few scientists gave considerable thought to this idea of more massive objects

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having higher escape velocities. One of these researchers was English astronomer John Michell, who carried out a detailed study of the properties of stars. It was by then clear that some stars in the heavens are more massive than the Sun. Michell did not know if there is an upper limit to a star's size. But at least in theory, he proposed, stars with truly tremendous mass might exist, and if so, their gravities would be huge. Moreover, the escape velocities of such giant stars would be correspondingly huge.

John Michell: the Forgotten Pioneer

The first person to realize that objects like black holes might exist—English scientist John Michell—is all but forgotten now, except by astronomers. In this excerpt from In Search of the Edge of Time, noted science writer John Gribbin summarizes Michell's career and contributions to science.

Born in 1724, Michell … is still known as the father of the science of seismology [the study of earthquakes]. He studied at the University of Cambridge, graduating in 1752, and his interest in earthquakes was stimulated by the disastrous seismic shock that struck Lisbon [Portugal] in 1755. Michell established that the damage had actually been caused by an earthquake centered underneath the Atlantic Ocean. He became Woodwardian Professor of Geology at Cambridge in 1762, a year after becoming a bachelor of divinity…. Michell made many contributions to astronomy, including the first realistic estimate of the distance to the stars, and the suggestion that some pairs of stars seen in the night sky … are really "binary stars," in orbit around each other…. The first mention of dark stars [i.e., black holes] was made in a paper by Michell read to the Royal Society … in 1783. This was an impressively detailed discussion of ways to work out the properties of stars, including their distances, sizes, and masses, by measuring the gravitational effect of light emitted from their surfaces.

That led Michell to ponder just how high a star's escape velocity could reach. And taking this line of reasoning to its logical extreme, he wondered what might happen if the star's escape velocity exceeded the speed of light—186,000 miles per second. In that case, he reasoned, even light could not escape the star. In a paper published in 1784, he wrote: "If there should really exist in nature any bodies whose … diameters are more than 500 times the diameter of the sun," they would have enormous gravities and escape velocities. Thus, "all light emitted from such a body would be made to return to it by its own power of gravity." And because the light cannot leave the star, "we could have no information from sight."9 In other words, the star would be dark and therefore invisible to human eyes and telescopes. Appropriately, Michell called these objects "dark stars."

Michell was not the only scientist of his day fascinated by the effects of extreme gravity. In 1795 French scientist Pierre-Simon Laplace arrived at the same basic conclusion independently. Someplace in the heavens, he wrote, there might exist

invisible bodies as large, and perhaps in as great number, as the stars. A luminous star of the same density [compactness] as the Earth, and whose diameter was two hundred and fifty times greater than that of the sun, would not, because of its [gravitational] attraction, allow any of its [light] rays to arrive at us; it is therefore possible that the largest luminous bodies of the universe may, through this cause, be invisible.10

Based on this conclusion, Laplace called these hypothetical objects les corps obscures, or "invisible bodies."

Bendable Space and Gravity Wells

Michell's and Laplace's descriptions of dark stars and invisible bodies were at the time completely theoretical. They had absolutely no evidence for these strange celestial bodies, and the vast majority of scientists thought that no such bodies existed. Not surprisingly, therefore, these precursors of black holes became a mere mathematical curiosity. And for more than a century afterward few scientists gave them any thought.

In the early twentieth century, however, the concept of black holes enjoyed an unexpected revival when a brilliant young German scientist named Albert Einstein proposed a new theory of gravity. Part of his general theory of relativity, published in 1915–1916, it did not disprove Newton's theory and formula for universal gravitation. Rather, Einstein's version simply explained the nature of space and the way gravity works within it differently than Newton's had.

For example, according to Newton gravity is a force exerted by objects and therefore emanates somehow from their centers. According to Einstein, however, gravity is not a directed force but a property of space itself, an idea that was revolutionary because it proposed that space actually has an unseen structure. Before Einstein, the common assumption among physicists and other scientists was that space is an empty void with no ability to affect the bodies moving within it. In contrast, Einstein argued that space has an invisible "fabric" with an elastic, or bendable, quality.

Further, Einstein stated, bodies possessing mass move through space and interact with its hidden fabric by sinking into it and creating a depression. Scientists came to call such a well-like depression a "gravity well." In this view, the depth of a gravity well depends on a body's mass; obviously, the more massive the body is, the deeper the body will sink and the deeper the well it will create. In this way, said Einstein, very massive objects, like planets and stars, distort or curve space's elastic fabric, and this curvature is what people experience as gravity. Arny gives this simplified analogy:

Imagine a waterbed on which you have placed a baseball. The baseball makes a small depression

Einstein: Visionary of Space and Time

No other scientist has contributed more to human understanding of the behavior of light, the curvature of space, and the existence of black holes than physicist Albert Einstein. He was born in Ulm, Germany, in 1879. Soon his father, who manufactured electronic goods, moved the family to Munich, and later to Milan, Italy. As a young man, Albert studied in Switzerland and in 1900 graduated from Zurich Polytechnic Institute.

In 1905 he published three ground-breaking scientific papers, one on the nature of light, another on the mechanics of atom-sized molecules, and a third stating most of the principles that came to be known as his special theory of relativity. Perhaps the most famous component of the theory of special relativity is that mass and energy are equivalent. In 1915 Einstein published his visionary general theory of relativity, in which he showed that gravity is a function of four-dimensional space and time and that space is curved. Among the equations for general relativity were some that predicted the existence of black holes.

Einstein received the Nobel Prize in physics in 1921 and died in 1955. Throughout the twentieth century, one scientific experiment and discovery after another verified his predictions with amazing accuracy, including the discovery of black holes. Today he is regarded as one of the greatest scientists in history.

in the otherwise flat surface of the bed. If a marble is now placed near the baseball, it will roll along the curved surface into the depression. The bending of its environment made by the baseball therefore creates an "attraction" between the baseball and the marble. Now suppose we replace the baseball with a bowling ball. It will make a bigger depression and the marble will roll in further and be moving faster as it hits the bottom. We therefore infer from the analogy that the strength of the attraction between the bodies depends on the amount by which the surface is curved. Gravity also behaves this way, according to the general theory of relativity. According to that theory, mass creates a curvature of space, and gravitational motion occurs as bodies move along the curvature.11

Now replace this analogy with one involving real objects moving through outer space. Consider two planets of differing size approaching each other. The smaller planet encounters the curve of the larger planet's gravity well and rolls "downhill" toward the

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larger object. (This produces exactly the same effect as the larger planet "pulling in" the smaller one in Newton's gravitational model, so Newton's formula can still be applied and its results for most objects are still valid.) In Einstein's gravitational model, if the smaller planet is moving fast enough, it will soon roll out of the larger planet's gravity well and continue on its way. If it is not moving at the proper escape velocity, however, it will be trapped in the well, in which case it will either go into orbit around the larger planet or crash into it.

Could Superdense Bodies Exist?

The new theory of curved space created a great stir in scientific circles. Many physicists, astronomers, and other scientists felt that Einstein's ideas were compelling and they wanted to test and prove the theory. If space is indeed curved and massive bodies create gravity wells, they reasoned, a very deep gravity well should deflect a beam of light. In other words, though light travels swiftly enough to allow it to escape such a well, the well should bend the beam enough for scientists to measure it.

What was needed for the test was a very massive body, at least by human standards. And because it is the largest object in the solar system, the Sun was the logical choice. The historic experiment took place on May 29, 1919, during a solar eclipse that was visible from the western coast of central Africa. "Bright stars were visible in the sky near the eclipsed sun," Asimov explains, "and their light on its way to Earth skimmed past the sun. Einstein's theory predicted that this light would be bent very slightly toward the sun as it passed."12 Sure enough, after analyzing the data gathered during the eclipse, astronomers found that the light from the more distant stars did bend slightly as it passed by the Sun. In fact, the light beams were deflected by nearly the exact amount Einstein had predicted.

Einstein's theory of curved space had been confirmed. (Several other experiments proving the validity of his general theory of relativity have been conducted since that time.) The theory of relativity also forced scientists to readdress the questions raised long before by Michell and Laplace about the extreme effects of gravity. The experiment during the eclipse had demonstrated that the Sun's gravity well bends light slightly. It stood to reason, therefore, that a much more massive object would bend light even more. And this naturally led to the theoretical possibility that supermassive, superdense bodies might exist. If so, such a body would possess an extremely deep gravity well, perhaps so deep that light could not escape. In 1939 physicist J. Robert Oppenheimer and his student George M. Volkoff published a scientific paper predicting the existence of superdense stars that would have extremely deep, perhaps even bottomless, gravity wells.

Yet there was still no direct observational proof of such bizarre cosmic bodies. So in the years that followed, the concept of dark stars and their potentially

weird effects on space and light remained in the province of science fiction stories and films. The first attempt to deal with the idea on film was an episode of the original Star Trek television series first broadcast in 1967. Star Trek's Captain Kirk and his crew referred to the strange object they encountered as a "black star," which turned out to be prophetic. At the time, interest in such objects was reviving among a handful of physicists, and only a few months after the Star Trek episode aired, noted Princeton University physicist John A. Wheeler coined the term "black hole." The name was perfectly descriptive and highly catchy, and it immediately became popular. Thereafter, the concept of black holes captured the attention of increasing numbers of physicists, astronomers, and other scientists, as well as science fiction fans. As Wheeler himself later remarked:

The advent of the term black hole in 1967 was terminologically trivial but psychologically powerful. After the name was introduced, more and more astronomers and astrophysicists came to appreciate that black holes might not be a figment of the imagination but astronomical objects worth spending time and money to seek.13

Indeed, time and money turned out to be important keys to unlocking the secrets of black holes. Their prediction in theory by scientists over the course of nearly two centuries had been only a first step. The next necessary steps, or goals, were: more serious and concentrated study of the concept, including a better understanding of how these strange objects form; and a serious attempt to detect them. Since the late 1960s, these goals have been largely fulfilled by a series of exciting researches and discoveries that have significantly altered and improved human understanding of the universe.