Black Hole

by Marcia Bartusiak

  After poring over historic records, Halley figured that a comet sighted in 1682 had much in common with comets previously observed in 1531 and 1607. They shared the same orbital characteristics, going around the Sun in the opposite direction to the planets, and appeared every seventy-five to seventy-six years. Upon calculating the comet’s orbit based on Newton’s laws, he predicted in 1705 that the comet would return at the end of 1758. And so it did, right on schedule sixteen years after Halley’s death, thirty-one years after Newton’s. This feat bedazzled and instantly silenced Newton’s critics. Who could argue with a theory that allowed for a spot-on prediction about the solar system’s behavior more than half a century in advance? It was at that moment that Newton’s law of gravity, despite its lack of a mechanism, was at last victorious.

  With Newton’s laws in place, scientists in the eighteenth century came to view the universe as intrinsically knowable, ticking away like a well-oiled timepiece. Many astronomers began spending long hours huddled at their desks using Newton’s mathematical rules to work out planetary motions and to forecast the tides. Stars, as well, became convenient objects for testing the laws of gravity. And it was during such a stellar endeavor that a precursor to the black hole—the Model-T version, in a way—emerged. The possible existence of such a bizarre object arose when an Englishman named John Michell applied Newton’s laws to the most extreme case imaginable.

  Michell stood in the very thick of a wondrous age of scientific discovery, and he dabbled in it all. He was a geologist, astronomer, mathematician, and theorist who regularly hobnobbed with the greats of the Royal Society of London, such men as Henry Cavendish, Joseph Priestley, and even the society’s American fellow Benjamin Franklin (during the diplomat’s two long stays in London). The claim could be made, science historian Russell McCormmach has written, that Michell was “the most inventive of the eighteenth-century natural philosophers.” He recognized early on, for example, that Earth’s strata could bend, fold, rise, and dip. If Michell is remembered at all today, it is for his suggestion in 1760 that earthquakes propagate as elastic waves through the Earth’s crust. That earned Michell the title “father of modern seismology.” By deeply scrutinizing and comparing various accounts of the great temblor that leveled Lisbon, Portugal, in 1755, Michell was able to compute the time, location, and depth of the quake’s epicenter, situated to the west in the Atlantic Ocean.

  Michell also designed a delicate instrument that could measure the gravitational constant in Newton’s equations, allowing him in essence to “weigh” the Earth. He died before he could carry out the experiment, but his friend Cavendish ultimately obtained the torsion balance, made modifications, and successfully measured our planet’s mass with it.

  The torsion balance, based on a design by John Michell, that was used by Henry Cavendish in 1797–98 to weigh the Earth. (Philosophical Transactions of the Royal Society of London)

  Despite such accomplishments, however, Michell had the unfortunate habit of burying original insights (such as the inverse-square law of magnetic force decades before it was rediscovered) in journal papers that focused on more mundane research, and so received little notice. Some of his greatest ideas were casually mentioned in asides or footnotes. As a consequence, long-lasting fame eluded him.

  Michell had begun his scientific investigations at Queens’ College in Cambridge. Son of an Anglican rector, he entered Queens’ in 1742 at the age of seventeen and after graduation remained there to teach for many years. A contemporary described him as a “short Man, of a black Complexion, and fat. … He was esteemed a very ingenious Man, and an excellent Philosopher.” While in Cambridge, Michell even tutored a young Erasmus Darwin, Charles Darwin’s grandfather, who called his mentor “a comet of the first magnitude.”

  But by 1763, ready to marry, Michell decided to leave teaching and devote himself to the church. He ultimately settled in the village of Thornhill in West Yorkshire, where he served as a clergyman until his death in 1793 at the age of sixty-eight. Yet, over those decades with the Church of England, the reverend continued to indulge his wide-ranging scientific curiosity. He had a nose for interesting questions and was willing to stick his neck out in speculation, though always grounded in his first-rate mathematical skills. One of Michell’s more intriguing conjectures at this time, right when Great Britain was recovering from its war with colonial America, was imagining what today we call a black hole.

  This idea grew out of an earlier prediction that Michell had made. Astronomers in the eighteenth century were starting to see more and more double stars as they scanned the celestial sky with their ever-improving telescopes. The common wisdom of the time declared that such stars were actually at varying distances from Earth and closely aligned in the sky by chance alone—that it was just an illusion that they were connected in any way. But, with remarkable insight, Michell argued that nearly all those doubles had to be gravitationally bound together.

  He was suggesting that some stars exist in pairs, a completely novel notion for astronomers in those days. In a groundbreaking paper published in 1767, Michell worked out the high probability that, given how most other stars were arranged on the sky, the twin stars were physically near each other—“the odds against the contrary opinion,” he stressed, “being many million millions to one.” (As usual, he displayed his computations in a footnote.) In carrying out this calculation, Michell was the first person to add statistics to astronomy’s repertoire of mathematical tools. This paper, according to astronomy historian Michael Hoskin, was “arguably the most innovative and perceptive contribution to stellar astronomy … in the eighteenth century.”

  At the same time, Michell recognized that double stars would be quite handy for learning lots of good things about the properties of stars—how bright they are, how much they weigh, how vast is their girth. Michell suspected that there were stars both brighter and dimmer than our Sun. He cunningly ventured that a white star was brighter than a red one. (“Those fires, which produce the whitest light,” he pointed out in his paper, “are much the brightest.”) So, two stars orbiting each other were the perfect laboratory for testing his ideas from afar and arriving at answers. Yet, nearly all astronomers in his day weren’t concerned with such questions. They were too busy discovering new planetary moons or tracking the motions of the planets with exquisite precision. To them, the stars themselves were not terribly interesting and served merely as a convenient backdrop for their measurements of the solar system and its components. The Sun, Moon, and planets were astronomers’ prime observing targets at the time.

  The great British astronomer William Herschel, a friend of Michell’s, was the rare exception to that rule. He often veered away from conventional astronomical work. Within a dozen years of Michell’s paper on double stars, Herschel began monitoring and cataloging the stars positioned close together in the sky. Michell extolled Herschel’s growing data bank as “a most valuable present to the astronomical world.” So valuable that Michell extended his ideas on double stars in a paper, published in 1784, with the marathonic title “On the Means of discovering the Distance, Magnitude, &c. of the Fixed Stars, in consequence of the Diminution of the Velocity of their Light, in case such a Diminution should be found to take place in any of them, and such other Data should be procured from Observations, as would be farther necessary for that Purpose.” (Whew!) It was in this work that Michell hinted at the possibility of a black hole—or at least an eighteenth-century, Newtonian version of one.

  The eminent Henry Cavendish, discoverer of hydrogen and its connection to water, read Michell’s paper before the Royal Society over a succession of meetings, in November and December 1783 as well as January 1784. (It was then published in the Royal Society’s Philosophical Transactions, taking up twenty-three pages in print.) Michell was devoted to the society and at least once a year traveled the arduous two hundred miles (three hundred kilometers) from Yorkshire to London to either attend its meetings or meet with society friends. But for those
winter meetings the reverend inexplicably stayed home. It could have been ill health or lack of travel funds, or possibly he just wanted to avoid a raucous skirmish then in full swing to unseat the society’s president, the botanist Sir Joseph Banks. There was also the matter of preliminary tests of his idea. They weren’t detecting what he had hoped to measure. But some historians have speculated that Michell recognized the daring nature of his paper and thought the society would more readily accept his idea if his close friend and highly respected colleague presented it.

  The eighteenth-century scientific paper in which John Michell first suggested the existence of the Newtonian version of a “black hole.” (Philosophical Transactions of the Royal Society of London)

  The radical technique that Michell was proposing to study the stars involved the speed of light. If astronomers closely monitored the two stars in a binary system moving around each other over the years, noted Michell, they could calculate the masses of the stars. It was the most basic application of Newton’s laws of gravity. If he measured the width of the orbit and the time it takes for the two stars to orbit each other, he could estimate their masses. And if each star’s gravitational pull affected the other’s motion, suggested Michell, that pull should also affect light. This was an era when light was assumed to be composed of “corpuscles,” swarms of particles—largely because Newton, whose opinion was revered, had endorsed that idea.

  Now imagine these particles journeying off a star and out into space. Michell assumed that gravity would attract these corpuscles just like matter. The bigger the star, the stronger the gravitational hold upon the light, slowing down its speed. There would be a “diminution of the velocity of [the stars’] light,” as the title of his paper announced. Measure the velocity of a beam of starlight entering a telescope, and voilà, you acquire a means of weighing the star.

  Now, this is where the “black hole” possibility arises: Michell took his scenario to the utmost limit and estimated when the mass of the star would be so great that “all light … would be made to return towards it, by its own proper gravity”—like a spray of water shooting up from a fountain, reaching a maximum height, and then plunging back down to the bowl. With not one radiant corpuscle escaping from the star, it would remain forever invisible, like a dark pinpoint upon the sky. According to Michell’s calculations, this transformation would occur when the star was about five hundred times wider than our Sun and just as dense throughout. In our solar system, such a star would extend past the orbit of Mars.

  In 1796, in the midst of the French Revolution, the mathematician Pierre-Simon de Laplace independently arrived at a similar conclusion. He briefly mentioned these corps obscurs, or hidden bodies, in his famous Exposition du système du monde (The system of the world), essentially a handbook on the cosmology of his day. “A luminous star, of the same density as the Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun,” he wrote, “would not, in consequence of its attraction, allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the universe, may, through this cause, be invisible.” It was only after an appeal from a dogged colleague, the astronomer Baron Franz Xaver von Zach, that Laplace three years later worked out a rigorous mathematical proof to back up his initial, cursory statement. Laplace’s estimate for the width of the dark star differed from Michell’s because he assumed a greater density for sunlike bodies.

  But did it even make sense to predict the existence of stars that could never be seen? Laplace may have had second thoughts when light came to be viewed as waves, not corpuscles. Or perhaps he simply experienced a loss of interest, for in subsequent editions of Système du monde, which he published up until his death in 1827, he expunged his invisible-star speculation and never referred to it again. Michell, in contrast, displayed greater ingenuity in his 1784 paper. There he suggested a clever way to “see” such invisible stars. If one revolved around a luminous star, he noted, its gravitational effect on the bright star’s motions would be noticeable. In other words, the bright star would appear over time to jiggle back and forth on the sky, due to the dark star’s tugs. It’s one of the very ways that astronomers today track down black holes.

  In the end, though, Michell and Laplace were getting ahead of themselves—contemplating problems before the physics was in place to answer them. They didn’t yet realize that supergiant stars have far lower densities than the ones they envisioned. They also never considered that the same invisibility effect could happen if a star were smaller but very, very dense. If an ordinary star were somehow compressed into a smaller volume, the velocity needed to escape from its surface would increase appreciably. But astronomers then just assumed that all stars shared the same density as the Sun or Earth. Could anything be denser than the elements found on Earth? It seemed unthinkable in the late eighteenth century.

  Both Michell and Laplace were working with an inadequate law of gravity and the wrong theory of light. They didn’t yet know that light never slows down in empty space. Proving the existence of such dark stars required more advanced theories of light, gravity, and matter. The modern conception of the black hole—a real “hole” in space-time, rather than just a big, dark lump of stellar matter—would not emerge for nearly a century. It had to wait for the entrance of the twentieth century’s most inventive natural philosopher, Albert Einstein.

  2

  Newton, Forgive Me

  Physicists could proudly point to two major accomplishments by the end of the nineteenth century: Newton’s classical mechanics (established more than two centuries earlier) and the equations of electromagnetism formulated by the Scottish theoretician James Clerk Maxwell in the 1860s. In the physical sciences, each was the monumental theory of its age. It was Maxwell who figured out what light truly was, linking it to the long-known phenomena of electricity and magnetism. He predicted the existence of electromagnetic waves, whose “velocity is so nearly that of light,” he reported, “that it seems we have strong reason to conclude that light itself … is an electromagnetic disturbance in the form of waves.” And from his equations alone, Maxwell had revealed a new, fundamental constant in nature—the speed of light.

  Because the scientific principles set forth by both Newton and Maxwell yielded extremely accurate predictions in experiment after experiment, it was easy to think that little remained to be done on these topics. Even Maxwell in 1874, during an address at the opening of what is now the Cavendish Physical Laboratory at Cambridge University, wondered if “the only occupation which will … be left to men of science will be to carry on these measurements to another place of decimals.”

  But to an inquisitive German student of physics in the 1890s, there was something not quite right about these laws. Taken together, they seemed somewhat out of kilter in his mind. His suspicions involved many complexities, such as the true nature of the ether believed to fill space and how light traveled through it. But, at its core, what disturbed the young Albert Einstein was that these two great works of physics didn’t appear to share the same rules on handling space and time. Fearless at challenging the greats of his day, even as a student, Einstein was sure that the prevailing theory linking Newton’s mechanics with Maxwell’s electromagnetism— electrodynamics—was “not correct, and that it should be possible to present it in a simpler way.” He yearned to make the two theories fully compatible with one another.

  This wasn’t a sudden decision on his part. The root of this challenge went back to his adolescence. In some autobiographical notes, Einstein recalled being caught up in a particular reverie: If a man could keep pace with a beam of light, what would he see? Would he observe an electromagnetic wave frozen in place, like some glacial swell? “There seems to be no such thing,” he remembered thinking, at the youthful age of sixteen. According to Newton, you could catch up to the light, much like two runners in a relay race. But from Maxwell’s perspective, that wasn’t so clear. Experiments measuring how fast light traveled thr
ough the “ether” were suggesting that there was no catching up.

  After spending years, on and off, thinking about this issue, Einstein at last arrived at a solution. But more than that, he did so by making the most basic assumptions possible. No grand leaps of theoretical prowess were required to reach an answer. Einstein’s historic 1905 paper—on what came to be called special relativity—is actually exquisite in its simplicity. All of his hypotheses are based on physics that was available to anyone in the nineteenth or early twentieth century. Indeed, the same concerns bedeviled other physicists who were close to a solution, but all kept missing the key ingredient. Einstein’s one inventive assumption was an entirely new conception of space and time. With that single change, all fell into place; the mismatch between Newton and Maxwell vanished.

  Special relativity proposed that all the laws of physics (for both mechanics and electromagnetic processes) are the same for two frames of reference: one at rest and one moving at a constant velocity. Those schooled in Newtonian physics already knew that a ball thrown upward on a train moving forward at a steady 100 miles (160 kilometers) per hour behaves exactly the same as a ball thrown into the air from a motionless playground. Einstein wanted that agreement to be true for electromagnetism as well. But that meant that the behavior of a beam of light—that is, its measured velocity of 186,282 miles (299,792 kilometers) per second—must be the same in each place, both on the speedy train and on the ground. Why? If the laws of physics are to remain the same in both settings—on both the steadily moving train and the playground—the speed of light must be identical in both environments. “[We will] introduce another postulate … ,” wrote Einstein in his 1905 paper, “that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”