Death By Black Hole & Other Cosmic Quandaries

by Neil DeGrasse Tyson

  Copernicus himself was not unmindful of the trouble he was about to cause. In the book’s dedication, addressed to Pope Paul III, Copernicus notes:

  I can well appreciate, Holy Father, that as soon as certain people realize that in these books which I have written about the Revolutions of the spheres of the universe I attribute certain motions to the globe of the Earth, they will at once clamor for me to be hooted off the stage with such an opinion. (1999, p. 23)

  But soon after the Dutch spectacle maker Hans Lippershey had invented the telescope in 1608, Galileo, using a telescope of his own manufacture, saw Venus going through phases, and four moons that orbited Jupiter and not Earth. These and other observations were nails in the geocentric coffin, making Copernicus’s heliocentric universe an increasingly persuasive concept. Once Earth no longer occupied a unique place in the cosmos, the Copernican revolution, based on the principle that we are not special, had officially begun.

  NOW THAT EARTH was in solar orbit, just like its planetary brethren, where did that put the Sun? At the center of the universe? No way. Nobody was going to fall for that one again; it would violate the freshly minted Copernican principle. But let’s investigate to make sure.

  If the solar system were in the center of the universe, then no matter where we looked on the sky we would see approximately the same number of stars. But if the solar system were off to the side somewhere, we would presumably see a great concentration of stars in one direction—the direction of the center of the universe.

  By 1785, having tallied stars everywhere on the sky and crudely estimated their distances, the English astronomer Sir William Herschel concluded that the solar system did indeed lie at the center of the cosmos. Slightly more than a century later, the Dutch astronomer Jacobus Cornelius Kapteyn—using the best available methods for calculating distance—sought to verify once and for all the location of the solar system in the galaxy. When seen through a telescope, the band of light called the Milky Way resolves into dense concentrations of stars. Careful tallies of their positions and distances yield similar numbers of stars in every direction along the band itself. Above and below it, the concentration of stars drops symmetrically. No matter which way you look on the sky, the numbers come out about the same as they do in the opposite direction, 180 degrees away. Kapteyn devoted some 20 years to preparing his sky map, which, sure enough, showed the solar system lying within the central 1 percent of the universe. We weren’t in the exact center, but we were close enough to reclaim our rightful place in space.

  But the cosmic cruelty continued.

  Little did anybody know at the time, especially not Kapteyn, that most sight lines to the Milky Way do not pass all the way through to the end of the universe. The Milky Way is rich in large clouds of gas and dust that absorb the light emitted by objects behind them. When we look in the direction of the Milky Way, more than 99 percent of all stars that should be visible to us are blocked from view by gas clouds within the Milky Way itself. To presume that Earth was near the center of the Milky Way (the then-known universe) was like walking into a large, dense forest and, after a few dozen steps, asserting that you’ve reached the center simply because you see the same number of trees in every direction.

  By 1920—but before the light-absorption problem was well understood—Harlow Shapley, who was to become director of the Harvard College Observatory, studied the spatial layout of globular clusters in the Milky Way. Globular clusters are tight concentrations of as many as a million stars and are seen easily in regions above and below the Milky Way, where the least amount of light is absorbed. Shapley reasoned that these titanic clusters should enable him to pinpoint the center of the universe—a spot that, after all, would surely have the highest concentration of mass and the strongest gravity. Shapley’s data showed that the solar system is nowhere close to the center of the globular clusters’ distribution, and so is nowhere close to the center of the known universe. Where was this special place he found? Sixty thousand light-years away, in roughly the same direction as—but far beyond—the stars that trace the constellation Sagittarius.

  Shapley’s distances were too large by more than a factor of 2, but he was right about the center of the system of globular clusters. It coincides with what was later found to be the most powerful source of radio waves in the night sky (radio waves are unattenuated by intervening gas and dust). Astrophysicists eventually identified the site of peak radio emissions as the exact center of the Milky Way, but not until one or two more episodes of seeing-isn’t-believing had taken place.

  Once again the Copernican principle had triumphed. The solar system was not in the center of the known universe but far out in the suburbs. For sensitive egos, that could still be okay. Surely the vast system of stars and nebulae to which we belong comprised the entire universe. Surely we were where the action was.

  Nope.

  Most of the nebulae in the night sky are like island universes, as presciently proposed in the eighteenth century by several people, including the Swedish philosopher Emanuel Swedenborg, the English astronomer Thomas Wright, and the German philosopher Immanuel Kant. In An Original Theory of the Universe (1750), for instance, Wright speculates on the infinity of space, filled with stellar systems akin to our own Milky Way:

  We may conclude…that as the visible Creation is supposed to be full of sidereal Systems and planetary Worlds,…the endless Immensity is an unlimited Plenum of Creations not unlike the known Universe…. That this in all Probability may be the real Case, is in some Degree made evident by the many cloudy Spots, just perceivable by us, as far without our starry Regions, in which tho’ visibly luminous Spaces, no one Star or particular constituent Body can possibly be distinguished; those in all likelyhood may be external Creation, bordering upon the known one, too remote for even our Telescopes to reach. (p. 177)

  Wright’s “cloudy Spots” are in fact collections of hundreds of billions of stars, situated far away in space and visible primarily above and below the Milky Way. The rest of the nebulae turn out to be relatively small, nearby clouds of gas, found mostly within the Milky Way band.

  That the Milky Way is just one of multitudes of galaxies that comprise the universe was among the most important discoveries in the history of science, even if it made us feel small again. The offending astronomer was Edwin Hubble, after whom the Hubble Space Telescope is named. The offending evidence came in the form of a photographic plate taken on the night of October 5, 1923. The offending instrument was the Mount Wilson Observatory’s 100-inch telescope, at the time the most powerful in the world. The offending cosmic object was the Andromeda nebula, one of the largest on the night sky.

  Hubble discovered a highly luminous kind of star within Andromeda that was already familiar to astronomers from surveys of stars much closer to home. The distances to the nearby stars were known, and their brightness varies only with their distance. By applying the inverse-square law for the brightness of starlight, Hubble derived a distance to the star in Andromeda, placing the nebula far beyond any known star within our own stellar system. Andromeda was actually an entire galaxy, whose fuzz could be resolved into billions of stars, all situated more than 2 million light-years away. Not only were we not in the center of things, but overnight our entire Milky Way galaxy, the last measure of our self-worth, shrank to an insignificant smudge in a multibillion-smudge universe that was vastly larger than anyone had previously imagined.

  ALTHOUGH THE MILKY WAY turned out to be only one of countless galaxies, couldn’t we still be at the center of the universe? Just six years after Hubble demoted us, he pooled all the available data on the motions of galaxies. Turns out that nearly all of them recede from the Milky Way, at velocities directly proportional to their distances from us.

  Finally we were in the middle of something big: the universe was expanding, and we were its center.

  No, we weren’t going to be fooled again. Just because it looks as if we’re in the center of the cosmos doesn’t mean we are. As a matt
er of fact, a theory of the universe had been waiting in the wings since 1916, when Albert Einstein published his paper on general relativity—the modern theory of gravity. In Einstein’s universe, the fabric of space and time warps in the presence of mass. This warping, and the movement of objects in response to it, is what we interpret as the force of gravity. When applied to the cosmos, general relativity allows the space of the universe to expand, carrying its constituent galaxies along for the ride.

  A remarkable consequence of this new reality is that the universe looks to all observers in every galaxy as though it expands around them. It’s the ultimate illusion of self-importance, where nature fools not only sentient human beings on Earth, but all life-forms that have ever lived in all of space and time.

  But surely there is only one cosmos—the one where we live in happy delusion. At the moment, cosmologists have no evidence for more than one universe. But if you extend several well-tested laws of physics to their extremes (or beyond), you can describe the small, dense, hot birth of the universe as a seething foam of tangled space-time that is prone to quantum fluctuations, any one of which could spawn an entire universe of its own. In this gnarly cosmos we might occupy just one universe in a “multiverse” that encompasses countless other universes popping in and out of existence. The idea relegates us to an embarrassingly smaller part of the whole than we ever imagined. What would Pope Paul III think?

  OUR PLIGHT PERSISTS, but on ever larger scales. Hubble summarized the issues in his 1936 work Realm of the Nebulae, but these words could apply at all stages of our endarkenment:

  Thus the explorations of space end on a note of uncertainty…. We know our immediate neighborhood rather intimately. With increasing distance our knowledge fades, and fades rapidly. Eventually, we reach the dim boundary—the utmost limits of our telescopes. There, we measure shadows, and we search among ghostly errors of measurement for landmarks that are scarcely more substantial. (p. 201)

  What are the lessons to be learned from this journey of the mind? That humans are emotionally fragile, perennially gullible, hopelessly ignorant masters of an insignificantly small speck in the cosmos.

  Have a nice day.

  FOUR

  THE INFORMATION TRAP

  Most people assume that the more information you have about something, the better you understand it.

  Up to a point, that’s usually true. When you look at this page from across the room, you can see it’s in a book, but you probably can’t make out the words. Get close enough, and you’ll be able to read the chapter. If you put your nose right up against the page, though, your understanding of the chapter’s contents does not improve. You may see more detail, but you’ll sacrifice crucial information—whole words, entire sentences, complete paragraphs. The old story about the blind men and the elephant makes the same point: if you stand a few inches away and fixate on the hard, pointed projections, or the long rubbery hose, or the thick, wrinkled posts, or the dangling rope with a tassel on the end that you quickly learn not to pull, you won’t be able to tell much about the animal as a whole.

  One of the challenges of scientific inquiry is knowing when to step back—and how far back to step—and when to move in close. In some contexts, approximation brings clarity; in others it leads to oversimplification. A raft of complications sometimes points to true complexity and sometimes just clutters up the picture. If you want to know the overall properties of an ensemble of molecules under various states of pressure and temperature, for instance, it’s irrelevant and sometimes downright misleading to pay attention to what individual molecules are doing. As we will see in Section 3, a single particle cannot have a temperature, because the very concept of temperature addresses the average motion of all the molecules in the group. In biochemistry, by contrast, you understand next to nothing unless you pay attention to how one molecule interacts with another.

  So, when does a measurement, an observation, or simply a map have the right amount of detail?

  IN 1967 BENOIT B. MANDELBROT, a mathematician now at IBM’s Thomas J. Watson Research Center in Yorktown Heights, New York, and also at Yale University, posed a question in the journal Science: “How long is the coast of Britain?” A simple question with a simple answer, you might expect. But the answer is deeper than anyone had imagined.

  Explorers and cartographers have been mapping coastlines for centuries. The earliest drawings depict the continents as having crude, funny-looking boundaries; today’s high-resolution maps, enabled by satellites, are worlds away in precision. To begin to answer Mandelbrot’s question, however, all you need is a handy world atlas and a spool of string. Unwind the string along the perimeter of Britain, from Dunnet Head down to Lizard Point, making sure you go into all the bays and headlands. Then unfurl the string, compare its length to the scale on the map, and voilà! you’ve measured the island’s coastline.

  Wanting to spot-check your work, you get hold of a more detailed ordnance survey map, scaled at, say, 2.5 inches to the mile, as opposed to the kind of map that shows all of Britain on a single panel. Now there are inlets and spits and promontories that you’ll have to trace with your string; the variations are small, but there are lots of them. You find that the survey map shows the coastline to be longer than the atlas did.

  So which measurement is correct? Surely it’s the one based on the more detailed map. Yet you could have chosen a map that has even more detail—one that shows every boulder that sits at the base of every cliff. But cartographers usually ignore rocks on a map, unless they’re the size of Gibraltar. So, I guess you’ll just have to walk the coastline of Britain yourself if you really want to measure it accurately—and you’d better carry a very long string so that you can run it around every nook and cranny. But you’ll still be leaving out some pebbles, not to mention the rivulets of water trickling among the grains of sand.

  Where does all this end? Each time you measure it, the coastline gets longer and longer. If you take into account the boundaries of molecules, atoms, subatomic particles, will the coastline prove to be infinitely long? Not exactly. Mandelbrot would say “indefinable.” Maybe we need the help of another dimension to rethink the problem. Perhaps the concept of one-dimensional length is simply ill-suited for convoluted coastlines.

  Playing out Mandelbrot’s mental exercise involved a newly synthesized field of mathematics, based on fractional—or fractal (from the Latin fractus, “broken”)—dimensions rather than the one, two, and three dimensions of classic Euclidean geometry. The ordinary concepts of dimension, Mandelbrot argued, are just too simplistic to characterize the complexity of coastlines. Turns out, fractals are ideal for describing “self-similar” patterns, which look much the same at different scales. Broccoli, ferns, and snowflakes are good examples from the natural world, but only certain computer-generated, indefinitely repeating structures can produce the ideal fractal, in which the shape of the macro object is made up of smaller versions of the same shape or pattern, which are in turn formed from even more miniature versions of the very same thing, and so on indefinitely.

  As you descend into a pure fractal, however, even though its components multiply, no new information comes your way—because the pattern continues to look the same. By contrast, if you look deeper and deeper into the human body, you eventually encounter a cell, an enormously complex structure endowed with different attributes and operating under different rules than the ones that hold sway at the macro levels of the body. Crossing the boundary into the cell reveals a new universe of information.

  HOW ABOUT EARTH itself? One of the earliest representations of the world, preserved on a 2,600-year-old Babylonian clay tablet, depicts it as a disk encircled by oceans. Fact is, when you stand in the middle of a broad plain (the valley of the Tigris and Euphrates rivers, for instance) and check out the view in every direction, Earth does look like a flat disk.

  Noticing a few problems with the concept of a flat Earth, the ancient Greeks—including such thinkers as Pythagoras and Herodotus—
pondered the possibility that Earth might be a sphere. In the fourth century B.C., Aristotle, the great systematizer of knowledge, summarized several arguments in support of that view. One of them was based on lunar eclipses. Every now and then, the Moon, as it orbits Earth, intercepts the cone-shaped shadow that Earth casts in space. Across decades of these spectacles, Aristotle noted, Earth’s shadow on the Moon was always circular. For that to be true, Earth had to be a sphere, because only spheres cast circular shadows via all light sources, from all angles, and at all times. If Earth were a flat disk, the shadow would sometimes be oval. And some other times, when Earth’s edge faced the Sun, the shadow would be a thin line. Only when Earth was face-on to the Sun would its shadow cast a circle.

  Given the strength of that one argument, you might think cartographers would have made a spherical model of Earth within the next few centuries. But no. The earliest known terrestrial globe would wait until 1490–92, on the eve of the European ocean voyages of discovery and colonization.

  SO, YES, EARTH is a sphere. But the devil, as always, lurks in the details. In Newton’s 1687 Principia, he proposed that, because spinning spherical objects thrust their substance outward as they rotate, our planet (and the others as well) will be a bit flattened at the poles and a bit bulgy at the equator—a shape known as an oblate spheroid. To test Newton’s hypothesis, half a century later, the French Academy of Sciences in Paris sent mathematicians on two expeditions—one to the Arctic Circle and one to the equator—both assigned to measure the length of one degree of latitude on Earth’s surface along the same line of longitude. The degree was slightly longer at the Arctic Circle, which could only be true if Earth were a bit flattened. Newton was right.