Death by Black Hole: And Other Cosmic Quandaries (5 page)

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 matter 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.

M
ost 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.

The faster a planet spins, the greater we expect its equatorial bulge to be. A single day on fast-spinning Jupiter, the most massive planet in the solar system, lasts 10 Earth-hours; Jupiter is 7 percent wider at its equator than at its poles. Our much smaller Earth, with its 24-hour day, is just 0.3 percent wider at the equator—27 miles on a diameter of just under 8,000 miles. That’s hardly anything.

One fascinating consequence of this mild oblateness is that if you stand at sea level anywhere on the equator, you’ll be farther from Earth’s center than you’d be nearly anywhere else on Earth. And if you really want to do things right, climb Mount Chimborazo in central Ecuador, close to the equator. Chimborazo’s summit is four miles above sea level, but more important, it sits 1.33 miles farther from Earth’s center than does the summit of Mount Everest.

SATELLITES HAVE MANAGED
to complicate matters further. In 1958 the small Earth orbiter
Vanguard 1
sent back the news that the equatorial bulge south of the equator was slightly bulgier than the bulge north of the equator. Not only that, sea level at the South Pole turned out to be a tad closer to the center of Earth than sea level at the North Pole. In other words, the planet’s a pear.

Next up is the disconcerting fact that Earth is not rigid. Its surface rises and falls daily as the oceans slosh in and out of the continental shelves, pulled by the Moon and, to a lesser extent, by the Sun. Tidal forces distort the waters of the world, making their surface oval. A well-known phenomenon. But tidal forces stretch the solid earth as well, and so the equatorial radius fluctuates daily and monthly, in tandem with the oceanic tides and the phases of the Moon.

So Earth’s a pearlike, oblate-spheroidal hula hoop.

Will the refinements never end? Perhaps not. Fast forward to 2002. A U.S.-German space mission named GRACE (Gravity Recovery and Climate Experiment) sent up a pair of satellites to map Earth’s geoid, which is the shape Earth would have if sea level were unaffected by ocean currents, tides, or weather—in other words, a hypothetical surface where the force of gravity is perpendicular to every mapped point. Thus, the geoid embodies the truly horizontal, fully accounting for all the variations in Earth shape and subsurface density of matter. Carpenters, land surveyors, and aqueduct engineers will have no choice but to obey.

ORBITS ARE ANOTHER
category of problematic shape. They’re not one-dimensional, nor merely two-or three-dimensional. Orbits are multidimensional, unfolding in both space and time. Aristotle advanced the idea that Earth, the Sun, and the stars were locked in place, attached to crystalline spheres. It was the spheres that rotated, and their orbits traced—what else?—perfect circles. To Aristotle and nearly all the ancients, Earth lay at the center of all this activity.

Nicolaus Copernicus disagreed. In his 1543 magnum opus,
De Revolutionibus,
he placed the Sun in the middle of the cosmos. Copernicus nonetheless maintained perfect circular orbits, unaware of their mismatch with reality. Half a century later, Johannes Kepler put matters right with his three laws of planetary motion—the first predictive equations in the history of science—one of which showed that the orbits are not circles but ovals of varying elongation.

We have only just begun.

Consider the Earth-Moon system. The two bodies orbit their common center of mass, their barycenter, which lies roughly 1,000 miles below the spot on Earth’s surface closest to the Moon at any given moment. So instead of the planets themselves, it’s actually their planet-moon barycenters that trace the Keplerian elliptical orbits around the Sun. So now what’s Earth’s trajectory? A series of loop-the-loops—thirteen of them in a year, one for each cycle of lunar phases—rolled together with an ellipse.

Meanwhile, not only do the Moon and Earth tug on each other, but all the other planets (and their moons) tug on them too. Everybody’s tugging on everybody else. As you might suspect, it’s a complicated mess, and will be described further in Section 3. Plus, each time the Earth-Moon system takes a trip around the Sun, the orientation of the ellipse shifts slightly, not to mention that the Moon is spiraling away from Earth at a rate of one or two inches per year and that some orbits in the solar system are chaotic.

All told, this ballet of the solar system, choreographed by the forces of gravity, is a performance only a computer can know and love. We’ve come a long way from single, isolated bodies tracing pure circles in space.

THE COURSE OF
a scientific discipline gets shaped in different ways, depending on whether theories lead data or data lead theories. A theory tells you what to look for, and you either find it or you don’t. If you find it, you move on to the next open question. If you have no theory but you wield tools of measurement, you’ll start collecting as much data as you can and hope that patterns emerge. But until you arrive at an overview, you’re mostly poking around in the dark.

Nevertheless, one would be misguided to declare that Copernicus was wrong simply because his orbits were the wrong shape. His deeper concept—that planets orbit the Sun—is what mattered most. From then on, astrophysicists have continually refined the model by looking closer and closer. Copernicus may not have been in the right ballpark, but he was surely on the right side of town. So, perhaps, the question still remains: When do you move closer and when do you take a step back?

NOW IMAGINE YOU’RE
strolling along a boulevard on a crisp autumn day. A block ahead of you is a silver-haired gentleman wearing a dark blue suit. It’s unlikely you’ll be able to see the jewelry on his left hand. If you quicken your pace and get within 30 feet of him, you might notice he’s wearing a ring, but you won’t see its crimson stone or the designs on its surface. Sidle up close with a magnifying glass and—if he doesn’t alert the authorities—you’ll learn the name of the school, the degree he earned, the year he graduated, and possibly the school emblem. In this case, you’ve correctly assumed that a closer look would tell you more.