Chapter 3 -- The Height of the Sky

From Fire in the Mind: Science, Faith, and the Search for Order (Knopf 1995/Vintage 1996)

Copyright 1995 by George Johnson

"When all the stars were ready to be placed in the sky First Woman said, 'I will use these to write the laws that are to govern mankind for all time. These laws cannot be written on the water as that is always changing its form, nor can they be written in the sand as the wind would soon erase them, but if they are written in the stars they can be read and remembered forever.'" -- From a Navajo creation story

It seems so clear when you first observe it, one of the few constellations that actually looks its name: Orion the Hunter. Two stars, Betelgeuse and Bellatrix, mark his shoulders; Saiph and Rigel his legs. And cinching the waist, three stars of approximately equal brightness form his belt. So naturally do these lights seem to link into this hourglass pattern that it is strange to realize that, except from the narrow perspective of our own solar system, Orion's parts are not close to one another at all. Though the stars in Orion's belt are each approximately 1,500 light-years distant, the belt is nowhere near the rest of his body. One shoulder, Bellatrix, is estimated to be about 350 light-years from the earth. Betelgeuse, the other shoulder, is in rough proximity -- 420 light-years away -- if 70 light-years (the distance light would travel in seven decades) can be so easily disregarded. One of Orion's knees, Rigel, is 1,000 light-years from us; the other is perhaps twice that far away. At Orion's feet lies his faithful dog, Canis Major; its principal star, Sirius, is a mere 8.6 light-years away.

When we look at Orion, the astronomers tell us, we are seeing stars not only separated by distance but separated in time. In geology, we visit the past by cutting through the layers of sediment beneath us; the deeper we go, the farther we go back in time. In cosmology, the farther we look, the farther we see back in time. According to the picture we have drawn of the heavens, the photons from distant Rigel that strike our retinal cells were emitted a millennium ago. When we gaze through our telescopes, it feels as though we are reaching out into the heavens. But, of course, the photons we are capturing and amplifying are already here in our own atmosphere. All we can really do is sit here on earth and scrutinize the electromagnetic signals that happen to cross our threshold -- the light waves, radio waves, x-rays, and gamma rays that bring us news of what we have come to believe are galaxies flying away from us in all directions, propelled by the ancient explosion we have named the big bang. After measuring the galaxies' velocities and how far away they seem, we can reverse the film in our mind's eye and imagine the whole universe contracting to a point; we can count back and estimate that the explosion must have occurred some 15 billion years ago. But what a curious explosion it is said to have been. We think of something exploding in space over a period of time. But before the big bang there was no time, no space. The explosion created not only matter and energy but the universe in which it expands.

Assuming, like Einstein, that nothing can travel faster than light, the big bang theory implies that the farthest we can possibly see is 15 billion light-years in every direction. That doesn't mean that there is nothing beyond that limit. From our vantage point on earth, we might detect an energy source 10 billion light-years away, in the direction we quaintly call north, then swing our instruments around and detect another source 10 billion light-years to the south. These two objects would be separated from each other by 20 billion light-years; they can't be touched by each other's light. Since we are presumably not at the center of the universe, we can assume that there are objects 20 billion light-years from us. But we cannot see them. The light emitted by whatever is beyond our horizon hasn't had time to reach us.

In trying to explain matter, the stuff we can pick up with our hands, science is quickly propelled into abstract realms where we can find pattern only by putting our faith in symmetries that exist in the barely accessible spaces of mathematics. Extrapolating a cosmos from pinpoints of light also takes great ingenuity and imagination. Over the years we have slowly developed a grand picture of the universal scheme -- the big bang theory. But inevitably the universe refuses to be squeezed into our formulations. And so, as with particle physics, we end up honing and revising, stacking abstraction on top of abstraction, always striving for a better fit.

Plank by plank we use theory and observation to elevate ourselves toward the heavens, rising as high as we can above the terrain. But strip away the tissue of concepts and suppositions and the long chains of inferences that get us to these heights and what do we see, standing in the foothills of the Sangre de Cristo mountains, gazing at the sky? Stars that seem stationary, unless we try to track them with a telescope or leave a camera mounted on a tripod with its shutter propped open. And then what we see is the motion of our planet making it appear that the heavens move around us in a great celestial sphere. The sky shows us only two dimensions, giving no indication that these lights aren't tiny objects all the same distance away. Our only hope is to measure what is near and trust that we can use this data to bootstrap ourselves higher into the sky.

After gazing for a while at all the tiny silent lights, one is sometimes startled from the reverie by a star that suddenly seems to break out of the pack, disturbing the cerebral networks. The light moves too fast to be a planet -- a wanderer, the Greeks called them, as they tried to make sense of stars that seemed to come unstuck from the celestial pack and meander across the sky. It is too steady to be a meteor. Instinctively laboring to classify this sudden anomaly, the brain throws out a hypothesis -- a satellite? -- and recalls childhood memories of seeing Echo 1, the astonishment that something made by people had joined the heavenly light show, as though, as in an old Ray Bradbury story, someone had painted the Coca-Cola emblem on the moon.

But we quickly reject that notion, as the ears pick up the sound of metal ripping sky -- an airplane flying northeast from Albuquerque. The brain, satisfied, settles back into equilibrium, the wonder dampened -- except for a lingering feeling of how eerie it really is, that inside that tiny light are maybe three hundred people, each with a different reason for going to Omaha.

Things shrink as they get farther away, a relationship that seems embedded so deeply into the structure of this fishbowl we call space that we rarely ever think about it. From the window of a car, the fence posts along the highway pass one after another at sixty-five miles per hour, but behind them the telephone poles move slower and the hills beyond more slowly still -- tier by tier all the way to the mountains on the horizon, solid earth divided into a continuum of bands by this phenomenon called motion.

Things farther away seem smaller and appear to move at slower speeds. With this simple rule, written into our nervous systems by growing up on this planet, we can calculate how far away the plane is if we compare its true size (we could radio the pilot for information) with the shrunken image we see. Or we could compare its true speed with the speed at which it seems to cut across the sky. Here, though, we need more information. All else being equal, a plane that happens to be flying perpendicular to our line of sight will seem to move faster than one flying off at an angle; a plane flying straight away from us, precisely along our line of vision, will appear not to be moving at all. And so we have to divide the motion into two components: transverse (across the sky) and radial (toward or away from the observer).

It is comforting to think that the same neural circuitry that evolved to help us navigate through woods and mountains can be used to pull a third dimension from the flat canopy overhead; like the Jemez mountains unfolding in the evening twilight, the sky also reveals hidden peaks and canyons. These days we are confident enough of the behavior of electromagnetic waves that we can gauge the distance to the moon by bouncing radio waves off it and measuring the echo's delay. But there are simpler ways. A triangle has three sides, three angles; if we know just a few of these measures, we can calculate the rest. So measure the position of the moon against the distant stars, which seem as steady as the mountains on the horizon, and have someone a known distance away simultaneously take the same measurement. Using the difference between the two apparent positions, the parallax, we can calculate that the moon is 240,000 miles away -- a year's drive if we allow ourselves time to eat and rest. Similarly, we can measure the distance of the planets and show that the sun is 93 million miles (eight light-minutes) from us.

But parallax will get us only a tiny fraction of the way up the ladder. Even the closest stars are too distant to detect a parallactic shift from any two points on earth -- our planet isn't wide enough. To reach farther into space, we have to use the earth's orbit around the sun as a basis of comparison. Observe Alpha Centauri six months apart, from opposite points in the earth's orbit, and you find a tiny difference in its position against the backdrop of the heavens. How tiny? Look from the horizon to an imaginary point directly overhead; your eyes have traversed a 90-degree angle. Now imagine one of those degrees and divide it into 60 minutes and each of those minutes into 60 seconds. The parallax of Alpha Centauri is less than a second of a degree. Plugging that tiny number into the trigonometric equations yields a distance of 4.3 light-years. Likewise we can show Sirius to be 8.6 light-years from us; Altair, in the constellation Aquila, 16.6 light-years. But beyond 100 light-years, even the parallax from the earth's motion around the sun is too small to detect.

How then can we judge the distance of something like Betelgeuse, and how can we talk of quasars billions of light-years away? The sky is sprayed with lights of all brightnesses -- or magnitudes, as the astronomers say. But we can't tell distance from brightness unless we can radio the star, like the pilot of that plane, and ask for its intrinsic luminosity -- how bright it says it is.

For all but the closest stars around us, our measurements depend on theory and mathematics more abstract than simple trigonometry. We start with a celestial beacon whose distance we have measured, often by the most indirect of methods. Then, using our theories of astrophysics, we analyze the characteristics of its light and guess what its intrinsic brightness might be. The object then becomes what astronomers call a standard candle. If we can find a similar object in another part of the sky, we can hypothesize that it is of the same intrinsic brightness; if it appears a little dimmer, we can assume that it is farther away than our reference object. If our newly measured light is part of a cluster of stars or a galaxy, then perhaps some of its neighbors can serve as standard candles. We now have an estimate of their distance from earth; if we know enough about their physics we can guess at their true intensity and use them to reach out farther still. Layer by layer, we build a house of cards, each resting on a shakier foundation and each testifying to our theoretical bravado.

If we look at the Big Dipper and sight along the pole stars, the points that form the end of the ladle, we see Polaris, the North Star. Like the blinking red lights on the radio towers on the Sandia mountains, Polaris cycles bright to dim -- not in seconds but in four-day cycles. Nearby, in the constellation Cepheus, the star Delta Cephei was observed as long ago as 1784 to vary rhythmically in brightness, going from dim to bright to dim again every six days. In 1912, while studying photographs of the Magellanic Clouds, two galaxies spotted in the skies of the southern hemisphere by Ferdinand Magellan's crew, Henrietta Swann Leavitt of the Harvard College Observatory saw a number of these pulsating stars -- the so-called Cepheid variables -- and found an interesting correlation: the slower the blinking, the brighter the star. Since all these Cepheids were in the same formation, the Magellanic Clouds, the stars were presumed to be of roughly equal distance from earth. Assuming that Leavitt's relationship held throughout the universe, astronomers could now find two Cepheids with the same periods and suppose they were of equal intrinsic brightness. If one appeared dimmer than the other, it would indeed be farther away. Using the inverse-square law -- an object twice as far away as another is one fourth as bright -- one could calculate their relative distances from earth.

While Cepheids might give clues to relative distance, they say nothing about absolute distance. The problem was that no one knew how far the Magellanic Clouds were from earth. Before astronomers could use the Cepheid yardstick, they had to calibrate it, determining as surely as possible the distance of at least one of these blinking stars. It would be comforting to say that astronomers simply found a nearby Cepheid, measured its distance by parallax and came up with a standard candle. But in fact, Polaris, the closest Cepheid, is far too distant to detect the slightest parallax; it was found through other methods to be some 800 light-years away.

To calculate the distances to the nearest Cepheids in the Milky Way, astronomers needed a baseline much longer than the diameter of the earth's orbit. And so they looked to the movement of the sun. The sun, dragging the solar system along with it, circles the center of the galactic spiral of the Milky Way. Wait long enough and the position of closer stars against the backdrop of more distant stars and galaxies should shift ever so slightly. From this parallax, it seemed, one should be able to calculate their distances.

Why believe the sun is moving? In 1783, William Herschel showed that when one looked toward the constellation Hercules it was possible to find stars that seemed to move, as the years went by, as though they were fanning out from an imaginary point, like snowflakes seen through the windshield of a moving car; at an opposite point in the sky, toward the constellation Columba, the stars seemed to be converging in a point, like snowflakes viewed through a rearview mirror. Hershel interpreted this as an optical illusion caused by the sun's motion through the blizzard of stars.

Now we calculate the speed of this apparent movement using another phenomenon called the Doppler effect. Moving toward us, the crests and troughs of sound waves are pushed together so the frequency of the signal increases. As the source recedes the waves are stretched toward the lower end of the scale; the frequency goes down. If we think of light as wavelike, we can take this earthly phenomenon of Doppler's and apply it to the sky. Stars speeding from us should have their light waves stretched out, falling in pitch toward the low-frequency red end of the scale; stars moving toward us should be shifted toward the blue. Using the Doppler effect, one can estimate the average amount that stars in Hercules are blue-shifted and calculate the sun's motion through the galaxy as 20 kilometers per second.

Now, if all of this is correct, we can measure the position of a star and then measure it again years later. Then we use the speed of our sun to calculate the distance between these two vantage points. All things being equal, the star's apparent change in position would yield the parallax, and from this we calculate its distance from our solar system.

There is, however, an imposing problem. The stars are not fixed in space. Like the sun, they too are moving; over the eons, the shapes of the constellations subtly change. How can we know how much of a star's shift in position is due to the actual motion of the star and how much to the parallactic illusion?

As with the speed of a distant airplane, we first must distinguish between transverse motion, cutting across our field of vision, and radial motion, travelling along our line of sight. Here, the Doppler effect is our first recourse: by measuring a star's red or blue shift, we can let physics tell us its radial velocity, how fast it is moving toward or away from us. But we can't know the absolute value of the transverse velocity, the motion across the sky, unless we know the star's distance -- nearby stars appear to move faster than distant stars, just like the fenceposts that speed by on the highway.

Of course, it is the distance that we are trying to gauge in the first place. How can we break out of this loop? If we look at a group of stars, which we have reason to believe are all about the same distance away from us, we can make the simplifying assumption that the directions of their intrinsic motions are random -- some are moving this way, some are moving that way. Statistically, the motions should cancel one another out. And so, as we follow our sun through the galaxy, we can ignore how much of the apparent movement of these groups of stars is due to their own motion and attribute their shift in position to parallax. Using this mathematical sleight of hand, Harlow Shapley of Mount Wilson Observatory calculated the average distance of thirteen Cepheids in the Milky Way and used that figure to calibrate Leavitt's period-luminosity relationship, which he hoped would apply to all Cepheids everywhere. According to this yardstick, the Magellanic Clouds were about 30,000 light-years away. The distance is now believed to be seven times greater, a gauge of the difficulty of the art.

In fact, Cepheids are now calibrated by using other measurements that are at least as indirect. By studying nearby examples of various kinds of stars -- there are supergiants, red giants, blue giants, white dwarfs -- whose distances can be measured by parallax or some other means, astronomers believe they have found a relationship between a star's temperature, its type, and its intrinsic brightness. A star's temperature is taken by analyzing its spectrum, using the laws of black-body radiation that preoccupied Planck. Assuming that these rules hold true outside our neighborhood, we can guess the distances of farther stars: Use the star's spectrum to put it in the proper class, then compare the star's apparent brightness with the intrinsic brightness that theory predicts stars of that variety should have. Finally, we use the inverse-square law to calculate how far away it is.

And so we go, from moon to sun to stars. The farther we reach from earth, the deeper our measurements become embedded in our theories of stellar physics, which are based, in turn, on thermodynamics, quantum mechanics, and the nuclear physics we believe energizes stars. Even these methods, with all their uncertainties and assumptions, can only take us so far. Thirty million light-years is about as far as terrestrial telescopes can resolve single stars (though the Hubble telescope has now extended the range). Beyond that we use whole galaxies as standard candles. What kind of galaxy is it? How much energy is emanated by similar galaxies, whose distances we are somewhat more certain of? But then we are left with this dilemma: according to the big bang theory, the light of the nearest, most familiar galaxies, the ones we use as our standard, is far younger than the light from the distant galaxies. We cannot know whether galaxies in more recent times behave as galaxies did near the beginning of time. Our measurements become even less certain, immersed ever more deeply in theory as we reach farther out on our limb.

The method we most depend on to measure these unimaginable stretches is redshift. In the early 1920s, the American astronomer Edwin Hubble used Cepheids to show that nebulae are huge, distant galaxies and not small nearby hazes of light, as his rival, Harlow Shapley, thought. Having measured the distances to nearby galaxies, Hubble then used a spectrometer to analyze the color of their light. Making the assumption that stars farther out and further back in time are made of the same stuff as those closer in, hydrogen and helium, it would seem that they should show the same patterns of spectral lines. In fact, Hubble showed in the 1920s that the farther a galaxy was from the earth, as reckoned by the pulsations of its Cepheids, the more its spectral rainbow appears shifted toward the red end of the spectrum. Rather than attribute this phenomena to age, concluding that for some reason ancient, more distant galaxies radiate redder light, astronomers quickly realized that, with the proper assumptions, Hubble's observations could be taken as strong support of an expanding universe. Farther stars should appear to be receding from us more rapidly, the Doppler effect ensuring that their light is shifted toward the red end of the scale. By measuring to what degree redshift is correlated with distance, Hubble invented the yardstick we use to reach to the very edge of the observable universe, measuring the distance of anything whose electromagnetic waves we can detect. The redder an object, the faster it is receding; the faster it is receding the farther away it is. The theory of Cepheids, supplemented by some sophisticated statistical reasoning, brought us to the nearby galaxies. When we use redshift as a gauge of farther distances, we are assuming the truth of the big bang. Without the theoretical framework, the individual observations would be meaningless.

Hubble used his method to calculate that the observable universe was 2 billion light-years in radius, and so (according to the big bang) 2 billion years old. But geologists had used their own measuring stick -- the rate at which uranium decays into lead -- to calculate that the earth itself was twice that old. Something had to give somewhere. Conveniently for astronomy, it was later decided that there was more than one kind of Cepheid, each of which had to be calibrated differently. Hubble was confusing the two. Once the new numbers were plugged into the equations, the universe doubled in size overnight. It took several more adjustments of the so-called Hubble constant to come up with today's universe: 10 to 20 billion light years in radius. We can expect that the revisions will continue.

In the ensuing decades, the picture of a primal explosion and an expanding universe became so compelling that data stuck to it like iron filings to a magnet, arranging themselves in this wonderful new way. In 1948 George Gamow, Ralph Alpher, and Robert Herman predicted that, if the universe had indeed begun with a big bang, space should be permeated with its afterglow, in the form of measureable background radiation. When, in 1964, Arno Penzias and Robert Wilson found that an experimental microwave antenna at Bell Laboratories in New Jersey was plagued with a background hiss, no matter in which direction it was pointed, they speculated that the problem was pigeons roosting inside. The birds were evicted and the droppings cleaned out, but the static persisted. A consultation with radioastronomers at Princeton University led to the conclusion that Wilson and Penzias were measuring fossil radiation from the big bang. The mystery of the constant hissing was not only absorbed and explained away -- it became one of the most persuasive pieces of evidence for the big bang.

Over the years the celestial net has become thicker and thicker with mutually supporting threads. Whenever possible, distances are gauged by several independent methods. When they converge on similar answers, we can take that as reassurance that the weave is tight, the network robust. The lower levels of our celestial tower have become more solid, we hope, the playing cards replaced by bricks and mortar.

When observation clashes with theory, or with common sense, ways must be found to account for the discrepancy. In 1930 Robert J. Trumpler, an astronomer at Lick Observatory, was studying groups of stars called open clusters when he found a strange correlation between their diameters and their distances from the earth: for no apparent reason, it appeared that nearby clusters had small diameters, distant clusters had large diameters, and that there was a gradation of diameters in between. This would be a strange law indeed, implying that the earth had a special place in the universe: at the center of concentric rings of increasingly wider star clusters. Perhaps Trumpler wondered, there was something wrong with the assumptions behind his calculations. He had gauged how far away a cluster was by comparing what he believed was its intrinsic luminosity with how bright it appeared from earth. Then he measured its apparent diameter and calculated how wide it really should be. But what if there was something in space -- interstellar dust -- absorbing some of the starlight, throwing off the distance measurement? Then a cluster would actually be much closer than it appeared to be. And if it were closer, it would not have to be as large as originally supposed to emit the same amount of light. If we assume instead that all the clusters are of roughly the same diameter, then interstellar dust would create an optical illusion: those farther away would appear larger because their light would have more interstellar dust to traverse.

To gauge how much our distance measurements are thrown off by interstellar debris, we must know how much dust there is between us and the object in question. But how do we measure the amount of dust without knowing the distance, which is what we are trying to determine in the first place? Our assumptions must be expanded. We assume that starlight is reddened by interstellar dust just as the sun and moon are reddened by dust in the earth's atmosphere. So we predict from our theories of stellar physics the color a star should be and use the reddening to measure the density of dust. We cross-check the estimate with other measurements, taken from other perspectives, adding more threads to the net.

And so we tinker with our models. From our vantage point on this tiny planet we construct a universe. When, in 1963, objects with redshifts so severe that they had to be billions of light-years away were each found to be emitting the energy of a hundred galaxies, a few astronomers found their faith shaken. What could possibly emit so much light? Some were tempted to conclude that the Hubble method was wrong, that our celestial house of cards, with measurements built on measurements built on measurements, was about to collapse. Perhaps the relationship between distance, velocity and redshift had been miscalibrated. Or perhaps redshifts were caused not by the Doppler effect at all, but by some unknown peculiarity of nuclear physics. If redshifts were not a true measure of distance, then these absurdly powerful beacons might be much, much closer by. The alternative was to accept that these sources -- now we call them quasi-stellar objects, or quasars -- are indeed fantastically energetic objects at the very edge of the observable universe and a whole branch of astrophysics has been created to explain what they could possibly be.

When, in the early 1980s, astronomers were faced with the embarrassing problem that some quasars seemed to be emitting jets of matter that moved faster than light, some were tempted again to assume a much smaller universe; if the quasars were actually nearby stars, then the jets would be moving much more slowly. The tension was relieved when a way was found to dismiss the jets' illegal velocities as an optical illusion caused by the angle at which earthlings happened to be viewing the events.

We can sympathize with Ptolemy and his layers of epicycles. When we can't get the models we build to yield what our instruments detect, we make our own adjustments, hoping that history will show us more prescient than the geocentrists. How deft our brains are at smoothing out the irregularities, absorbing the anomalies, bringing the strange back into the land of the familiar as we search the world for patterns, always trying to extend them to new corners of the universe.

But there must be something at the base of our theoretical towers, a foundation to build upon, something we can take as fundamental. When the superluminal jets appeared, no one seriously suggested overthrowing Einstein's special theory of relativity. Why are we so confident that the speed of light is inviolable?

Until Einstein the measure of all things was not light but aether, Aristotle's fifth essence. Aristotle's first four elements, earth, air, fire, and water, had been abandoned long ago as fundamental ingredients in the universal recipe. But the ethereal quintessence, said to fill the space within atoms and between stars, was harder to forsake. Something, it was believed, must act as a carrier of the light waves that beam across space. Something must be doing the waving. As Maxwell himself rhapsodized, the universe is "full of this wonderful medium; so full that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity. It extends unbroken from star to star. . . ."

By the time Maxwell made his grand unification of electricity and magnetism, his belief in aether was becoming harder to sustain. In 1887, the Americans Albert Michelson and Edward Morley performed the famous experiment that seemed to show that there is nothing filling the cracks of the universe, no celestial backdrop -- just empty space. Using an apparatus of prisms and mirrors, the two scientists split a lightbeam, sending one part moving in the direction of the earth's orbit around the sun and the other perpendicular to it. They had assumed that the "aether wind," caused by the motion of the earth through the invisible medium, would slow down the first beam (it was struggling upstream). But they found to their surprise that the speed of the two beams was precisely the same.

Interpreting so delicate an experiment is never a straightforward affair. When an experiment fails to confirm a compelling hypothesis -- Michelson and Morley had fully expected to find aether -- it is a sign that there may be a discrepancy between our picture of nature and the way nature really is. But as philosophers like Willard Quine and Pierre Duhem have pointed out, this misalignment might exist anywhere in the vast web of facts and assumptions that are implicit in the design, execution, and interpretation of the experiment.

In a heroic attempt to preserve the idea of Aristotle's fifth essence, the physicists George Fitzgerald and Hendrik Lorentz suggested that the Michelson-Morley result was an optical illusion caused by a hitherto undiscovered universal truth: things shrink, ever so slightly, in the direction they are traveling in. The light beam moving with the earth was indeed retarded by the aether, but the measuring instrument shrunk in that direction -- the distance the beam had to travel was less. The Fitzgerald-Lorentz contraction conspired to make it appear that there was no aether. This assumption was not as ad hoc as it might seem. After all, scientists knew from Faraday that a moving charge created a magnetic field. Perhaps as a measuring stick moved, the charges inside generated a field that squeezed the molecules closer together. True, no one seemed to be able to measure the contraction. But perhaps this was part of nature's conspiracy: as the earth moved through space, we and everything else in our world were shrinking in the same direction.

With his special theory of relativity, Einstein suggested that the conspiracy was much subtler than Fitzgerald or Lorentz had supposed. And in doing so he introduced his new absolute, the speed of light, setting a platform on which to erect our towers of observation. As hard as you look you will never see your own instruments shrink. But, he suggested, if you could somehow observe a laboratory in another reference frame -- in a spaceship, perhaps, moving by at a fixed velocity -- it would appear that those scientists were performing their measurements with shrunken instruments. And they, looking at you, would think that their instruments were just fine; it was your lab that appeared to be moving and your instruments that had contracted. Who was really moving and shrinking? To Einstein that was a meaningless question. The Michelson-Morley experiment should be taken at its face: there is no aether, no privileged reference frame to measure motion by. Motion can only be gauged relative to something else.

No matter how many times we hear them, the implications of Einstein's theory never fail to amaze: an object in relative motion will also increase in mass and its clocks will slow down. Two events that appear to be simultaneous in one reference frame may appear separate if viewed from another. Space, time, and mass are not any more absolute than the illusory aether; they are just relationships we measure with yardsticks, clocks, and scales -- instruments whose readings depend on their relative motion. But the point of all this was not nihilism. The ultimate aim of the conspiracy was a lawfulness more deeply embedded than before. Einstein saw that allowing familiar quantities like time and space to bend would ensure that from any of the universe's infinite number of moving vantage points, science would be the same. In the universe according to Einstein, all observers, whatever their relative motion, would discover the same natural laws. As two laboratories observe each other flying by, length will contract, time slow, mass increase by just enough to guarantee that the rules that govern the universe appear the same in both domains. Looking at the world beyond their own reference frames, scientists moving at different velocities will measure different quantities, see different numbers on their dials, but the relationships between the quantities -- the structure of the system -- will be the same: length contracts, mass increases, and time dilates just enough to even things out.

Of course there has to be a limit to these dilations and contractions. As you observe a particle speeding faster and faster, at some point its mass will become infinite, its length zero, its clocks frozen still. In Einstein's theory, this limiting speed was the speed of light. Nothing can go faster, and no matter how fast you are moving, the speed of light is the one thing that will always appear the same.

Lorentz had postulated that there must be an aether -- that which was doing the vibrating -- and he assumed that the logic of classical physics was true. The outcome of the Michelson-Morley experiment -- light beams that moved the same speed no matter how fast the body that emitted them -- was the anomaly to explain. Einstein abandoned these assumptions as prejudices and showed that the same facts could be built into an entirely different structure if we turned the anomaly into a postulate: light travels at the same speed regardless of the speed of the observer.

In this reconstruction of the universe, what had been taken as absolutes were now considered relative. But just as important is what became invariant. If some things change -- space, time -- others, by definition, must remain the same. With everything moving relative to everything else, there must be some kind of glue holding things together, a standard that allows for a sensible world.

There are compelling reasons why it should be light -- or, more generally, electromagnetism -- that is accorded this dispensation. As far as we can tell, light is the fastest means by which something can make its presence known, by which one event can affect another. In all the thought experiments with laboratories moving by one another at different speeds, the means by which they are aware of one another's existence is electromagnetism: they can observe each other with telescopes, or send radio signals. For that matter, how are we aware of anything beyond our planet, where our atmosphere allows us also to communicate with more parochial signals like sound and smell? We receive signals, information, in the form of lightbeams, radio waves -- electromagnetism.

If there were no upper limit to the speed at which information can be sent, the universe would allow instantaneous action at a distance; or, even worse, a reversal of cause and effect -- the future could send signals to the past. It is true that quantum theory presents us with possibilities almost as weird. But for there to be a lawful universe with a strict wall between past and future, cause and effect, there must be an upper limit to the speed of signalling, the speed of causality, the speed of light. Whatever we call it, this constant of the universe is now considered all but sacrosanct. If our house of cards should ever tumble, we will rebuild on the same underfooting. There is little in science about which we feel so sure.

Morley and a colleague of Michelson's, Dayton Clarence Miller, later repeated the Michelson-Morley experiment to see if its disappointing results could be explained away by some unappreciated parameter. After all, the original experiment had been performed in a basement. Perhaps if it were repeated on a hilltop. . . . But the results were the same. Still, as late as 1925, two decades after Einstein's papers on special relativity, Miller, then the president of the American Physical Society, announced that he had found definite proof that aether existed after all. But by this time, the speed of light had thoroughly dislodged aether as the universal gold standard. Einstein easily dismissed the findings, noting that they might be attributed to temperature variations in the measuring device.

It is natural that in creating an image of the universe, scientists would begin with themselves at the center, humanity as the absolute. Over the centuries, as the illusion became harder and harder to sustain, we could still hope that our most direct experiences -- the passage of time, the passage through space -- were absolute. If we weren't sitting still at the center of creation then at least we could measure our motion against the stationary aether.

But in the new view, nothing was at rest. Without aether, we can only measure our motion in relation to something else, which is moving in relation to something else. But for all this relativity, we remain absolutists at heart. In recasting our map of the heavens in Einsteinian terms, we have been careful to maintain the centrality of cause and effect and the existence of universal scientific laws.

But it is a constant struggle to interpret the data we gather so that it obeys the laws we believe we have divined. With the platform of special relativity solidly beneath their feet, astronomers have gone on to beguile us with a universe far more bizarre than their predecessors could have imagined. Einstein taught us that light reigns supreme. But in trying to account for an increasingly discordant stream of astronomical observations, scientists have been forced to conclude that most of the universe consists of matter that for unknown reasons seems to emit no light.

The need for dark matter began to insinuate itself into cosmology in before World War II when the Dutch astronomer Jan Oort and the Swiss-American Fritz Zwicky noticed that galaxies behaved as though they were far more massive than they appeared. If our distance measurements can be trusted, galaxies, including our own Milky Way, are spinning faster than Newton's laws would predict -- so fast, in fact, that they shouldn't exist, having flown apart long ago. Either we must demote our laws of gravity (as established by Newton and modified by Einstein's Theory of General Relativity) to the status of local aberrations or we must invent something that is holding the galaxies together -- unseen matter that seems to emit no radiation, or emits it too weakly for us to detect. We can know it only by its secondary effects, phenomena that make no sense in the current theoretical framework unless we come up with more gravity, more mass. Over the years, further measurements have suggested that, from these arguments alone, the ratio of this unseen matter to visible matter is 10 to 1.

But that is just the beginning of the problem. For years, cosmologists pointed to the smoothness of the background radiation, the ubiquitous microwaves that we interpret as the afterglow of the primordial explosion, as stunning support for the big bang. Everywhere we pointed our dish antennas, it seemed to rain down on us with the same temperature. But the more they looked, the more cosmologists worried that the radiation might be a bit too smooth. A perfectly smooth afterglow would seem to signal a smooth early universe, which made it difficult to explain why we observe largescale structures today -- the galaxies and galaxies of galaxies that seem to extend as far as we can see.

And so cosmology underwent a subtle shift in emphasis. For years astronomers had marvelled at how uniform the background radiation was -- after all, this was considered among the strongest evidence for the big bang. They performed experiments to establish this smoothness over and over again. Now they needed signs of subtle irregularities -- imperfections that might have been magnified into the lumpiness we see today. Using satellites and ever more sensitive detectors, they scrutinized the radiation at a finer and finer grain. And the closer they looked, the smoother the radiation appeared. Any irregularities must have been very tiny indeed.

At the same time, the structures whose genesis needed to be explained grew larger and larger. In the late 1980s it was discovered that a large number of galaxies are not moving away from us in the uniform manner that the big bang theory predicts. To account for this aberration, theorists were forced to conclude that something rather enormous was pulling them off course. And so they announced the existence of a conglomeration of mass, several hundred million light-years in size, that they called the Great Attractor. Other astronomers found evidence of a giant chain of galaxies: the Great Wall.

It was hard to escape the conclusion that even 15 billion years -- the age of the universe predicted by the big bang -- wasn't nearly enough time for gravity to cause such enormous configurations of matter to coalesce. Something seemed to be missing. A few theorists were inspired to posit the existence of a fifth force to help matter clump together. Others proposed modifications to the laws of gravity. A more conservative gambit was to propose that some kind of dark matter provided the extra ingredient needed for the congealing.

At first it seemed hopeful that this dark matter was like ordinary matter, that its emanations were simply too feeble for our instruments to detect. Perhaps the universe was filled with very dim stars or black holes, those gravitational whirlpools said to suck in everything around them, including light. Perhaps enough mass was tied up in these vortices to balance the equations.

It is a measure of how rarefied our explanations have become that black holes would be considered conservative candidates for dark matter. Detecting black holes requires immersing oneself deeply into the wells of theory. And even then, the only black holes one can unambiguously see are those within the equations of Einstein's Theory of General Relativity, which imply that if a collapsing star is massive enough it will go on collapsing forever, tearing a dimensionless pinhole into the space-time fabric.

But to many cosmologists, even this explanation, which once would have seemed daringly exotic, did not go far enough. There is little reason, other than theoretical convenience, to believe that there are enough black holes or dim stars to make up for the gravitational deficit. In an attempt to rectify still other problems with the universal creation story, many cosmologists have been forced to conclude that dark matter is something far stranger.

Depending on its total density of matter, a universe can be in one of three states: If the density is low, space will be negatively curved and the universe will be "open," becoming more and more rarefied as it keeps expanding forever. If the density is high enough, space will be positively curved and the universe will be "closed": the expansion will rapidly fizzle out and all of creation will fall back in on itself in a big crunch. Or the universe might have just the density required for space to be "flat," yielding a universe poised between open and closed. Years of observations and calculations have persuaded many theorists that the universe is indeed flat, with the outward Hubble expansion balanced by the inward coalescing pull of gravity. More compellingly, perhaps, it seems that if the universe were not flat then it either should have collapsed long ago or become so rarefied that there could be no galaxies, no stars, no us.

Here is the problem: If the universe is flat, there doesn't seem to be nearly enough ordinary matter -- dark and luminous combined -- to provide the necessary gravity to balance the expansion. Luminous stars can account for roughly 1 percent of the needed density. Throwing in 10 times as much hypothetical dark matter -- the dim stars and black holes that have been inferred but not seen -- brings the density up to 10 percent of that required for flatness. So what is the other 90 percent? It seems it would have to be something quite exotic. In fact, according to other arguments, the relative abundance of light elements in the universe -- hydrogen, deuterium, helium, and lithium -- requires that the primordial fireball that exploded some 15 billion years ago consisted of no more than a tiny fraction of ordinary, "baryonic" matter -- the protons and neutrons we once had every reason to believe make up most of the mass of the universe. Otherwise nuclear reactions should have produced different ratios of light elements than those we measure.

We don't know what this nonbaryonic dark matter could be. For awhile, it was hoped that dark matter might consist of the elusive neutrinos that are so difficult to detect. Originally invented as accounting fictions, to balance the books of beta decay, neutrinos were now confidently believed to stream through the densest matter as though it were empty space. Neutrinos were thought to be massless, like photons, but perhaps if they had the slightest mass their huge abundance could provide the extra gravity needed to get the big bang theory to generate the enormous structures we see.

But after years of searching, it is still unclear whether neutrinos have a slight mass. And even if they do, there are other arguments that may rule out neutrinos as too light and too swift (too "hot") to bring about the congealing of matter. Instead, many cosmologists have concluded, there must be some kind of undiscovered dark matter. Like neutrinos, it would interact only weakly with ordinary matter (or not at all) -- explaining why it has gone undetected -- but unlike neutrinos, it would be massive and move far more slowly. To play the proper role in the theory, this substance would have to be immune to interference from the high density of photons believed to have existed in the universe's infancy. Thus it would be not only dark but transparent, absorbing or emitting no light. In the early history of the universe, this invisible "cold dark matter" would have clumped together easily, providing the seeds for galactic structure. Candidates for the mysterious glue include monopoles (north and south magnetic poles that have become separated one from the other), particles called axions, or the "sparticles" predicted by supersymmetry: selectrons, squarks, gravitinos, and such.

The big bang theory is impressive in its ability to account for the redshifts of the galaxies that Hubble first measured and the ubiquitous radiation that Penzias and Wilson found. If cold dark matter were enough to explain how the big bang generated the galactic structures we see in the sky, then the search for a satisfying creation myth might have reached an important milestone. But there was still the problem of the smooth background radiation. Even if one spiked the big bang theory with a hefty dose of cold dark matter, a featureless primordial fireball would produce a featureless universe. There still had to be some kind of measurable irregularities for things as big as the Great Attractor and the Great Wall to have formed. Coming to the rescue in 1992, a satellite called the Cosmic Background Explorer (Cobe) found the tiniest variations -- 30 millionths of a degree kelvin -- but only after an enormous amount of computer enhancement to separate what was accepted as signal from what was discarded as noise. Most of the data, by far, was static produced by the instruments or by the Milky Way and other celestial bodies. The experimenters couldn't actually point to any particular variation in the background radiation and say whether it was real or artifact. But taken together the variations could be interpreted statistically as evidence of irregularities, stirring so much excitement that a press conference was called to herald the results.

Later experiments more firmly established the existence of what came to be called the cosmic ripples. But they are too minuscule to explain, on their own, how primordial lumpiness was magnified into the huge structures we find. An enormous amount of dark matter -- or something extra -- is still required. And we still don't know what it is. Using computers, cosmologists simulate the early conditions of the universe, tinkering with various mixes of cold and hot dark matter, trying to bring about the structure we see. But the recipe continues to elude them.

The big bang theory remains very much a work in progress. In addition to the structure problem, there are other cosmological mysteries to explain. Despite the variations measured by COBE, the background radiation still appears smoother than it has any right to be. Unless the initial flash of the big bang just happened to be extremely uniform, a coincidence or divine decree that few scientists are willing to suppose, then there must have been a way for the hotter parts of the early universe to radiate heat to the cooler parts, evening things out. But one of the most striking implications of the big bang is that most regions of the universe have never been in contact. There is no way they could have exchanged heat. An observer anywhere in the universe should find itself surrounded by an imaginary sphere 15 billion light-years in radius -- the distance light has traveled since the big bang. Objects that are farther apart, say 20 billion light-years, can never have been in contact. When the universe was 15 minutes old they would have been 30 light-minutes apart, twice as far as light would have time to travel. No mixing of background radiation could possibly have occurred.

In the early 1980's, Alan Guth, of the Massachusetts Institute of Technology, began developing a possible mechanism to explain how the universe became so smooth: Suppose the universe we live in is only a tiny part of the initial creation that began with the big bang. According to the so-called inflationary universe version of the big bang theory, an infinitesimal bit of this primordial megaverse, small enough to have a uniform temperature, was pinched off in the earliest microseconds; then, propelled by the brief existence of a kind of antigravity, arising from quantum effects, this tiny region was inflated at enormous speed, expanding instantaneously, perhaps 1050 times, into the seed of the universe we live in today. Guth's scenario also provides an explanation for why the universe is flat. Any positive or negative curvature that existed would have been flattened out, and tiny quantum ripples amplified into the irregularities that later became the seeds for galaxies. Other pieces from the big bang may also have been inflated into other universes, perhaps with their own unique laws, but they are beyond our horizons and can never be seen.

Many cosmologists hold out hope that a way will be found to account for galaxy formation without having to declare that most of the universe is invisible. But if science is ultimately compelled to conclude that as much as 99 percent of matter indeed consists of particles that emit or absorb no light, then we are confronted with a startling reversal of figure and ground. Most of what we know about the universe comes to us through photons filtering through our atmosphere or striking the receptors of our occasional space probes. We are creatures of light. We depend on sunlight to power the earth's biochemical reactions and electromagnetism to learn of the universe and, in turn, to make our existence known. How strange that in mapping a universe whose one seeming certainty is the speed of light, we are faced with the possibility that only an insignificant portion can be known this way.

What we took for creation -- the stars and galaxies we see and imagine around us -- might be only a froth on a wave made of mysterious dark matter, an essence that can be inferred through logic but, at best, only obliquely detected. We and the universe we know might be no more than a bit of static, noise in the cosmic signal, as central to the universal scheme as the pigeons Penzias and Wilson expelled from their microwave antenna.

Few deny the magnificence of the big bang, its power to explain so much we see. Perhaps this is as good as we have a right to expect a theory of the universe to be. But we cannot escape the fact that the one explanation it seems a creation story should include -- how our universe of stars and galaxies and galactic clusters came to be -- continues to elude us. What the big bang theory strains to explain is the very platform on which we make our observations and construct our towers of abstraction -- the very platform on which we, the builders of the big bang theory, stand. So we make adjustments to our vision of the celestial fireworks. We rearrange and embellish until we come up with a version of the big bang theory that can explain flatness, smoothness, and, most importantly, the origin of structure -- but only if as much as 99 percent of the universe is essentially invisible. Should we of the one percent congratulate ourselves on being clever enough to discern the rest? Or should we worry that we have been backed into a theoretical cul de sac where the only way out is to make such extravagant assumptions? We evolved on the earth with a marvelous ability to find patterns. But our brains were not selected for their ability to understand cosmology or particle physics. There is the constant danger that we are being too clever, too good at absorbing discrepancies to our theoretical inventions. We cannot always know when, like Ptolemy, we are adding epicycles, elaborations to keep our theories standing.

And yet we maintain the conviction -- at least as a working hypothesis -- that we can comprehend the whole. So vivid is the picture we have drawn of the heavens, with its stunningly brilliant quasars, its infinitely deep black holes, that an alien reading our literature might think we had traveled great distances. But, in fact, we have sent space probes no farther than just beyond the solar system, we have stepped no farther than the moon. The rest of the picture is built from the photons that happen to come our way -- magnified by telescopes, sifted for patterns.

With all this effort, the cosmological model we have constructed has become so firmly lodged in the brain that mere humans can be heard to confidently speculate about the very origin of the universe. What caused the big bang? That is where science once left off and religion began. But who could be satisfied with a science that could say no more than Genesis: Let there be light! And so in recent years, cosmologists have looked to their colleagues in particle physics, wondering if quantum theory, the tool that has proved so powerful in explaining the universe inside atoms could be stretched to try and understand the most fundamental particle of all: the infinitely dense pinpoint whose mysterious explosion is said to have given rise to all we see and imagine. How do you get something -- in this case, everything -- from nothing?

It seems that nature not only abhors a vacuum, it doesn't allow one to exist. It is not just that space is filled with cosmic dust. According to quantum theory, the vacuum we once thought was empty actually seethes with energy, constantly creating pairs of "virtual particles" -- matter and antimatter -- that jump out and flash their tails for an instant before annihilating one another and returning to the void. Heisenberg's uncertainty principle guarantees that this energy is untappable: a particle's timespan and energy, like its position and momentum, are reciprocally related. So any particles that the vacuum creates will be either so low in energy or so short in duration that they will go undetected.

Apply relativity and quantum theory to the primordial mass and you get a cosmic loophole big enough for all creation to jump through. Suppose that a tiny amount of energy -- a virtual particle -- randomly arose from the vacuum. According to Einstein's special theory of relativity, this energy will be associated with mass (E = mc2), and according to Einstein's general theory of relativity, the mass will bend space-time, giving rise to gravity. Thus all of the mass-energy created spontaneously from the void could conceivably be offset by the resulting gravitational pull -- the net value would be zero, so no conservation laws would be broken. Heisenberg's principle tells us that an infinitesimal amount of energy can exist for an infinite amount of time.

The universe then would be a quantum fluctuation and, like all things in quantum theory, it could be described as either a particle or a wave. Just as scientists talk about the wave function of the electron, they talk about the wave function of the universe, assuming that a set of mathematical tools devised to explain the nucleus can be applied to the whole of creation.

But then we are left to wonder: how can one have a quantum fluctuation before there was space and time in which anything could fluctuate? Pushed to the edge, we come up against the limits of our terrestrial language. But who would have thought that it would take us this far?

When we look upon the grand architectures of cosmology and particle physics with the advantage of hindsight, developments take on an illusory sense of inevitability, as though the picture that emerged, with all its strengths and weaknesses, is the only one that could have been. When we read in the history books how the great Harlow Shapley believed that the Milky Way was the universe, we want to grab his hand and say, "No. Don't you see! Those nebulae that look so small and nearby are really huge galaxies far away. If you calibrate your Cepheids correctly and allow for all that cosmic dust, you'll see that our own galaxy is really much smaller than you believe." We struggle in vain to imagine what it would have been like to be in his shoes -- or in Thomson's or Rutherford's -- observing the phenomena without the filters that would later channel everything we see.

But what a false sense this gives us of the scientific quest, of the never-ending effort to map our inner and outer worlds. Looking back, knowing what we know, it is hard to shake the conviction that the astronomers and the particle physicists are uncovering a pre-existing order, converging on the way the universe really is. If we could go back in time and see the enterprise through their eyes, we would have a stronger sense of science as a glorious human construction, an artful fitting of the data into a carefully crafted mental framework, a construction of towers that just possibly might have been built another way. And so we must turn from science past to science future, to ventures so new that there is no way to know how the story will come out.

Just as New Mexico's stars and stark geology set the mind to wondering about the pictures we have drawn of the world, its laboratories invite us to see through the eyes of contemporary scientists, those whose work is so pregnant with potential upheaval that it puts them up against the very edge of the aquarium, theorizing into empty conceptual space. Northern New Mexico happens to be a haven for some of these explorers. Faced with a universe inevitably more complex than the brains trying to capture it in their mesh, these scientists, like their predecessors, struggle to sort order from randomness. And, in the process, some of them go even further, examining more closely just what we mean by randomness and order, and why it is possible to have a science at all.