the expansion of the universe - columbia...

12

THE EXPANSION OF THE UNIVERSE

IT is A CHILLY EVENING in the late 1920s, on the top of Mount Wil-son in southern California. After dinner, Edwin Hubble walks along

the dirt path from the little monastery to the great domed building ofthe hundred-inch Hooker telescope, the largest telescope on earth. Thedome alone is ninety-five feet in diameter and a hundred feet high.Wearing his camel-hair coat and black beret, Hubble enters the shedlikedoor. He climbs the metal stairway to the concrete floor of the telescopemount, climbs another flight of stairs to the platform surrounding theinstrument, then one more set of steps to the "observing platform."Except for a single assistant, he is alone. Outside, darkness is falling. Athis signal, the massive dome slowly opens with a long rumbling sound.The sky is a deep purple gash flecked with stars. Hubble calls out hisorders to the assistant below, the hours and degrees of the pointingangle he wants, and the telescope wheels around to its target, whiningmetal against metal, clicking and clanking on its seventeen-foot gears.

Tonight, Hubble will make photographs of distant galaxies, so dis-tant that their light has spent millions of years traveling through spaceto the earth. The astronomer studies the view through the eyepiece.When the position is correct, he strikes a match, lights his pipe, and sitsdown in his low bentwood chair. From now on, a clock drive will auto-matically revolve the telescope at precisely the correct rate to compen-sate for the earth's rotation, so that the galaxies do not slide out of view.But the clock drive is silent. The lights in the observatory are extin-guished, leaving the astronomer in darkness except for the faint glow ofhis pipe and the gauzy light of the stars overhead. Here he will sit forhours through the cold silent night. From time to time, he will call outnew orders to his assistant, stand, and stare through the eyepiece. Thetelescope itself looms above him like a giant squatting bird. Its torso,the light tube, extends for some thirty feet. Its massive hind legs and

The Expansion of the Universe 231

haunches, the support structure, cling to the floor with a steel grip. Thisbird weighs one hundred tons. Hubble is a large man himself, six feettwo inches tall, barrel-chested, a former heavyweight boxer. But sittingbeneath the tail of the giant bird as it peers into space, he is the size ofan ant.

On February 4, 1931, in the small library of the Mount Wilson Obser-vatory, a stone's throw from the Hooker telescope, Albert Einsteinannounced that his original conception of a static universe was nolonger valid. Forty-one-year-old Edwin Hubble, as well as a half dozenother leading astronomers, stood nearby. As a result of the discoveriesof Edwin Hubble, Einstein went on, the universe must be considered tobe in motion. The cosmos was expanding. Space itself was stretching,with distant galaxies flying away from each other like dots painted onthe skin of a swelling balloon. According to a reporter from the Associ-ated Press, "a gasp of astonishment swept through the library." And thenews flashed over the world.

In 1543, Copernicus proposed that the sun, rather than the earth, wasthe center of our planetary system. In all of the following centuries,Edwin Hubble's discovery of the expansion of the universe was probablythe most important event in astronomy. If the universe is expanding,then it is changing. Indeed, the universe must have evolved through aseries of grand epochs, each unimaginably different from the last. Inparticular, the universe was smaller and denser in the past. At one time,the galaxies were touching. Farther in the past, stars had not yet formedout of the dense clouds of primordial gas. Farther still in the past, elec-trons would be boiled off the outer parts of atoms. Go far enough intothe past, and all of the matter that we see in the cosmos was crushedtogether into a volume tinier than an atom. That point in time, or justbefore, was the "beginning," now called the Big Bang. By measuring therate that the universe is expanding, astronomers can calculate that theBig Bang occurred about fifteen billion years ago. Thus, Hubble's dis-covery had enormous meaning, not only for science but also for philos-ophy, theology, and even human psychology.

Edwin Hubble had taken a winding route to the moment in themountaintop library with Einstein. Born in Marshfield, Missouri, inlate 1889 and schooled in Chicago, he could easily have been a profes-sional athlete or a lawyer or a half dozen other occupations instead ofan astronomer. By sixteen, Edwin was the star of the Central High

232 THE DISCOVERIES

School basketball team in Chicago. In a single track meet his senioryear, he won the pole vault, the shot put, the standing high jump, therunning high jump, the discus, and the hammer throw, and on May 6,1906, he established the Illinois state record in the high jump. After com-piling a superb academic record at the University of Chicago, he won aRhodes Scholarship, which had been a personal obsession. Anotherobsession, astronomy, met strong resistance by his father, who was alawyer and insurance agent. At Oxford, Edwin read not astronomy ormathematics but jurisprudence. He explained to a friend that on hisreturn home he would have to earn money to support his family. ButEdwin still made time for winning track events at Oxford, and he held anexhibition boxing match with a French champion. When Hubble cameback to the United States in 1913, he opened a law office in Louisville,Kentucky, where his parents had moved. The law, however, could neverfill his stomach. After a year Hubble went back to the University ofChicago as a graduate student. Astronomy it would be.

Edwin Hubble seems to have been an almost superhuman individual:handsome, physically powerful and athletic, bright, restless, ambitious,arrogant, aloof. At an early age he read widely in the classics and historyas well as in science. A classmate in high school remembers that Edwinrejected his teachers' authority and questioned them with a smart aleckattitude. Another classmate, Albert Colvin, recalls that Edwin had "away of acting as though he had all the answers . . . He always seemed tobe looking for an audience to which he could expound some theory orother." According to his sister Betsy, Edwin "tried to do things to provehe was capable of doing them," and often retold stories about himselfwith exaggerated and heroic proportions.

Hubble eventually succeeded in his ambitions beyond any possibleexaggeration. Ironically, when he published his famous paper of 1929,claiming a linear relation between distances and receding velocities ofthe galaxies, he suspected that he'd done something important, but hedidn't know what it was.

Before Hubble's discovery, nearly every human culture on earth hadbelieved in a universe without change, a cosmos in stasis. The stars in thesky certainly appear to be fixed and unmoving, aside from the statelyrevolution caused by the spin of the earth. As Aristotle wrote in On theHeavens, "Throughout all past time, according to the records handeddown from generation to generation, we find no trace of change either in


the whole of the outermost heaven or in any one of it proper parts."Indeed, scientists and poets alike took the fixed heavens as the suprememetaphor for constancy and permanence, in contrast to the ephemeralnature of all phenomena on earth. Copernicus, who was willing to chal-lenge so much of our astronomical thinking, wrote that "the state ofimmobility is regarded as more noble and godlike than that of changeand instability, which for that reason should belong to the Earth ratherthan to the [Universe]." And in Shakespeare's Julius Caesar, Caesar saysto Cassius:

But I am constant as the northern star,Of whose true-fix'd and resting qualityThere is no fellow in the firmament.

Einstein, in his 1917 theory of cosmology, simply assumed that the uni-verse did not change on the grand scale. Indeed, he was so certain that theuniverse had to be static that he was willing to revise and complicate theelegant equations of his 1915 theory of gravity, general relativity, in orderto account for the presumed immobility of the heavens. Those equationsshow how matter and energy generate gravity, and how that gravity in turnaffects the geometry of space and time. In his revision, Einstein added anumber to his equations, sometimes called the lambda term or the cosmo-logical constant. The lambda term acts as a kind of repulsive force, bal-ancing the attractive force of gravity and thus allowing the stars andnebulae of the universe to hold steady at fixed positions. As the greatGerman-born physicist said at the end of his paper: "That [lambda] termis necessary only for the purpose of making possible a quasi-static distri-bution of matter, as required by the fact of the small velocities of stars."

Unbeknownst to Einstein, who was not an astronomer, certain recentastronomical data were already suggesting that the material of the uni-verse did not sit quietly in balanced equilibrium. Since 1912, a onetimefarm boy from Mulberry, Indiana, named Vasco Melvin Slipher hadbeen amassing evidence that some of the "nebulae" were flying awayfrom the solar system at fantastic speeds. Slipher had been given accessto the twenty-four-inch telescope of the Lowell Observatory in Arizona.(The twenty-four inches refers to the diameter of the lens or mirror ofthe telescope. Larger diameters can gather more light and thus seefainter objects, as well as resolve finer details.)

234 THE DISCOVERIES

Nebulae are the permanent, cloudlike, misty patches of light in thesky. Many have been known since antiquity. Galileo, with his first tele-scope, showed that some of the nebulae are congregations of individualstars, too dim and close together to distinguish with the naked eye. Themost dramatic cosmic nebula is the faint band of light that arches acrossthe night sky, called the Milky Way, or sometimes just the Galaxy. TheMilky Way is the great spiral-shaped system of stars that is home to ourown star, the sun. Today, we know the Milky Way contains about a hun-dred billion stars. We also know that there are actually three kinds ofnebulae: the globular clusters, which are spherical systems of about amillion stars located within the Milky Way; the galactic nebulae, whichare clouds of dust and gas also located within the Milky Way; and theextragalactic nebulae, other giant systems of stars outside of the MilkyWay. The extragalactic nebulae are, in fact, other galaxies. But in 1912much of this was unknown. Most significantly, distances to these objectswere unknown. Until the mid-1920s, astronomers hotly debated whetherthe nebulae were located within the Milky Way or were instead separate"island universes" beyond.

By 1914, Slipher had measured the velocities of thirteen of the nebu-lae. More precisely, Slipher had measured the colors of the nebulae.What do colors have to do with speeds? When a moving source of lightis traveling toward you, its colors shift up in frequency toward the blueend of the spectrum; when it is moving away, its colors shift down to thered. This phenomenon—called the Doppler shift in honor of ChristianJohann Doppler, who first discussed it in 1842—is exactly analogousto the change in pitch of the whistle of a moving train. As the trainapproaches, its pitch rises above the pitch at rest; as the train movesaway, its pitch drops. From the amount of the shift in color (for light) orpitch (for sound), one can calculate the speed of the moving object.Using this method, Slipher concluded that the average spiral-shapednebula was moving away from the earth at a speed of about 600 kilome-ters per second, a hundred times faster than the speed of any otherknown type of object in the sky.

By the early 1920s, Slipher had measured the recessional velocities ofabout forty nebulae, with the same general results. His findings were con-sidered important, but no one knew their significance. Were the spiral neb-ulae relatively small andnearby constellations of stars, like the globularclusters, or instead large stellar systems like the Milky Way, at great dis-tance from our own galaxy? Hubble, as well as other astronomers, puz-zled over the meaning of Slipher's results. As the eminent astronomer


Arthur Eddington wrote in his influential The Mathematical Theory ofRelativity in 1923: "One of the most perplexing problems of cosmogonyis the great speed of the spiral nebulae." Perplexing largely because thedistances were not known.

Indeed, the major obstacle for much of astronomy was the determi-nation of distance. When we detect light from an astronomical body likea star or a nebula, we measure only its apparent brightness. To know itsdistance, we must also know its intrinsic luminosity, just as we mustknow the wattage of a lightbulb in order to infer its distance from howbright it appears to our eye.

As described in detail in Chapter 6, in 1912 Henrietta Leavitt of theHarvard College Observatory discovered a method to measure the dis-tance to a certain kind of star called a Cepheid variable. Cepheids varyin the intensity of their light in a regular and repeating way, with periods(cycle times) between about three and fifty days. In brief, Leavitt found arelationship between a Cepheid's period and its intrinsic luminosity. Thedistance to a Cepheid could then be computed as follows: Measure itsperiod and apparent brightness. From Leavitt's period-luminosity law,and the measured period, infer its intrinsic luminosity. From its intrinsicluminosity and its measured apparent brightness, infer its distance.

In 1918, the American astronomer Harlow Shapley systematicallysearched for Cepheids at various locations in the Milky Way to map outthe size of the galazy. He concluded that the Milky Way is about 300,000light-years in diameter. Recall that a light-year is the distance that lightcan travel in a year, roughly ten thousand billion miles. Another unit ofdistance sometimes used is the parsec, equal to about 3.3 light-years. Forreference, the nearest star to our sun, Alpha Centauri, is about fourlight-years away.

Having determined the approximate size of the Milky Way, Shapleyargued for various reasons that the nebulae were all within our galaxy.According to Shapley there were no island universes, no extragalacticnebulae. It was Edwin Hubble in 1924 who proved Shapley wrong.

After receiving his Ph.D. in astronomy from the University ofChicago in 1917, Hubble was offered a position at the Mount WilsonObservatory of the Carnegie Institution of Washington. But Hubblewanted to serve in World War I. He received a deferment for his posi-tion. With his usual bravado, Hubble joined the American Expedi-tionary Force in France and quickly rose to the rank of major. In

240 THE DISCOVERIES

A 6 C

Figure 12.1

Lemaitre was at Cambridge University on another fellowship, he placedhis paper in the hands of Sir Arthur Eddington. Eddington was one ofthe best-known and most influential astronomers of the day. Amongmany accomplishments, in 1919 he had triumphantly measured thebending of starlight by the sun, in an amount predicted by Einstein'stheory of general relativity, and in 1923 he had published his widely readbook on relativity. For some reason, Eddington paid little attention toLemaitre's paper and apparently misplaced it.

At last, we return to Edwin Hubble. When Hubble began measuring thedistances to Slipher's redshifted nebulae in the late 1920s, what he knewwas this: these nebulae had enormous redshifts, implying their large out-ward velocities in all directions. He knew, from his own measurements,that many nebulae were extragalactic and thus important in the big pic-ture of the universe. He knew about the de Sitter effect, popularized inEddington's 1923 book. He did not know about Friedmann's paper orLemaitre's paper. Thus, it seems unlikely that he could have had in hishead the concept of an expanding universe. Even with data suggesting alinear relation between outward velocity and distance, it is still a largeconceptual and philosophical leap to go from there to the notion of adynamic universe, a universe in which space itself is stretching, anexpanding universe. In this regard, it is useful to recall that the de Sittereffect took place within a static cosmos. De Sitter, also, had no notion ofan expanding universe.

Hubble begins his 1929 paper by presenting Slipher's results in termsof the "K term." This term was a speed of 600-800 kilometers per sec-ond that had to be subtracted from the speeds of all of Slipher's spiralnebulae in order to cancel out their enormous outward velocities andmake them appear as an ordinary group of astronomical objects with


random velocities. Hubble calls this term a "paradox" because there wasno explanation for it. However, there was some evidence that the K termmight vary with distance. That is, the outward speeds for the nebulaewere not all the same.

Some astronomers, including A. Dose, Knut Lundmark, and GustafStromberg, had previously attempted to see if the redshifts correlatedwith distance. Indeed, that is the project Hubble has set for himself—and the linear correlation turns out to be his great triumph. Hubblerightfully regards these earlier attempts as "unconvincing." First of all,Lundmark, in his 1925 work, estimated distances to the nebulae by thequestionable technique of comparing their apparent diameters andapparent brightnesses to standard galaxies of standard diameter andbrightness. This method assumes that all galaxies are the same, accord-ing to which a galaxy that appears half as big is twice as far away. Hub-ble, for the most part, relies on the far more reliable method of Cepheidvariables and Leavitt's period-luminosity law. And, of course, he has theenormous advantage of sitting beneath the hundred-inch Hooker tele-scope. Second, Lundmark, in his attempt to see if the K term variedwith distance, fit for both a linear and quadratic dependence on distanceand reached the baffling conclusion that the K term should actuallystart decreasing beyond a certain distance.

Note that Hubble refers to the redshifts as "apparent radial veloci-ties." Hubble is very much an observational (experimental) astronomer,not a theorist, and it is the redshift, not the radial velocity, that isdirectly measured. Indeed, Hubble is skeptical of all theories.

Hubble goes on to mention the various methods that he will use tomeasure distances. Besides using the reliable Cepheid variables and theO stars, he will assume that the brightest stars in a nebula all have thesame luminosity, of about 30,000 times the luminosity of the sun. Heexpresses this maximum luminosity in terms of the standard astronomi-cal notation, M- -6.3, where M, the "absolute magnitude," is related tothe luminosity L (expressed in units of the luminosity of the sun) byM=4.75 - 2.5 log (L). Hubble later also uses the "apparent magnitude,"m, which depends, like apparent brightness, on distance as well as lumi-nosity. In particular, if r is the distance to the object in parsecs, then, m =M-5 + 5 log (r). Some of these astronomical notations have been previ-ously discussed in Chapter 6.

Table 1 of the paper gives Hubble's principal results. In the first col-umn are the twenty-four nebulae in the sample, arranged in order of

2*2 THE DISCOVERIES

increasing distance. The third column givesthe distance to each nebula,the fourth gives the velocity, in kilometers per second. A positive veloc-ity means the nebula is moving away from the earth and its colors areshifted to the red. A negative velocity means the nebula is movingtoward the earth and its colors are shifted to the blue. From the distanceand apparent magnitude, m, the latter being directly measured, Hubblecan calculate the absolute magnitude, M, of each nebula. (The absolutemagnitude is equivalent to its intrinsic luminosity.)

The redshift of a nebula measures its velocity relative to the earth.But the earth is attached to the sun, and the sun is moving through theMilky Way at some to-be-determined speed and direction, called thesolar motion. To get the velocities of the nebulae relative to the MilkyWay, and not just to the sun, the solar motion must be subtracted out.That is the purpose of the long equation with X, Y, and Z. The A, D,and Vo represent the direction and speed of the sun through the MilkyWay. Here and elsewhere, Hubble is working and thinking very muchwithin the mind-set of galactic structure. He uses the mathematicalnotation and concepts of motion within the Milky Way, even though hewill ultimately apply them to objects far beyond the Milky Way. We mustremember that only a few years earlier, it was not established that thenebulae lay beyond the Milky Way. Extragalactic astronomy, at thistime, is an extremely new field, one that Hubble pioneered.

As can be seen from the table, although there are some exceptionalcases, the nebular velocities are mostly outward and mostly increase withincreasing distance. Hubble then makes the claim that "the data in thetable indicate a linear correlation between distances and velocities . . . "That is, Hubble is proposing something more than simply that the veloc-ities increase with increasing distance. He proposes that his data suggesta particular law: the velocities are proportional to distance. Double thedistance and the velocity doubles. That is the meaning of a "linear cor-relation."

Hubble has made a great leap of faith in his proposal, even though heis aware of the "scanty material, so poorly distributed." In fact, the datapoints in Figure 1 of his paper have fairly large deviations about thestraight (linear) line that Hubble has drawn through them. But the situ-ation is actually even more precarious than Hubble realized at the time.Lemaitre's result that the recessional velocity of the nebulae should beproportional to their distance holds only for a universe whose mass isevenly distributed, so that the cosmos can expand uniformly in all direc-


tions. Hubble's data went out to a distance of about two million parsecs,or about six million light-years. Astronomers now know that the distri-bution of matter in the universe does not begin to look uniform untilone reaches distances of at least 100 million light-years. At that distance,the lumpiness caused by individual galaxies begins to average out anddisappear, just as the individual grains of sand on a beach disappearwhen viewed from a height of twenty feet or more. For smaller distances,the linear relationship between outward velocity and distance predictedfor a homogeneous (uniform) and expanding universe is not valid. Hub-ble doesn't know about the expanding universe model of Lemaitre or itspredictions. He has made a lucky guess in claiming a linear law, and evenhis own data don't support the guess very well.

By 1931, Hubble and Milton Humason used new methods to extendtheir observations to 100 million light-years. Figure 12.2a shows Hub-ble's data of 1929, Figure 12.2b gives the extended data of Hubble andHumason two years later. As can be seen, the linear law in Figure 12.2bis more obvious and now justified.

As an important check on his proposal, Hubble then applies his linearlaw to nebulae too faint for their distances to be determined directly.From their outward velocities, he can see where they fall on his graphand assign them distances. From the distances, he can compute theirluminosities, an intrinsic property of the nebulae. He can then comparethose luminosities with the luminosities of nebulae whose distances canbe determined directly and finds much similarity.

All of the theoretical discussion in Hubble's paper is relegated to thevery last paragraph. Here, he mentions de Sitter's model and only de Sit-ter's model. De Sitter, apparently, exerted some influence over Hubble.First, the Dutch scientist's work had been published in English and

244 THE DISCOVERIES

popularized by Eddington. Second, de Sitter and later Eddington hadapplied de Sitter's mathematical and abstruse results to actual data, theredshifts of known nebulae. This gesture must have warmed the heartof the data-oriented Hubble. And finally, Hubble visited Leiden in thesummer of 1928, where de Sitter personally encouraged him to extendSlipher's redshifts to higher redshifts and fainter nebulae.

Thus, through the de Sitter effect, Hubble is aware that his "numericaldata may be introduced into discussions of the general curvature ofspace" and thus may be of great importance to cosmology. However,Hubble does not mention the idea of an expanding universe. It seemslikely that he did not know of that concept.

There are several ironies here. First, as has been mentioned, in 1929Hubble did not have nearly good enough data to support his claim of alinear relation between velocity and distance. Second, the sole theorythat he used to interpret his findings, de Sitter's model, was later over-thrown in favor of Friedmann's and Lemaitre's models. Thus, even if hisclaim turned out to be true, Hubble probably did not understand its sig-nificance at the time.

In late 1929, well after Hubble's paper had appeared in print, Lemaitresent Eddington a second copy of his 1927 model for an expandinguniverse. Now, with Hubble's results published, everything clicked inEddington's mind. Here was a (theoretical) solution of Einstein's equa-tions predicting a linear relation between redshift and distance as a conse-quence of a homogeneous and expanding universe. On the experimentalside, Hubble had recently claimed such a relation in the wispy glimmersof the distant nebulae. Eddington immediately publicized Lemaitre'spaper and convinced him to publish it in English. Friedmann's paperwas recalled by Einstein and others and duly celebrated. By early 1931,Einstein was prepared to make his announcement in the library of theMount Wilson Observatory, recanting his static model, tossing awayfor good measure the lambda term—which he had always consideredan ugly appendage to his graceful theory of gravity—and honoringEdwin Hubble. ("Your husband's work is beautiful," Einstein said toHubble's wife in a trip to Pasadena later in 1931.) Within a year or two,the idea of an expanding universe, with a beginning in time, was beinganxiously digested by the public. The journalist George Gray, writingin the February 1933 issue of the Atlantic, described the discovery as"a radically new picture of the cosmos—a universe in expansion, a


vast bubble blowing, distending, scattering, thinning out into gossamer,losing itself."

Hubble, like many scientists, drew a sharp line between what he consid-ered the objective world of science and the subjective world of thehumanities. In his major autobiography, Realm of the Nebulae, pub-lished in 1936, Hubble wrote:

Science is the one human activity that is truly progressive. The body ofpositive knowledge is transmitted from generation to generation, andeach contributes to the growing structure . . . Agreement is secured bymeans of observation and experiment. The tests represent externalauthorities which all men must acknowledge . . . Science, since it dealsonly with such judgments, is necessarily barred from the world of val-ues. There, no external authority is known. Each man appeals to his pri-vate god and recognizes no superior court of appeal.

Modern philosophers and historians of science would partly disagreewith Hubble's severe distinction between science and other professions.Although the actual data of science may be objective, the "human activ-ity" involved in the enterprise of science is full of the same prejudices,passions, and personal judgments that mark other human endeavors.Indeed, such personal factors may be essential to empower and propel aman like Edwin Hubble through his scientific career.

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