Illustrated Theory of Everything: The Origin and Fate of the Universe (2 page)

The Theory of Everything: The Origin and Fate of the Universe

Chapter 2 - SECOND LECTURE - THE EXPANDING UNIVERSE

Our sun and the nearby stars are all part of a vast collection of stars calledthe Milky Way galaxy. For a long time it was thought that this was thewhole universe. It was only in 1924 that the American astronomer EdwinHubble demonstrated that ours was not the only galaxy. There were, in fact,many others, with vast tracks of empty space between them. In order to provethis he needed to determine the distances to these other galaxies. We candetermine the distance of nearby stars by observing how they change positionas the Earth goes around the sun. But other galaxies are so far away that, unlikenearby stars, they really do appear fixed. Hubble was forced, therefore, to useindirect methods to measure the distances.

Now the apparent brightness of a star depends on two factors-luminosity andhow far it is from us. For nearby stars we can measure both their apparentbrightness and their distance, so we can work out their luminosity. Conversely,if we knew the luminosity of stars in other galaxies, we could work out theirdistance by measuring their apparent brightness. Hubble argued that therewere certain types of stars that always had the same luminosity when they werenear enough for us to measure. If, therefore, we found such stars in anothergalaxy, we could assume that they had the same luminosity. Thus, we couldcalculate the distance to that galaxy. If we could do this for a number of starsin the same galaxy, and our calculations always gave the same distance, wecould be fairly confident of our estimate. In this way, Edwin Hubble workedout the distances to nine different galaxies.

We now know that our galaxy is only one of some hundred thousand millionthat can be seen using modern telescopes, each galaxy itself containing somehundred thousand million stars. We live in a galaxy that is about one hundredthousand light-years across and is slowly rotating; the stars in its spiral armsorbit around its center about once every hundred million years. Our sun is justan ordinary, average-sized, yellow star, near the outer edge of one of the spiralarms. We have certainly come a long way since Aristotle and Ptolemy, whenwe thought that the Earth was the center of the universe.

Stars are so far away that they appear to us to be just pinpoints of light. Wecannot determine their size or shape. So how can we tell different types of starsapart? For the vast majority of stars, there is only one correct characteristicfeature that we can observe-the color of their light. Newton discovered thatif light from the sun passes through a prism, it breaks up into its componentcolors-its spectrum-like in a rainbow. By focusing a telescope on anindividual star or galaxy, one can similarly observe the spectrum of the lightfrom that star or galaxy. Different stars have different spectra, but the relativebrightness of the different colors is always exactly what one would expect tofind in the light emitted by an object that is glowing red hot. This means thatwe can tell a star’s temperature from the spectrum of its light. Moreover, wefind that certain very specific colors are missing from stars’ spectra, and thesemissing colors may vary from star to star. We know that each chemical elementabsorbs the characteristic set of very specific colors. Thus, by matching each ofthose which are missing from a star’s spectrum, we can determine exactlywhich elements are present in the star’s atmosphere.

In the 1920s, when astronomers began to look at the spectra of stars in othergalaxies, they found something most peculiar: There were the same character-istic sets of missing colors as for stars in our own galaxy, but they were allshifted by the same relative amount toward the red end of the spectrum. Theonly reasonable explanation of this was that the galaxies were moving awayfrom us, and the frequency of the light waves from them was being reduced, orred-shifted, by the Doppler effect. Listen to a car passing on the road. As thecar is approaching, its engine sounds at a higher pitch, corresponding to ahigher frequency of sound waves; and when it passes and goes away, it soundsat a lower pitch. The behavior of light or radial waves is similar. Indeed, thepolice made use of the Doppler effect to measure the speed of cars by measur-ing the frequency of pulses of radio waves reflected off them.

In the years following his proof of the existence of other galaxies, Hubble spenthis time cataloging their distances and observing their spectra. At that timemost people expected the galaxies to be moving around quite randomly, and soexpected to find as many spectra which were blue-shifted as ones which werered-shifted. It was quite a surprise, therefore, to find that the galaxies allappeared red-shifted. Every single one was moving away from us. More surpris-ing still was the result which Hubble published in 1929: Even the size of thegalaxy’s red shift was not random, but was directly proportional to the galaxy’sdistance from us. Or, in other words, the farther a galaxy was, the faster it wasmoving away. And that meant that the universe could not be static, as every-one previously thought, but was in fact expanding. The distance between thedifferent galaxies was growing all the time.

The discovery that the universe was expanding was one of the great intellec-tual revolutions of the twentieth century. With hindsight, it is easy to wonderwhy no one had thought of it before. Newton and others should have realizedthat a static universe would soon start to contract under the influence ofgravity. But suppose that, instead of being static, the universe was expanding.If it was expanding fairly slowly, the force of gravity would cause it eventuallyto stop expanding and then to start contracting. However, if it was expandingat more than a certain critical rate, gravity would never be strong enough tostop it, and the universe would continue to expand forever. This is a bit likewhat happens when one fires a rocket upward from the surface of the Earth. Ifit has a fairly low speed, gravity will eventually stop the rocket and it will startfalling back. On the other hand, if the rocket has more than a certain criticalspeed-about seven miles a second-gravity will not be strong enough to pull itback, so it will keep going away from the Earth forever.

This behavior of the universe could have been predicted from Newton’s theoryof gravity at any time in the nineteenth, the eighteenth, or even the late sev-enteenth centuries. Yet so strong was the belief in a static universe that it per-sisted into the early twentieth century. Even when Einstein formulated thegeneral theory of relativity in 1915, he was sure that the universe had to bestatic. He therefore modified his theory to make this possible, introducing a so-called cosmological constant into his equations. This was a new “antigravity”force, which, unlike other forces, did not come from any particular source, butwas built into the very fabric of space-time. His cosmological constant gavespace-time an inbuilt tendency to expand, and this could be made to exactlybalance the attraction of all the matter in the universe so that a static universewould result.

Only one man, it seems, was willing to take general relativity at face value.While Einstein and other physicists were looking for ways of avoiding generalrelativity’s prediction of a nonstatic universe, the Russian physicist AlexanderFriedmann instead set about explaining it.

THE FRIEDMANN MODELSThe equations of general relativity, which determined how the universeevolves in time, are too complicated to solve in detail. So what Friedmanndid, instead, was to make two very simple assumptions about the universe:that the universe looks identical in whichever direction we look, and thatthis would also be true if we were observing the universe from anywhere else.On the basis of general relativity and these two assumptions, Friedmannshowed that we should not expect the universe to be static. In fact, in 1922,several years before Edwin Hubble’s discovery, Friedmann predicted exactlywhat Hubble found.

The assumption that the universe looks the same in every direction is clearly nottrue in reality. For example, the other stars in our galaxy form a distinct band oflight across the night sky called the Milky Way. But if we look at distant galax-ies, there seems to be more or less the same number of them in each direction.So the universe does seem to be roughly the same in every direction, providedone views it on a large scale compared to the distance between galaxies.For a long time this was sufficient justification for Friedmann’s assumption-as a rough approximation to the real universe. But more recently a lucky acci-dent uncovered the fact that Friedmann’s assumption is in fact a remarkablyaccurate description of our universe. In 1965, two American physicists, ArnoPenzias and Robert Wilson, were working at the Bell Labs in New Jersey onthe design of a very sensitive microwave detector for communicating withorbiting satellites. They were worried when they found that their detector waspicking up more noise than it ought to, and that the noise did not appear tobe coming from any particular direction. First they looked for bird droppingson their detector and checked for other possible malfunctions, but soon ruledthese out. They knew that any noise from within the atmosphere would bestronger when the detector is not pointing straight up than when it is, becausethe atmosphere appears thicker when looking at an angle to the vertical.The extra noise was the same whichever direction the detector pointed, so itmust have come from outside the atmosphere. It was also the same day andnight throughout the year, even though the Earth was rotating on its axis andorbiting around the sun. This showed that the radiation must come frombeyond the solar system, and even from beyond the galaxy, as otherwise itwould vary as the Earth pointed the detector in different directions.In fact, we know that the radiation must have traveled to us across most ofthe observable universe. Since it appears to be the same in different direc-tions, the universe must also be the same in every direction, at least on a largescale. We now know that whichever direction we look in, this noise nevervaries by more than one part in ten thousand. So Penzias and Wilson hadunwittingly stumbled across a remarkably accurate confirmation ofFriedmann’s first assumption.

At roughly the same time, two American physicists at nearby PrincetonUniversity, Bob Dicke and Jim Peebles, were also taking an interest inmicrowaves. They were working on a suggestion made by George Gamow,once a student of Alexander Friedmann, that the early universe should havebeen very hot and dense, glowing white hot. Dicke and Peebles argued that weshould still be able to see this glowing, because light from very distant partsof the early universe would only just be reaching us now. However, theexpansion of the universe meant that this light should be so greatly red-shift-ed that it would appear to us now as microwave radiation. Dicke and Peebleswere looking for this radiation when Penzias and Wilson heard about theirwork and realized that they had already found it. For this, Penzias andWilson were awarded the Nobel Prize in 1978, which seems a bit hard onDicke and Peebles.

Now at first sight, all this evidence that the universe looks the same whichev-er direction we look in might seem to suggest there is something special aboutour place in the universe. In particular, it might seem that if we observe allother galaxies to be moving away from us, then we must be at the center of theuniverse. There is, however, an alternative explanation: The universe mightalso look the same in every direction as seen from any other galaxy. This, as wehave seen, was Friedmann’s second assumption.

We have no scientific evidence for or against this assumption. We believe itonly on grounds of modesty. It would be most remarkable if the universelooked the same in every direction around us, but not around other points inthe universe. In Friedmann’s model, all the galaxies are moving directly awayfrom each other. The situation is rather like steadily blowing up a balloonwhich has a number of spots painted on it. As the balloon expands, the dis-tance between any two spots increases, but there is no spot that can be said tobe the center of the expansion. Moreover, the farther apart the spots are, thefaster they will be moving apart. Similarly, in Friedmann’s model the speed atwhich any two galaxies are moving apart is proportional to the distancebetween them. So it predicted that the red shift of a galaxy should be directlyproportional to its distance from us, exactly as Hubble found.

Despite the success of his model and his prediction of Hubble’s observations,Friedmann’s work remained largely unknown in the West. It became knownonly after similar models were discovered in 1935 by the American physicistHoward Robertson and the British mathematician Arthur Walker, in responseto Hubble’s discovery of the uniform expansion of the universe.

Although Friedmann found only one, there are in fact three different kinds ofmodels that obey Friedmann’s two fundamental assumptions. In the firstkind-which Friedmann found-the universe is expanding so sufficientlyslowly that the gravitational attraction between the different galaxies causesthe expansion to slow down and eventually to stop. The galaxies then start tomove toward each other and the universe contracts. The distance between twoneighboring galaxies starts at zero, increases to a maximum, and then decreasesback down to zero again.

In the second kind of solution, the universe is expanding so rapidly that thegravitational attraction can never stop it, though it does slow it down a bit.The separation between neighboring galaxies in this model starts at zero, andeventually the galaxies are moving apart at a steady speed.

Finally, there is a third kind of solution, in which the universe is expandingonly just fast enough to avoid recollapse. In this case the separation also startsat zero, and increases forever. However, the speed at which the galaxies aremoving apart gets smaller and smaller, although it never quite reaches zero.

A remarkable feature of the first kind of Friedmann model is that the universeis not infinite in space, but neither does space have any boundary. Gravity isso strong that space is bent round onto itself, making it rather like the surfaceof the Earth. If one keeps traveling in a certain direction on the surface of theEarth, one never comes up against an impassable barrier or falls over the edge,but eventually comes back to where one started. Space, in the first Friedmannmodel, is just like this, but with three dimensions instead of two for the Earth’ssurface. The fourth dimension-time-is also finite in extent, but it is like aline with two ends or boundaries, a beginning and an end. We shall see laterthat when one combines general relativity with the uncertainty principle ofquantum mechanics, it is possible for both space and time to be finite withoutany edges or boundaries. The idea that one could go right around the universeand end up where one started makes good science fiction, but it doesn’t havemuch practical significance because it can be shown that the universe wouldrecollapse to zero size before one could get round. You would need to travelfaster than light in order to end up where you started before the universe cameto an end-and that is not allowed.