if one looks at the sky on a clear, moonless night, thebrightest objects one sees are likely to be the planets venus,mars, jupiter, and saturn. there will also be a very largenumber of stars, which are just like our own sun but muchfarther from us. some of these fixed stars do, in fact, appearto change very slightly their positions relative to each other asearth orbits around the sun: they are not really fixed at all!

this is because they are comparatively near to us. as the earthgoes round the sun, we see them from different positionsagainst the background of more distant stars. this is fortunate,because it enables us to measure directly the distance of thesestars from us: the nearer they are, the more they appear tomove. the nearest star, called proxima centauri, is found to beabout four light-years away (the light from it takes about fouryears to reach earth), or about twenty-three million millionmiles. most of the other stars that are visible to the naked eyelie within a few hundred light-years of us. our sun, forcomparison, is a mere light-minutes away! the visible starsappear spread all over the night sky, but are particularlyconcentrated in one band, which we call the milky way. aslong ago as 1750, some astronomers were suggesting that theappearance of the milky way could be explained if most of thevisible stars lie in a single disklike configuration, one example ofwhat we now call a spiral galaxy. only a few decades later, theastronomer sir william herschel confirmed this idea bypainstakingly cataloging the positions and distances of vastnumbers of stars. even so, the idea gained complete acceptanceonly early this century.

our modern picture of the universe dates back to only 1924,when the american astronomer edwin hubble demonstratedthat ours was not the only galaxy. there were in fact manyothers, with vast tracts of empty space between them. in orderto prove this, he needed to determine the distances to theseother galaxies, which are so far away that, unlike nearby stars,they really do appear fixed. hubble was forced, therefore, touse indirect methods to measure the distances. now, theapparent brightness of a star depends on two factors: howmuch light it radiates (its luminosity), and how far it is fromus. for nearby stars, we can measure their apparent brightnessand their distance, and so we can work out their luminosity.

conversely, if we knew the luminosity of stars in other galaxies,we could work out their distance by measuring their apparentbrightness. hubble noted that certain types of stars always havethe same luminosity when they are near enough for us tomeasure; therefore, he argued, if we found such stars inanother galaxy, we could assume that they had the sameluminosity - and so calculate the distance to that galaxy. if wecould do this for a number of stars in the same galaxy, andour calculations always gave the same distance, we could befairly confident of our estimate.

in this way, edwin hubble worked out the distances to ninedifferent galaxies. we now know that our galaxy is only one ofsome hundred thousand million that can be seen using moderntelescopes, each galaxy itself containing some hundred thousandmillion stars. fig. 3.1 shows a picture of one spiral galaxy thatis similar to what we think ours must look like to someoneliving in another galaxy. we live in a galaxy that is about onehundred thousand light-years across and is slowly rotating; thestars in its spiral arms orbit around its center about onceevery several hundred million years. our sun is just anordinary, average-sized, yellow star, near the inner edge of oneof the spiral arms. we have certainly come a long way sincearistotle and ptolemy, when thought that the earth was thecenter of the universe!

stars are so far away that they appear to us to be justpinpoints of light. we cannot see their size or shape. so howcan we tell different types of stars apart? for the vast majorityof stars, there is only one characteristic feature that we canobserve - the color of their light. newton discovered that if lightfrom the sun passes through a triangular-shaped piece of glass,called a prism, it breaks up into its component colors (itsspectrum) as in a rainbow. by focusing a telescope on anindividual star or galaxy, one can similarly observe the spectrumof the light from that star or galaxy. different stars havedifferent spectra, but the relative brightness of the differentcolors is always exactly what one would expect to find in thelight emitted by an object that is glowing red hot. (in fact, thelight emitted by any opaque object that is glowing red hot hasa characteristic spectrum that depends only on its temperature- a thermal spectrum. this means that we can tell a star’stemperature from the spectrum of its light.) more-over, we findthat certain very specific colors are missing from stars’ spectra,and these missing colors may vary from star to star. since weknow that each chemical element absorbs a characteristic set ofvery specific colors, by matching these to those that are missingfrom a star’s spectrum, we can determine exactly whichelements are present in the star’s atmosphere.

in the 1920s, when astronomers began to look at thespectra of stars in other galaxies, they found something mostpeculiar: there were the same characteristic sets of missingcolors as for stars in our own galaxy, but they were all shiftedby the same relative amount toward the red end of thespectrum. to understand the implications of this, we must firstunderstand the doppler effect. as we have seen, visible lightconsists of fluctuations, or waves, in the electromagnetic field.

the wavelength (or distance from one wave crest to the next)of light is extremely small, ranging from four to seventen-millionths of a meter. the different wavelengths of light arewhat the human eye sees as different colors, with the longestwavelengths appearing at the red end of the spectrum and theshortest wavelengths at the blue end. now imagine a source oflight at a constant distance from us, such as a star, emittingwaves of light at a constant wavelength. obviously thewave-length of the waves we receive will be the same as thewavelength at which they are emitted (the gravitational field ofthe galaxy will not be large enough to have a significant effect).

suppose now that the source starts moving toward us. whenthe source emits the next wave crest it will be nearer to us, sothe distance between wave crests will be smaller than when thestar was stationary. this means that the wavelength of thewaves we receive is shorter than when the star was stationary.

correspondingly, if the source is moving away from us, thewavelength of the waves we receive will be longer. in the caseof light, therefore, means that stars moving away from us willhave their spectra shifted toward the red end of the spectrum(red-shifted) and those moving toward us will have theirspectra blue-shifted. this relationship between wavelength andspeed, which is called the doppler effect, is an everydayexperience. listen to a car passing on the road: as the car isapproaching, its engine sounds at a higher pitch (correspondingto a shorter wavelength and higher frequency of sound waves),and when it passes and goes away, it sounds at a lower pitch.

the behavior of light or radio waves is similar. indeed, thepolice make use of the doppler effect to measure the speed ofcars by measuring the wavelength of pulses of radio wavesreflected off them.

ln the years following his proof of the existence of othergalaxies, rubble spent his time cataloging their distances andobserving their spectra. at that time most people expected thegalaxies to be moving around quite randomly, and so expectedto find as many blue-shifted spectra as red-shifted ones. it wasquite a surprise, therefore, to find that most galaxies appearedred-shifted: nearly all were moving away from us! moresurprising still was the finding that hubble published in 1929:

even the size of a galaxy’s red shift is not random, but isdirectly proportional to the galaxy’s distance from us. or, inother words, the farther a galaxy is, the faster it is movingaway! and that meant that the universe could not be static, aseveryone previously had thought, is in fact expanding; thedistance between the different galaxies isg all the time.

the discovery that the universe is expanding was one of thegreat intellectual revolutions of the twentieth century. withhindsight, it is easy wonder why no one had thought of itbefore. newton, and others should have realized that a staticuniverse would soon start to contract under the influence ofgravity. but suppose instead that the universe is expanding. if itwas expanding fairly slowly, the force of gravity would cause iteventually to stop expanding and then to start contracting.

however, if it was expanding at more than a certain criticalrate, gravity would never be strong enough to stop it, and theuniverse would continue to expand forever. this is a bit likewhat happens when one fires a rocket upward from thesurface of the earth. if it has a fairly low speed, gravity willeventually stop the rocket and it will start falling back. on theother hand, if the rocket has more than a certain critical speed(about seven miles per second), gravity will not be strongenough to pull it back, so it will keep going away from theearth forever. this behavior of the universe could have beenpredicted from newton’s theory of gravity at any time in thenineteenth, the eighteenth, or even the late seventeenth century.

yet so strong was the belief in a static universe that itpersisted into the early twentieth century. even einstein, whenhe formulated the general theory of relativity in 1915, was sosure that the universe had to be static that he modified histheory to make this possible, introducing a so-calledcosmological constant into his equations. einstein introduced anew “antigravity” force, which, unlike other forces, did not comefrom any particular source but was built into the very fabric ofspace-time. he claimed that space-time had an inbuilt tendencyto expand, and this could be made to balance exactly theattraction of all the matter in the universe, so that a staticuniverse would result. only one man, it seems, was willing totake general relativity at face value, and while einstein andother physicists were looking for ways of avoiding generalrelativity’s prediction of a nonstatic universe, the russianphysicist and mathematician alexander friedmann instead setabout explaining it.

friedmann made two very simple assumptions about theuniverse: that the universe looks identical in whichever directionwe look, and that this would also be true if we were observingthe universe from anywhere else. from these two ideas alone,friedmann showed that we should not expect the universe tobe static. in fact, in 1922, several years before edwin hubble’sdiscovery, friedmann predicted exactly what hubble found!

the assumption that the universe looks the same in everydirection is clearly not true in reality. for example, as we haveseen, the other stars in our galaxy form a distinct band of lightacross the night sky, called the milky way. but if we look atdistant galaxies, there seems to be more or less the samenumber of them. so the universe does seem to be roughly thesame in every direction, provided one views it on a large scalecompared to the distance between galaxies, and ignores thedifferences on small scales. for a long time, this was sufficientjustification for friedmann’s assumption - as a roughapproximation to the real universe. but more recently a luckyaccident uncovered the fact that friedmann’s assumption is infact a remarkably accurate description of our universe.

in 1965 two american physicists at the bell telephonelaboratories in new jersey, arno penzias and robert wilson,were testing a very sensitive microwave detector. (microwavesare just like light waves, but with a wavelength of around acentimeter.) penzias and wilson were worried when they foundthat their detector was picking up more noise than it ought to.

the noise did not appear to be coming from any particulardirection. first they discovered bird droppings in their detectorand checked for other possible malfunctions, but soon ruledthese out. they knew that any noise from within theatmosphere would be stronger when the detector was notpointing straight up than when it was, because light rays travelthrough much more atmosphere when received from near thehorizon than when received from directly overhead. the extranoise was the same whichever direction the detector waspointed, so it must come from outside the atmosphere. it wasalso the same day and night and throughout the year, eventhough the earth was rotating on its axis and orbiting aroundthe sun. this showed that the radiation must come frombeyond the solar system, and even from beyond the galaxy, asotherwise it would vary as the movement of earth pointed thedetector in different directions.

in fact, we know that the radiation must have traveled to usacross most of the observable universe, and since it appears tobe the same in different directions, the universe must also bethe same in every direction, if only on a large scale. we nowknow that whichever direction we look, this noise never variesby more than a tiny fraction: so penzias and wilson hadunwittingly stumbled across a remarkably accurate confirmationof friedmann’s first assumption. however, be-cause the universeis not exactly the same in every direction, but only on averageon a large scale, the microwaves cannot be exactly the same inevery direction either. there have to be slight variationsbetween different directions. these were first detected in 1992by the cosmic background explorer satellite, or cobe, at alevel of about one part in a hundred thousand. small thoughthese variations are, they are very important, as will beexplained in chapter 8.

at roughly the same time as penzias and wilson wereinvestigating noise in their detector, two american physicists atnearby princeton university, bob dicke and jim peebles, werealso taking an interest in microwaves. they were working on asuggestion, made by george gamow (once a student ofalexander friedmann), that the early universe should have beenvery hot and dense, glowing white hot. dicke and peeblesargued that we should still be able to see the glow of the earlyuniverse, because light from very distant parts of it would onlyjust be reaching us now. however, the expansion of theuniverse meant that this light should be so greatly red-shiftedthat it would appear to us now as microwave radiation. dickeand peebles were preparing to look for this radiation whenpenzias and wilson heard about their work and realized thatthey had already found it. for this, penzias and wilson wereawarded the nobel prize in 1978 (which seems a bit hard ondicke and peebles, not to mention gamow!).

now at first sight, all this evidence that the universe looksthe same whichever direction we look in might seem to suggestthere is some-thing special about our place in the universe. inparticular, it might seem that if we observe all other galaxies tobe moving away from us, then we must be at the center ofthe universe. there is, however, an alternate explanation: theuniverse might look the same in every direction as seen fromany other galaxy too. this, as we have seen, was friedmann’ssecond assumption. we have no scientific evidence for, oragainst, this assumption. we believe it only on grounds ofmodesty: it would be most remarkable if the universe lookedthe same in every direction around us, but not around otherpoints in the universe! in friedmann’s model, all the galaxiesare moving directly away from each other. the situation israther like a balloon with a number of spots painted on itbeing steadily blown up. as the balloon expands, the distancebetween any two spots increases, but there is no spot that canbe said to be the center of the expansion. moreover, thefarther apart the spots are, the faster they will be movingapart. similarly, in friedmann’s model the speed at which anytwo galaxies are moving apart is proportional to the distancebetween them. so it predicted that the red shift of a galaxyshould be directly proportional to its distance from us, exactlyas hubble found. despite the success of his model and hisprediction of hubble’s observations, friedmann’s work remainedlargely unknown in the west until similar models werediscovered in 1935 by the american physicist howardrobertson and the british mathematician arthur walker, inresponse to hubble’s discovery of the uniform expansion of theuniverse.

although friedmann found only one, there are in fact threedifferent kinds of models that obey friedmann’s twofundamental assumptions. in the first kind (which friedmannfound) the universe is expanding sufficiently slowly that thegravitational attraction between the different galaxies causes theexpansion to slow down and eventually to stop. the galaxiesthen start to move toward each other and the universecontracts. fig. 3.2 shows how the distance between twoneighboring galaxies changes as time increases. it starts at zero,increases to a maximum, and then decreases to zero again. inthe second kind of solution, the universe is expanding sorapidly that the gravitational attraction can never stop it, thoughit does slow it down a bit. fig. 3.3 shows the separationbetween neighboring galaxies in this model. it starts at zero andeventually the galaxies are moving apart at a steady speed.

finally, there is a third kind of solution, in which the universeis expanding only just fast enough to avoid recollapse. in thiscase the separation, shown in fig. 3.4, also starts at zero andincreases forever. however, the speed at which the galaxies aremoving apart gets smaller and smaller, although it never quitereaches zero.

a remarkable feature of the first kind of friedmann model isthat in it the universe is not infinite in space, but neither doesspace have any boundary. gravity is so strong that space isbent round onto itself, making it rather like the surface of theearth. if one keeps traveling in a certain direction on thesurface of the earth, one never comes up against animpassable barrier or falls over the edge, but eventually comesback to where one started.

in the first kind of friedmann model, space is just like this,but with three dimensions instead of two for the earth’ssurface. the fourth dimension, time, is also finite in extent, butit is like a line with two ends or boundaries, a beginning andan end. we shall see later that when one combines generalrelativity with the uncertainty principle of quantum mechanics, itis possible for both space and time to be finite without anyedges or boundaries.

the idea that one could go right round the universe andend up where one started makes good science fiction, but itdoesn’t have much practical significance, because it can beshown that the universe would recollapse to zero size beforeone could get round. you would need to travel faster than lightin order to end up where you started before the universecame to an end - and that is not allowed!

in the first kind of friedmann model, which expands andrecollapses, space is bent in on itself, like the surface of theearth. it is therefore finite in extent. in the second kind ofmodel, which expands forever, space is bent the other way, likethe surface of a saddle. so in this case space is infinite. finally,in the third kind of friedmann model, with just the critical rateof expansion, space is flat (and therefore is also infinite).

but which friedmann model describes our universe? will theuniverse eventually stop expanding and start contracting, or willit expand forever? to answer this question we need to knowthe present rate of expansion of the universe and its presentaverage density. if the density is less than a certain criticalvalue, determined by the rate of expansion, the gravitationalattraction will be too weak to halt the expansion. if the densityis greater than the critical value, gravity will stop the expansionat some time in the future and cause the universe torecollapse.

we can determine the present rate of expansion bymeasuring the velocities at which other galaxies are movingaway from us, using the doppler effect. this can be done veryaccurately. however, the distances to the galaxies are not verywell known because we can only measure them indirectly. soall we know is that the universe is expanding by between 5percent and 10 percent every thousand million years. however,our uncertainty about the present average density of theuniverse is even greater. if we add up the masses of all thestars that we can see in our galaxy and other galaxies, thetotal is less than one hundredth of the amount required to haltthe expansion of the universe, even for the lowest estimate ofthe rate of expansion. our galaxy and other galaxies, however,must contain a large amount of “dark matter” that we cannotsee directly, but which we know must be there because of theinfluence of its gravitational attraction on the orbits of stars inthe galaxies. moreover, most galaxies are found in clusters, andwe can similarly infer the presence of yet more dark matter inbetween the galaxies in these clusters by its effect on themotion of the galaxies. when we add up all this dark matter,we still get only about one tenth of the amount required tohalt the expansion. however, we cannot exclude the possibilitythat there might be some other form of matter, distributedalmost uniformly throughout the universe, that we have not yetdetected and that might still raise the average density of theuniverse up to the critical value needed to halt the expansion.

the present evidence therefore suggests that the universe willprobably expand forever, but all we can really be sure of isthat even if the universe is going to recollapse, it won’t do sofor at least another ten thousand million years, since it hasalready been expanding for at least that long. this should notunduly worry us: by that time, unless we have colonizedbeyond the solar system, mankind will long since have diedout, extinguished along with our sun!

all of the friedmann solutions have the feature that at sometime in the past (between ten and twenty thousand millionyears ago) the distance between neighboring galaxies must havebeen zero. at that time, which we call the big bang, the densityof the universe and the curvature of space-time would havebeen infinite. because mathematics cannot really handle infinitenumbers, this means that the general theory of relativity (onwhich friedmann’s solutions are based) predicts that there is apoint in the universe where the theory itself breaks down. sucha point is an example of what mathematicians call a singularity.

in fact, all our theories of science are formulated on theassumption that space-time is smooth and nearly fiat, so theybreak down at the big bang singularity, where the curvature ofspace-time is infinite. this means that even if there were eventsbefore the big bang, one could not use them to determinewhat would happen afterward, because predictability wouldbreak down at the big bang.

correspondingly, if, as is the case, we know only what hashappened since the big bang, we could not determine whathappened beforehand. as far as we are concerned, eventsbefore the big bang can have no consequences, so they shouldnot form part of a scientific model of the universe. we shouldtherefore cut them out of the model and say that time had abeginning at the big bang.

many people do not like the idea that time has a beginning,probably because it smacks of divine intervention. (the catholicchurch, on the other hand, seized on the big bang model andin 1951officially pronounced it to be in accordance with thebible.) there were therefore a number of attempts to avoid theconclusion that there had been a big bang. the proposal thatgained widest support was called the steady state theory. it wassuggested in 1948 by two refugees from nazi-occupied austria,hermann bondi and thomas gold, together with a briton, fredhoyle, who had worked with them on the development ofradar during the war. the idea was that as the galaxies movedaway from each other, new galaxies were continually forming inthe gaps in between, from new matter that was beingcontinually created. the universe would therefore look roughlythe same at all times as well as at all points of space. thesteady state theory required a modification of general relativityto allow for the continual creation of matter, but the rate thatwas involved was so low (about one particle per cubic kilometerper year) that it was not in conflict with experiment. thetheory was a good scientific theory, in the sense described inchapter 1: it was simple and it made definite predictions thatcould be tested by observation. one of these predictions wasthat the number of galaxies or similar objects in any givenvolume of space should be the same wherever and wheneverwe look in the universe. in the late 1950s and early 1960s asurvey of sources of radio waves from outer space was carriedout at cambridge by a group of astronomers led by martinryle (who had also worked with bondi, gold, and hoyle onradar during the war). the cambridge group showed that mostof these radio sources must lie outside our galaxy (indeedmany of them could be identified with other galaxies) and alsothat there were many more weak sources than strong ones.

they interpreted the weak sources as being the more distantones, and the stronger ones as being nearer. then thereappeared to be less common sources per unit volume of spacefor the nearby sources than for the distant ones. this couldmean that we are at the center of a great region in theuniverse in which the sources are fewer than elsewhere.

alternatively, it could mean that the sources were morenumerous in the past, at the time that the radio waves left ontheir journey to us, than they are now. either explanationcontradicted the predictions of the steady state theory.

moreover, the discovery of the microwave radiation by penziasand wilson in 1965 also indicated that the universe must havebeen much denser in the past. the steady state theorytherefore had to be abandoned.

another attempt to avoid the conclusion that there musthave been a big bang, and therefore a beginning of time, wasmade by two russian scientists, evgenii lifshitz and isaackhalatnikov, in 1963. they suggested that the big bang mightbe a peculiarity of friedmann’s models alone, which after allwere only approximations to the real universe. perhaps, of allthe models that were roughly like the real universe, onlyfriedmann’s would contain a big bang singularity. infriedmann’s models, the galaxies are all moving directly awayfrom each other - so it is not surprising that at some time inthe past they were all at the same place. in the real universe,however, the galaxies are not just moving directly away fromeach other - they also have small sideways velocities. so inreality they need never have been all at exactly the same place,only very close together. perhaps then the current expandinguniverse resulted not from a big bang singularity, but from anearlier contracting phase; as the universe had collapsed theparticles in it might not have all collided, but had flown pastand then away from each other, producing the presentexpansion of the the universe that were roughly likefriedmann’s models but took account of the irregularities andrandom velocities of galaxies in the real universe. they showedthat such models could start with a big bang, even though thegalaxies were no longer always moving directly away from eachother, but they claimed that this was still only possible incertain exceptional models in which the galaxies were all movingin just the right way. they argued that since there seemed tobe infinitely more friedmann-like models without a big bangsingularity than there were with one, we should conclude thatthere had not in reality been a big bang. they later realized,however, that there was a much more general class offriedmann-like models that did have singularities, and in whichthe galaxies did not have to be moving any special way. theytherefore withdrew their claim in 1970.

the work of lifshitz and khalatnikov was valuable because itshowed that the universe could have had a singularity, a bigbang, if the general theory of relativity was correct. however, itdid not resolve the crucial question: does general relativitypredict that our universe should have had a big bang, abeginning of time? the answer to this carne out of acompletely different approach introduced by a britishmathematician and physicist, roger penrose, in 1965. using theway light cones behave in general relativity, together with thefact that gravity is always attractive, he showed that a starcollapsing under its own gravity is trapped in a region whosesurface eventually shrinks to zero size. and, since the surface ofthe region shrinks to zero, so too must its volume. all thematter in the star will be compressed into a region of zerovolume, so the density of matter and the curvature ofspace-time become infinite. in other words, one has asingularity contained within a region of space-time known as ablack hole.

at first sight, penrose’s result applied only to stars; it didn’thave anything to say about the question of whether the entireuniverse had a big bang singularity in its past. however, at thetime that penrose produced his theorem, i was a researchstudent desperately looking for a problem with which tocomplete my ph.d. thesis. two years before, i had beendiagnosed as suffering from als, commonly known as lougehrig’s disease, or motor neuron disease, and given tounderstand that i had only one or two more years to live. inthese circumstances there had not seemed much point inworking on my ph.d.- i did not expect to survive that long.

yet two years had gone by and i was not that much worse.

in fact, things were going rather well for me and i had gottenengaged to a very nice girl, jane wilde. but in order to getmarried, i needed a job, and in order to get a job, i neededa ph.d.

in 1965 i read about penrose’s theorem that any bodyundergoing gravitational collapse must eventually form asingularity. i soon realized that if one reversed the direction oftime in penrose’s theorem, so that the collapse became anexpansion, the conditions of his theorem would still hold,provided the universe were roughly like a friedmann model onlarge scales at the present time. penrose’s theorem had shownthat any collapsing star must end in a singularity; thetime-reversed argument showed that any friedmann-likeexpanding universe must have begun with a singularity. fortechnical reasons, penrose’s theorem required that the universebe infinite in space. so i could in fact, use it to prove thatthere should be a singularity only if the universe was expandingfast enough to avoid collapsing again (since only thosefriedmann models were infinite in space).

during the next few years i developed new mathematicaltechniques to remove this and other technical conditions fromthe theorems that proved that singularities must occur. thefinal result was a joint paper by penrose and myself in 1970,which at last proved that there must have been a big bangsingularity provided only that general relativity is correct andthe universe contains as much matter as we observe. therewas a lot of opposition to our work, partly from the russiansbecause of their marxist belief in scientific determinism, andpartly from people who felt that the whole idea of singularitieswas repugnant and spoiled the beauty of einstein’s theory.

however, one cannot really argue with a mathematical theorem.

so in the end our work became generally accepted andnowadays nearly everyone assumes that the universe startedwith a big bang singularity. it is perhaps ironic that, havingchanged my mind, i am now trying to convince other physiciststhat there was in fact no singularity at the beginning of theuniverse - as we shall see later, it can disappear once quantumeffects are taken into account.

we have seen in this chapter how, in less than half acentury, man’s view of the universe formed over millennia hasbeen transformed. hubble’s discovery that the universe wasexpanding, and the realization of the insignificance of our ownplanet in the vastness of the universe, were just the startingpoint. as experimental and theoretical evidence mounted, itbecame more and more clear that the universe must have hada beginning in time, until in 1970 this was finally proved bypenrose and myself, on the basis of einstein’s general theory ofrelativity. that proof showed that general relativity is only anincomplete theory: it cannot tell us how the universe startedoff, because it predicts that all physical theories, including itself,break down at the beginning of the universe. however, generalrelativity claims to be only a partial theory, so what thesingularity theorems really show is that there must have been atime in the very early universe when the universe was so smallthat one could no longer ignore the small-scale effects of theother great partial theory of the twentieth century, quantummechanics. at the start of the 1970s, then, we were forced toturn our search for an understanding of the universe from ourtheory of the extraordinarily vast to our theory of theextraordinarily tiny. that theory, quantum mechanics, will bedescribed next, before we turn to the efforts to combine thetwo partial theories into a single quantum theory of gravity.