a well-known scientist (some say it was bertrand russell)once gave a public lecture on astronomy. he described howthe earth orbits around the sun and how the sun, in turn,orbits around the center of a vast collection of stars called ourgalaxy. at the end of the lecture, a little old lady at the backof the room got up and said: “what you have told us isrubbish. the world is really a flat plate supported on the backof a giant tortoise.” the scientist gave a superior smile beforereplying, “what is the tortoise standing on.” “you’re very clever,young man, very clever,” said the old lady. “but it’s turtles allthe way down!”

most people would find the picture of our universe as aninfinite tower of tortoises rather ridiculous, but why do we thinkwe know better? what do we know about the universe, andhow do we know it? where did the universe come from, andwhere is it going? did the universe have a beginning, and if so,what happened before then? what is the nature of time? will itever come to an end? can we go back in time? recentbreakthroughs in physics, made possible in part by fantasticnew technologies, suggest answers to some of theselongstanding questions. someday these answers may seem asobvious to us as the earth orbiting the sun - or perhaps asridiculous as a tower of tortoises. only time (whatever that maybe) will tell.

as long ago as 340 bc the greek philosopher aristotle, inhis book on the heavens, was able to put forward two goodarguments for believing that the earth was a round sphererather than a hat plate. first, he realized that eclipses of themoon were caused by the earth coming between the sun andthe moon. the earth’s shadow on the moon was always round,which would be true only if the earth was spherical. if theearth had been a flat disk, the shadow would have beenelongated and elliptical, unless the eclipse always occurred at atime when the sun was directly under the center of the disk.

second, the greeks knew from their travels that the north starappeared lower in the sky when viewed in the south than itdid in more northerly regions. (since the north star lies overthe north pole, it appears to be directly above an observer atthe north pole, but to someone looking from the equator, itappears to lie just at the horizon. from the difference in theapparent position of the north star in egypt and greece,aristotle even quoted an estimate that the distance around theearth was 400,000 stadia. it is not known exactly what lengtha stadium was, but it may have been about 200 yards, whichwould make aristotle’s estimate about twice the currentlyaccepted figure. the greeks even had a third argument thatthe earth must be round, for why else does one first see thesails of a ship coming over the horizon, and only later see thehull?

aristotle thought the earth was stationary and that the sun,the moon, the planets, and the stars moved in circular orbitsabout the earth. he believed this because he felt, for mysticalreasons, that the earth was the center of the universe, andthat circular motion was the most perfect. this idea waselaborated by ptolemy in the second century ad into acomplete cosmological model. the earth stood at the center,surrounded by eight spheres that carried the moon, the sun,the stars, and the five planets known at the time, mercury,venus, mars, jupiter, and saturn (fig. 1.1). the planetsthemselves moved on smaller circles attached to their respectivespheres in order to account for their rather complicatedobserved paths in the sky. the outermost sphere carried theso-called fixed stars, which always stay in the same positionsrelative to each other but which rotate together across the sky.

what lay beyond the last sphere was never made very clear,but it certainly was not part of mankind’s observable universe.

ptolemy’s model provided a reasonably accurate system forpredicting the positions of heavenly bodies in the sky. but inorder to predict these positions correctly, ptolemy had to makean assumption that the moon followed a path that sometimesbrought it twice as close to the earth as at other times. andthat meant that the moon ought sometimes to appear twice asbig as at other times! ptolemy recognized this flaw, butnevertheless his model was generally, although not universally,accepted. it was adopted by the christian church as the pictureof the universe that was in accordance with scripture, for ithad the great advantage that it left lots of room outside thesphere of fixed stars for heaven and hell.

a simpler model, however, was proposed in 1514 by a polishpriest, nicholas copernicus. (at first, perhaps for fear of beingbranded a heretic by his church, copernicus circulated hismodel anonymously.) his idea was that the sun was stationaryat the center and that the earth and the planets moved incircular orbits around the sun. nearly a century passed beforethis idea was taken seriously. then two astronomers - thegerman, johannes kepler, and the italian, galileo galilei -started publicly to support the copernican theory, despite thefact that the orbits it predicted did not quite match the onesobserved. the death blow to the aristotelian/ptolemaic theorycame in 1609. in that year, galileo started observing the nightsky with a telescope, which had just been invented. when helooked at the planet jupiter, galileo found that it wasaccompanied by several small satellites or moons that orbitedaround it. this implied that everything did not have to orbitdirectly around the earth, as aristotle and ptolemy had thought.

(it was, of course, still possible to believe that the earth wasstationary at the center of the universe and that the moons ofjupiter moved on extremely complicated paths around theearth, giving the appearance that they orbited jupiter. however,copernicus’s theory was much simpler.) at the same time,johannes kepler had modified copernicus’s theory, suggestingthat the planets moved not in circles but in ellipses (an ellipseis an elongated circle). the predictions now finally matched theobservations.

as far as kepler was concerned, elliptical orbits were merelyan ad hoc hypothesis, and a rather repugnant one at that,because ellipses were clearly less perfect than circles. havingdiscovered almost by accident that elliptical orbits fit theobservations well, he could not reconcile them with his idea thatthe planets were made to orbit the sun by magnetic forces. anexplanation was provided only much later, in 1687, when sirisaac newton published his philosophiae naturalis principiamathematica, probably the most important single work everpublished in the physical sciences. in it newton not only putforward a theory of how bodies move in space and time, buthe also developed the complicated mathematics needed toanalyze those motions. in addition, newton postulated a law ofuniversal gravitation according to which each body in theuniverse was attracted toward every other body by a force thatwas stronger the more massive the bodies and the closer theywere to each other. it was this same force that caused objectsto fall to the ground. (the story that newton was inspired byan apple hitting his head is almost certainly apocryphal. allnewton himself ever said was that the idea of gravity came tohim as he sat “in a contemplative mood” and “was occasionedby the fall of an apple.”) newton went on to show that,according to his law, gravity causes the moon to move in anelliptical orbit around the earth and causes the earth and theplanets to follow elliptical paths around the sun.

the copernican model got rid of ptolemy’s celestial spheres,and with them, the idea that the universe had a naturalboundary. since “fixed stars” did not appear to change theirpositions apart from a rotation across the sky caused by theearth spinning on its axis, it became natural to suppose thatthe fixed stars were objects like our sun but very much fartheraway.

newton realized that, according to his theory of gravity, thestars should attract each other, so it seemed they could notremain essentially motionless. would they not all fall together atsome point? in a letter in 1691 to richard bentley, anotherleading thinker of his day, newton argued that this wouldindeed happen if there were only a finite number of starsdistributed over a finite region of space. but he reasoned thatif, on the other hand, there were an infinite number of stars,distributed more or less uniformly over infinite space, this wouldnot happen, because there would not be any central point forthem to fall to.

this argument is an instance of the pitfalls that you canencounter in talking about infinity. in an infinite universe, everypoint can be regarded as the center, because every point hasan infinite number of stars on each side of it. the correctapproach, it was realized only much later, is to consider thefinite situation, in which the stars all fall in on each other, andthen to ask how things change if one adds more stars roughlyuniformly distributed outside this region. according to newton’slaw, the extra stars would make no difference at all to theoriginal ones on average, so the stars would fall in just as fast.

we can add as many stars as we like, but they will still alwayscollapse in on them-selves. we now know it is impossible tohave an infinite static model of the universe in which gravity isalways attractive.

it is an interesting reflection on the general climate ofthought before the twentieth century that no one had suggestedthat the universe was expanding or contracting. it was generallyaccepted that either the universe had existed forever in anunchanging state, or that it had been created at a finite time inthe past more or less as we observe it today. in part this mayhave been due to people’s tendency to believe in eternal truths,as well as the comfort they found in the thought that eventhough they may grow old and die, the universe is eternal andunchanging.

even those who realized that newton’s theory of gravityshowed that the universe could not be static did not think tosuggest that it might be expanding. instead, they attempted tomodify the theory by making the gravitational force repulsive atvery large distances. this did not significantly affect theirpredictions of the motions of the planets, but it allowed aninfinite distribution of stars to remain in equilibrium - with theattractive forces between nearby stars balanced by the repulsiveforces from those that were farther away. however, we nowbelieve such an equilibrium would be unstable: if the stars insome region got only slightly nearer each other, the attractiveforces between them would become stronger and dominateover the repulsive forces so that the stars would continue tofall toward each other. on the other hand, if the stars got abit farther away from each other, the repulsive forces woulddominate and drive them farther apart.

another objection to an infinite static universe is normallyascribed to the german philosopher heinrich olbers, who wroteabout this theory in 1823. in fact, various contemporaries ofnewton had raised the problem, and the olbers article was noteven the first to contain plausible arguments against it. it was,however, the first to be widely noted. the difficulty is that inan infinite static universe nearly every line of sight would endon the surface of a star. thus one would expect that thewhole sky would be as bright as the sun, even at night.

olbers’ counter-argument was that the light from distant starswould be dimmed by absorption by intervening matter.

however, if that happened the intervening matter wouldeventually heat up until it glowed as brightly as the stars. theonly way of avoiding the conclusion that the whole of the nightsky should be as bright as the surface of the sun would be toassume that the stars had not been shining forever but hadturned on at some finite time in the past. in that case theabsorbing matter might not have heated up yet or the lightfrom distant stars might not yet have reached us. and thatbrings us to the question of what could have caused the starsto have turned on in the first place.

the beginning of the universe had, of course, been discussedlong before this. according to a number of early cosmologiesand the jewish/christian/muslim tradition, the universe startedat a finite, and not very distant, time in the past. oneargument for such a beginning was the feeling that it wasnecessary to have “first cause” to explain the existence of theuniverse. (within the universe, you always explained one eventas being caused by some earlier event, but the existence of theuniverse itself could be explained in this way only if it hadsome beginning.) another argument was put forward by st.

augustine in his book the city of god. he pointed out thatcivilization is progressing and we remember who performed thisdeed or developed that technique. thus man, and so alsoperhaps the universe, could not have been around all that long.

st. augustine accepted a date of about 5000 bc for thecreation of the universe according to the book of genesis. (itis interesting that this is not so far from the end of the lastice age, about 10,000 bc, which is when archaeologists tell usthat civilization really began.)aristotle, and most of the other greek philosophers, on theother hand, did not like the idea of a creation because itsmacked too much of divine intervention. they believed,therefore, that the human race and the world around it hadexisted, and would exist, forever. the ancients had alreadyconsidered the argument about progress described above, andanswered it by saying that there had been periodic floods orother disasters that repeatedly set the human race right backto the beginning of civilization.

the questions of whether the universe had a beginning intime and whether it is limited in space were later extensivelyexamined by the philosopher immanuel kant in his monumental(and very obscure) work critique of pure reason, published in1781. he called these questions antinomies (that is,contradictions) of pure reason because he felt that there wereequally compelling arguments for believing the thesis, that theuniverse had a beginning, and the antithesis, that it had existedforever. his argument for the thesis was that if the universedid not have a beginning, there would be an infinite period oftime before any event, which he considered absurd. theargument for the antithesis was that if the universe had abeginning, there would be an infinite period of time before it,so why should the universe begin at any one particular time?

in fact, his cases for both the thesis and the antithesis arereally the same argument. they are both based on hisunspoken assumption that time continues back forever, whetheror not the universe had existed forever. as we shall see, theconcept of time has no meaning before the beginning of theuniverse. this was first pointed out by st. augustine. whenasked: “what did god do before he created the universe?”

augustine didn’t reply: “he was preparing hell for people whoasked such questions.” instead, he said that time was aproperty of the universe that god created, and that time didnot exist before the beginning of the universe.

when most people believed in an essentially static andunchanging universe, the question of whether or not it had abeginning was really one of metaphysics or theology. one couldaccount for what was observed equally well on the theory thatthe universe had existed forever or on the theory that it wasset in motion at some finite time in such a manner as to lookas though it had existed forever. but in 1929, edwin hubblemade the landmark observation that wherever you look, distantgalaxies are moving rapidly away from us. in other words, theuniverse is expanding. this means that at earlier times objectswould have been closer together. in fact, it seemed that therewas a time, about ten or twenty thousand million years ago,when they were all at exactly the same place and when,therefore, the density of the universe was infinite. this discoveryfinally brought the question of the beginning of the universeinto the realm of science.

hubble’s observations suggested that there was a time, calledthe big bang, when the universe was infinitesimally small andinfinitely dense. under such conditions all the laws of science,and therefore all ability to predict the future, would breakdown. if there were events earlier than this time, then theycould not affect what happens at the present time. theirexistence can be ignored because it would have noobservational consequences. one may say that time had abeginning at the big bang, in the sense that earlier times simplywould not be defined. it should be emphasized that thisbeginning in time is very different from those that had beenconsidered previously. in an unchanging universe a beginning intime is something that has to be imposed by some beingoutside the universe; there is no physical necessity for abeginning. one can imagine that god created the universe atliterally any time in the past. on the other hand, if theuniverse is expanding, there may be physical reasons why therehad to be a beginning. one could still imagine that god createdthe universe at the instant of the big bang, or even afterwardsin just such a way as to make it look as though there hadbeen a big bang, but it would be meaningless to suppose thatit was created before the big bang. an expanding universe doesnot preclude a creator, but it does place limits on when hemight have carried out his job!

in order to talk about the nature of the universe and todiscuss questions such as whether it has a beginning or anend, you have to be clear about what a scientific theory is. ishall take the simpleminded view that a theory is just a modelof the universe, or a restricted part of it, and a set of rulesthat relate quantities in the model to observations that wemake. it exists only in our minds and does not have any otherreality (whatever that might mean). a theory is a good theoryif it satisfies two requirements. it must accurately describe alarge class of observations on the basis of a model thatcontains only a few arbitrary elements, and it must makedefinite predictions about the results of future observations. forexample, aristotle believed empedocles’s theory that everythingwas made out of four elements, earth, air, fire, and water. thiswas simple enough, but did not make any definite predictions.

on the other hand, newton’s theory of gravity was based onan even simpler model, in which bodies attracted each otherwith a force that was proportional to a quantity called theirmass and inversely proportional to the square of the distancebetween them. yet it predicts the motions of the sun, themoon, and the planets to a high degree of accuracy.

any physical theory is always provisional, in the sense that itis only a hypothesis: you can never prove it. no matter howmany times the results of experiments agree with some theory,you can never be sure that the next time the result will notcontradict the theory. on the other hand, you can disprove atheory by finding even a single observation that disagrees withthe predictions of the theory. as philosopher of science karlpopper has emphasized, a good theory is characterized by thefact that it makes a number of predictions that could inprinciple be disproved or falsified by observation. each timenew experiments are observed to agree with the predictions thetheory survives, and our confidence in it is increased; but ifever a new observation is found to disagree, we have toabandon or modify the theory.

at least that is what is supposed to happen, but you canalways question the competence of the person who carried outthe observation.

in practice, what often happens is that a new theory isdevised that is really an extension of the previous theory. forexample, very accurate observations of the planet mercuryrevealed a small difference between its motion and thepredictions of newton’s theory of gravity. einstein’s generaltheory of relativity predicted a slightly different motion fromnewton’s theory. the fact that einstein’s predictions matchedwhat was seen, while newton’s did not, was one of the crucialconfirmations of the new theory. however, we still usenewton’s theory for all practical purposes because the differencebetween its predictions and those of general relativity is verysmall in the situations that we normally deal with. (newton’stheory also has the great advantage that it is much simpler towork with than einstein’s!)the eventual goal of science is to provide a single theorythat describes the whole universe. however, the approach mostscientists actually follow is to separate the problem into twoparts. first, there are the laws that tell us how the universechanges with time. (if we know what the universe is like atany one time, these physical laws tell us how it will look at anylater time.) second, there is the question of the initial state ofthe universe. some people feel that science should beconcerned with only the first part; they regard the question ofthe initial situation as a matter for metaphysics or religion. theywould say that god, being omnipotent, could have started theuniverse off any way he wanted. that may be so, but in thatcase he also could have made it develop in a completelyarbitrary way. yet it appears that he chose to make it evolvein a very regular way according to certain laws. it thereforeseems equally reasonable to suppose that there are also lawsgoverning the initial state.

it turns out to be very difficult to devise a theory todescribe the universe all in one go. instead, we break theproblem up into bits and invent a number of partial theories.

each of these partial theories describes and predicts a certainlimited class of observations, neglecting the effects of otherquantities, or representing them by simple sets of numbers. itmay be that this approach is completely wrong. if every-thingin the universe depends on everything else in a fundamentalway, it might be impossible to get close to a full solution byinvestigating parts of the problem in isolation. nevertheless, it iscertainly the way that we have made progress in the past. theclassic example again is the newtonian theory of gravity, whichtells us that the gravitational force between two bodies dependsonly on one number associated with each body, its mass, butis otherwise independent of what the bodies are made of. thusone does not need to have a theory of the structure andconstitution of the sun and the planets in order to calculatetheir orbits.

today scientists describe the universe in terms of two basicpartial theories - the general theory of relativity and quantummechanics. they are the great intellectual achievements of thefirst half of this century. the general theory of relativitydescribes the force of gravity and the large-scale structure ofthe universe, that is, the structure on scales from only a fewmiles to as large as a million million million million (1 withtwenty-four zeros after it) miles, the size of the observableuniverse. quantum mechanics, on the other hand, deals withphenomena on extremely small scales, such as a millionth of amillionth of an inch. unfortunately, however, these two theoriesare known to be inconsistent with each other - they cannotboth be correct. one of the major endeavors in physics today,and the major theme of this book, is the search for a newtheory that will incorporate them both - a quantum theory ofgravity. we do not yet have such a theory, and we may stillbe a long way from having one, but we do already knowmany of the properties that it must have. and we shall see, inlater chapters, that we already know a fair amount about thepredications a quantum theory of gravity must make.

now, if you believe that the universe is not arbitrary, but isgoverned by definite laws, you ultimately have to combine thepartial theories into a complete unified theory that will describeeverything in the universe. but there is a fundamental paradoxin the search for such a complete unified theory. the ideasabout scientific theories outlined above assume we are rationalbeings who are free to observe the universe as we want andto draw logical deductions from what we see.

in such a scheme it is reasonable to suppose that we mightprogress ever closer toward the laws that govern our universe.

yet if there really is a complete unified theory, it would alsopresumably determine our actions. and so the theory itselfwould determine the outcome of our search for it! and whyshould it determine that we come to the right conclusions fromthe evidence? might it not equally well determine that we drawthe wrong conclusion.? or no conclusion at all?

the only answer that i can give to this problem is based ondarwin’s principle of natural selection. the idea is that in anypopulation of self-reproducing organisms, there will be variationsin the genetic material and upbringing that different individualshave. these differences will mean that some individuals arebetter able than others to draw the right conclusions about theworld around them and to act accordingly. these individualswill be more likely to survive and reproduce and so theirpattern of behavior and thought will come to dominate. it hascertainly been true in the past that what we call intelligenceand scientific discovery have conveyed a survival advantage. itis not so clear that this is still the case: our scientificdiscoveries may well destroy us all, and even if they don’t, acomplete unified theory may not make much difference to ourchances of survival. however, provided the universe has evolvedin a regular way, we might expect that the reasoning abilitiesthat natural selection has given us would be valid also in oursearch for a complete unified theory, and so would not lead usto the wrong conclusions.

because the partial theories that we already have aresufficient to make accurate predictions in all but the mostextreme situations, the search for the ultimate theory of theuniverse seems difficult to justify on practical grounds. (it isworth noting, though, that similar arguments could have beenused against both relativity and quantum mechanics, and thesetheories have given us both nuclear energy and themicroelectronics revolution!) the discovery of a complete unifiedtheory, therefore, may not aid the survival of our species. itmay not even affect our life-style. but ever since the dawn ofcivilization, people have not been content to see events asunconnected and inexplicable. they have craved anunderstanding of the underlying order in the world. today westill yearn to know why we are here and where we camefrom. humanity’s deepest desire for knowledge is justificationenough for our continuing quest. and our goal is nothing lessthan a complete description of the universe we live in.