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Just Six Numbers


Our Cosmic Habitat

Martin Rees (1999 and 2001)


On the blurred boundaries of ancient maps, cartographers wrote "There be dragons." After the pioneer navigators had encircled the globe and delineated the main continents and oceans, later explorers filled in the details. But there was no longer any hope of finding a new continent, or any expectation that the Earth's size and shape would ever be drastically reappraised.
At the end of the twentieth century we have, remarkably, reached the same stage in mapping our universe: the grand outlines are now coming into focus. This is the collective achievement of thousands of astronomers, physicists and engineers, using many different techniques. (ix)

Our emergence and survival depend on very special "tuning" of the cosmos—a cosmos that may be even vaster than the universe that we can actually see. (x)

We are each made up of between 1028 and 1029 atoms. This "human scale" is, in a numerical sense, poised midway between the masses of atoms and stars. It would take roughly as many human bodies to make up the mass of the Sun as there are atoms in each of us. But our Sun is just an ordinary star in the galaxy that contains a hundred billion stars altogether. There are at least as many galaxies in our observable universe as there are stars in a galaxy. More than 1078 atoms lie within the range of our telescope.
Living organisms are configured into layer upon layer of complex structure. Atoms are assembled into complex molecules; these react, via complex pathways in every cell, and indirectly lead to the entire interconnected structure that makes up a tree, an insect or a human. We straddle the cosmos and the microworld—intermediate in size between the Sun, at a billion metres in diameter, and a molecule at a billionth of a metre. It is actually no coincidence that nature attains its maximum complexity on this intermediate scale: anything larger, if it were on a habitable planet, would be vulnerable to breakage or crushing by gravity. (6-7)

The empirical support for a Big Bang ten to fifteen billion years ago is as compelling as the evidence that geologists offer on our Earth's history. This is an astonishing turnaround: our ancestors could weave theories almost unencumbered by facts, and until quite recently cosmology seemed little more than speculative mathematics. (10)

The amazing and fascinating complexity of biological evolution, and the variety of life on Earth, makes us realize that everything in the inanimate world is, in comparison, very simple. And this simplicity—or, at least, relative simplicity—is a feature of the objects that astronomers study. Things are hard to understand because they are complex, not because they are big. The challenge of fully elucidating how atoms assembled themselves—here on Earth, and perhaps on other worlds—into living beings intrictate enough to ponder their origins is more daunting than anything in cosmology. For just that reason, I don't think it's presumptuous to aspire to understand our large-scale universe.
The concept of a "plurality of inhabited worlds" is still the province of speculative thinkers, as it has been through the ages. The year 2000 marks the fourth centenary of the death of Giordano Bruno, burnt at the stake in Rome. He believed that:
In space there are countless constellations, suns and planets; we see only the suns because they give light; the planets remain invisible, for they are small and dark. There are also numberless earths circling around their suns, no worse and no less than this globe of ours. For no reasonable mind can assume that heavenly bodies that may be far more magnificent than ours would not bear upon them creatures similar or even superior to those upon our human earth. (19)

Any remote beings who could communicate with us would have some concepts of mathematics and logic that paralleled our own. And they would also share a knowledge of the basic particles and forces that govern our universe. Their habitat may be very different (and the biosphere even more different) from ours here on Earth; but they, and their planet, would be made of atoms just like those on Earth. For them, as for us, the most important particles would be protons and electrons: one electron orbiting a proton makes a hydrogen atom, and electric currents and radio transmitters involve streams of electrons. A proton is 1,836 times heavier than an electron, and the number 1,836 would have the same connotations to any 'intelligence' able and motivated to transmit radio signals. All the basic forces and natural laws would be the same. Indeed, this uniformity - without which our universe would be a far more baffling place - seems to extend to the remotest galaxies that astronomers can study. (Later chapters in this book will, however, speculate about other 'universes', forever beyond range of our telescopes, where different laws may prevail.) (21)

Why are carbon and oxygen so common here on Earth, but gold and uranium so rare? The answer involves stars that exploded before our Sun formed. The Earth, and we ourselves, are the ashes from those ancient stars. Our galaxy is an ecosystem, recycling atoms again and again through generations of stars. (46)

The often-used analogy with an explosion is misleading inasmuch as it conveys the image that the Big Bang was triggered at some particular centre. But as far as we can tell, any observer—whether on Earth, on Andromeda, or even on the galaxies remotest from us—would see the same pattern of expansion. The universe may once have been squeezed to a single point, but everyone had an equal claim to have started from that point; we can't identify the origin of the expansion with any particular location in our present universe. (67)

The name "Big Bang" was introduced in the 1950s by the celebrated Cambridge theorist Fred Hoyle . . . as a derisive description of a theory he didn't like. Hoyle himself favoured a "steady state" universe, in which new atoms and new galaxies were imagined to form continuously in the gaps as the universe expanded, so that its average properties never changed. There was at that time no evidence either way—cosmology was the province of armchair speculators—because observations didn't probe far enough for the evolution (if it existed) to show up. But the steady-state theory fell from favour as soon as evidence emerged that the universe was actually different in the past. (68)

Helium is the only element that, according to calculations, would be created prolifically in a Big Bang. This is gratifying because it explains why there is so much helium and why the helium is so uniform in its abundance. Attributing helium to the Big Bang thus solved a long-standing problem, and emboldened cosmologists to take the first few seconds of cosmic history seriously. (69)

In about five billion years the Sun will die; and the Earth with it. At about the same time (give or take a billion years) the Andromeda galaxy, our nearest big galactic neighbour, which belongs to the same cluster as our galaxy and which is actually falling towards us, will crash into the Milky Way. (71)

So all the atoms in the universe could result from a tiny bias in favour of matter over antimatter. We, and the visible universe around us, may exist only because of a difference in the ninth decimal place between the numbers of quarks and of antiquarks. (85)

The Big Bang theory has lived dangerously for more than thirty years. Various measurements could have refuted it if they had turned out differently. Here are five of them:
• Astronomers might have discovered an object whose helium abundance was zero, or at any rate well below 23 per cent ot that of hydrogen. This would have been fatal, because fusion of hydrogen in stars can readily boost helium above its pre-galactic abundance but there is no way of converting all the helium back to hydrogen.
• The background radiation measured so accurately by COBE might have turned out to have a spectrum that differed from the expected "black body" or thermal form.
• Physicists might have discovered something about neutrinos that was incompatible with the Big Bang. In the "fireball", neutrinos would outnumber the atoms by a huge factor - around a billion - just as the photons do. If each neutrino weighed even a millionth as much as an atom, they would, in total, contribute too much mass to the present universe - more, even than could be hidden in dark matter.
• The deuterium abundance could have been out of line with the amount expected to survive from the Big Bang.
• The temperature fluctuations over the sky could have implied a value of Q that was incompatible with what is inferred from the present-day structure in the universe, rather than being consistent with the value of 1/100,000.
The Big Bang theory has survived these tests. (117)

In the somewhat harsh view of his most distinguished biographer, the physicist Abraham Pais, Einstein "might as well have gone fishing" for the last thirty years of his life. (121)

In the 1950s, cosmology was outside the mainstream of physics—only a few "eccentrics" like George Gamow paid any attention to it. In contrast, cosmological issues now engage the interest of many leading mainstream theoretical physicists. (127)

It may seem counterintuitive that an entire universe ten billion light-years across (and which probably spreads even further beyond our horizon) can have emerged from an infinitesimal speck. What makes this possible is that, however much inflation has occurred, the universe's net energy can still be zero. (130)

We've realized ever since Einstein that empty space can have a structure such that it can be warped and distorted. Even if shrunk to a "point", it is latent with particles and forces—still a far richer construct than the philosopher's "nothing". (131)

The leap in scale from the microworld to our horizon is as nothing compared with the leap beyond that to the real limit of our universe. Though not infinite, our domain of space and time extends far beyond what we can see. The time before light reaches us from the "edge" is then a number of years written not just within ten zeros, nor even with a hundred, but with millions.
But this isn't all. Even this colossal universe, whose extent requires a million-digit number to express it, may not be "everything there is". It is the outcome of one episode of inflation; but that episode—that Big Bang—may itself just be one event in an infinite ensemble. Indeed, this ia a natural consequence of the "eternal inflation" espoused especially by the Russian cosmologist Andrei Linde. (132) [I have had salvia divinorum trips that felt exactly like experiencing an infinite succession of universes.]

In the present era Edward Witten, the currently acknowledged intellectual leader of mathematical physics, has said that "good wrong ideas are extremely scarce, and good wrong ideas that even remotely rival the majesty of string theory have never been seen." (145)

There are various ways of reacting to the apparent fine tuning of our six numbers. One hard-headed response is that we couldn't exist if these numbers weren't adjusted in the appropriate 'special' way: we manifestly are here, so there's nothing to be surprised about. Many scientists take this line, but it certainly leaves me unsatisfied. I'm impressed by a metaphor given by the Canadian philosopher John Leslie. Suppose you are facing a firing squad. Fifty marksman take aim, but they all miss. If they hadn't all missed, you would not have survived to ponder the matter. But you wouldn't just leave it at that-you'd still be baffled, and would seek some further reason for your good fortune.

Others adduce the 'tuning' of the numbers as evidence for a beneficent Creator, who formed the universe with the specific intention of producing us (or, less anthropocentrically, of permitting intricate complexities to unfold). This is in the tradition of William Paley and other advocates of the so-called 'argument from design' for God's existence. Variants of it are now espoused by eminent scientist-theologians such as John Polkinghorn; he writes that the universe is 'not just "any old world," but it's special and finely tuned for life because it is the creation of a Creator who wills that it be so'.

If one doesn't accept the 'providence' argument, there is another perspective, which—though still conjectural—I find compellingly attractive. It is that our Big Bang may not have been the only one. Separate universes may have cooled down differently, ending up governed by different laws and defined by different numbers. This may not seem an "economical" hypothesis—indeed, nothing might seem more extravagant than invoking multiple universes—but it is a natural deduction from some (albeit speculative) theories, and opens up a new vision of our universe as just one "atom" selected from an infinite multiverse. (148-9)

These studies of "eternal inflation" . . . already show us that some sets of assumptions, consistent with everything else we know, yield many universes that sprout from separate Big Bangs into disjoint regions of space-time. These universes would never be directly observable, even in principle; we couldn't even meaningfully say whether they existed "before," "after" or "alongside" our own. However, if the input theory that predicted multiple universes could be "battle-tested" by convincingly explaining things we could observe, then we should take the other (unobservable) universes seriously, just as we give credence to what our current theories predict about quarks inside atoms, or the regions shrouded inside black holes. (151-2)
[An interestingly opposite approached compared to some who would have us trust propositions by faith, regarding things that cannot be seen, when propositions from the same source(s) that are verifiable turn out to be false.]

If there are indeed many universes, the next question that arises is: How much variety do they display? The answer again depends on the character of the physical laws at a deeper and more unified level than we yet understand. Perhaps some "final theory" will give unique formulae for all of our six numbers. If it were to, then the other universes, even if they existed, would in essence be just replicas of ours, and the apparent "tuning" would be no less a mystery than if our single universe were the whole of reality. We'd still be perplexed that a set of numbers imprinted in the extreme conditions of the Big Bang happened to lie in the narrow range that allowed such interesting consequences ten billion years later.
But there's another possibility. The underlying laws that apply throughout the multiverse may turn out to be more permissive. Each universe may evolve in a distinctive way, being characterized by a different set of numbers from those that are so crucial moulding our own universe. We are used to explaining contingencies here on the Earth (why there is a particular mountain, for instance), and even features in sapce (the shape of a nebula, the pattern of the galaxies), as "accidents of history." We can't explain such things any more deeply, although we don't doubt that they are the outcome of some underlying laws. By extension, the strength of the forces and the masses of elementary particles (as well as Ω, Q and λ) could be secondary outcomes of the final theory (maybe a version of superstring theory) that governs the entire multiverse. (152)


The planets found so far, orbiting solar-type stars, are all roughly the size of Jupiter or Saturn. Bur there is every reason to suspect that these are the largest planets in other "solar systems" whose smaller planets are not yet detectable. (12)

We were all, when young, taught the layout of our own solar system—the sizes of the nine major planets and how they move in orbit around the Sun. But, twenty years from now we shall be able to tell our grandchildren far more interesting things on a starry night. Nearby stars will no longer just be points of light—we will think of them as the Suns of other solar systems. We will know the orbits of each star's retinue of planets, and the sizes (and even some topographic details) of the bigger ones. (13)

We cannot yet be sure what fraction of planetary systems would permit an Earthlike planet to survive undisturbed for billions of years in a near-circular orbit; but among the many millions of planetary systems (formed with one, two, or three high-mass planets), there would surely be some planets on Earthlike orbits, with temperatures such that water neither boils nor stays frozen. (13)

Astronomy has a longer history than any other science, except perhaps medicine. It was the first to involve precise measurement, and perhaps the first to do more good than harm. (56)

When we observe Andromeda, we may wonder if Andromedans are looking back at us, maybe with still bigger telescopes. Perhaps they are. But the remotest galaxies viewed in the Hubble Deep Field could not yet have evolved anything so advanced. We are viewing them at a very primitive stage, before there's been time for many stars to have completed their lives and for the stellar furnaces to have forged the atoms needed for complex chemistry. (63)

How did 13 billion years of evolution lead from such a simple recipe to our complex habitat where—here on Earth and perhaps on other worlds—atoms assemble into creatures able to ponder their origins? Maybe there are aliens in orbits around distant Suns who already know the answers. But for us, they are challenges for the new millenium. (64)

In 1990 John Mather and his colleagues used the Cosmic Background Explorer (COBE) satellite to make truly remarkable measurements with errors smaller than the thickness of the line on the graph (fig. 5.1). This confirms beyond any reasonable doubt that everything—all the stuff that galaxies are now made of—was once a compressed gas, hotter than the Sun's core. The expansion has cooled and diluted the radiation and stretched its wavelength. But this primordial heat—the afterglow of creation—is still around: it fills all of space and has nowhere else to go! Most of us see it every day, as it causes one percent of the interference on our television screens.
Penzias and Wilson were radio astronmers, with expertise in electronics rather than cosmology. Their success stemmed from persistence and technical skills. It wasn't surprising that it took others to convince them of what their discovery meant. In fact, Wilson has recalled that the full import of his achievement really sank in only when he read a report of it in the New York Times. Many of us, at a lower level, have similiar experiences. Any researcher has to focus on specific technical details, but the occupational risk is that, through a narrow focus on tractable bite-sized problems, one loses the broader perspective. That is why—in their own intersets—professional scientists should try to convey their work to non-specialists. Even if we do it badly, the effort is salutary: it reminds us that our efforts are worthwhile only insofar as they help to illuminate the big picture. (67-9)

The intellectual stakes are high. Dark matter is the No. 1 problem in astronomy today, and it ranks high as a physics problem, too. If we could solve it—and I'm optimistic that we will within the next decade—we would know what our universe is mostly made of, and we would discover, as a bonus, something quite new about the microworld of particles. (75)

Five billion years from now, when the Sun dies, the galaxies will be more widely dispersed and intrinsically somewhat fainter because their stellar population will have aged, and less gas will survive to form bright new stars. But what might happen still farther ahead? We can't predict what role life will eventually carve out for itself: it could become extinct, or it could achieve such dominance that it can influence the entire cosmos. The latter is the province of science fiction, but it can't be dismissed as absurd. After all, it has taken little more than one billion years for natural selection to lead from the first multicellular organisms to Earth's present biosphere, which includes us. By the time the Sun dies, five times longer will have elapsed—time enough for Earth's biosphere (and any others that exist) to be inconceivably transformed, even if future species emerged on the timescale of biological natural selection. Future changes would occur faster still if they are artificially directed—on a cultural or historical timescale. (113-14)

A more disconcerting prospect is that empty space could be vulnerable to a catastrophic transfiguration. Very pure water can "supercool" below its freezing point, but it will suddenly freeze when a speck of dust is put into it. In an analogous way, our present "vacuum" may be merely meta-stable and could then transform to a quite different universe, governed by different laws, perhaps with a large negative lambda that would cause everything to implode rather than accelerate outwards. (120)

Our remote descendants are likely to have an eternal future (unless they come within the clutches of a black hole). Nonetheless, it is worth noting that the alternative fate—being snuffed out in a Big Crunch—could be an enriching experience. We have seen that events happen ever more slowly in the ever-expanding universe; the total number of discrete events or "thoughts" could then be bounded, even in an infinite future. John Barrow and Frank Tipler have emphasized that, in a collapsing universe, the converse is possible: there can be an infinite number of "happenings" within a finite time. Cosmologists are used to the idea that a lot could happen in the initial instants after the Big Bang; as we extrapolate back to more extreme densities, time must be measured by a series of progressively smaller, more robust, and faster-ticking clocks. An infinite set of numbers can add up to a finite sum. Likewise, in the final instants before the crunch, we could not only see our entire earlier life flash by, but we could experience an infinite number of new events. (122)
[And salvia once again says hello.]

I would bet reasonable odds that by the year 2010 we will be very confident of what the dominant dark matter is, the value of Ω, and the properties of the dark energy in the vacuum. If that happens, it will signal a great triumph for cosmology: we will have taken the measure of our universe, just as, over the last few centuries, we have learned the size and shape of our Earth and Sun. And, subject to some provisos mentioned in the next chapter, we will know the long-range cosmic forecast. (135)

Unified theories now engage young scientists, not just established dignitaries who can afford to risk over-reaching themselves and achieving nothing. (151)

There are other conjectures that suggest a multiplicity of universes. For instance, whenever a black hole forms, processes deep inside it might trigger the creation of another universe into a space disjoint from our own. If that new universe were like ours, stars, galaxies, and black holes would form in it, and those black holes would in turn spawn another generation of universes, and so on, perhaps ad infinitum. Alternatively, if there were extra spatial dimensions that were not tightly rolled up, we may be living in one of many separate universes embedded in a higher-dimensional space.
All these theories are tentative and should be prefaced by something akin to a health warning. But they give us tantalizing glimpses of a dramatically enlarged cosmic perspective. The entire history of our universe could be just an episode, one facet, of the infinite multiverse. Were this indeed so, some features of our universe would be less surprising. Let me sketch why I think this is so.
The distinctive details of our universe, and of everything in it (ourselves included), seem to be the outcome of what might be called an accident. The size and shape of our home Galaxy are the outcome of quantum fluctuations imprinted when the universe was the size of a golf ball; so is the layout of galaxies in the Local Group around us. The gases that ended up in our Sun had been, for billions of years, churned up by the shearing motions in our rotating Galaxy and buffeted by supernova explosions. Our Earth (along with the other inner planets, Mercury, Venus and Mars) is an agglomeration of rocks and asteroids; the largest crash scooped out the material that made the Moon. . . . Obviously, we can never explain all the contingencies that led from a Big Bang to our own birth here 13 billion years later. The outcome depended crucially on a recipe encoded in the Big Bang, and this recipe seems to have been rather special. . . . A degree of fine-tuning—in the expansion speed, the material content of the universe, and the strengths of the basic forces—seems to have been a prerequisite for the emergence of the hospitable cosmic habitat in which we live. (158-9)

Guth and Edward Harrison have even conjectured that universes could be made in the laboratory by imploding a lump of material to make a small black hole. Is our entire universe perhaps the outcome of some experiment in another universe? (170)

None of these scenarios has been simply dreamed up out of the air: each has a serious, albeit speculative, theoretical motivation. However, one of them, at most, can be correct. Quite possibly none is: there are alternative theories that would lead to just one universe. (171)

There are three great frontiers in science: the very big, the very small and the very complex. Cosmology involves them all. First, cosmologists must pin down the basic numbers such as [OMEGA], and find what the dark matter is. I think there is a good chance of achieving this goal within ten years. Second, theorists must elucidate the exotic physics of the very earliest stages, which entails a new synthesis between cosmos and microworld. It would be presumptuous for me to place bets here. But cosmology is also the grandest environmental science, and its third aim is to understand how a Big Bang described by a simple recipe evolved, over 13 billion years, into our complex cosmic habitat.: the filamentary layout of galaxies through space, the galaxies themselves, the stars, planets, and the prerequisites for life's emergence. No mystery in cosmology presents a more daunting challenge than the task of fully elucidating how atoms assembled—here on Earth and perhaps on other worlds—into living beings intricate enough to ponder their origins. (180-1)

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