The Grand Design - Stephen Hawking, Leonard Mlodinow (2010)
Chapter 7. The Apparent Miracle
HE CHINESE TELL OF A TIME during the Hsia dynasty (ca. 2205—ca. 1782 BC) when our cosmic environment suddenly changed. Ten suns appeared in the sky. The people on earth suffered greatly from the heat, so the emperor ordered a famous archer to shoot down the extra suns. The archer was rewarded with a pill that had the power to make him immortal, but his wife stole it. For that offense she was banished to the moon.
The Chinese were right to think that a solar system with ten suns is not friendly to human life. Today we know that, while perhaps offering great tanning opportunities, any solar system with multiple suns would probably never allow life to develop. The reasons are not quite as simple as the searing heat imagined in the Chinese legend. In fact, a planet could experience a pleasant temperature while orbiting multiple stars, at least for a while. But uniform heating over long periods of time, a situation that seems necessary for life, would be unlikely. To understand why, let’s look at what happens in the simplest type of multiple-star system, one with two suns, which is called a binary system. About half of all stars in the sky are members of such systems. But even simple binary systems can maintain only certain kinds of stable orbits, of the type shown below. In each of these orbits there would likely be a time in which the planet would be either too hot or too cold to sustain life. The situation is even worse for clusters having many stars.
Our solar system has other “lucky” properties without which sophisticated life-forms might never have evolved. For example, Newton’s laws allow for planetary orbits to be either circles or ellipses (ellipses are squashed circles, wider along one axis and narrower along another). The degree to which an ellipse is squashed is described by what is called its eccentricity, a number between zero and one. An eccentricity near zero means the figure resembles a circle, whereas an eccentricity near one means it is very flattened. Kepler was upset by the idea that planets don’t move in perfect circles, but the earth’s orbit has an eccentricity of only about 2 percent, which means it is nearly circular. As it turns out, that is a stroke of very good fortune.
Seasonal weather patterns on earth are determined mainly by the tilt of the earth’s axis of rotation relative to the plane of its orbit around the sun. During winter in the Northern Hemisphere, for example, the North Pole is tilted away from the sun. The fact that the earth is closest to the sun at that time—only 91.5 million miles away, as opposed to around 94.5 million miles away from the sun in early July—has a negligible effect on the temperature compared with the effect of its tilt. But on planets with a large orbital eccentricity, the varying distance from the sun plays a much larger role. On Mercury, for example, with a 20 percent eccentricity, the temperature is over 200 degrees Fahrenheit warmer at the planet’s closest approach to the sun (perihelion) than when it is at its farthest from the sun (aphelion). In fact, if the eccentricity of the earth’s orbit were near one, our oceans would boil when we reached our nearest point to the sun, and freeze over when we reached our farthest, making neither winter nor summer vacations very pleasant. Large orbital eccentricities are not conducive to life, so we are fortunate to have a planet for which orbital eccentricity is near zero.
We are also lucky in the relationship of our sun’s mass to our distance from it. That is because a star’s mass determines the amount of energy it gives off. The largest stars have a mass about a hundred times that of our sun, while the smallest are about a hundred times less massive. And yet, assuming the earth-sun distance as a given, if our sun were just 20 percent less or more massive, the earth would be colder than present-day Mars or hotter than present-day Venus.
Traditionally, given any star, scientists define the habitable zone as the narrow region around the star in which temperatures are such that liquid water can exist. The habitable zone is sometimes called the “Goldilocks zone,” because the requirement that liquid water exist means that, like Goldilocks, the development of intelligent life requires that planetary temperatures be “just right.” The habitable zone in our solar system, pictured above, is tiny. Fortunately for those of us who are intelligent life-forms, the earth fell within it!
Newton believed that our strangely habitable solar system did not “arise out of chaos by the mere laws of nature.” Instead, he maintained, the order in the universe was “created by God at first and conserved by him to this Day in the same state and condition.” It is easy to understand why one might think that. The many improbable occurrences that conspired to enable our existence, and our world’s human-friendly design, would indeed be puzzling if ours were the only solar system in the universe. But in 1992 came the first confirmed observation of a planet orbiting a star other than our sun. We now know of hundreds of such planets, and few doubt that there exist countless others among the many billions of stars in our universe. That makes the coincidences of our planetary conditions—the single sun, the lucky combination of earth-sun distance and solar mass—far less remarkable, and far less compelling as evidence that the earth was carefully designed just to please us human beings. Planets of all sorts exist. Some—or at least one—support life. Obviously, when the beings on a planet that supports life examine the world around them, they are bound to find that their environment satisfies the conditions they require to exist.
It is possible to turn that last statement into a scientific principle: Our very existence imposes rules determining from where and at what time it is possible for us to observe the universe. That is, the fact of our being restricts the characteristics of the kind of environment in which we find ourselves. That principle is called the weak anthropic principle. (We’ll see shortly why the adjective “weak” is attached.) A better term than “anthropic principle” would have been “selection principle,” because the principle refers to how our own knowledge of our existence imposes rules that select, out of all the possible environments, only those environments with the characteristics that allow life.
Though it may sound like philosophy, the weak anthropic principle can be used to make scientific predictions. For example, how old is the universe? As we’ll soon see, for us to exist the universe must contain elements such as carbon, which are produced by cooking lighter elements inside stars. The carbon must then be scattered through space in a supernova explosion, and eventually condense as part of a planet in a new-generation solar system. In 1961 physicist Robert Dicke argued that the process takes about 10 billion years, so our being here means that the universe must be at least that old. On the other hand, the universe cannot be much older than 10 billion years, since in the far future all the fuel for stars will have been used up, and we require hot stars for our sustenance. Hence the universe must be about 10 billion years old. That is not an extremely precise prediction, but it is true—according to current data the big bang occurred about 13.7 billion years ago.
As was the case with the age of the universe, anthropic predictions usually produce a range of values for a given physical parameter rather than pinpointing it precisely. That’s because our existence, while it might not require a particular value of some physical parameter, often is dependent on such parameters not varying too far from where we actually find them. We furthermore expect that the actual conditions in our world are typical within the anthropically allowed range. For example, if only modest orbital eccentricities, say between zero and 0.5, will allow life, then an eccentricity of 0.1 should not surprise us because among all the planets in the universe, a fair percentage probably have orbits with eccentricities that small. But if it turned out that the earth moved in a near-perfect circle, with eccentricity, say, of 0.00000000001, that would make the earth a very special planet indeed, and motivate us to try to explain why we find ourselves living in such an anomalous home. That idea is sometimes called the principle of mediocrity.
The lucky coincidences pertaining to the shape of planetary orbits, the mass of the sun, and so on are called environmental because they arise from the serendipity of our surroundings and not from a fluke in the fundamental laws of nature. The age of the universe is also an environmental factor, since there are an earlier and a later time in the history of the universe, but we must live in this era because it is the only era conducive to life. Environmental coincidences are easy to understand because ours is only one cosmic habitat among many that exist in the universe, and we obviously must exist in a habitat that supports life.
The weak anthropic principle is not very controversial. But there is a stronger form that we will argue for here, although it is regarded with disdain among some physicists. The strong anthropic principle suggests that the fact that we exist imposes constraints not just on our environment but on the possible form and content of the laws of nature themselves. The idea arose because it is not only the peculiar characteristics of our solar system that seem oddly conducive to the development of human life but also the characteristics of our entire universe, and that is much more difficult to explain.
The tale of how the primordial universe of hydrogen, helium, and a bit of lithium evolved to a universe harboring at least one world with intelligent life like us is a tale of many chapters. As we mentioned earlier, the forces of nature had to be such that heavier elements—especially carbon—could be produced from the primordial elements, and remain stable for at least billions of years. Those heavy elements were formed in the furnaces we call stars, so the forces first had to allow stars and galaxies to form. Those grew from the seeds of tiny inhomogeneities in the early universe, which was almost completely uniform but thankfully contained density variations of about 1 part in 100,000. However, the existence of stars, and the existence inside those stars of the elements we are made of, is not enough. The dynamics of the stars had to be such that some would eventually explode, and, moreover, explode precisely in a way that could disburse the heavier elements through space. In addition, the laws of nature had to dictate that those remnants could recondense into a new generation of stars, these surrounded by planets incorporating the newly formed heavy elements. Just as certain events on early earth had to occur in order to allow us to develop, so too was each link of this chain necessary for our existence. But in the case of the events resulting in the evolution of the universe, such developments were governed by the balance of the fundamental forces of nature, and it is those whose interplay had to be just right in order for us to exist.
One of the first to recognize that this might involve a good measure of serendipity was Fred Hoyle, in the 1950s. Hoyle believed that all chemical elements had originally been formed from hydrogen, which he felt was the true primordial substance. Hydrogen has the simplest atomic nucleus, consisting of just one proton, either alone or in combination with one or two neutrons. (Different forms of hydrogen, or any nucleus, having the same number of protons but different numbers of neutrons are called isotopes.) Today we know that helium and lithium, atoms whose nuclei contain two and three protons, were also primordially synthesized, in much smaller amounts, when the universe was about 200 seconds old. Life, on the other hand, depends on more complex elements. Carbon is the most important of these, the basis for all organic chemistry.
Though one might imagine “living” organisms such as intelligent computers produced from other elements, such as silicon, it is doubtful that life could have spontaneously evolved in the absence of carbon. The reasons for that are technical but have to do with the unique manner in which carbon bonds with other elements. Carbon dioxide, for example, is gaseous at room temperature, and biologically very useful. Since silicon is the element directly below carbon on the periodic table, it has similar chemical properties. However, silicon dioxide, quartz, is far more useful in a rock collection than in an organism’s lungs. Still, perhaps life-forms could evolve that feast on silicon and rhythmically twirl their tails in pools of liquid ammonia. Even that type of exotic life could not evolve from just the primordial elements, for those elements can form only two stable compounds, lithium hydride, which is a colorless crystalline solid, and hydrogen gas, neither of them a compound likely to reproduce or even to fall in love. Also, the fact remains that we are a carbon life-form, and that raises the issue of how carbon, whose nucleus contains six protons, and the other heavy elements in our bodies were created.
The first step occurs when older stars start to accumulate helium, which is produced when two hydrogen nuclei collide and fuse with each other. This fusion is how stars create the energy that warms us. Two helium atoms can in turn collide to form beryllium, an atom whose nucleus contains four protons. Once beryllium is formed, it could in principle fuse with a third helium nucleus to form carbon. But that doesn’t happen, because the isotope of beryllium that is formed decays almost immediately back into helium nuclei.
The situation changes when a star starts to run out of hydrogen. When that happens the star’s core collapses until its central temperature rises to about 100 million degrees Kelvin. Under those conditions, nuclei encounter each other so often that some beryllium nuclei collide with a helium nucleus before they have had a chance to decay. Beryllium can then fuse with helium to form an isotope of carbon that is stable. But that carbon is still a long way from forming ordered aggregates of chemical compounds of the type that can enjoy a glass of Bordeaux, juggle flaming bowling pins, or ask questions about the universe. For beings such as humans to exist, the carbon must be moved from inside the star to friendlier neighborhoods. That, as we’ve said, is accomplished when the star, at the end of its life cycle, explodes as a supernova, expelling carbon and other heavy elements that later condense into a planet.
This process of carbon creation is called the triple alpha process because “alpha particle” is another name for the nucleus of the isotope of helium involved, and because the process requires that three of them (eventually) fuse together. The usual physics predicts that the rate of carbon production via the triple alpha process ought to be quite small. Noting this, in 1952 Hoyle predicted that the sum of the energies of a beryllium nucleus and a helium nucleus must be almost exactly the energy of a certain quantum state of the isotope of carbon formed, a situation called a resonance, which greatly increases the rate of a nuclear reaction. At the time, no such energy level was known, but based on Hoyle’s suggestion, William Fowler at Caltech sought and found it, providing important support for Hoyle’s views on how complex nuclei were created.
Hoyle wrote, “I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars.” At the time no one knew enough nuclear physics to understand the magnitude of the serendipity that resulted in these exact physical laws. But in investigating the validity of the strong anthropic principle, in recent years physicists began asking themselves what the universe would have been like if the laws of nature were different. Today we can create computer models that tell us how the rate of the triple alpha reaction depends upon the strength of the fundamental forces of nature. Such calculations show that a change of as little as 0.5 percent in the strength of the strong nuclear force, or 4 percent in the electric force, would destroy either nearly all carbon or all oxygen in every star, and hence the possibility of life as we know it. Change those rules of our universe just a bit, and the conditions for our existence disappear!
By examining the model universes we generate when the theories of physics are altered in certain ways, one can study the effect of changes to physical law in a methodical manner. It turns out that it is not only the strengths of the strong nuclear force and the electromagnetic force that are made to order for our existence. Most of the fundamental constants in our theories appear fine-tuned in the sense that if they were altered by only modest amounts, the universe would be qualitatively different, and in many cases unsuitable for the development of life. For example, if the other nuclear force, the weak force, were much weaker, in the early universe all the hydrogen in the cosmos would have turned to helium, and hence there would be no normal stars; if it were much stronger, exploding supernovas would not eject their outer envelopes, and hence would fail to seed interstellar space with the heavy elements planets require to foster life. If protons were 0.2 percent heavier, they would decay into neutrons, destabilizing atoms. If the sum of the masses of the types of quark that make up a proton were changed by as little as 10 percent, there would be far fewer of the stable atomic nuclei of which we are made; in fact, the summed quark masses seem roughly optimized for the existence of the largest number of stable nuclei.
If one assumes that a few hundred million years in stable orbit are necessary for planetary life to evolve, the number of space dimensions is also fixed by our existence. That is because, according to the laws of gravity, it is only in three dimensions that stable elliptical orbits are possible. Circular orbits are possible in other dimensions, but those, as Newton feared, are unstable. In any but three dimensions even a small disturbance, such as that produced by the pull of the other planets, would send a planet off its circular orbit and cause it to spiral either into or away from the sun, so we would either burn up or freeze. Also, in more than three dimensions the gravitational force between two bodies would decrease more rapidly than it does in three dimensions. In three dimensions the gravitational force drops to ¼ of its value if one doubles the distance. In four dimensions it would drop to ⅛, in five dimensions it would drop to and so on. As a result, in more than three dimensions the sun would not be able to exist in a stable state with its internal pressure balancing the pull of gravity. It would either fall apart or collapse to form a black hole, either of which could ruin your day. On the atomic scale, the electrical forces would behave in the same way as gravitational forces. That means the electrons in atoms would either escape or spiral into the nucleus. In neither case would atoms as we know them be possible.
The emergence of the complex structures capable of supporting intelligent observers seems to be very fragile. The laws of nature form a system that is extremely fine-tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it. Were it not for a series of startling coincidences in the precise details of physical law, it seems, humans and similar life-forms would never have come into being.
The most impressive fine-tuning coincidence involves the so-called cosmological constant in Einstein’s equations of general relativity. As we’ve said, in 1915, when he formulated the theory, Einstein believed that the universe was static, that is, neither expanding nor contracting. Since all matter attracts other matter, he introduced into his theory a new antigravity force to combat the tendency of the universe to collapse onto itself. This force, unlike other forces, did not come from any particular source but was built into the very fabric of space-time. The cosmological constant describes the strength of that force.
When it was discovered that the universe was not static, Einstein eliminated the cosmological constant from his theory and called including it the greatest blunder of his life. But in 1998 observations of very distant supernovas revealed that the universe is expanding at an accelerating rate, an effect that is not possible without some kind of repulsive force acting throughout space. The cosmological constant was resurrected. Since we now know that its value is not zero, the question remains, why does it have the value that it does? Physicists have created arguments explaining how it might arise due to quantum mechanical effects, but the value they calculate is about 120 orders of magnitude (a 1 followed by 120 zeroes) stronger than the actual value, obtained through the supernova observations. That means that either the reasoning employed in the calculation was wrong or else some other effect exists that miraculously cancels all but an unimaginably tiny fraction of the number calculated. The one thing that is certain is that if the value of the cosmological constant were much larger than it is, our universe would have blown itself apart before galaxies could form and—once again—life as we know it would be impossible.
What can we make of these coincidences? Luck in the precise form and nature of fundamental physical law is a different kind of luck from the luck we find in environmental factors. It cannot be so easily explained, and has far deeper physical and philosophical implications. Our universe and its laws appear to have a design that both is tailor-made to support us and, if we are to exist, leaves little room for alteration. That is not easily explained, and raises the natural question of why it is that way.
Many people would like us to use these coincidences as evidence of the work of God. The idea that the universe was designed to accommodate mankind appears in theologies and mythologies dating from thousands of years ago right up to the present. In the Mayan Popol Vuh mythohistorical narratives the gods proclaim, “We shall receive neither glory nor honor from all that we have created and formed until human beings exist, endowed with sentience.” A typical Egyptian text dated 2000 BC states, “Men, the cattle of God, have been well provided for. He [the sun god] made the sky and earth for their benefit.” In China the Taoist philosopher Lieh Yü-K’ou (c. 400 BC) expressed the idea through a character in a tale who says, “Heaven makes the five kinds of grain to grow, and brings forth the finny and the feathered tribes, especially for our benefit.”
In Western culture the Old Testament contains the idea of providential design in its story of creation, but the traditional Christian viewpoint was also greatly influenced by Aristotle, who believed “in an intelligent natural world that functions according to some deliberate design.” The medieval Christian theologian Thomas Aquinas employed Aristotle’s ideas about the order in nature to argue for the existence of God. In the eighteenth century another Christian theologian went so far as to say that rabbits have white tails in order that it be easy for us to shoot them. A more modern illustration of the Christian view was given a few years ago when Cardinal Christoph Schönborn, archbishop of Vienna, wrote, “Now, at the beginning of the 21st century, faced with scientific claims like neo-Darwinism and the multiverse [many universes] hypothesis in cosmology invented to avoid the overwhelming evidence for purpose and design found in modern science, the Catholic Church will again defend human nature by proclaiming that the immanent design in nature is real.” In cosmology the overwhelming evidence for purpose and design to which the cardinal was referring is the fine-tuning of physical law we described above.
The turning point in the scientific rejection of a human-centered universe was the Copernican model of the solar system, in which the earth no longer held a central position. Ironically, Copernicus’s own worldview was anthropomorphic, even to the extent that he comforts us by pointing out that, despite his heliocentric model, the earth is almost at the universe’s center: “Although [the earth] is not at the center of the world, nevertheless the distance [to that center] is as nothing in particular when compared to that of the fixed stars.” With the invention of the telescope, observations in the seventeenth century, such as the fact that ours is not the only planet orbited by a moon, lent weight to the principle that we hold no privileged position in the universe. In the ensuing centuries the more we discovered about the universe, the more it seemed ours was probably just a garden-variety planet. But the discovery relatively recently of the extreme fine-tuning of so many of the laws of nature could lead at least some of us some back to the old idea that this grand design is the work of some grand designer. In the United States, because the Constitution prohibits the teaching of religion in schools, that type of idea is called intelligent design, with the unstated but implied understanding that the designer is God.
That is not the answer of modern science. We saw in Chapter 5 that our universe seems to be one of many, each with different laws. That multiverse idea is not a notion invented to account for the miracle of fine-tuning. It is a consequence of the no-boundary condition as well as many other theories of modern cosmology. But if it is true, then the strong anthropic principle can be considered effectively equivalent to the weak one, putting the fine-tunings of physical law on the same footing as the environmental factors, for it means that our cosmic habitat—now the entire observable universe—is only one of many, just as our solar system is one of many. That means that in the same way that the environmental coincidences of our solar system were rendered unremarkable by the realization that billions of such systems exist, the fine-tunings in the laws of nature can be explained by the existence of multiple universes. Many people through the ages have attributed to God the beauty and complexity of nature that in their time seemed to have no scientific explanation. But just as Darwin and Wallace explained how the apparently miraculous design of living forms could appear without intervention by a supreme being, the multiverse concept can explain the fine-tuning of physical law without the need for a benevolent creator who made the universe for our benefit.
Einstein once posed to his assistant Ernst Straus the question “Did God have any choice when he created the universe?” In the late sixteenth century Kepler was convinced that God had created the universe according to some perfect mathematical principle. Newton showed that the same laws that apply in the heavens apply on earth, and developed mathematical equations to express those laws that were so elegant they inspired almost religious fervor among many eighteenth-century scientists, who seemed intent on using them to show that God was a mathematician.
Ever since Newton, and especially since Einstein, the goal of physics has been to find simple mathematical principles of the kind Kepler envisioned, and with them to create a unified theory of everything that would account for every detail of the matter and forces we observe in nature. In the late nineteenth and early twentieth century Maxwell and Einstein united the theories of electricity, magnetism, and light. In the 1970s the standard model was created, a single theory of the strong and weak nuclear forces, and the electromagnetic force. String theory and M-theory then came into being in an attempt to include the remaining force, gravity. The goal was to find not just a single theory that explains all the forces but also one that explains the fundamental numbers we have been talking about, such as the strength of the forces and the masses and charges of the elementary particles. As Einstein put it, the hope was to be able to say that “nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).” A unique theory would be unlikely to have the fine-tuning that allows us to exist. But if in light of recent advances we interpret Einstein’s dream to be that of a unique theory that explains this and other universes, with their whole spectrum of different laws, then M-theory could be that theory. But is M-theory unique, or demanded by any simple logical principle? Can we answer the question, why M-theory?