Victor J. Stenger

The Anthropic Coincidences:

A Natural Explanation


Published in TheSkeptical Intelligencer,  Vol. 3 Issue No. 3 July 1999.

 Recently the media has reported that scientists have discovered supernatural purpose to the universe. The so-called anthropic coincidences, in which the constants of nature seem to be extraordinarily fine-tuned for the production of life, are cited, in these reports, as evidence. However, no such interpretation can be found in scientific literature. Based on all we currently know about fundamental physics and cosmology, the most logically consistent and parsimonious picture of the universe as we know it is a natural one, with no sign of design or purposeful creation provided by scientific observations.
 
 

Poking Out of The Noise

At least two-and-a-half millennia have passed since a few thinkers, such as Thales and Heraclitus in ancient Greece, had the idea that the world around us might be understood wholly in terms of familiar substances and forces such as water and fire. They were the first to grasp the possibility that mysterious, undetectable agents need not be invoked in the explanation of phenomena. It was a revolutionary notion--and the world was far from ready to embrace it. At this stage, humanity still clutched the superstitions carried out of cave and forest. And so, with a few exceptions, naturalism lay largely dormant for two millennia while human cultures continued to be dominated by supernatural thinking.

In Christian Europe during the Middle Ages, the study of empirical phenomena did not necessarily exclude the supernatural. Indeed, most if not all of the scientists, or "natural philosophers," of the period were clerics or otherwise connected with the Church. Nevertheless, serious conflict between the fledgling science and religion broke out in the sixteenth century when the Church condemned Galileo for maintaining that Copernicus' proposition that the earth circled the sun represented a physical and not just mathematical description of the solar system. However, religion and science soon reconciled. Newton interpreted his great mechanical discoveries, which were based on the earlier work of Descartes, Galileo, and others, as uncovering God's design for the physical universe. The success of Newtonian science was rapid and dramatic. People began to speak of the need to read two books authored by God--Scripture and the Book of Nature.

Science offers natural explanations for phenomena previously attributed to supernatural agency. Static electricity, not Thor's spear, produces a lightning flash. Natural selection, not divine intervention, impels the development of life. The neural network of the brain, not some disembodied spirit, enables mental processes. Scientific explanations are frequently unpopular; witness Darwinism. It seems that they occupy a privileged place for the simple reason that they work so well, not because people find them appealing. Technological progress, fed by scientific discovery, testifies to the power of natural explanations for events. This has given science enormous stature and credibility. People listen to what science has to say, even if they do not always like what they hear, in particular, that they are not the center of the universe.

With the exception of the minority who insist on literal interpretation of scripture, religious scholars have largely deferred to science on those matters where the scientific consensus has spoken. Theologians are quite adept at reinterpreting the teachings of their faiths in the light of new knowledge. There is nothing wrong with this. Most scientists and theologians agree that both groups are in the business of learning, not preaching. Theologians argue, with some merit, that religion still has a role to play in moral matters and in the search to find the place of humanity in the scheme of things. Most scientists regard questions about the purpose of the universe to be beyond the scope of science. Nevertheless, when they read the press reports about science and religion converging, some religious believers take heart that, when everything is said and done, the purpose they desire will stick its head up out of the scientific background noise.
 
 

The Supposed Signal of Purpose

For about a decade now, an ever-increasing number of scientists and theologians have been asserting, in popular articles and books, that they can detect a signal of cosmic purpose poking its head out of the noisy data of physics and cosmology. This claim has been widely reported in the media (see, for example, Begley 1998, Easterbrook 1998), perhaps misleading lay people into thinking that some kind of new scientific consensus is developing in support of supernatural beliefs. In fact, none of this reported evidence can be found in the pages of scientific journals, which continue to successfully operate within an assumed framework in which all physical phenomena are natural.

The purported signal of cosmic purpose cannot be demonstrated from the data alone. Such observations require considerable interpretation to arrive at that conclusion. Those not very familiar with recent deliberations in the philosophy of science might be inclined to scoff and say that the observations speak for themselves, with no interpretation necessary. Facts are facts, they might argue, and neither God nor purpose are scientific facts.

However, scientists and philosophers of science have been unable to define a clear demarcation between observation and theory. Most now agree that all scientific observations are "theory-laden." That is, empirical results cannot be cleanly separated from the theoretical framework used to classify and interpret them. This new development in the philosophy of science has opened the door for theologians and believing scientists to reinterpret scientific data in terms of their preferred model of intelligent design and divine purpose to the universe. Some claim the data fit this model better than alternatives. Most say it is at least as good.

The data whose interpretation is being debated in the religion-science dialogue are not scraps of fading documents, nor the uncertain translations of ancient fables that over time have evolved into sacred texts. Rather, they consist of measurements made by sophisticated research teams using advanced scientific instruments. The new theistic argument is based on the fact that earthly life is so sensitive to the values of the fundamental physical constants and properties of its environment that even the tiniest changes to any of these would mean that life as we see it around us would not exist. This is said to reveal a universe in which the fundamental physical constants of nature are exquisitely fine-tuned and delicately balanced for the production of life. As the argument goes, the chance that any initially random set of constants would correspond to the set of values they happen to have in our universe is very small; thus this precise balancing act is exceedingly unlikely to be the result of mindless chance. Rather, an intelligent, purposeful, and indeed personal Creator probably made things the way they are. The argument is well captured by a cartoon mathematician Roger Penrose's book The Emperor's New Mind which shows a cartoon of the Creator pointing a finger toward an "absurdly tiny volume in the "phase space of possible universes" to produce the universe in which we live (Penrose 1989, 343).

Most who make the fine-tuning argument are content to say that intelligent, purposeful, supernatural design has become an equally viable alternative to a random, purposeless, natural evolution of the universe and humankind suggested by conventional science. However, a few theists have gone much farther to insist that God is now required by the data. Moreover, this God must be the God of the Christian Bible. No way, this group says, can the universe be the product of purely natural, impersonal processes. Typical of this view is The Creator and the Cosmos: How the Greatest Scientific Discoveries of the Century Reveal God, a book by physicist and astronomer Hugh Ross. Ross cannot imagine fine-tuning happening any other way than by a "personal Entity . . . at least a hundred trillion times more 'capable' than are we human beings with all our resources." He concludes that "the Entity who brought the universe into existence must be a Personal Being, for only a person can design with anywhere near this degree of precision" (Ross 1995, 118).

The delicate connections among certain physical constants, and between those constants and life, are collectively called the anthropic coincidences. Before examining the merits of the interpretation of these coincidences as evidence for intelligent design, I will review how the notion first came about. For a detailed history and a wide-ranging discussion of all the issues, see The Anthropic Cosmological Principle by John D. Barrow and Frank J. Tipler (Barrow 1986). I also refer the reader there for the original references. But be forewarned that this exhaustive tome has many errors, especially in equations, some of which remain uncorrected in later editions.
 
 

The Anthropic Coincidences

In 1919, Hermann Weyl expressed his puzzlement that the ratio of the electromagnetic force to the gravitational force between two electrons is such a huge number, N1 = 1039 (Weyl 1919). This means that the strength of the electromagnetic force is greater than the strength of the gravitational force by 39 orders of magnitude. Weyl wondered why this should be the case, expressing his intuition that "pure" numbers, like pi, that do not depend any system of units, occurring in the description of physical properties should most naturally occur within a few orders of magnitude of unity. Unity, or zero, you can expect "naturally." But why 1039? Why not 1057 or 10-123? Some principle must select out 1039.

In 1923, Arthur Eddington commented: "It is difficult to account for the occurrence of a pure number (of order greatly different from unity) in the scheme of things; but this difficulty would be removed if we could connect it to the number of particles in the world--a number presumably decided by accident (Eddington 1923, 167). He estimated that number, now called the "Eddington number," to be N =1079. Well, N is not too far from the square of N1. This was the first of the anthropic coincidences, that N approximately equals the square of N1.

These musings may bring to mind the measurements made on the Great Pyramid od Egypt in 1864 by Scotland's Astronomer-Royal, Piazzi Smyth. He found accurate estimates of pi and the distance from the earth to the sun, and other strange "coincidences" buried in his measurements (Smyth 1978). However, we now know that these were simply the result of Smyth's selective toying with the numbers (Steibing 1994, 108-110; De Jager, 1992). Still, even today some people believe that the pyramids hold secrets about the universe. Ideas like this never seem to die, no matter how deep in the sand they may be buried.

Look around at enough numbers and you are bound to find some that appear connected. Most physicists, therefore, did not regard the large numbers puzzle seriously until one of their most brilliant members, Paul Dirac, took an interest. Few physicists ignored anything Dirac had to say.

Dirac discovered that N1 is the same order of magnitude as another pure number N2 that gives the ratio of a typical stellar lifetime to the time for light to traverse the radius of a proton. That is, he found two seemingly unconnected large numbers to be of the same order of magnitude (Dirac 1937). If one number being large is unlikely, how much more unlikely is another to come along with about the same value?

In 1961, Robert Dicke pointed out that N2 is necessarily large in order that the lifetime of typical stars be sufficient to generate heavy chemical elements such as carbon. Furthermore, he showed that N1 must be of the same order of N2 in any universe with heavy elements (Dicke 1961).

The heavy elements did not get fabricated straightforwardly. According to the big bang theory (despite what you may hear, the consensus of cosmologists now regard the big bang as very well established), only hydrogen, deuterium ( the isotope of hydrogen consisting of one proton and one neutron), helium, and lithium were formed in the early universe. Carbon, nitrogen, oxygen, iron, and the other elements of the chemical periodic table were not produced until billions of years later. These billions of years were needed for stars to form assemble these heavier elements out of neutrons and protons. When the more massive stars expended their hydrogen fuel, they exploded as supernovae, spraying the manufactured elements into space. Once in space, these elements cooled and accumulated into planets.

 Billions of additional years were needed for our home star, the sun, to provide a stable output of energy so that at least one of its planets could develop life. But if the gravitational attraction between protons in stars had not been many orders of magnitude weaker than the electric repulsion, as represented by the very large value of N1, stars would have collapsed and burned out long before nuclear processes could build up the periodic table from the original hydrogen and deuterium. The formation of chemical complexity is only possible in a universe of great age--or at least in a universe with other parameters close to the values they have in this one.

Great age is not all. The element-synthesizing processes in stars depend sensitively on the properties and abundances of deuterium and helium produced in the early universe. Deuterium would not exist if the difference between the masses of a neutron and a proton were just slightly displaced from its actual value. The relative abundances of hydrogen and helium also depend strongly on this parameter. The relative abundances of hydrogen and helium also require a delicate balance of the relative strengths of gravity and the weak interaction, the interaction responsible for nuclear beta decay. A slightly stronger weak force and the universe would be 100 percent hydrogen. In that case, all the neutrons in the early universe will have decayed leaving none around to be saved in deuterium nuclei for later use in the element-building processes in stars. A slightly weaker weak force and few neutrons would have decayed, leaving about the same numbers of protons and neutrons. In that case, all the protons and neutrons would have been bound up in helium nuclei, with two protons and two neutrons in each. This would have lead to a universe that was 100 percent helium, with no hydrogen to fuel the fusion processes in stars. Neither of these extremes would have allowed for the existence of stars and life as we know it based on carbon chemistry.

The electron also enters into the tightrope act needed to produce the heavier elements. Because the mass of the electron is less than the neutron proton mass difference, a free neutron can decay into a proton, electron, and anti-neutrino. If this were not the case, the neutron would be stable and most of the protons and electrons in the early universe would have combined to form neutrons, leaving little hydrogen to act as the main component and fuel of stars. It is also essential that the neutron be heavier than the proton, but not so much heavier that neutrons cannot be bound in nuclei, where conservation of energy prevents the neutrons from decaying.

In 1952, astronomer Fred Hoyle used anthropic arguments to predict that an excited carbon nucleus has an excited energy level at around 7.7 MeV. I have already noted that a delicate balance of physical constants was necessary for carbon and other chemical elements beyond lithium in the periodic table to be cooked in stars. Hoyle looked closely at the nuclear mechanisms involved and found that they appeared to be inadequate.

 The basic mechanism for the manufacture of carbon is the fusion of three helium nuclei into a single carbon nucleus:

3He4 --> C12

 (The superscripts give the number of nucleons, i.e., protons and neutrons in each nucleus, which is indicated by its chemical symbol; the total number of nucleons is conserved, i.e., remains constant, in a nuclear reaction). However, the probability of three bodies coming together simultaneously is very low and some catalytic process in which only two bodies interact at a time must be assisting. An intermediate process had earlier been suggested in which two helium nuclei first fuse into a beryllium nucleus which then interacts with the third helium nucleus to give the desired carbon nucleus:

2He4- -> Be8

 He4+ Be8 --> C12

 Hoyle showed that this still was not sufficient unless the carbon nucleus had an excited state at 7.7 MeV to provide for a high reaction probability. A laboratory experiment was undertaken, and sure enough a previously unknown excited state of carbon was found at 7.66 MeV (Barrow 252).

Nothing can gain you more respect in science than the successful prediction of a new phenomenon. Here, Hoyle used standard nuclear theory. But his reasoning contained another element whose significance is still hotly debated. Without the 7.7 MeV nuclear state of carbon, our form of life based on carbon would not have existed. Yet nothing in fundamental nuclear theory, as it is still known today, directly determines the existence of this state. It cannot be deduced from the axioms of the theory.

 Like the other coincidences, this particular nuclear state seems hardly likely to be the result of chance. In 1974, Brandon Carter (Carter 1974) introduced the notion of the anthropic principle which hypothesized that the anthropic coincidences are not the result of chance but somehow built into the structure of the universe. Barrow and Tipler (21) have identified three different forms of the anthropic principle and refer to Carter's version as the "strong" anthropic principle, defined as follows:

Strong Anthropic Principle (SAP): The Universe must have those properties which allow life to develop within it at some stage in its history.

This suggests that the coincidences are not accidental but the result of a law of nature. But it is a strange law indeed, unlike any other in physics. It suggests that life exists as some Aristotelian "final cause."

Barrow and Tipler (22) claim that this can have three interpretations:

(A) There exists one possible Universe 'designed' with the goal of generating and sustaining 'observers."

This is the interpretation adopted by most theistic believers.

(B) Observers are necessary to bring the Universe into being.

This is traditional solipsism, but also is a part of today's New Age mysticism.

(C) An ensemble of other different universes is necessary for the existence of our Universe.

This speculation is part of contemporary cosmological thinking, as I will discuss below. It represents the idea that the coincidences are accidental. We just happen to live in the particular universe that was suited for us.

The current dialogue focusses on the choice between (A) and (C), with (B) not taken seriously in the scientific community. However, before discussing the relative merits of the three choices, let me complete the story on the various forms of the anthropic principle discussed by Barrow and Tipler. They identify two other versions:

Weak Anthropic Principle (WAP): The observed values of all physical and cosmological quantities are not equally probable but take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so.

The WAP has not impressed too many people. All it seems to say is that if the universe was not the way it is, we would not be here talking about it. If the fine structure constant were not 1/137, people would look different. If I did not live at 508 Pepeekeo Place, I would live someplace else.

Final Anthropic Principle (FAP): Intelligent, information-processing must come into evidence in the Universe, and, once it comes into existence, it will never die out.

This is sometimes also referred to as the Completely Ridiculous Anthropic Principle.

Predictions of the FAP

In The Anthropic Cosmological Principle, Barrow and Tipler speculated only briefly about the implications of the FAP. Tipler later propounded its consequences in a controversial book with the provocative title: The Physics of Immortality: Modern Cosmology, God and the Resurrection of the Dead. Here Tipler carries the implications of the FAP about as far as one can imagine they could go (Tipler 1994).

Tipler argues that the robots that will evolve from our current computer technology will ultimately spread themselves throughout the universe, each new generation of robot producing ever superior versions of itself. After the passage of a billion billion years or so, the universe will become uniformly populated with an extremely advanced life form. Humanity, of course, will be long gone.
At that point, Tipler assumes the universe will begin to contract toward what is called the "big crunch," the reverse of the big bang. The collapse of the universe does not happen in any old way, however. It is very carefully controlled in order to maintain causal contact across the universe and provide sufficient energy for what life must then accomplish in order to avoid extinction.

The advanced life form that has evolved from our twenty-first century robots should be able manage this, according to Tipler. Who can deny the possibility of anything a billion billion years in the future? The universe then converges on what the French Jesuit Pierre Teilhard de Chardin called the Omega Point. Tipler associates the Omega Point, as did Teilhard, with God.

Being the ultimate form of power and knowledge, the Omega Point would also be the ultimate in Love. Loving us, it would proceed to resurrect all humans who ever lived (along with their favorite pets and popular endangered species). This is accomplished by means of a perfect computer simulation, what Tipler calls an emulation.

Since each of us is defined by our DNA, the Omega Point simply emulates all possible humans that could ever live, which of course includes you and me in every variation. Our memories have long since dissolved into entropy, but Omega has us relive our lives in an instant, along with all the other possible lives we could have lived. Those that Omega-God deems deserving will get to live even better lives, including lots of sex with the most desirable partners we can imagine.

All this, Tipler claims, is a predictable consequence of the FAP. Fortunately, we do not have to wait a billion billion years to test the theory. One prediction is that the universe is "closed." That is, someday in the distant future it will stop expanding and begin contracting. This depends on the average density of matter and energy in the universe, a quantity which can be estimated from a wide range of observations that are improving every year.

When Tipler wrote his book, a closed universe was not supported by the data, but the uncertainties were still large enough that the possibility could not be strongly ruled out. Since then, observations have made it even more unlikely that the universe is closed. An open, "flat" universe that is poised just on the border between expansion and contraction is predicted by the inflationary big-bang theory. Right now, the FAP prediction of a closed universe does not look as if it will be fulfilled.

You might ask if an ever-expanding universe can be made consistent with the FAP. No doubt it can, but then it makes no testable predictions and so it becomes little more than speculation. Tipler's theory at least had the virtue of being falsifiable. It now seems to be heading for falsification.
 
 

Interpreting the Coincidences: (A) They Are Designed

Let us now review the first of the three possible explanations for the anthropic coincidences listed by Barrow and Tipler: (A) There exists one possible Universe 'designed' with the goal of generating and sustaining 'observers'."

Many theists see the anthropic coincidences as evidence for purposeful design to the universe. They ask: how can the universe possibly have obtained the unique set of physical constants it has, so exquisitely fine-tuned for life as they are, except by purposeful design--design with life and perhaps humanity in mind? (See, for example, Swinburne 1990, Ellis 1993, Ross 1995).

 Let us examine the implicit assumptions here. First and foremost, and fatal to the design argument all by itself, we have the wholly unwarranted assumption that only one type of life is possible--the particular form of carbon-based life we have here on earth.

Carbon would seem to be the chemical element best suited to act as the building block for the type of complex molecular systems that develop lifelike qualities. Even today, new materials assembled from carbon atoms exhibit remarkable, unexpected properties, from superconductivity to ferromagnetism. However, to assume that only carbon life is possible is simply "carbocentrism" that results from the fact that you and I are structured on carbon.

Given the known laws of physics and chemistry, we can easily imagine life based on silicon (computers, the Internet?) or other elements chemically similar to carbon. However, these still require cooking in stars and thus a universe old enough for star evolution. The N1 = N2 coincidence would still hold in this case, although the anthropic principle would have to be renamed the "cyberthropic" principle, or some such, with computer rather than humans and cockroaches the purpose of existence. Indeed, Tipler would probably agree with this.

Only hydrogen, helium, and lithium were synthesized in the early big bang. They are probably chemically too simple to be assembled into diverse structures. So, it seems that any life based on chemistry would require an old universe, with long-lived stars producing the needed materials.
Still, it seems like "chemicentrism" to rule out other forms of matter than molecules in the universe as building blocks of complex systems. While atomic nuclei, for example, do not exhibit the diversity and complexity seen in the way atoms assemble into molecular structures, perhaps they might be able to do so in a universe with different properties.

Sufficient complexity and long life may be the only ingredients needed for a universe to have some form of life. Those who argue that life is highly improbable need to open their minds to the fact that life might be likely with many different configurations of laws and constants of physics. Furthermore, nothing in anthropic reasoning indicates any special preference for human life, or indeed intelligent or sentient life of any sort. As Earmon has expressed this: "Imagine, if you will, the wonderment of a species of mud worms who discover that if the constant of thermometric conductivity of mud were different by a small percentage they would not be able to survive." (Earmon 1987, 314).

The development of intelligent life does not seem to have proceeded smoothly and elegantly from the fundamental constants in the way that the phrase "fine-tuning" may be thought to imply. Several billion years elapsed before the conditions of intelligent life came together, and that the process of fashioning these conditions seems to have been accompanied by a staggering degree of waste (all that space, dust and seemingly dead cosmic bodies). By human standards, it seems remarkably inefficient. Also, in the case of human life, it appears that (amongst other things) Earth would have suffered frequent catastrophic collisions with comets had it not been for the gravitational effect of Jupiter. This hardly seems consistent with divine creation. Setting in motion a myriad of threatening comets and then positioning a huge planet as a protection against the danger you have thus created seems like the work of a cosmic jerry-builder. (For more about the contingency of life on Earth, see Taylor, 1998).

 Even before we examine the other possibilities in detail, we can see another fatal fallacy in the fine-tuning argument. It is a probability argument that rests on a misconception of the concept of probability . Suppose we were to begin with a ensemble of universes in which the physical constants for each vary over a wide range of possible values. Then the probability that one universe selected randomly from that set would be our universe is admittedly very small. The fine-tuning argument then concludes that our specific universe was deliberately selected from the set by some external agent, namely God.

However, a simple example shows that this conclusion does not logically follow. Suppose that a lottery is conducted in which each entrant is assigned a number from one to one million. Each has kicked in a dollar and the winner gets the whole pot of $1 million. The number is selected and you are the lucky winner! Now it is possible that the whole thing was fixed and your mother chose the winning number. But absent any evidence for this, no one has the right to make that accusation. Yet that's what the fine-tuning argument amounts to. Without any evidence, God is accused of fixing the lottery.

Somebody had to win the lottery, and you lucked out. Similarly, if a universe was going to happen, some set of physical constants was going to be selected. The physical constants, randomly selected, could have been the ones we have. And they led to the form of life we have.

In another example, estimate the probability that the particular sperm and egg that formed you would unite--that your parents, grandparents and all your ancestors down to the primeval stew that formed the first living things would come together in the right combination. Would that infinitesimally small number be the probability that you exist? Of course not. You exist with 100% probability. (For further discussion of probability and the fine-tuning argument, see Le Podevin 1996 and Parsons 1998).

 Ikeda and Jefferys (1997) have done a formal probability theory analysis that demonstrates these logical flaws and others in the fine tuning argument. They have also noted an amusing inconsistency that shows how promoters of design often use mutually contradictory logic.

On the one hand you have the creationists and god-of-the-gaps evolutionists who argue that nature is too uncongenial for life to have developed totally naturally, and so therefore supernatural input must have occurred. Then you have the fine-tuners (often the same people) arguing that the constants and laws of nature are exquisitely congenial to life, and so therefore they must have been supernaturally created. They can't have it both ways.

The fine-tuning argument rests on the assumption that any form of life is possible only for a very narrow, improbable range of physical parameters. We can safely conclude that this assumption is completely unjustified. None of this rules out option (A) as the source of the anthropic coincidences. But it does show that the arguments that are used to support that option are very weak and certainly insufficient to rule out of hand all alternatives. If all those alternatives are to fall, making (A) the choice by default, then they will have to fall of their own weight.

Interpreting the Coincidences: (B) They Are All in the Head


Let us look next at the second of the explanations for the anthropic coincidences listed by Barrow and Tipler: (B) Observers are necessary to bring the Universe into being.

As the philosophers Berkeley and Hume realized, the possibility that reality is all in the mind cannot be disproved. However, any philosophy based on this notion is wrought with problems, not the least of which is why then is the universe not the way each of us wants it to be? Furthermore, whose mind is the one that is doing the imagining? Berkeley decided it had the be the mind of God, which makes this interpretation of the anthropic coincidences indistinguishable from the previous one. However, another possibility that is more in tune with Eastern religion than Western is that we are all part of a single cosmic mind.

This idea has become very popular in the new age movement. Triggered by the publication of The Tao of Physics by physicist Fritjof Capra (1975), a whole industry has developed in which the so-called mysteries and paradoxes of quantum mechanics are used to justify the notion that our thoughts control reality. The most successful practitioner of this philosophy is Dr. Deepak Chopra, who has done very well promoting what he calls "quantum healing" (Chopra 1989, 1993).

Option (B) is certainly not taken seriously in the current science-religion dialogues. However, let me include a brief discussion for the sake of completeness (see Stenger 1995 for more details).

Basically, the new ideas on cosmic mind and the quantum begin with the confusing interpretive language used by some of the founders of quantum mechanics, most particularly Niels Bohr. In what is termed the Copenhagen interpretation, a physical body does not obtain a property, such as position in space, until it is observed. Although quantum mechanics has continued to agree with all measurements to very high precision, the Copenhagen interpretation has been further interpreted to mean that reality is all in our heads.

Moreover, according to the idea of "quantum consciousness," our minds are all tuned in holistically to all the minds of the universe, with each individual forming part of the cosmic mind of God. As applied to the anthropic coincidences, the constants of physics are what they are because the cosmic mind wills them so.

Today few quantum physicists take the notion of a cosmic quantum mind seriously. The success of quantum mechanics does not depend in any way on the Copenhagen interpretation or its more mystical spinoffs. Other interpretations exist, like Bohm's hidden variables Bohm 1993), the many worlds interpretation (Deutsch 1997), and the consistent histories interpretation (Omnès 1994). Unfortunately, no consensus interpretation of quantum mechanics exists among physicists and philosophers. Suffice it to say that the admittedly "strange" behavior of the quantum world is mysterious only because it is unfamiliar, and can be interpreted without the introduction of any mystical ideas, including cosmic mind.
 
 

Interpreting the Coincidences: (C) They Are Natural


Finally let me move to the possibility that we can understand the anthropic coincidences naturally. I have very carefully discussed the other options first in order to make it clear that, by themselves, they are highly flawed and provide us little reason to accept their premises. I might stop here and claim the natural explanation wins by default. This can be somewhat justified on the principle of parsimony. Since all scientific explanations until now have been natural, then it would seem that the best bet is a natural explanation for the anthropic coincidences. Such an explanation would probably require the fewest in the way of extraordinary hypotheses--such as the existence of a spirit world either inside or outside the physical universe.
 
 

The Laws of Nature


The standard model of elementary particles and fields has, for the first time in history, given us a theory that is consistent with all experiments. More than that, in developing the standard model physicists have gained significant new insights into the nature of the so-called laws of nature.

Prior to these recent developments, the physicist's conception of the laws of nature was pretty much that of most lay people: They were assumed to be rules for the behavior of matter and energy that are part of the very structure of the universe, laid out at the creation. However, in the past several decades we have gradually come to understand that what we call "laws of physics" are basically our own descriptions of certain symmetries observed in nature and how these symmetries, in some cases, happen to be broken. And, as we will see, the particular laws we have found do not require an agent to bring them into being. In fact, they are exactly what would be expected in the absence of an agent.

The most powerful of all the laws of nature are the great conservation principles of energy, momentum, angular momentum, charge, and other quantities that are measured in fundamental interactions. These apply whenever a system of bodies is sufficiently isolated from its environment. Thus the total energy, momentum, angular momentum, charge, etc. of the molecules in a completely insulated chamber of fixed volume will remain constant as the molecules move about. Individual molecules can exchange these quantities when they interact with others. Thus a molecule can lose energy and momentum by colliding with another, while the struck molecule will gain the same amounts. A chemical reaction can occur in which the charges of the molecules also change, but the total charge remains constant.

The position of a body in space is usually represented in terms of coordinates, such as the latitude, longitude, and altitude of an aircraft in the sky. For over a century now, physicists have known that whenever their description of a body does not depend on a particular coordinate, say x, then the momentum that corresponds to that coordinate, px, is conserved. That is, this particular momentum component, called the "momentum conjugate to x," does not change as the body moves.

 For example, consider a space probe far from earth moving in a straight line at constant velocity vx with respect to its home ship in which we are riding. Let the position of the probe with respect to some arbitrary marker, say asteroid Randi, be x. The motion of the probe will look the same whether viewed from our ship at x=0 or another vessel at x =137,000 kilometers. The probe's velocity vx and momentum px = mvx, where m is the mass of the probe, will be the same independent of x.

Similarly, our description of the probe's motion need not include the time at which it is being observed. As long as it keeps moving with constant velocity, in magnitude and direction, its motion will look the same whether viewed at UT0645 or UT1720. This independence of the time "coordinate" is expressed as conservation of energy, where energy is "the momentum conjugate to t." (In relativistic kinematics, energy is the "timelike coordinate" of a four-dimensional momentum in which each component is conjugate to four-dimensional spacetime).

The motion of the probe in this example is said to possess both space-translation and time-translation symmetries. This means that our description of its motion does not depend on any special position in space or moment in time. Under the same conditions, the probe would behave the same way on a planet in the Andromeda galaxy a million years in the future.

The probe also possesses rotational symmetry, behaving the same way when observed from other angles where its motion points in a different direction. Rotational symmetry implies angular momentum conservation.

Now consider the universe as a whole. Unless it is being acted on by some outside agent, it will behave the same regardless of where we place it in some imagined super spacetime or how we happen to orient it. That is, the universe is expected to possess all three symmetries described above. It follows that energy, momentum, angular momentum, and any other quantities of the type that are conjugate to these coordinates will be conserved globally , that is, as a whole and at each point in space and time.

 In other words, the global conservation "laws" are exactly what one expects for an isolated universe with no outside agent acting. Only a violation of these laws would imply an outside agent. The data so far are consistent with no agent.

Global conservation laws follow from what we call global symmetries, like space translation and time translation. As I said, this was pretty much known a hundred years ago but not much was made of it. In this century, with the development of quantum mechanics, the same connection between symmetries and conservation laws was shown to still exist and to be even more profound.

In more recent years, the importance of broken symmetries has come to be recognized. This has been put together with our understanding of unbroken global symmetries to produce a coherent scheme in which everything we know seems to broadly fit.

Broken symmetry is actually very common at the everyday scale. Not all cars travel in straight lines at constant speed. They roll to a stop when the engine cuts off, as energy is lost to friction. Neither are the material structures we see around us fully symmetric. The earth is not a sphere but a flattened spheroid. A tree looks different from different angles. Our faces look different in a mirror. Mirror symmetry is broken when a system is not precisely left-right or mirror symmetric, like our faces. That is no surprise, and indeed we can view much of what we call material structure as a combination of broken and unbroken symmetries. Again, think of a snowflake. Structure and beauty seem to be combinations of both unbroken and broken symmetries, of both order and randomness.

 The big revelation to physicists in the 1950s was that a few rare nuclear and fundamental particle interactions are not mirror symmetric. This discovery triggered an awakening to the possibilities of symmetry breaking at the fundamental scale in other situations. In many cases, this was merely a reexpression of old facts in a new language. For example, a symmetry such as momentum conservation can be broken locally without destroying the overall space-translation symmetry of the universe. When momentum conservation is locally broken, as with a falling body, we say we have a force acting. Indeed Newton's second law of motion specifies that force is equal to the time rate of change of momentum. In this case global momentum conservation is maintained, as interacting bodies in an isolated system have an equal and opposite reaction, as expressed by Newton's third law.

Thus gravity, and the other forces of nature, came to be recognized--and described theoretically--as broken local symmetries. The standard model was built on a framework of local broken symmetry.

Symmetry breaking can be likened to a pencil balanced vertically on its eraser end. This situation possesses rotational symmetry about the vertical axis, that is, it looks the same from any angle you view it as you walk around the able holding the pencil. However, the balance is precarious. With no help from the outside other than random breezes, the pencil will eventually fall over. The direction it points along is random--unpredictable, undesigned--but the symmetry is broken and a new, special direction is then singled out.
 
 

In the Beginning

For almost two decades, the inflationary big bang has been the standard model of cosmology (Guth 1981, 1997; Linde 1987, 1990, 1994). We keep hearing, again from the unreliable popular media, that the big bang being is in trouble and the inflationary model is dead. In fact, no viable substitute has been proposed that has near the equivalent explanatory power.

The inflationary big bang offers a plausible, natural scenario for the uncaused origin and evolution of the universe, including the formation of order and structure--without the violation of any laws of physics. Indeed, as we saw above, these laws themselves are now understood far more deeply than before and we are beginning to grasp how they too could have come about naturally. This particular version of a natural scenario for the origin of the universe has not yet risen to the exalted status of a scientific theory. However, the fact that it is consistent will all current knowledge and cannot be ruled out at this time demonstrates that no rational basis exists for introducing the added hypothesis of supernatural creation. Such a hypothesis is simply not required by the data.

 According to this scenario, by means of a random quantum fluctuation the universe "tunneled" from pure vacuum ("nothing") to what is called a false vacuum, a region of space that contains no matter or radiation but is not quite "nothing." The space inside this bubble of false vacuum was curved, or warped. A small amount of energy was contained in that curvature, somewhat like the energy stored in a strung bow. This ostensible violation of energy conservation is allowed by the Heisenberg uncertainty principle for sufficiently small time intervals.

The bubble then inflated exponentially and the universe grew by many orders of magnitude in a tiny fraction of a second. (For a not-too-technical discussion, see Stenger 1990). As the bubble expanded, its curvature energy was converted into matter and radiation, inflation stopped, and the more linear big bang expansion we now experience commenced. The universe cooled and its structure spontaneously froze out, as formless water vapor freezes into snowflakes whose unique patterns arise from a combination of symmetry and randomness.

In our universe, the first galaxies began to assemble after about a billion years, eventually evolving into stable systems where stars could live out their lives and populate the interstellar medium with the complex chemical elements such as carbon which are needed for the formation of life.

So how did our universe happen to be so "fine-tuned" as to produce these wonderful, self-important carbon structures? As I explained above, we have no reason to assume that ours is the only possible form of life and perhaps life of some sort would have happened whatever form the universe took--however the crystals on the arm of the snowflake happened to be arranged by chance.

At some point, according to this scenario, the symmetries of the initial nothingness began to be "spontaneously" broken. Those of the current standard model of elementary particles and forces were among the last broken, when the universe was about 10-12 second old and much "colder" than earlier. The distances and energies involved at this point have been probed in existing colliding beam accelerators, which represents about the deepest into big-bang physics we have so far been able to explore in detail. Higher energy colliders will be necessary to push farther, and we are far from directly probing the earliest time scales where the ultimate symmetry breakdown can be explored. Still, it may surprise to reader that the physical principles which have been in place since a trillionth of a second after the universe began are very well understood.

 By about 10-6 second, the early universe had gone through all the symmetry breaking required to produce the fundamental laws and constants we still observe today, 13-15 billion years later. Nuclei and atoms still needed more time to get organized, but after 300,000 years the lighter atoms had assembled and ceased to interact with the photons that went off on their own to become the cosmic microwave background. The first galaxies began to assemble after about billion years, evolving eventually into stable systems where stars could live out their lives and populate the interstellar medium with the heavier elements like carbon needed for the formation of life.

Regardless of the fact that we cannot explore the origin of the universe by any direct means, the undoubted success of the theory of broken symmetry as manifested in the standard model of particle physics provides us with a mechanism that we can apply, at least in broad terms, to provide a natural explanation for the development natural law within the universe, without a lawgiver being invoked to institute those laws from the outside.

 We have seen that the conservation laws correspond to global symmetries that would automatically be present in the absence of any outside agent. The total chaos that was the state of the universe at the earliest definable time possessed space translation, time translation, rotational, and all the other symmetries that result when a system depends on none of the corresponding coordinates. Nothing is more symmetric than nothing. Nothing has more conservation laws than nothing. Expressing this in an information science context, total chaos and complete symmetry correspond to zero information. Any kind of action by an external agent would result in non-zero information and some broken symmetry. We have no evidence for this, again no need to introduce the uneconomical hypothesis of a creator.

 The force laws as exist in the standard model are represented as spontaneously broken symmetries, that is, symmetries that are broken randomly and without cause or design. When the pencil fell over, the direction it pointed to broke the original symmetry and selected out a particular axis. In a more apt example, consider what happens when a ferromagnet cools below a certain critical temperature called the Curie point.. The iron undergoes a change of phase and a magnetic field suddenly appears that points in a specific, though random, direction, breaking the original symmetry in which no direction was singled out ahead of time, none predictable by any known theory.

 The forces of nature are akin to the magnetic field of a ferromagnet. The "direction" they point to after symmetry breaking was not determined ahead of time. The nature of the forces themselves was not pre-specified. They just happened to freeze out the way they did. Just as no agent is implied by the global symmetries, in fact quite the opposite, none is implied by the broken symmetries, which in fact look very much like the opposite.

Now theists may argue that I am simply assuming the absence of divine causation and not proving it. I am not claiming to prove that such causation does not exist. Rather I am simply demonstrating that, based on current scientific knowledge, none is necessary.

 In natural scenario I have provided, the values of the constants of nature in question are not the only ones that can occur. A huge range of values are in fact possible, as are all the possible laws that can result from symmetry breaking. The constants and forces that we have were selected by accident--as the pencil fell--when the expanding universe cooled and the structure we see at the fundamental level froze out. Just as the force laws did not exist before symmetry breaking, so too the constants did not exist. They, after all, come along with the forces. In the current theoretical scheme, particles also appear, with the forces, as the carriers of the quantities like mass and charge and indeed the forces themselves. They provided the means by which the broken symmetries materialize and manifest their structure.

What About Life?


Someday we may have the opportunity to study different forms of life that evolved on other planets. Given the vastness of the universe, and the common observation of supernovas in other galaxies, we have no reason to assume life only exists on earth. Although it seems hardly likely that the evolution of DNA and other details were exactly replicated elsewhere, carbon and the other the elements of our life form are well distributed, as evidenced by the composition of comic rays and the spectral analysis of interstellar gas.

We also cannot assume that life would have been impossible in our universe had the symmetries broken differently. Certainly we cannot speak of such things in the normal scientific mode in which direct observations are described by theory. But, at the same time, it is not illegitimate, not unscientific, to examine the logical consequences of existing theories that are well-confirmed by data from our own universe.

The extrapolation of theories beyond their normal domains can turn out to be wildly wrong. But it can also turn out to be spectacularly correct. The fundamental physics learned in earthbound laboratories has proved to be valid at great distances from earth and at times long before the earth and solar system had been formed. Those who argue that science cannot talk about the early universe, or life on the early earth because no humans were there to witness these events, greatly underestimate the power of scientific theory.

I have made a modest attempt to obtain some feeling for what a universe with different constants would be like. It happens that the physical properties of matter, from the dimensions of atoms to the length of the day and year, can be estimated from the values of just four fundamental constants. Two of these constants are the strengths of the electromagnetic and strong nuclear interactions. The other two are the masses of the electron and proton (Press and Lightman1983).

Of course, many more constants are needed to fill in the details of our universe. And our universe, as we have seen, might have had different physical laws. We have little idea what those laws might be; all we know is the laws we have. Still, varying the constants that go into our familiar equations will give many universes that do not look a bit like ours. The gross properties of our universe are determined by these four constants, and we can vary them to see what a universe might grossly look like with different values of these constants.

I have created a program, MonkeyGod, which can be executed on the World Wide Web at <http:/ /www.phys.hawaii.edu/vjs/www/monkey.html>. Try your own hand at generating universes! Just choose different values of the four constants and see what happens. While these are really only "toy" universes, the exercise illustrates that there could be many different universes possible even within the existing laws of physics.

As an example, I have analyzed 100 universes in which the values of the four parameters were generated randomly from a range five orders of magnitude above to five orders of magnitude below their values in our universe, that is, over a total range of ten orders of magnitude. Over this range of parameter variation, N1 is at least 1033 and N2 at least 1020 in all cases. That is, both are still very large numbers. Although many pairs do not have N1 = N2, an approximate coincidence between these two quantities is not very rare (for more details, see Stenger 1995).

The distribution of stellar lifetimes for these same 100 universes has also been examined. While a few are low, most are probably high enough to allow time for stellar evolution and heavy element nucleosynthesis. Over half the universes have stars that live at least a billion years. Long life is not the only requirement for life, but it certainly is not an unusual property of universes.

Recall Barrow and Tipler's option (C), which held that an ensemble of other, different universes is necessary in any natural explanation for the existence of our universe. Another myth that has appeared frequently in the literature (see, for example, Swinburne 1990) holds that only a multiple-universe scenario can explain the coincidences without a supernatural creator. No doubt this can do it, as we will see below. But even if there were only one universe, the likelihood of some form of life in that single universe is not necessarily small. If many universes beside our own exist, then the anthropic coincidences are a no-brainer.
 
 

An Infinity of Universes


Within the framework of established knowledge of physics and cosmology, our universe could be one of many in an infinite super universe or "multiverse" (Linde 1994). Each universe within the multiverse can have a different set of constants and physical laws. Some might have life of a different form than us, others might have no life at all or something even more complex or so different that we cannot even imagine it. Obviously we are in one of those universes with life.

Several commentators have argued that a multiverse cosmology violates Occam's razor (see, typically, Ellis 1993, 97). This is wrong. The entities that Occam's law of parsimony forbids us from "multiplying beyond necessity" are theoretical hypotheses, not universes. For example, although the atomic theory of matter multiplied the number of bodies we must consider in solving a thermodynamic problem by 1024 or so per gram, it did not violate Occam's razor. Instead, it provided for a simpler, more powerful, more economic exposition of the rules that were obeyed by thermodynamic systems.

As Max Tegmark (1998) has argued, a theory in which all possible universes exist is actually more parsimonious than one in which only one exists. Just as was the case for the breaking of the global conservation laws, a single universe requires more explanation- additional hypotheses.

Let me give a simple example that illustrates his point. Consider the two statements: (a) y = x2 and (b) 4 = 22. Which is simpler? the answer is (a), because it carries far more information with the same number of characters than the special case (b). Applied to multiple universes, a multiverse in which all possible universes exist is analogous to (a), while a single universe is analogous to (b).
The existence of many universes is in fact consistent with all we know about physics and cosmology. No new hypotheses are needed to introduce them. It takes an added hypothesis to rule them out--a super law of nature that says only one universe can exist. That would be an uneconomical hypothesis! Another way to express this is with lines from T. H. White's The Once and Future King: "Everything not forbidden is compulsory."

An infinity of random universes is suggested by the modern inflationary model of the early universe (Linde 1987, 1990, 1994 ; Guth 1981, 1997; Smith 1990; Smolin 1992, 1997). As we have seen, a quantum fluctuation can produce a tiny, empty region of curved space that will exponentially expand, increasing its energy sufficiently in the process to produce energy equivalent to all the mass of a universe in a tiny fraction of second. Andre Linde proposed that a background spacetime "foam" empty of matter and radiation will experience local quantum fluctuations in curvature, forming many bubbles of false vacuum that individually inflate into mini-universes with random characteristics (Linde 1987, 1990, 1994; Guth 1997). In this view, our universe is one of those expanding bubbles, the product of a single monkey banging away at the keys of a single word processor.
 
 

The Descent of the Universe


Smith (1990) and Smolin (1992) have independently suggested a mechanism for the evolution of universes by natural selection. They propose a multi-universe scenario in which each universe is the residue of an exploding black hole that was previously formed in another universe.

An individual universe is born with a certain set of physical parameters--its "genes." As it expands, new black holes are formed within. When these black holes eventually collapse, the genes of the parent universe get slightly scrambled by fluctuations that are expected in the state of high entropy inside a black hole. So when the descendant black hole explodes, it produces a new universe with a different set of physical parameters--similar but not exactly the same as its parent universe. (To my knowledge, no one has yet developed a sexual model for universe reproduction.)

The black hole mechanism provides for both mutations and progeny. The rest is left to survival of the survivor. Universes with parameters near their "natural" values can easily be shown to produce a small number of black holes and so have few progeny to which to pass their genes. Many will not even inflate into material universes, but quickly collapse back on themselves. Others will continue to inflate, producing nothing. However, by chance some small fraction of universes will have parameters optimized for greater black hole production. These will quickly predominate as their genes get passed from generation to generation.

The evolution of universes by natural selection provides a mechanism for explaining the anthropic coincidences that may appear far out, but Smolin suggests several tests. In one, he predicts that the fluctuations in the cosmic microwave background should be near the value expected if the energy fluctuation responsible for inflation in the early universe is just below the critical value for inflation to occur.

It is no coincidence that the idea of the evolution of universes is akin to Darwin's theory of biological evolution. In both cases we are faced with explaining how unlikely, complex, non-equilibrium structures can form without invoking even less likely supernatural forces. Natural selection may offer a natural explanation.
 
 

Tegmark's Ensembles

Tegmark has recently proposed what he calls "the ultimate ensemble theory" in which all universes that mathematically exist also physically exist (Tegmark 1997). By "mathematical existence," Tegmark means "freedom from contradiction." So, universes cannot contain square circles, but anything that does not break a rule of logic exists in some universe.

Tegmark claims his theory is scientifically legitimate since it is falsifiable, makes testable predictions, and is economical in the sense that I have already mentioned above--a theory of many universes contains fewer hypotheses than a theory of one. He finds that many mathematically possible universes will not be suitable for the development of what he calls "self-aware structures," his euphemism for intelligent life. For example, he argues that only a universe with three spatial and one time dimension can contain self-aware structures because other combinations are too simple, too unstable, or too unpredictable. Specifically, in order that the universe be predictable to its self-aware structures, only a single time dimension is deemed possible. In this case, one or two space dimensions is regarded as too simple, and four or more space dimensions is reckoned as too unstable. However, Tegmark admits that we may simply lack the imagination to consider universes radically different from our own.

Tegmark examines the types of universes that would occur for different values of key parameters and concludes, as have others, that many combinations will lead to unlivable universes. However, the region of the parameter space where ordered structures can form is not the infinitesimal point only reachable by a skilled artisan, as asserted by proponents of the designer universe.
 
 

Conclusion

The new convergence of science and religion that has been reported in the media is more between believing scientists and theologians than believers and nonbelievers. Theistic scientists who deeply wish to find evidence for design and purpose to the universe now think they have. Many say that they see strong hints of purpose in the way the physical constants of nature seem to be exquisitely fine-tuned for the evolution and maintenance of life. Although not so specific that they select out human life, these properties are called the "anthropic coincidences" and various forms of the "anthropic principle" have been suggested as the underlying rational.
Theists argue that the universe seems to have been specifically designed so that intelligent life would form. Some have gone so far as to claim that this is already "proved" by the existence of the anthropic coincidences. The theist claim translates into a modern version of the ancient argument from design for the existence of God. However, the new version is as deeply flawed as its predecessors, making many unjustified assumptions and being inconsistent with existing knowledge. One gross and fatal assumption is that only one kind of life, ours, is possible in every configuration of possible universes.

Another form of the anthropic principle holds that observers, by their very act of observation, bring the universe into being. This has become a popular notion in New Age philosophy and is supposedly justified by certain interpretations of quantum mechanics. However, other interpretations of quantum mechanics are viable and the best evidence that we do not make our own universe is the fact that the universe is not what most of us want it to be.

We have examined possible natural explanations for the anthropic coincidences. A wide variation of constants of physics has been shown to lead to universes that are long-lived enough for life to evolve and exhibit "anthropic" coincidences, though human life would certainly not exist in such universes.

The most powerful "laws of physics," the conservation laws, were shown to be evidence against design rather than for it. They are directly related to the "symmetries of nothing" that would exist in the absence of design. Furthermore, the observed forces, particles, and other structure in our universe are consistent with the accidental, or spontaneous, breaking of symmetries at local points in spacetime. This also mitigates against design or creation.

Although not needed to negate the fine-tuning argument, which falls of its own weight, from all that we know of fundamental physics and cosmology other universes besides are own are not ruled out. The theory of a multiverse composed of many universes with different laws and physical properties is actually more parsimonious, more consistent with Occam's razor, than a single universe. We would need to hypothesize a new principle to rule out all but a single universe. If, indeed, there exist multiple universes, then we are simply in that particular universe of all the logically consistent possibilities that had the properties needed to produce us.
 
 

Acknowledgments

I have greatly benefitted from discussions with Ricardo Aler Mur, Samantha Atkins, John Chalmers, Scott Dalton, Keith Douglas, Ron Ebert, Simon Ewins, Jim Humphreys, Bill Jefferys, Kenneth Porter, Wayne Spencer, and Ed Weinmann.

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