Perhaps the most widely discussed argument from design in the last thirty years has been that based on the fine-tuning of the cosmos for life. The literature presenting the evidence for fine-tuning is fairly extensive, with books by theoretical physicist Paul Davies (1982), physicists John Barrow and Frank Tipler (1986), astrophysicist Martin Rees (1999), and philosopher John Leslie (1989), being some of the most prominent. Yet, despite this abundance of literature, several leading scientists are still skeptical of the purported evidence of fine-tuning. Nobel Prize winning physicist Steven Weinberg, for instance, says that he is "not impressed with these supposed instances of fine-tuning" (1999, p. 46). Other physicists, such as MIT's astrophysicist Alan Guth, have presented similar reservations. ⁽²⁾ As explicated in the appendix, there are good reasons for this skepticism: the arguments for several of the most widely cited cases of purported fine-tuning are seriously flawed.

To counteract this form of skepticism, I will attempt to present six of what seem to me to be among the strongest cases of fine-tuning. The way in which I judge the strength of a particular case of purported fine-tuning is primarily based on how secure the physical calculations, or type of reasoning, is behind the case of fine-tuning in question. In several cases below, the purported instance of fine-tuning is secure because it is based on a highly straightforward line of reasoning that involves a minimum number of assumptions. The existence of secure cases of fine-tuning, along with philosopher John Leslie's comment that "clues heaped upon clues can constitute weighty evidence despite doubts about each element in the pile" (1988, p. 300), should go a long way toward answering these critics. Before looking at the evidence, however, we first need a rough definition of fine-tuning, and some important criteria for when a parameter of physics can be considered fine-tuned in the sense relevant to the design argument (or the argument for many universes). ⁽³⁾

As a first approximation, we can think of the claim that a parameter of physics is "fine-tuned" as the claim that the range of values of the parameter that is life-permitting, or intelligent life-permitting, is very small compared with some non-arbitrarily chosen theoretically "possible" range of values R. In each of the cases below, we will indicate how the physical situation itself suggests a plausible lower bound for the overall range R, and hence a plausible lower bound for the degree of fine-tuning. A full treatment of the fine-tuning, however, would need to justify the choice of the lower bound of the overall range R in considerably more depth, but that is beyond the scope this paper. ⁽⁴⁾

Now, the inference to design (or many universes) does not require that a parameter be fine-tuned in the full sense as defined above. First, all that needs to be shown is that conditions would be much less optimal for the evolution of intelligent life if a parameter were to have fallen outside of some narrow range r (as compared to the theoretically "possible" range R). The reason for this has to do with the nature of the inference to design (or many universes). The inference to design or many-universes typically involves two steps. First, the claim is made that it is very coincidental, or surprising, for some parameter of physics to fall within the life-permitting range (instead of somewhere else in the theoretically "possible" range R) under the non-design, non-many-universe hypothesis, but not surprising or coincidental under the design or many-universe hypothesis. Then, a general rule of confirmation is implicitly or explicitly invoked, according to which if a body of evidence E is highly surprising or coincidental under an hypothesis H₂, but not under an hypothesis H₁, then that body of evidence E confirms H₁ over H₂: that is, E gives us significant reason to prefer H₁ over H₂. ⁽⁵⁾ The surpisingness or coincidental character of the values of the parameters of physics, however, would still remain if their actual values were merely optimal for the evolution of intelligent life, and thus the soundness of the above inference would be unaffected. Further, this optimality criterion largely avoids the objections based on the possibilities of non-carbon based life forms: a change in a parameter that decreased the likelihood of carbon-based intelligent life forms, would clearly be less optimal for intelligent life unless it resulted in a compensating increase in the likelihood of other kinds of intelligent life, such as those based on silicon or liquids other than water. But this is highly unlikely, given the well-known difficulties involved in the existence of any kind of alternative to carbon-based life.

Second, all we actually need to show is that a parameter falls near the edge of a life-permitting region, not that the life-permitting region is small compared to some non-arbitrarily defined region R. For example, as I will discuss below, we only have well-developed reasons to believe that a relatively small decrease in the weak force strength would severely inhibit the possibility of life. Thus at present we only have a solid argument for what I will call one-sided fine-tuning of the weak force, instead of what could be called two-sided fine-tuning, in which either a decrease or an increase of the strength of the weak force would be severely life-inhibiting. (The way we defined fine-tuning above was essentially as two-sided fine-tuning.)

The basic reason we only need evidence for one-sided fine-tuning is that it is still seems highly coincidental for a parameter to fall very near the edge of the life-permitting region under the non-design, non-many-universes hypothesis. ⁽⁶⁾ But, it does not seem highly coincidental under the joint hypothesis of design and two-sided fine-tuning (or many-universes and two-sided fine-tuning). The reason for this is that the existence of two-sided fine-tuning implies that all life-permitting values are near the edge (since the life-permitting region is so small), and the design hypothesis renders it not coincidental that the parameter is in the life-permitting region. So, taken together, these two hypotheses remove the coincidence of a parameter falling near the edge of the life-permitting region. Thus, by the rule of inference mentioned above, the existence of one-sided fine-tuning confirms the joint hypothesis of design and two-sided fine-tuning over the non-design, non-many-universes hypothesis.

It is worth noting that these explanations of one-sided fine tuning (design and two-sided fine-tuning and many-universes and two sided fine-tuning) are at least in part testable, since they lead us to expect the existence of two-sided fine-tuning in those cases in which there is a significant degree of one-sided fine-tuning. (Since writing this, I have submitted for publication a detailed demonstration of this point regarding the testability of these explanations of fine-tuning.) This distinction between one- and two-sided fine-tuning will be very important, since in some of the most important cases of fine-tuning, we only have well-developed arguments for one-sided fine-tuning.

Now we are ready to consider six solid cases of fine-tuning. The cases I discuss are those in which we can make a quantitative estimate of the degree of fine-tuning. There are many other significant, more qualitative, cases such as presented by Michael Denton (1998) that we will not discuss here. We will begin with the cosmological constant.

A. Cosmological Constant

Note: Since Wordperfect does not convert Greek characters from Wordperfect to html. Thus, I substituted the Greek symbol Lamda that typically denotes the cosmological constant with CC in the text below.

The cosmological constant is the first case of fine-tuning that we will examine. The smallness of the cosmological constant is widely regarded as the single greatest problem confronting current physics and cosmology. The cosmological constant, CC, is a term in Einstein's equation, that when positive, acts as a repulsive force causing space to expand and when negative acts as an attractive force causing space to contract. Now, apart from some sort of extraordinarily precise fine-tuning or new physical principle, today's theories of fundamental physics and cosmology lead one to expect that the vacuum--that is, the state of space-time free of ordinary matter fields--has an extraordinarily large energy density. This energy density in turn acts as an effective cosmological constant, thus leading one to expect an extraordinarily large effective cosmological constant, one so large that, if positive, it would cause space to expand at such an enormous rate that almost every object in the universe would fly apart, and if negative, it would cause the universe to almost instantaneously collapse back in on itself. This would clearly make the evolution of life impossible.

What makes it so difficult to avoid postulating some sort of highly precise fine-tuning of the cosmological constant is that almost every type of field in current physics--the electromagnetic field, the Higgs fields associated with the weak force, the inflaton field hypothesized by inflationary cosmology, the dilaton field hypothesized by superstring theory, and the fields associated with elementary particles such as electrons-- each contribute to the vacuum energy. Although no one knows how to calculate the energy density of the vacuum, when physicists make estimates of the contribution to the vacuum energy from these fields, they get values of the energy density anywhere from 10⁵⁰ to 10¹²⁰ higher than its maximum life permitting value, CC_max. ⁽⁷⁾ (Here, CC_max is expressed in terms of the energy density of empty space.)

Although each field contributes in a different way to the total vacuum energy, for the purposes of illustration we will look at just two examples. As our first example, consider the inflaton field of inflationary cosmology. Inflationary universe models postulate that the inflaton field had an enormously high energy density in the first 10^-35 to 10^-37 seconds of our universe (Guth, 1997, p. 185), causing space to expand by a factor of around 10⁶⁰. By about 10^-35 seconds or so, however, the value of the inflaton field fell to a relatively small value corresponding to a local minimum of energy of the inflaton field. Theoretically the local minimum of the inflaton field could be anything from zero to 10⁵²CC_max, or even 10¹²³CC_max, depending on the inflationary model under consideration. (See, Sahni and Starobinsky, 1999, section 7.0, and Rees, 1999, p. 154.). ⁽⁸⁾ The fact that it is less than CC_max, therefore, suggests a high degree of fine-tuning, to at least one part in 10⁵³. ⁽⁹⁾

A similar sort of fine-tuning occurs in the case of the the symmetry breaking of the weak force in the widely accepted Weinberg-Salem-Glashow electroweak theory. According to this theory, the electromagnetic force and the weak force acted as one force prior to symmetry breaking of a postulated Higgs field in the very early universe when temperatures were still extremely high. Before symmetry breaking, the vacuum energy of the Higgs field had its maximum value V₀. This value was approximately 10⁵³ CC_max. After symmetry breaking, the Higgs field falls into some local minimum of energy density, which theoretically could be anywhere from zero to 10⁵³ CC_max, being solely determined by V₀ and other free parameters of the electroweak theory. ⁽¹⁰⁾

Once again, the fact that this energy density is less that CC_max, instead of somewhere else in the range zero to 10⁵³ CC_max, suggests an extraordinarily high degree of fine-tuning.

To account for the near-zero value of the cosmological constant one could hypothesize some unknown physical principle or mechanism that requires that the cosmological constant be zero. One problem with this hypothesis is that recent cosmological evidence from distant supernovas strongly indicates that the effective cosmological constant is not exactly zero (Sahni and Starobinsky, 1999, and Krauss, 1999). Thus, the principle or mechanism could not simply be one that specifies that the cosmological constant must be zero, but would have to be one that specified that it be less than some small upper bound. This hypothesis, however, seems to simply relocate the cosmological constant problem to that of explaining why this upper bound is less than CC_max instead of being much, much larger. ⁽¹¹⁾ Second, current inflationary cosmologies require that the effective cosmological constant be relatively large at very early epochs in the universe, since it is a large cosmological constant that drives inflation. Thus, any mechanism that forces it to be zero or near-zero now must allow for it to be large in early epochs. Accordingly, if there is a physical principle that accounts for the smallness of the cosmological constant, it must be: (i) attuned to the contributions of every particle to the vacuum energy; (ii) only operative in the later stages of the evolution of the cosmos (assuming inflationary cosmology is correct); and (iii) something that drives it extraordinarily close to zero, but not exactly zero, which would itself seem to require fine-tuning. Given these constraints on such a principle, it seems that if such a principle exists, it would have to be "well-designed" (or "fine-tuned") to yield a life-permitting cosmos. Thus, such a mechanism would most likely simply reintroduce the issue of design at a different level. ⁽¹²⁾

These difficulties confronting finding a physical principle or mechanism for forcing the cosmological constant to be near-zero have led many cosmologists, most notably Steven Weinberg, to reluctantly search for an anthropic many-universes explanation for its apparent fine-tuning (Weinberg, 1987, 1996).

B. Fine-Tuning of Strong Force

The next case of fine-tuning that we will examine is that of the strong force. The strong force is the force that keeps the nucleons--that is, the protons and neutrons--together in an atom. The effect of decreasing the strong force is straightforward, since the stability of elements depends on the strong force being strong enough to overcome the electromagnetic repulsion between the protons in a nucleus. A 50% decrease in the strong force, for instance, would undercut the stability of all elements, making the universe merely consist of hydrogen. (See Barrow and Tipler, 1986, pp. 326-27) A universe with only hydrogen, however, could not support the sort of organized, stable, complexity necessary for intelligent life.

Another effect of decreasing the strength of the strong force is that it would throw off the balance between the rates of production of carbon and oxygen in stars, as discussed immediately below. This would have severe life-inhibiting consequences. Although various life-inhibiting effects are claimed for increasing the strength of the strong force, the arguments are not nearly as strong or well-developed, except for the one below involving the existence of carbon and oxygen. Further, the argument most commonly cited - namely, that it would cause the binding of the diproton which would in turn result in an all helium universe - is faulty. (See the appendix.) At present, therefore, we have a solid argument for one-sided fine-tuning of the strong force, along with a significant and well-developed argument for two-sided fine-tuning based on the joint production of carbon and oxygen in stars (see next section). Finally, since the forces of nature span a range of 10⁴⁰ in strength, a 50% decrease is still about one part in 10⁴⁰ of the total range of forces, which is clearly a very high degree of (one-sided) fine-tuning. ⁽¹³⁾

C. Fine-Tuning of Carbon Production in Stars

The first significantly discussed, and probably most famous, case of fine-tuning involves the production of carbon and oxygen in stars. Since both carbon and oxygen play crucial roles in life-processes, the conditions for complex, multicellular life would be much less optimal without the presence of these two elements in sufficient quantities. (For a fairly complete of these reasons, see Michael Denton, 1998, chapters 5 and 6.) Yet, a reasonable abundance of both carbon and oxygen appears to require a fairly precise adjustment of the strong nuclear force, as we will now see.

Carbon and oxygen are produced by the processes of nuclear synthesis in stars via a delicately arranged process. At first, a star burns hydrogen to form helium. Eventually, when enough hydrogen is burned, the star contracts thereby increasing the core temperature of the star until helium ignition takes place, which results in helium being converted to carbon and oxygen. The process occurs by helium nuclei colliding first to form beryllium 8 (⁸Be), which is a metastable nuclei with a half-life of 10^-17 seconds. During ⁸Be's short life-span, it can capture another helium nuclei to form carbon 12. Some of the carbon 12 that is formed is then burned to oxygen 16 by collisions with other helium nuclei.

Helium burning in stars thus involves two simultaneous reactions:

(i) The carbon producing reaction chain, ⁴He + ⁴He --> ⁸Be, ⁸Be + ⁴He --> ¹²C,

and

(ii) The oxygen producing reaction, ¹²C + ⁴He --> ¹⁶O.

Now in order for appreciable amounts of both carbon and oxygen to be formed, the rates of these two processes must be well adjusted. If, for example, one were drastically to increase the rate of carbon production -- say by a thousandfold -- without increasing the rate of oxygen production, most of the helium would be burned to carbon before it had a chance to combine with carbon to burn to oxygen. On the other hand, if one decreased the rate of carbon synthesis by a thousandfold, very little carbon would be produced, since most of the carbon would be burned to oxygen before it could accumulate in significant quantities.

Astrophysicist Sir Fred Hoyle was the first to notice that this process involved several coincidences which allowed for this balance between the rate of synthesis of carbon and that of oxygen: namely, the precise position of the 0⁺ nuclear "resonance" states in carbon, the opportune positioning of a resonance state in oxygen, and the fact that ⁸Be has an anomalously long life-time of 10^-17 seconds as compared to the ⁴He + ⁴He collision time of 10^-21 seconds (Barrow and Tipler,1986, p. 252).

Now, the position of these resonance states, along with the life-time of ⁸Be, is further dependent on the strength of the strong nuclear force and the electromagnetic force. A quantitative treatment of the effect of changes in the strong force on the amount of carbon and oxygen produced in stars has been performed by three astrophysicists, H. Oberhummer, A. Csótó, and H. Schlattl (2000a). Using the latest stellar evolution codes, they calculated the effect on the production of carbon and oxygen in stars of a small decrease, and a small increase, of the strong nuclear force. Their codes took into account the effect of a change in the strength of the strong force on the relevant resonance levels of both carbon and oxygen, along with the change in temperature of helium ignition. They also examined a wide variety of different types of stars in which carbon and oxygen are produced. Based on this analysis, the authors conclude that

a change of more than 0.5% in the strength of the strong interaction or more than 4% in the strength of the Coulomb force would destroy either nearly all C or all O in every star. This implies that irrespective of stellar evolution the contribution of each star to the abundance of C or O in the ISM [interstellar medium] would be negligible. Therefore, for the above cases the creation of carbon-based life in our universe would be strongly disfavored" (2000a, p. 90).

The exact amount by which the production of either carbon and oxygen would be reduced by changes in these forces is 30 to 1000 fold, depending on the stellar evolution code used and the type of star (2000a, p. 88).

One hitch in the above calculation is that no detailed calculations have been performed on the effect of further increases or decreases in the strong nuclear force that go far beyond the 0.5% presented by Oberhummer, et. al. Specifically, if the strong nuclear force were decreased sufficiently, new carbon resonances might come into play thereby possibly allowing for new pathways to become available for carbon or oxygen formation. In fact, an additional 10% decrease or increase would likely bring such a new resonance of carbon into play. A 10% increase could also open up another pathway to carbon production during big bang nucleosynthesis via ⁵He or ⁵Li, both of which would become bound. Apart from detailed calculations, it is difficult to say what the abundance ratio would be if such resonances or alternative pathways came into play (Oberhummer, et al., 2000b). We can say, however, that decreases or increases from 0.5% to 10% would magnify the disparities in the oxygen/carbon ratios by magnifying the relevant disparities in the rate of carbon synthesis and oxygen synthesis. Thus we have a small island of life-permitting values with a width of 1%, with a distance of 10% between it and the next nearest possible life-permitting island. This would leave a two-sided fine-tuning of one part in ten for the strong force, which is significant without being enormous: for example, if one had six independent cases of one in ten two-sided fine-tuning, one would have a total two-sided fine-tuning of one part in one part in a million.)

Another hitch is the amount of carbon, or oxygen, actually needed for life. Even very small amounts of carbon or oxygen in the interstellar medium could, as a remote possibility, become concentrated in sufficient quantities to allow for complex life to evolve, though the existence of life would almost certainly be much less likely under this scenario. So, it seems, one can conclude with significant confidence that such changes in the strong nuclear force would make intelligent life much less likely, and thus that in our universe the strong interaction is optimized for carbon-based life giving an abundance ratio of carbon to oxygen of the same order (C:O about 1:2).

Overall, therefore, I conclude that the fine-tuning of the strong force for carbon and oxygen production, though not straightforward, seems to be on fairly solid ground because of the detailed calculations that have been performed. Nonetheless, more work needs to be done on the two "hitches" cited above to make it completely solid.

C. Fine Tuning of Proton-Neutron Mass Difference

The neutron is slightly heavier than the proton by about 1.293 MeV. If the mass of the neutron were increased by another 1 MeV - that is, by one part in a thousand of its actual mass of about 938 MeV - then one of the key steps by which stars burn their hydrogen to helium could not occur. The main process by which hydrogen is burned to helium in stars is proton-proton collisions in which two protons form a coupled system, the diproton, while flashing past each other. During that time, one of the protons can undergo a decay via the weak force to form a deuteron, which is a nucleus containing one proton and one neutron. The conversion takes place by the emission of a positron and an electron neutrino: ⁽¹⁴⁾

p + p --> deuteron + positron + electron neutrino + 0.42 MeV of energy.

About 1.0 MeV more energy is then released by positron/electron annihilation, making a total energy release of 1.42 MeV. This process can occur because the deuteron is less massive than two protons, even though the neutron itself is more massive. The reason is that the binding energy of the strong force between the proton and neutron in the deuteron is approximately 2.2 MeV, thus overcompensating by about 1 MeV for the greater mass of the neutron. If the neutron's mass were increased by around 1.42 MeV, however, then this reaction could not proceed at all, because it would become endothermic instead of exothermic (that is, it would absorb energy instead of producing it). Since it is only via the production of deuterium that hydrogen can be burnt to helium, it follows that if the mass of the neutron were increased beyond 1.4 MeV, stars could not exist. ⁽¹⁵⁾

On the other hand, a small decrease in the neutron mass of around 0.5 to 0.7 MeV would result in near equal number of protons and neutrons in the early stages of the big bang since neutrons would move from being energetically disfavored, to energetically favored. (Hogan, 1999, equation 19 and Barrow and Tipler, 1986, p. 400). The protons and neutrons would then combine to form deuterium which would in turn fuse via the strong force to form ⁴He, resulting in an all helium universe, which would have severe (intelligent) life inhibiting consequences since helium stars have a life-time of at most 300 million years and are much less stable than hydrogen burning stars. A decrease in the neutron mass beyond ~0.8 MeV, however, would result in neutrons becoming energetically favored, along with free protons being converted to neutrons, and hence an initially all neutron universe. (Barrow and Tipler, 1986, p. 400 and Hogan, 1999, equation 20.) Contrary to what Barrow and Tipler argue, however, it is unclear to what extent, if any, this would have life-inhibiting, effects. (See appendix, section b.)

Another plausible lower bound of the theoretically possible range R is given by the range of quark masses. According to the Standard Model of particle physics, the proton is composed of the two up quarks and one down quark (uud), whereas the neutron is composed of one up quark and two down quarks (udd). The reason the neutron is heavier than the proton is that the down quark has a mass of 4Mev more than the up quark, which compensates by about 1.7 MeV for the ~2.3 MeV contribution of the electric charge of the proton to its mass. (Most of the mass of the proton and neutron, however, is due to gluon exchange between the quarks.) The quark masses range from 6 MeV for the up quark, to 180,000 MeV for top quark(Peacock, 1999, p. 216). Thus, a 1.42 MeV in the neutron mass - which would correspond to a 1.42 increase in the down quark mass - is only a mere one part in one hundred and twenty-six thousand of the total range of quark masses, resulting in a lower bound for half-parameter fine-tuning of about one part in sixty-thousand.

D. Fine-tuning of Weak Force

One of the major arguments for the fine-tuning of the weak force begins with considering the nuclear dynamics of the early stages of the big bang. Because of the very high temperature and mass/energy density during the first seconds, neutrons and protons readily converted via the weak force into each other through interactions with electrons, positrons, neutrinos, and anti-neutrinos. The rate of this interconversion was dependent on, among other things, the temperature, the density, the mass difference between the proton and neutron, and strength of the weak force.

Because the neutron is slightly heavier than the proton, at equilibrium the number of neutrons will always be less than the number of protons: that is, the ratio of neutrons to protons will always be less than 1. This ratio will depend on the equilibrium temperature, being given by what is known as the Maxwell-Boltzmann distribution. The result is that the higher the temperature (that is, the more energy available to convert protons into neutrons), the closer the ratio will be to one, since the difference in rest mass between the neutron and proton becomes less and less significant as the energy available for interconversion becomes greater.

As the universe expands, however, the density of photons, electrons, positrons, and neutrinos needed to bring about this interconversion of protons to neutrons rapidly diminishes. This means at some point in the big bang expansion, the rate of interconversion becomes effectively zero, and hence the interconversion is effectively shut off. If one were to imagine suddenly shutting off the interaction at some point, one could see that the ratio of neutrons to protons would be frozen at the equilibrium value for the temperature at which the interaction was shut off. The temperature at which such a shutoff effectively occurs is known as the freeze-out temperature, T_f, and determines the ratio of neutrons to protons. The higher T_f, the closer the ratio will be to one.

Now, since the interconversion of protons to neutrons proceeds via the weak force, it is highly dependent on the strength of the weak force. The stronger the weak force, the greater the rate of interconversion at any given temperature and density. Thus, an increase in the weak force will allow this interaction to be non-negligible at lower temperatures, and hence cause the freeze-out temperature to decrease. Conversely, a decrease in the weak force will cause the freeze-out temperature to increase. Using the fact that the freezout temperature T_f is proportional to g_w^(-2/3), where g_w is the weak force coupling constant (Davies, 1982, p. 3), it follows that a thirty-fold decrease in the weak force would cause the freeze-out temperature to increase by a factor of ten. This would in turn cause cause the neutron/proton ratio to become 0.9. (Davies, 1982, p. 64) Thus, almost all of the protons would quickly combine with neutrons to form deuterium, which, as in the case of the hydrogen bomb, will almost immediately fuse to form ⁴He during the very early stages of the big bang. Consequently, stars would be almost entirely composed of helium. As is well-known, Helium stars have a maximum lifetime of only around 300 million years and are much less stable than hydrogen burning stars such as the sun. This would make conditions much, much less optimal for the evolution of intelligent life.

Thus, we have a good case for a one-sided fine-tuning of the weak force. Although there are some reasons to think that a significant increase in the weak force might have life-inhibiting effects, they are currently not nearly as strong. Finally, relative to the total range of forces - which spans a range of 10⁴⁰ - this one-sided fine-tuning of the weak force is quite impressive, being better than one part in 10³⁸ of the total range of forces in nature. ⁽¹⁶⁾

F. Fine-Tuning of Gravity:

The main way in which significantly increasing the strength of gravity would have an intelligent life-inhibiting effect has to do with the strength of a planet's gravitational pull. If we increased the strength of gravity on earth a billionfold, for instance, the force of gravity would be so great that any land-based organism anywhere near the size of human beings would be crushed. (The strength of materials depends on the electromagnetic force via the fine-structure constant, which would not be affected by a change in gravity.) As Martin Rees notes, "In an imaginary strong gravity world, even insects would need thick legs to support them, and no animals could get much larger." (Rees, 2000, p. 30). Of course, organisms that exist in water would experience a severely diminished gravitational force if the density of the organism was very close to that of water. It is unlikely, however, that technologically advanced organisms, such as us, could evolve in a water-based environment given that the overall density of the organism was very close to that of water.

Further, even if aquatic organisms did evolve, such a drastic increase in gravity would still present a problem: any difference in density between various parts of the organism, or between the organism and the surrounding water, would be amplified a billion-fold from what it would be in our world. This would create enormous gravitational differentials. For example, if the liquid inside the organism were one part in a thousand less salty than the surrounding ocean, it would experience a gravitational pull of around a million times the equivalent force on earth of a land-based organism. This would certainly preclude the possibility of bones or cartilage, (Inserting air pockets into the cartilage or bone to compensate would cause it to be crushed under an enormous pressure of about 1,500,000 kilograms per square centimeter (or about 5,000,000 pounds per square inch) a mere one centimeter below the surface.

Now, the above argument assumes that the size of the planet on which life formed would be an earth-sized planet. Could life develop on a much smaller planet? In our imaginary strong gravity universe, a planet that exerted the same gravitational force as the earth on its inhabitants would have to have a radius a billionth of that of the earth, or about half an inch or one centimeter in radius. ⁽¹⁷⁾ Clearly such a planet could not support the energy requirements of even one organism like us, let alone allow for the evolution of organisms of our complexity. On the other hand, a planet with a gravitational pull of a thousand times that of earth -- which would make the existence of organisms of our size very improbable-- would have a diameter of about 40 feet or 12 meters, once again not large enough to sustain the sort of large-scale ecosystem necessary for organisms such as ourselves to evolve.

Of course, a billion-fold increase in the strength of gravity is a lot, but compared to the total range of strengths of the forces in nature (which span a range of 10⁴⁰ as we saw above), this still amounts to a one-sided fine-tuning of one part in 10³¹. On the other hand, if the strength of gravity were zero (or negative, making gravity repulsive), no stars or other solid bodies could exist. Thus, zero could be considered a lower bound on the strength of gravity. Accordingly, the life-permitting values of the gravitational force are restricted to at least the range 0 to 10⁹ G_0, which is one in 10³¹ of the total range of forces. (Here G₀ denotes the current strength of gravity.) This means that there is a two-sided fine-tuning of gravity of at least one part in 10³¹.

We have examined what seem to be six solid cases of fine-tuning of the constants of physics, though we did not examine many other cases of this type of fine-tuning. Further, we did not examine more qualitative cases of fine-tuning, such as those extensively discussed by Michael Denton (1998) - for example, the many special properties of elements such as carbon and oxygen that allow for life. Nor did we look at the way in which the universe has just the right laws for life - for example, if any one of the four forces (gravity, electromagnetism, the strong force, and the weak force) did not exist, life would not be possible. ⁽¹⁸⁾ These other cases of apparent fine-tuning further bolster the case for the universe being delicately arranged for the existence of complex life-forms such as ourselves.

One might wonder about the effect of the development of some grand unified theory that explains the above cases of fine-tuning would have on the case for design. Even if such a theory were developed, it would still be a huge coincidence that the grand unified theory implied just those values of these parameters of physics that are life-permitting, instead of some other value. As astrophysicists Bernard Carr and Martin Rees note "even if all apparently anthropic coincidences could be explained [in terms of some grand unified theory], it would still be remarkable that the relationships dictated by physical theory happened also to be those propitious for life." (1979, p. 612)

So, it is very unlikely that these cases of fine-tuning and others like them will lose their significance with the further development of science.

In this appendix, we will discuss several of the most seriously mistaken lines of reasoning that are prominent, and often repeated, in the literature on fine-tuning. What this shows is that one must demand careful calculations and examination of assumptions before relying on any purported claim of fine-tuning.

A. Strong Force

The most commonly cited mistake in the literature concerns the effect of increasing the strength of the strong force. This mistake goes back to various (perhaps misinterpreted) statements of Freeman Dyson in his Scientific American article "Energy in the Universe" (1971, p. 56) and is repeated in various forms by the most prominent writers on the subject, such as physicists John Barrow and and Frank Tipler (1986, p. 321 -322), Paul Davies (1982, pp. 70 -71), astrophysicist Martin Rees (1999, pp. 48-49), and philosopher John Leslie (1989, p.34). This argument begins with the correct claim that if the strong force were slightly increased, then the diproton would become bound, which means that it could exist for more than a very brief period of time. As it is, the diproton is unbound by a mere 93 KeV, and so, according to Barrow and Tipler (1986, p. 321), an increase of the strong force by a few percent would be sufficient to cause it to be bound. Then it is claimed that because of this, all the hydrogen would have been burnt to helium in the big bang, and hence no long-lived stable stars would exist. According to Barrow and Tipler, for example, if the diproton were bound, "all the hydrogen in the Universe would be burnt to He² during the early stages of the Big Bang and no hydrogen compounds or long-lived stable stars would exist today" (P. 322.).

The first problem with this line of reasoning is that ²He [that is, the diproton] is unstable, and would decay relatively quickly to deuterium (heavy hydrogen) via the weak force. So, the binding of the diproton would not have resulted in an all ²He universe. On the other hand, deuterium could easily fuse via the strong force to form ⁴He. So, wouldn't all the deuterium in turn be fused during the early stages of the big bang to form ⁴He, thus resulting in an all helium universe, as Davies seems to suggest?

The problem with this second argument is that none of these authors present, or reference, any calculations of the half-life of the diproton. Preliminary calculations by nuclear physicist Richard Jones at the University of Connecticut yield a lower bound for the half-life around 13000 seconds, with the actual half-life estimated to be within one or two orders of magnitude of this (private communication). As Barrow and Tipler note, however, there is only a short window of time of approximately 500 seconds when the temperature and density of the big bang are high enough for significant deuterium to be converted to ⁴He (1986, p. 398.) Since only a small proportion of diprotons would have been able decay in 500 seconds, little deuterium would have been formed to convert to ⁴He.

Of course, most of these diprotons would eventually decay to form deuterium, resulting in predominately deuterium stars. Stars that burned deuterium instead of hydrogen would be considerably different from ours, however, with a central temperature about one tenth that of the sun. Preliminary calculations performed by astrophysicist Helmut Schlattl using the latest stellar evolution codes show that deuterium stars with the same mass as the sun would have life-times of around 300 million years, instead of the sun's 10 billion years (private communication). This would seriously hamper the evolution of intelligent life. On the other hand, a deuterium star with a 10 billion-year lifetime would have a mass of 0.04 that of the sun, and a luminosity of 7% of the luminosity of the sun, with a similar surface temperature. (Private communication). This would require that any planet containing carbon-based life be about four times closer to its sun. It is unclear whether such a star would be as conducive to life as our sun.

B. Gravity:

In discussing a strong gravity world, Martin Rees claims that

"The number of atoms needed to make a star (a gravitationally bound fusion reactor) would be a billion times less in this imagined universe.... Heat would leak more quickly from these "mini-stars": in this hypothetical strong-gravity world, stellar lifetimes would be a million times shorter. Instead of living for ten billion years, a typical star would live for about 10,000 years. A mini-Sun would burn faster, and would have exhausted its energy before even the first steps in organic evolution had got under way." (2000, pp. 30-31).

The problem with this reasoning can be easily seen in the following commonly used simple model of a star, in which the star is assumed to have uniform density. In such a star, the condition of hydrostatic equilibrium dictates that:

T_c ~ GM/R (Eq. 5.104 of Barrow and Tipler, 1986, p. 328)

Where ~ represents proportional to, G is the gravitational constant, T_c is the central temperature of the star, M is its mass, R is its radius, and G is the gravitational constant. (I am assuming the star is composed of a single material, hydrogen.)

The lifetime of our model star is:

L_i ~ M/[T_s⁴ R²],

That is, the lifetime is proportional to the mass- which determines the total amount of nuclear fuel - divided by the amount of energy radiated from the surface, which is proportional to the fourth power of the surface temperature T_s times the surface area, R².

Dividing L_i by T_c, we obtain:

L_i/T_c ~1/[GT_s⁴R],

or

L_i ~ 1/[GR] x T_c/T_s⁴, where x represents multiplication.

Thus, if we increased the gravitational constant by a millionfold, the conditions of hydrostatic equilibrium could be met by a star with the same life-time, surface temperature, and core temperature, but with one millionth the radius. The mass of such a star would decrease by a factor of 10¹², as required by the first relation above linking T_c with G, M, and R. The density would correspondingly increase by a millionfold.

Because of the increase in density, the fusion rate per unit of volume of the star would change at constant central temperature, since it is proportional to the density. However, equilibrium between the fusion rate and the rate of energy loss could be easily obtained with one or two orders of magnitude adjustments in core temperature, since the rate of fusion is highly dependent on temperature. (In the case of the typical hydrogen-hydrogen reaction in a star, it varies with the fourth power of the temperature at the sort of temperatures and pressures we find in our sun, whereas for helium burning it varies with the fourtieth power of temperature [Hanson, 1994, p. 22].) ⁽¹⁹⁾ So, it appears that stable, long-lived stars would still be possible in our hypothetical strong gravity world.

C. Proton/Neutron Mass Difference

Barrow and Tipler and others have argued that a small decrease in the neutron mass relative to the proton would also eliminate the possibility of life. Specifically, they argue that if the difference between the neutron mass and the proton mass were less than the mass of the electron, then protons would spontaneously convert to neutrons by the weak force via electron capture. Thus, they claim, the universe would simply consist of neutrons, which in turn

". . .would lead to a World in which stars and planets could not exist. These structures, if formed, would decay into neutrons by pe^- [that is, proton - electron] annihilation. Without electrostatic forces to support them, solid bodies would collapse rapidly into neutron stars . . . or black holes . . .if that were to happen no atoms would ever have formed and we would not be here to know it." (p. 400).

As appealing as this line of reasoning initially sounds, it does not stand up to careful scrutiny. Barrow and Tipler are correct in asserting that protons would initially convert to neutrons. They neglect to consider, however, that the reaction n + n -> d + e^- + anti-neutrino could take place. The reason is that the deuteron has a 2.2 MeV less mass than the sum of two neutrons, as can be seen by the fact that the dineutron fails to be bound, yet the deuteron is bound by 2.2 MeV. (Barrow and Tipler, 1986, p. 321) Hence the decay allows for a conversion of 0.511 MeV for an electron, some amount for a neutrino, and some for the kinetic energy of the electron. Similar processes of conversion would happen in larger conglomerations of neutrons: neutrons would be converted to protons to fill lower energy levels that are already filled with neutrons as much as the Pauli-exclusion principle will allow. If this sort of decay can occur, then the only effects we can immediately deduce that a moderate decrease of the neutron mass would have are that stars would burn very differently and stable nuclei, including hydrogen, would shift towards having a higher proportion of neutrons than we presently find. I know of no current well-developed argument, however, that these effects would inhibit the existence of intelligent life. This is an area that needs further exploration.

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