1. Introduction

Why do the physical constants in our world have the numerical values which they do? This question may eventually be answered at a fundamental level if a Theory of Everything (TOE) can be developed. But until a TOE appears, the following gedanken experiment is of interest: if the physical constants were to take on different values from what they now have, it is conceivable that intelligent life might perhaps not have been able to develop at all. That is, if the physical constants were different, the intelligent being known as Man (Greek= anthropos) might not even be here to raise the question in the first sentence above. This gedanken perspective is referred to as the anthropic principle, which claims essentially that the physical constants have the values they do in order that Man can emerge. In other words, there is a fundamental selection effect at work by the very fact that we even ask the above question: and just as an observer plays a key role in "collapsing" a quantum system into a particular state in the process of making a measurement, so the very existence of an intelligent observer in the universe may "force" us into a universe which can only belong to a certain class.

In the context of this principle, a natural corollary to consider is the following: by how much could one (or more) of the physical constants be altered without interfering with the emergence of intelligent life? If even "small" changes in one of the constants were to have the consequence that intelligent life could not develop, then we might plausibly conclude that the universe is "finely tuned" for intelligent life. But if, on the other hand, intelligent life can develop even when one (or more) of the constants is changed by a "large" amount, then the concept of the universe being "tuned for intelligent life" would lose much of its significance.

An extensive history of the anthropic principle has been provided by Barrow and Tipler (1986), where a broad range of astrophysical questions are examined in quantitative detail from an anthropic perspective. In the present paper, we are interested mainly in what BT had to say about "tuning" the nuclear forces, and the effects which this would have on abundances of certain elements and stellar evolution. We are interested in three problems.

First, as regards nuclear physics, BT argue (p. 322) that if the strong force coupling constant αs were stronger by only 13%, the diproton (= He² ) would become bound, leading to "catastrophic consequences--- all the hydrogen in the Universe would have been burnt to He² during the early stages of the Big Bang and no hydrogen compounds or long-lived stars would exist today". Without hydrogen, there would be no water in our world. Therefore, "If the diproton existed we would not!" (Italics and exclamation point are both in the original.) Second, we ask: by how much could the strong force increase above its current value and still retain the possibility that the main sequence life-time of a solar-like star would remain long enough for abiotic processes to allow life to emerge? Third, since the principal "elements of life" include hydrogen, carbon and oxygen, we ask: what abundances would H, C, and O be expected to have if we "tune" the strong force away from its current value? Might relatively small changes in the strong force lead to much more drastic variations in the C/O ratio, so as to render unlikely the emergence of life forms as we know them (in which bio-molecules are characterized by C/O ratios ≈1 )?

2. Big Bang Nucleosynthesis: How Hard is it to Destroy Hydrogen?

Does the existence of stable He² automatically mean that the hydrogen in the universe will be destroyed? In order to answer that, a parameter study of changes in Big Bang Nucleosynthesis (BBN) was undertaken (MacDonald and Mullan 2009) in which the strong charge parameter G (~√αs ) was increased to as much as 50% of its current value. For G values in the range 1.043-1.065, the dineutron (nn) is bound. For G>1.065 both nn and He² are bound. Binding energies (BE) can be evaluated as a function of G by adopting a square-well potential: for G≈1.5, He² and nn both have BE = 5-6 MeV. Simultaneously, it is crucial to note that BE of the deuteron also increases rapidly above its standard value of 2.2 MeV . For G≈1.5, BE(D) ≈ 30 MeV. Why is BE(D) so much larger than BE(He²)? Because the nuclear force is stronger when spins are parallel: this is allowed in D, but not in He² or in nn (where identical particles are involved). The large BE(D) value has an important effect in BBN: D can survive photodestruction at much earlier times, and therefore build up abundance more rapidly than in "our world". In order to quantify the effects of increased G on BBN, we note that in the presence of a bound diproton, the reaction p+p-> He²+γ occurs via the strong force: as a result, the reaction proceeds much faster than the standard reaction which occurs in "our world" p+p->d+e⁺+ν. The latter is controlled by the weak force, with rates which are slower by fw ≈10₁₈. The expected beta-decay lifetimes of He² and nn can be estimated from the decay properties of the nuclei O14 and C14. Putting these into the BBN equations, it emerges that, with large enough G (≈1.3), there can be two phases of He₄ production, one when the universe is a few seconds old, and another phase when the universe is almost 1000 seconds old. The additional phase of He₄ production can lead to He₄ becoming the most abundant element. But in order to reduce H abundance to (say) 1/10 of its abundance in our world, G must be at least as large as 1.5. In principle, therefore, an increase in the strong force could lead to H yielding to He as the most abundant element in the universe. But this effect will not occur by changing the strong force by only a few percent. Instead, it requires that the strong force coupling constant αs must be at least as large as 2.25 times its current value. And even then, H would still remain at least 100 times more abundant (by number) than the other important "elements of life" (see Section 3). Therefore, H₂O could retain its prime position among the most abundant molecules in the cosmos. Thus, contrary to BT, even if He² were bound, we could still be here.

3. Evolution of Low-mass Stars: Enough Time for Life to Emerge?

In the Sun, the rate of the p+p reaction is controlled by the weak force (see e.g. Mullan 2009): one of the protons must turn into a neutron in order for the process to go ahead. This makes the rate of the reaction the slowest of all reactions in the Sun. But if the diproton were to be stable, then the p+p reaction could proceed via the strong force. In such a case, the p+p reaction rate would be many orders of magnitude faster than in "our world". As a result, the lifetime of a solar-like star could become so short that there might not be enough time for intelligent life (or even life of any kind) to develop on Earth.

Is this a serious argument in favor of nuclear conditions being "tuned" for intelligent life on Earth? Probably not. There is nothing which demands (as far as life is concerned) that the Earth must be in orbit around a star with a mass of 1 solar mass. All that is required for life to have a chance is (i) the environment must be suited for liquid water, (ii) there must be a planet in the habitable zone, and (iii) conditions must remain stable on the planet over intervals of at several billion years. Condition (i), which defines the so-called habitable zone, can be satisfied in principle around any star: it is simply a matter of combining the star’s luminosity L with an appropriate orbital radius of the planet D such that the incoming energy flux L/4πD² heats the planet surface to 273-373 K. There is no fine tuning here: stars of all kinds can satisfy condition (i) within some range of D values. Condition (ii) is harder to evaluate: most of the known exoplanets do not lie in the habitable zone (according to the data on the website exoplanets.org). The physics which determines the distribution of planet orbits around a star is not yet well enough developed to allow a priori evaluation of the probability that at least one planet around any particular star lies in the habitable zone: this probability presumably involves a complicated interplay between gravity, rotation, turbulence, and various loss mechanisms. In fact, we may only have the anthropic principle to guide us here! What about condition (iii)? This could be relevant if the emergence of life on any planet follows the sequence which occurred on Earth: single-cell life may have emerged essentially instantaneously after the end of the late heavy bombardment (LHB), and in any case no later than a few hundred million years after LHB (e.g. Buick 2007), whereas multi-cell organisms (required for intelligent life) may not have been present until some 3 giga-years had elapsed. If the multi-Gyr time-scale is characteristic of the emergence of intelligent life, then we require that the parent star of any planet with intelligent life must provide a steady source of energy over at least several Gyr. (Of course if panspermia is at work, and life is "delivered" to Earth from another plant, maybe intelligent life can develop on shorter time-scales: but it is hard to be quantitative about this.) A star provides a steady source of energy as long as it burns hydrogen, i.e. is on the main sequence: once the star evolves towards the red giant stage, the large increase in luminosity has the effect that life can no longer survive. Therefore, our interest is in stars whose main sequence lifetimes are at least as long as several Gyr.

To see how the physics of stellar evolution helps to offset even extreme variations in reaction rates, we note that non-degenerate stars have a regulatory mechanism built right in: such stars can respond to increased energy production in their cores by expanding. An increase in the p+p cross-section is mitigated by a decrease in the temperature of the stellar core: this reduces the thermonuclear reaction rate so that the star experiences only a small increase in luminosity. Even when we increase the p+p cross-section by fw ≈10¹⁸ (see Section 2), our stellar models indicate that the luminosity of a 1M_ʘ at the beginning of the proton burning phase is only of order 10² L_ʘ . This relatively small (compared to 10¹⁸) increase in luminosity occurs because the central temperature Tc ≈7 10⁵ K, i.e. only 5% of Tc (_ʘ).

When the p+p cross-section is increased by a factor of order 10¹⁸, we find that the main sequence phase consists of two distinct nuclear burning phases. In phase I, protons are converted to He₃nuclei by the reaction chains p(p,γ) He² (,e⁺v)d(d,n) He₃and p(p,γ) He²(,e⁺v d(dp)t (e^-v He₃. During phase I, the star is fully convective and all of the hydrogen is converted to He₃. The lifetime of this relatively short phase is about 0.08 M^-3/4 Gyr for a star of mass M (in units of M_ʘ). The initial luminosity (in solar units) is about 100 M^1.8 and increases by about a factor of 4 over the duration of this phase. At the end of phase I, the star contracts and the central temperature increases to about 9 10⁶ K, which is hot enough for the He₃+He₃reaction to convert He₃into He₄ plus H. Most of the main sequence is spent in this phase II, which has duration 0.2 M^-2.3 Gyr. The luminosity in phase II is about 20 M^2.2. For M = 1, the lifetime becomes so short (200 My) that condition (iii) above is not satisfied.

But this is not a serious problem: we simply switch our attention to stars of lower mass. Our models show that a star of mass 0.22M_ʘ has L in phase II of order L_ʘ , and a main sequence lifetime of ≈5 Gyr. This satisfies condition (iii) above. Therefore, if such a star has a planet orbiting at 1 AU (where water is liquid, given L ≈L_ʘ ), there would be plenty of time for life to develop on that planet as it has done on Earth. To be sure, our models indicate that the effective temperature of such a star is 8200 K. Coupled with the helium dominated atmosphere, this would lead to a higher flux of UV radiation, which might harm some biomolecules on the planet at 1 AU. Moreover, because of the reduced stellar mass, the orbital period of the planet would be 2.1 years. But there seems no reason why life should be definitively precluded from developing on such a planet, despite the fast pp reaction.

4. Carbon and Oxygen Synthesis

The anthropic principle has maximum direct relevance in the chemistry of life, which depends on the enormous diversity of carbon chemical compounds in nature. In the interests of generality, it is sometimes suggested that non-carbon-based life should also be included in the discussion, e.g. silicon-based life. But there are serious chemical difficulties with this hypothesis: SiO₂ is a solid, rather than a gas at the temperatures where water is liquid. Therefore Si-based life does not have access to intake of Si atoms from the atmosphere so as to allow for growth, unless the ambient temperatures were higher than 2000 K. But at such temperatures, the secondary and tertiary bonds in proteins and nucleic acids could not survive. Moreover, the fact that Si lies in the third row of the periodic table has two significant effects. (a) In general, electron energy levels are separated by smaller intervals of energy than those in C (by factors of order 3² /2² , i.e. by factors of 2-3): this leads to increased instability of Si-based compounds relative to analogous C-base compounds. (b) Si differs from C in having 3d orbitals, and these lead to channels of instability for Si-based molecules which are simply non-existent in Cbased molecules. In view of these properties, it seems highly unlikely that there exists any biosphere in which Si has replaced C (Barrow & Tipler, p.545). In the context of the anthropic principle, it seems safe to say that we would probably not exist in a universe where carbon was not available in sufficient abundance to be the basis for life’s molecules.

The prevalence of carbon-based life leads us to ask certain basic questions: (a) How is C synthesized? (Ans: the triple alpha reaction: α+α->Be⁸ followed by α+Be⁸ ->C¹²); (b) Where is C synthesized? (Ans: in stars where temperatures are at least as large as 10⁸ K, so as to overcome the Coulomb barriers. Such temperatures are not reached in solar-like stars until the star reaches the red giant branch); (c) How much C is synthesized in the cosmos as a result? (Ans: depends on the competition between the reactions which build up C and the reactions which destroy C.)

Also, we recognize that there is more to life on Earth than merely carbon: the elements H, N, and O are also crucial for biochemistry. Along with He and Ne (which play no role in life), H, C, N, and O are the 6 most abundant elements in the universe. The relative numbers of the "elements of life" (H, C, N, and O) in the Sun have been determined recently (Grevesse et al. 2010) to be 14800: 4.0: 1.0: 7.2. As regards H, we have already discussed above the abundance which emerges from the BBN. Now we turn to the two elements of life which have the largest cosmic abundances after H and He: C and O. The relatively large abundance of C in the universe (1 C for every 3700 H) was the first example of a quantitative prediction based explicitly on the anthropic principle: Hoyle (1953) predicted that in order for the 3α->C¹² reaction to produce C/H as large as ≈1/3700 in the universe, the C¹² nucleus must contain a bound state at ≈7.6-7.7 MeV above the ground level. This strikingly precise prediction was verified empirically. In the present paper, we are particularly interested in the ratio (by number) of C to O which occurs in living organisms. The molecules of life as we know it include (i) proteins (for structure and for catalysis), (ii) nucleic acids (for storage of information and replication), (iii) phospholipids (for membranes), and (iv) the phosphates of adenosine (AMP= adenosine mono-phosphate; ATP= adenosine tri-phosphate) and carbohydrates (for energy supply). Let us examine the C/O ratio in these constituents. (i) Proteins are composed of chains of amino acids, while nucleic acids are composed of chains of nucleotides. As a result, the life forms which we know on Earth are characterized by C/O number ratios that can be evaluated by simply counting carbons and oxygens in an "average" amino acid and in an "average" nucleotide. For the 20 amino acids which occur in living organisms, the "average" formula for the dominant elements (H, C, N, O) can be written as H_a C_b N_c O_d where a=9.7, b=5.3, c=1.5, d=2.5. This indicates that, in proteins, C/O ≈ 2. (ii) For nucleotides, we can derive an analogous "average" formula for the 5 bases which occur in DNA/RNA using the above form: we find subscripts a=5.0, b=4.6, c=3.4, d=1.2. Adding to this a ribose molecule (H₁₀ C₅ O₅ ) (and ignoring the difference of one oxygen between ribose in RNA and deoxyribose in DNA), plus a phosphate linkage (PO³ ), we arrive at an "average" ribonucleotide formula of the above form (ignoring P) with a=15, b=9.6, c=3.4, d=9.2. Thus, for the nucleic acids, C/O ≈ 1. (iii) Phospholipids, consisting of a hydrophilic branch (where O resides) and a hydrophobic branch (a long chain of hydrocarbons), can have C/O ratios well in excess of unity, depending on the length of the hydrophobic chain. However, the lipids are present mainly in the form of (2-dimensional) surfaces which contribute a relatively small amount to the total content of the (3-dimensional) cell: as a result, the large C/O ratios of lipids may have low weights when we consider the cell as a whole. (iv) AMP is basically the monomer of RNA which contains the lowest amount of oxygen, with C/O ≈ 1.4. Adding phosphates raises the O content, and in ATP, C/O ≈ 0.8. In carbohydrates, the ratio of C/O is exactly 1. Thus, depending on the relative mix of constituents in a singlecell organism, the C/O ratio lies in a narrow range which does not diverge significantly from unity.

This property suggests that the ability to form the constituent molecules of life as we know it will be largest in an environment where the C/O ratio is close to unity. In our Sun, the number ratio C/O is in fact observed to be in the range 0.44-0.69 (using the error bars quoted by Grevesse et al. 2010). And in the Milky Way galaxy as a whole, the C/O ratio is observed to be 0.6 (e.g. Croswell 1996). It is noteworthy that these C/O ratios in the world around us also do not differ significantly from a value of unity. Thus, it appears that the living organisms we know about have developed a chemistry which, in terms of C/O ratio, is adapted to (or driven by) the supply of materials.

In the context of the anthropic principle, we ask: could the C/O ratio be driven significantly far from unity if the strong force were different from the value it currently has? If that were possible, the molecules of biochemistry might have to be quite different from those which are familiar to us on Earth. The rate of C synthesis depends sensitively on the presence of a resonant level in C¹² which lies 0.3-0.4 MeV above the combined energy of the incoming Be⁸ +α nuclei. On the other hand, C is destroyed by adding another α and burning to O. The rate of C destruction by transforming to O depends on a bound level in O¹⁶ which lies about 0.05 MeV below the combined energy of C¹² +α.

Because this level lies below the input energy, the C->O burning occurs via a nonresonant process. This helps to slow down the α-burning which could destroy the C. But suppose the strong force could be varied in magnitude. With enough variation of the correct sign, the resonant level in C¹² might sink or rise to energies where the resonance is lost: the C abundance would decrease markedly. On the other hand, with appropriate variation in the strong force, the level in O¹⁶ might rise to an energy which is high enough that resonant reactions could occur in the C¹² +α ->O channel, thereby increasing the O abundance. To test this possibility quantitatively, Oberhummer et al. (2000) varied the strength of the nuclear force, computed the energy levels of the appropriate states in C and O, and then evaluated rates of reactions. The reaction network was inserted into a stellar evolution code for stars with masses of 20, 5, and 1.3 M_ʘ . In all 3 cases, an increase in the strength parameter of the nucleon-nucleon potential by 0.5% led to an increase in the C/O ratio to values as large as 1000, while a decrease in the strength parameter by 0.5% led to a decrease in the C/O ratio to values as small as 0.001. These swings by a factor of one million (!) in the C/O ratio accompanying changes of only ±0.5% in the nuclear force strength would indicate fine tuning indeed, as fine as in a commercial AM radio. Surely life in environments where C/O ratios are as small as 0.001 or as large as 1000 would have to rely on chemicals which could be quite different from those in "our world".

A follow-up study (Schlattl et al. 2004) incorporated the same nuclear force modifications as those of Oberhummer et al. (2000) into more detailed models of stars. The improved stellar models included effects of mass loss (either by a wind or by a supernova explosion), thermal pulses, and various episodes of dredge-up. To prepare the way for life in a future solar system, mass loss is essential in order to transport the C and O from their places of origin to the interstellar medium (ISM). In massive stars (15 and 25M_ʘ , Schlattl et al. found that the overall amounts of C and O which were synthesized are such that the ratio C/O ranges from about 0.1 to 10 when the nuclear force is changed by ±0.5%. In stars with masses of 5M_ʘ , applying the same changes to nuclear forces, Schlattl et al. find that, during thermal pulses on the asymptotic giant branch (AGB: when significant mass will be lost to the ISM), the C/O ratio in the star plus wind ranges from about 130 to 0.06. For stars of mass 1.3M_ʘ, the equivalent results for AGB evolution range from C/O = 170 to 0.04.

The actual ratio of C/O which will occur in any particular "solar system" will depend on the relative contributions of material from stars of various masses to the local ISM. Using a Salpeter mass function, the number of 1.3M_ʘ stars is expected to exceed the number of 25M_ʘ stars by about 1000, so even if a 1.3M_ʘ star loses only 0.1M(sun) in the AGB phase, whereas a 25M_ʘ star eventually loses essentially all of its mass, the mass balance in the ISM may be dominated by the 1.3M_ʘ stars. In such a case, no longer do we expect swings in the C/O ratio as large as factors of 10⁶ if we were able to "tune" the nuclear force (as reported by Oberhummer et al. 2000): now the swings are significantly smaller. Nevertheless, a range of even 100 in the C/O ratio, when compared to a "tweak" in the nuclear force by only ±0.5%, represents an "amplification" by a factor of 10⁴ in the C/O ratio. It is difficult to be specific, but if we were to examine life-forms in regions where the available initial material was characterized by C/O ratios of 170, or 130, or 10, or 0.1, or 0.06, or 0.04 (rather than close to 1, as in the solar neighborhood), it would not be surprising to find significant differences between the biomolecules which would predominate in such environments and the biomolecules which predominate on Earth.

5. Discussion

In the context of the anthropic principle, we have examined three possibilities which might suggest that nuclear forces in the world are "tuned for intelligent life". First, it was once feared that an increase in the strength of the nuclear force by even a few percent could cause all of the hydrogen in the Big Bang to bind into the diproton (i.e. He² ). This would cause the lightest helium isotope to be stable, and such an outcome could effectively destroy hydrogen, thereby precluding intelligent life. However, this fear has been significantly softened by detailed models. The models indicate that even if the nuclear force is altered by a factor in excess of 100 percent, a significant amount of hydrogen survives. Thus, the tuning (if it exists) which preserves hydrogen in the Big Bang (thereby preparing the way for life), can hardly be considered "fine tuning". Second, if the diproton were in fact to be stable, then the p-p chain in the Sun would proceed some 18 orders of magnitude faster than it does in our world. This led to the fear that the Sun would evolve so rapidly, on scales of millions of years, that there might be not enough time for any life (let alone intelligent life) to evolve. But again, detailed models have softened the blow here also. It is true that an object of one solar mass would burn up all its hydrogen within a few times 10⁷ years. But one then simply shifts attention to the evolution of a lower mass star (e.g. 0.22 solar masses) to find an object which radiates with the luminosity of the current Sun, and which has a hydrogen-burning lifetime of several billion years. On a planet orbiting at 1 AU around such a star, the environmental conditions could be essentially identical to our Earth, even if the diproton were stable. Thus, in the context of stellar evolution, the nuclear force strength does not appear to be tuned to any significant extent for intelligent life.

The strongest evidence for "tuning" of the nuclear force in our world emerges from a study of the relative abundances of C and O. Because resonant levels are involved, even slight shifts, of order 0.5%, in the strength of the nuclear force can alter the C/O ratio by factors of 10 or more, up or down relative to the current value. Such alterations could lead to quite different biochemical molecules from those which exist in our world: the potential impact of such different biomolecules on the development of intelligent life remains an interesting and open question.