Revised February, 2011

       

In Celebration of Psalm Nineteen:
God's handiwork in Creation

Chapter 4
CREATION OF THE ELEMENTS*

No doubt the manifestations of energy within the sun and stars, like the accompanying material phenomena there, can to-day only be surmised. For aught we know, these places may, as has been guessed, be the birthplace of elements and the seat of manifestations of energy quite different from what we have ever observed.

The very existence of a universe in which life can exist requires that it must have some quite remarkable properties. This chapter mentions a few of the most sweeping and general of these properties. Others will be mentioned in due course as our reconstruction of the Creation Narrative proceeds.

Collectively, these remarkable "coincidences" that are necessary for life to exist are called the Anthropic Principle. The classic (but not the first) treatment of this topic is Barrow and Tipler's The Anthropic Cosmological Principle, first published in 1986.

Some of these coincidences take the form of precisely chosen values for many physical and chemical properties. See Reasons to Believe for a (frequently updated) list of these prepared by Dr. Hugh Ross. See also the Wikipedia article on fine tuning.


Preview of Findings: Creation of the Elements
 This chapter makes a number of assertions about the early moments of the universe. Here is summary of the Creation Narrative's main points. Each of these points is further explained below.


Silent Speech

• Channels of Silent Speech
• Element Formation and Element Abundance.
• Direct Measurement of Astronomical Distances




Sharp Points

• Sun-Like Stars and Quantum Tunnelling
• The "Impossible Triple Alpha Process -- Helium Burning
"Monkeyed physics": Nuclear Resonance in Carbon
• The Slightly Low Nuclear Resonance in Oxygen
• The Importance of the Mysterious Neutrinos
• The Fitness of Carbon, Hydrogen and Oxygen for the Existence of Life
• The Laws of Nuclear Physics







Creation of the Elements: Channels of Silent Speech

The scientific understanding of the Big Bang (BB) and how the universe developed since that event -- and in particular how it produced the elements essential for life -- is due almost entirely to the fact that God preserved a number of channels of silent speech over billions of years, so that the speech could be heard and interpreted as scientists developed the tools and techniques to do so within the past century. The progress of modern science is dependent almost completely on the existence of these channels. The very existence of many of these channels depends upon "accidental" features of nature that could well have not existed and which together make our world peculiarly congenial to productive scientific investigation.


The Early Plasma Universe (0-380,000 y)

During the first 15 minutes after the Big Bang (BB) creation of the universe, essentially all of the hydrogen, deuterium, helium and lithium that exist in the universe today, were formed using the (now) well-known natural processes of thermonuclear physics. This stage of primordial element formation is discussed in Chapter 3. It is surprising (to mathematicians and physicists) that fairly basic, almost "idealized" calculations are so effective at describing the results of these early intensely hot times, in terms of the relative abundance and mix of these primordial elements forming under equilibrium conditions (the easiest to calculate)01.

At the end of this brief period, all of the matter in the universe
was a completely ionized plasma. The ambient temperature -- about a million degrees (106 °K) -- was far too low for element formation to continue, but it was far too high for the positively charged nuclei of the primordial elements to hold on to electrons and form neutral atoms.

Although atoms couldn't form,
the early universe was neutrally charged on all but the very smallest scale because of the strong mixing effect of the plasma stew of positively and negatively charged particles. The plasma at this time consisted of vast numbers of virtual helium and hydrogen atoms forming and unforming in a hot equilibrium -- very much like the plasma surfaces of stars, only much hotter02.

The force of gravity was at work from the very first minutes accentuating minute inhomogeneities in the (nearly) uniform density of matter and ultimately forming the material universe into what would become regions of gravitational attraction. This was a very slow process -- because gravity is itself a very weak force and because the universe was very nearly uniform03The formation of stars and galaxies was still hundreds of millions of years in the future.

The Formation of Primordial Atoms and a Transparent Universe (380,000-850,000 y)

Cosmic Background Radiation. About 380,000 years after the Big Bang, the ambient temperature of the universe dropped to about 4,000°K. At this point two events occurred.

First, the temperature dropped to a point at which atomic nuclei can capture electrons and hold them for some time before the electrons are blasted away by the intense radiation
. As more time passed, stable neutral atoms gradually froze out of the plasma stew. This was a slow process (unlike the rapid process when quarks froze out to form protons and neutrons in the first second) but eventually the plasma universe was replaced by a universe of neutral atoms04.

Second, at the beginning of this era, the universe was opaque, because every potential atom in the universe was constantly radiating and absorbing energy in the general frequencies of visible light so that no photon could survive more than a moment before being reabsorbed by a particle. Thus light came from everywhere and
in all directions - and light went nowhere. When the ambient temperature dropped below the range of visible light (the temperatures at which stable atoms form) the universe became transparent to light05. Most photons could survive for an indefinite time, speeding out into infinite space.

By a remarkable providence, we have a record of this time when the universe became transparent to light, in the
Cosmic Background Radiation (presently 2.6° K). This background radiation is the surviving remnants of the heat radiation from this era, red-shifted by the general expansion of space over the intervening 13.7 billion years06. By detailed analysis of this radiation, it is possible to measure the age and condition of the universe at that time (Figure 1). The minute variations in the background radiation depict inhomogeneities in the distribution of matter in the universe. These inhomogeneities were essential to allow the later formation of galaxies and stars (see note 3).

Orion Star Nursery
Figure 1
Full-Sky WMAP Cosmic Background Map
This image shows a temperature range of ± 200 microKelvin.

Star and Galaxy Formation (1 My to Present).

Over time the effects of gravity exaggerated the minor inhomogeneities and slowly caused the universe to separate out into numerous local regions or molecular clouds. As the regions contracted, the effects of gravity strengthened, and temperatures rose due to gravitational acceleration. This process is called 
gravitational collapse.

Molecular clouds are sometimes referred to as star nurseries, because they are the site of new star formation. The closest example of a star nursery is the Orion nebula, designated M42, situated in Orion's sword (Figure 2) within the same arm of the Milky Way galaxy that includes our Sun07. It is a site where many new stars are forming. This nebula is the remnant of previous stars, since  spectral analysis shows the presence of many elements other than hydrogen and helium, the only elements present in the first generation stars and galaxies.

Orion Star Nursery
Figure 2
Orion Nebula, M42 (distance 1300 lightyears)08.



The Orion Nebula (Figure 2)
 
The Orion Nebula is at a distance of 1340 ± 20 lightyears. It is located in the same branch of the Milky Way galaxy as our own sun. It is part of a ring of molecular clouds (called the Gould Belt) that encircle the Sun and is estimated to have formed about 30 million years ago.

Much of the dark matter in the Orion Nebula is back-lighted by the region of active star formation (the bright region in the upper center).

It was evident by the early 1900s that there are many different kinds of stars, although the details of how stars burn was not understood. Stars could be distinguished by illumination intensity (brightness), by color, and by composition -- presence and abundance of the various elements revealed from the star's light spectrum. In 1910, the astronomers Hertzsprung and Russell developed the 
Hertzsprung-Russell (H-R) diagram (Figure 3) which plots star brightness against star color. This diagram clearly shows certain patterns, which at the time could not be explained. Indeed, there was no general explanation at the time of how stars burn09.

Most of the stars, including the Sun, fall in the main sequence (the diagonal from upper left to lower right), but there are also groupings off that main sequence labelled dwarfs and giants based on brightness. An explanation of the H-S diagram's appearance and how stars change their position in the diagram over their lives, had to await an understanding of how stars burn, which occurred in the 1950s.

Hertzsprung-Russell Diagram
Figure 3
The Hertzsprung-Russell Diagram
Star colors are approximately as shown


Star Burning and Formation of the Elements.

At the end of the 19th Century, the source of the energy that is produced in stars, and particularly in the Sun, was one of the great mysteries in science.  Lord Kelvin, one of the century's premier physicists who did pioneering work in thermodynamics,  calculated that the Sun would burn up within 100 million (later reduced to 20 million) years, and yet evidence compiled by contemporary geologists almost certainly showed that the earth is many times older than this10.

Of course Lord Kelvin assumed conventional chemical burning as the source of energy. The missing factor was Einstein's equation for the equivalence of mass and energy, E = mc
2. One consequence of Einstein's equation is the fact that the elements incorporate vast amounts of energy that may be released during nuclear fusion (forming heavier elements from lighter) and nuclear fission (forming lighter elements from heavier), and that this, rather than chemical burning, accounts for the energy of star burning.

Even after the discovery of relativity, star burning was still a great mystery. In 1957 this mystery was finally solved in a landmark paper known as "B2FH"
11. Once again, the solution involved relatively simple mathematical calculations combined with brilliant and ingenious reasoning. The last-listed author, Fred Hoyle, provided the key insight to resolve the issue. Ironically, he was the only one of the authors who did not share a Nobel Prize for the work. The following Creation Narrative for the formation of the elements follows the derivations in B2FH.

Hydrogen Burning (Main Sequence Stars). The stars in the Main Sequence of the H-R Diagram obtain their energy by fusing hydrogen to form helium. This is how the Sun gets its energy. Hydrogen burning - see the box - is the first stage of a star's life and is the slowest star-burning process. It provides relatively steady output for a long time, measured in billions of years.

Over the lifetime of the Earth (4.5 billion years) the Sun has been a remarkably steady source of heat and light. Over that time its lumnosity has increased about 25%, closely matched by a decline in the radioactive heating of the Earth's surface from its own interior. The Earth should be habitable for at least another billion years, and then the helium "ashes" of hydrogen burning  which accumulate in the Sun's core, will heat up under gravitational pressure to reach the point where they will burn in turn. At this point, the Sun will migrate off the main-sequence and move upwards toward the red-giant region of the H-S diagram, gradually growing larger in size and luminosity.

The hydrogen burning in the Sun takes place near the Sun's core (temperature 13.6 million degrees -- around 0.01 MeV). The Sun as a whole is a hot plasma (ionized atoms) but nuclear burning occurs only near the core. At the surface of the Sun the temperature is a balmy 5,800° K, which accounts for its white color12.

Hydrogen Burning
 
Hydrogen Burning -- the p-p reaction -- converts hydrogen into helium and takes place at a temperature of
13.6 x 106 °K -- around 0.01 MeV. It is the nuclear reaction that occurs at the core of Sun-like stars. The curious (and at first puzzling) feature of hydrogen burning is that it takes place at temperatures that are too low for the kinetic energy of the protons (hydrogen nuclei) to overcome the coulomb barrier between them (which would require over 50 MeV).  The actual process  is quantum tunneling.

Two hydrogens fuse to form deuterium, ejecting a neutrino and positron and 0.42 MeV. The positron of course almost immediately annihilates by meeting an electron, producing two 0.51 MeV photons. The Deuterium fuses with another hydrogen to form Helium-3 and 5.49 MeV. Two of these then form Helium-4 and release 2 protons and 12.86 MeV.

Overall, the reaction is an exothermal reaction that converts 4 protons and 2 electrons into a Helium-4 and 2 neutrinos and produces 21.23 MeV.

Hydrogen Burning
Figure 4
Hydrogen Burning



Sharp Point
Sun-Like Stars and Quantum Tunnelling
A habitable planet must have a Sun that burns steadily for billions of years. Over the nearly 4 billion years that the Earth required to build a habitable environment, the output from the Sun has slowly increased about 25%, which is a close match to the slow decrease in the Earth's internal  core heating due to radioactive decay. The result is a temperature environment that has held within narrow limits over the entire 4 billion year period. This leads to two sharp points: (1) The fact of slow H-burning for life to develop; and (2) The maintenance of steady surface temperatures on earth for 4 By, in the face of an increasing output from the Sun and a decreasing heating due to radioactive decay.
Only the hydrogen burning process (p-p burning) can maintain a steady output for such lengths of time. All other burning processes in stars are much shorter in duration. Hydrogen burning is long-lived because the process is difficult to do and hence occurs at a slow rate. No other stage of stellar burning is comparable in duration13. The main-sequence stars on the H-R diagram (Figure 3) are hydrogen burning stars.

Hydrogen burning depends on quantum tunneling. This occurs at temperatures that are too small to overcome the coulomb repelling force, so the wave functions of the two protons tunnel through the coulomb barrier (with a low probability) to form a mass-2 nucleus. Classically this reaction would be impossible unless the two protons were exceedingly energetic (a kinetic energy equivalent to a temperature of 60 million degrees. In fact, quantum tunnelling occurs at 13.6 million degrees.

Quantum tunnelling is based on the fact that all particles (such as protons) have a particle-wave duality (just as photons do).  The wave representation of a proton is a three-dimensional space-filling probability distribution whose amplitude at a (3-dimensional) point X is interpreted as the probability density that the proton exists at X. This wave function peaks at the nominal location of the proton and then tails off towards zero in all directions. If (the wave functions of) two protons approach, the coulomb force distorts the wave function, but nonetheless the two wavefunctions fill space, and there is a small but non-zero probability that the protons are close enough to form a di-proton pair. This is unstable and almost immediately one of the protons decomposes into a neutron, positron and neutrino (called radioactive beta-plus decay in the table below), forming a Deuteron as shown in Figure 4. A second quantum tunnelling forms tritium, and two tritiums combine to form helium-4 plus two protons and a lot of energy.


Formation of Heavier Elements

Helium Burning and Carbon Formation. As the slow hydrogen burning process proceeds, the waste product helium gradually accumulates at the core. Since the temperature is too low for further burning, the accumulated helium contracts under gravity, and heats up from about 14 million to over 100 million degrees, and helium - helium burning occurs.

At this point a dilemma arises. As we noted in Chapter 3, the product of helium burning would normally be either Lithium (He + H with atomic weight 5, half-life about 6.83985×10-22 s) or Berillium (He + He, atomic weight 8, half-life 2.6×10-6 seconds). Both of these are exceedingly unstable and immediately dissociate again. This is the so-called Lithium Barrier at atomic numbers 5 and 8, that prevented the formation of heavier elements in the first few minutes after the Big Bang.

The only apparent way to get past this barrier is to have a triple collision of helium nuclei forming Carbon-12. The problem is that from elementary geometry, it is evident that triple collisions are very low probability events. Fred Hoyle, in 195314 saw the only possible way out of this dilemma, namely that the Carbon nucleus must have a nuclear resonance at around 7.65 MeV15. Subsequent investigation by Fowler established a resonance at 7.68 MeV. With this, the "Impossible" Triple Alpha Process was discovered -- see the box.

The drama of this discovery is narrated in the following account by Simon Mitton, author of Fred Hoyle: Conflict in the Cosmos: Life in Science (2005):

"Perhaps his most celebrated insight occurred in 1953. Fred Hoyle recognized that Salpeter's analysis in this work was incomplete. He pounced. If Salpeter's scenario were accurate, Hoyle supposed, stars would not produce enough carbon to match known cosmic abundances. Without known carbon abundances, human life—Fred Hoyle's life in particular—could not exist. Salpeter wrote:

"I calculated the rate for this indirect conversion of helium into carbon... in the summer of 1951 and published it in the following year. I noted in that paper that my calculated rate could easily be too low by a factor of 1000, say... but I did not have the chutzpah (or guts) to do anything about it: My energy production rate for red giant stars required a central temperature that was within the rather uncertain range given by stellar evolution theory at the time; my calculation would lead to most of the helium being converted to oxygen and neon instead of carbon, but I just did not have the guts to think of resonance levels that had not been found yet! A short while later Fred Hoyle demonstrated both chutzpah and insight... to show that there JUST HAD to be an appropriate resonance level in C[arbon], and he was able to predict its energy. Willy Fowler and his colleagues soon looked for Hoyle’s predicted resonance level and found it just where it should be."

"In a flash of inspiration Hoyle tried to make Salpeter's triple-alpha process work with an enhanced level in 12C. To his amazement he found that if the newly made 12C had a resonance at 7.65 MeV the reaction would proceed at just the correct rate. Hoyle crashed into Fowler's office without so much as a "by your leave" and urged him to measure the resonance levels in carbon. [Apparently Hoyle never published this insight -- which was verified two years later. dcb]

"More than half a century later, Salpeter recognized his role but has trouble forgiving himself for not seeing the door he left open for Hoyle. Astrophysicists who worked in that era say he's too hard on himself, and earned far more credit than he gives himself. 'The burning of helium into carbon is not really one [discovery] that I’m that proud of,' Salpeter told me. 'I goofed. In some ways I’m more embarrassed about that than about having done it.' I asked him why people still refer to it as the 'Salpeter process.' 'That’s just the nickname other people give to it,' he says. 'Hoyle figured it out. Let me put it this way, I’m a more pleasant guy than Fred Hoyle. Maybe they like me better. He was a slightly difficult guy to get along with. But a real genius.'"


Sharp Point
  The "Impossible" Triple Alpha Process -- Helium Burning

Without two very minor and peculiar characteristics of the elements Carbon and Oxygen, the entire program of synthesis of the elements in the stars would not have happened. None of the life elements, particularly carbon and oxygen, would be available to carry out the grand plan of life. As Fred Hoyle remarked, "The genesis [of about half of the elements] depends on the oddest array of apparently random quirks you could possibly imagine." See further remarks by Fred Hoyle in the box below.
Carbon Production. In an "ordinary" world, one would expect carbon to be created as a binary collision between a beryllium or boron atom. But both of these are rare.  This leaves a triple collision of 3 helium atoms -- but triple collisions are also quite rare, as was remarked in Chapter 3.

But we are not in an ordinary world! The production of carbon depends on two successive double collisions: two helium atoms collide to form beryllium-8. This is very unstable (about 7 E-17 seconds). But before disintegrating, it collides with another helium atom forming carbon-12. The key feature that allows this to take place is a particular resonance (7.65 MeV) in the energy levels of the carbon nucleus (see the text). This resonance is discussed in B2HF p. 565 -- see note 11.

Carbon production by Triple Alpha Process -- from Wikipedia

 


Oxygen, Neon and Magnesium. Carbon production is the gateway to all of the heavier elements. So it is good that the "impossible" triple alpha process works -- otherwise a rocky planet such as Earth could never have formed, and life could not have existed. But while the carbon bottleneck has been solved, there is another problem.  Carbon is literally the backbone of life -- it is the backbone of almost every structural molecule used in a living cell. So while it is necessary for heavier elements to be created from carbon, there must be a throttle that keeps an adequate amount of carbon around.

That throttle occurs in the production of Oxygen, which is formed by the reaction of Carbon with Helium: C + He -> O. Another nuclear resonance is involved in this reaction, but this time the end result is not to facilitate the reaction but slow it down somewhat. 


Basic Reactions in Carbon Burning16
 (T~900x106 °K; d~105 g/cc)
12C + 4He + γ -> 16O  (resonance)
(T~300x106 °K,   d~1000 g/cc)
12C + 12C -> 24Mg + γ
12C + 12C -> 20Ne + 4He
16O + 4He + γ <-> 20Ne (resonance)


Carbon is the "ash" of the triple-alpha process described above.  This ash sinks and accumulates to form a carbon core. At the temperatures that support the triple-alpha process, the carbon cannot react further, so it accumulates and compresses under gravitational pressure, until density reaches 105 g/cc and the temperature arises to about 900 x 106 °K.  At this temperature, the carbon reacts with helium (at the surface boundary between carbon and helium) to form neon, magnesium and oxygen. The oxygen reaction also enjoys a nuclear resonance, but this time (in contrast to the case with carbon formation), the resonance energy level is a little below the combined mass-energy of C and He. This slows the reaction down somewhat, which is good, because if the reaction were too easy, then all of the carbon would fuse into oxygen and carbon-based life would not be possible -- see the box.


Sharp Point          The Slightly Low Nuclear Resonance in Oxygen

The position of a nuclear resonance in Oxygen is the second "coincidence" that makes it possible to have carbon/oxygen based life. In the case of carbon, the resonance is slightly above the combined mass-energy of Beryllium and Helium. In the case of Oxygen, a similar resonance is slightly below the combined mass-energy of Carbon and Helium (7.68 MeV resonance vs. 7.65 MeV mass-energy). These two "accidents" determined  that the stars would produce similar amounts of Carbon and Oxygen. If the Oxygen resonance had been slightly higher, essentially all Carbon would have fused into Oxygen; if the resonance had been slightly lower, then only small amounts of Carbon would have fused into oxygen, which would have blocked not only oxygen production, but also the production of the higher elements.  The remarks of Hoyle refer to the combined effect of these two carefully chosen resonances17.


Other Elements up to the Iron Group.
The description to this point shows how synthesis of the lighter elements proceeds in stars. See the Summary of Nucleosynthesis in Stars for further remarks.


Nucleosynthesis in Stars -- Summary
 
Nucleosynthesis of the elements up to the Iron Group (Iron, Cobalt, Nickel) takes place within the stars in successive stages (See Figure 6). The burning (nuclear fusion) takes place in layers at the core, the hottest (highest atomic number) reactions at the core itself, with the others surrounding the core in shells of nuclear activity. At each stage, the "ash" sinks toward the core and is the fuel for the next stage of burning.

This process ends with the Iron Group (Iron, Cobalt, Nickel). These are the most efficiently packed nuclei, and mark the end of exothermic fusion. The heat released during the fusion adds to the heat energy of the star and keeps things burning. Fusion of elements above the Iron Group absorbs rather than releases energy, and so their nucleosynthesis (with the minor exception of Copper) cannot be sustained within the stars.


Silicon burns to form the Iron Group in the equilibrium process. The Iron Group elements sink to the center of the star and cannot sustain further nucleosynthesis, so the core collapses under gravity. If the star is large enough, the end result is a supernova explosion as the gravitational pressure forces the innermost electron levels into the nucleus.

The most common reaction involves fusion of Helium with a heavier element. This leads to elements with even atomic humber (Helium, Carbon, Oxygen, Neon, Magnesium, and Silicon). Nitrogen, an odd-numbered element forms from hydrogen fusing at the boundary between the H and He layers. Other elements and isotopes are the products of many different types of processes.  A summary of these processes is listed in the box below.

Mature star core burning
Figure 6
Nucleosynthesis at the Core of a Mature Star
Shortly before a Supernova

This end-stage of star nucleosynthesis typically occurs in supergiant red stars, which end their lives in supernovas. The bright red star Betelgeuse in the Orion Constellation is one such star (See Figure 7). Some sources conclude that some copper is also formed in such stars. Copper is the first endothermic element, along with all heavier elements, and cannot contribute to star burning, so such production is a parasite, so to speak, of the other exothermic star burning.

Orion with Betelgeuse
Figure 7
Constellation Orion with Super Red Giant Betelgeuse
Source of Lighter elements through Copper18
Note the hazy Orion Nebula in the Sword.



Formation of the Heavier Elements in Supernovas. The last stage of burning for a red giant star produces an Iron Group core. This core cannot carry on further nucleosynthesis because all  elements with higher atomic numbers can only fuse with the input of large amounts of energy.

If the core becomes sufficiently large (Type II supernovas from Red Giants), gravity forces the core to collapse further, until the K-orbit electrons get pushed into the nucleus at which point they combine violently with protons in the nucleus by electron capture -- reverse beta decay: p + e- -> n + neutrino. This proceeds rapidly, reducing most iron group protons to neutrons and ending up with helium, lots of free neutrons, and a large flux of neutrinos. The neutrinos escape, reducing the energy that balanced the gravitational forces, raising the temperature to ~1010 °K and density ~ 3x107 g/cc. The core collapses precipitately with a speed of about 0.4 c to the point where the core is packed at about nuclear density. At this point the neutrons reach maximum packing (by the Pauli Exclusion Principle) and the collapse rebounds with a massive neutrino flux. A shock wave propels outward at speeds approaching light speed. This is the supernova explosion. As the combination of neutrino bombardment and shock wave passes through the outer shells, elements with excesses of neutrons are formed by neutron capture. The excess neutrons then beta decay: n-> p + e- + anti-neutrino to form the heavy elements. The energy required to form the endothermic heavier elements comes from the energy of the shock wave and neutrino bombardment. This is the basic physics of the r-process.


Type II Supernova Physics
   
Massive Red Giant stars such as Betelgeuse end life in a type II supernova. These supernovas are essential buildingblocks of the elements with atomic numbers higher than the iron group. In particular, radioactive elements such as uranium are formed in supernovas.

Such elements are essential for life to exist because radioactive decay of these long-lived heavy elements have kept the earth to a uniformly moderate temperature during the long process of preparing it for advanced life.

 Sharp Point

Importance of the Mysterious Neutrinos

Wolfgang Pauli first postulated the existence of Neutrinos in 1930 to explain apparent violations of the conservation of energy, momentum and angular momentum during beta decay: n -> p + e + [?]. The first experimental detection of neutrinos (actually anti-neutrinos) was not made until 1956. Neutrinos are so elusive that direct detection takes elaborate equipment and even then they are detected only in very small numbers. The reason is that they are neutral, point particles (leptons, like electrons), have very little mass and travel close to the speed of light. For example, the massive neutrino burst associated with Supernova 1987A led to the detection of a total of 24 anti-neutrinos from 4 earth-based neutrino detectors.
 
Neutrinos rarely interact with matter: they will travel through large masses without interacting at all. Even neutrino-antineutrino annhilations are rare: in the rare occasions when they do join up, they generally form neutrino-antineutrino pairs rather than annhilate.

Without neutrinos and antineutrinos, supernovas would not exist and thus heavy elements would not form. Life could not exist.
An important function of neutrinos is to remove energy from the iron core of a massive red giant star, and indeed from the star itself. Very few neutrinos interact with other matter -- or indeed with anti-neutrinos. This is one reason why they are so difficult to detect.

The neutrinos simply pass through the star and escape into space. Most neutrinos and antineutrions generated in supernova explosions are still travelling through space at very high speed.

Because the neutrinos remove energy from the core, the core rapidly collapses under gravity, leading to cascading electron capture and finally neutrons arrive at maximum packing density, which results in the extreme energy bounce and shockwave of a supernova explosion.

If instead, the electron capture process released only energy instead of energy plus neutrinos, the buildup of energy in the core would tend to balance gravity and the electron capture would not become a runaway cascade. The end result would be that the iron core would slowly burn iron into lower atomic number materials, and an equilibrium would be maintained, greatly extending the life of the star. Supernovas would never occur and the heavy elements would (probably) never be made.



The Necessary Size and Age of the Universe.

Over the past hundred years scientists have discovered many (but certainly not all!) of the former secrets of the universe. For example, it is now known how the elements can be formed by nuclear processes that take place during the life and death of stars. This knowledge is thoroughly based on many thousands of scientific experiments conducted in high energy nuclear accelerators which can duplicate the thermonuclear energy and temperature conditions that prevailed in the early universe and in the stars.

Each element has its own thoroughly-studied development pathways -- known natural thermonuclear and radiative processes that form the element19. There are perhaps a dozen of these processes, some of which occurred at the very beginning of the universe, some of which take place in the interiors of stars, and some of which occur in the violent death-throes of a dying star20.

It takes about 10 billion years for these natural processes to produce the mix of elements that are found in the solar sytem and are needed to support life. It then takes another several billion years to form the solar system from these elements and prepare the ecosystem to support human life21. As we develop the Creation Narrative, the reasons for these lengths of time will be made clearer, but for now the important fact is that the project of Life requires a minimum of about 15 billion years, give or take a billion or two. In fact, the age of the universe (13.7 By) is at the lower end of this range, so that life has arrived, arguably, as soon as possible, at the first possible opportunity. As we develop the Creation Narrative, empirical observation indicates that "as soon as possible" -- i.e. no wasted time -- is a characteristic of creation.

It is worth noting the point of view developed in the Creation Narrative, which is that if natural processes are able provide a part of the Creation Narrative, then that is what God did, because he uses natural processes whenever they suffice to achieve the needed result.

As a consequence, with the universe expanding at about the speed of light, it is necessary that the human creation would look out and find a universe as large and as empty as our universe is. Clearly the miniscule size of our particular dwelling place in the universe does not imply man's insignificance in the scheme of things, despite the confident claims of some22. It could not be otherwise -- unless, ironically, God short-cut the natural processes and created the materials of life by fiat. In that case, though, the elements would show a false appearance of age, in contradiction to our assumption.

This leads to the question: What must be true of a universe that will allow it to produce the elements and last for 15 billion years? Such a universe must be very special indeed -- as indeed our own universe is.

Chemical Properties Necessary for Life to Exist

The existence of Life -- any conceivable form of life, not just the sort of life familiar to us -- requires some very special atomic and molecular properties. This is a vast subject that will arise frequently in the Creation Narrative. Here we will note only a few of the most fundamental properties. One of the early treatments of this matter was published in 1913 by Lawrence Henderson in his book The Fitness of the Environment. The quotes below and page references refer to Henderson's book. Many later authors have further developed the subject. One of my favorite is the little book by Harold J. Morowitz, Beginnings of Cellular Life (1992).

These treatments ask not just what is required for life of any sort, not just life as we know it on earth. One author even considers (and dismisses) the possibility of gaseous, liquid or solid (as in crystalline) life. The result of these investigations is that life depends in a fundamental way on certain chemical properties of a small number of elements and molecular compounds.

The required elements are: Hydrogen (H), Carbon (C), Oxygen (O) and Nitrogen (N). These are not just elements that appear in every form of life known on Earth (there are about 15 such elements), but elements and compounds whose properties are absolutely essential for any sort of life to exist. Notably missing from this list are some elements that were at one time thought to be possible candidates: for example Silicone (Si) as a substitute for Carbon, and Sulfur (S) as a substitute for Oxygen. We will defer the discussion of such things to a later chapter.

Water (H2O) is the most basic universal essential for life of any sort to exist. Water is truly a miracle molecule because of its numerous un-matched qualities (discussed in Henderson and many other authors). Henderson calls it "the only fit substance as the basis for life." [GET SPECIFIC REFERENCE]:

• It is a near-universal solvent, used to transport dissolved gases, nutrients and wastes to and within living cells "literally nothing to compare with water... nearly the whole science of chemistry has been built around water and aqueous solutions" (p.110).

• It is the best or nearly the best choice in many categories involving heat properties:
- Thermal conductivity
- Latent heat of melting (absorption of heat from melting)
- Specific heat (ability to hold heat)
This makes water and in particular the oceans into a remarkable heat regulator for both the Earth's environment and for living species. "The most obvious effect of the high specific heat of water is the tendency of the ocean and of all lakes and streams to maintain a nearly constant temperature." (p. 86).

• Because water expands on freezing, ice floats on the tops of oceans and lakes rather than sinking to the bottom. If ice sank then over the course of time, the bodies of water would gradually freeze from the bottom up, leaving only a thin layer of liquid water near the surface. In this event the oceans could not regulate the Earth's heat and weather.


Carbon in the form of Carbon dioxide (CO2) is an invaluable molecule that also has unmatched properties that are essential to life.
• It dissolves readily in water and forms a weak acid (carbonic acid which combines carbon dioxide and water). "Unlike oxygen, hydrogen, and nitrogen, carbonic acid enters water freely; unlike sulphurous oxide and ammonia, it escapes freely from water. Thus the waters can never wash carbonic acid out of the air, nor the air keep it from the waters. It everywhere accompanies water." (p. 138)
• It is gaseous at normal temperatures and is essential to respiration and in maintaining an ecological balance between plants and animals. "Were carbon dioxide not gaseous, its excretion would be the greatest of physiological tasks; were it not freely soluble, a host of the most universal existing physiological processes would be impossible." (p. 140).

Not surprisingly, Henderson does not develop the vital role of Nitrogen, except to mention that it is found in many carbon chains. The reason for this is that its role in genetic building-blocks was not fully understood until over 50 years later. A later chapter of this narrative discusses the vital role for nitrogen -- and its virtual unavailability on the early earth.

In summary, Henderson remarks (p. 276): "There is, in truth, not one chance in countless millions of millions that the many unique properties of carbon, hydrogen, and oxygen, and especially of their stable compounds water and carbonic acid, which chiefly make up the atmosphere of a new planet, should simultaneously occur in the three elements otherwise than through the operation of a natural law which somehow connects them together. There is no greater probability that these unique properties should be without due cause uniquely favorable to the organic mechanism. These are no mere accidents; an explanation is to seek. It must be admitted, however, that no explanation is at hand."

 
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SUPPLEMENTARY NOTES


 Sharp Point

Lawrence Henderson on The Fitness of Carbon, Hydrogen and Oxygen for the Existence of Life.
Lawrence Henderson wrote the book, The Fitness of the Environment in 1913. He was one of the first scientists to make an anthropic argument for the uniqueness of the conditions required for advanced life to exist (although he considered simple life to be abundant throughout the universe). Selected quotations are:

"logically, in some obscure manner, cosmic and biological evolution are one... not merely contingent, but resembling those which in human action we recognize as purposeful." (p. 278)

"But if to the coincidence of the unique properties of water we add that of the chemical properties of the three elements, a problem results under which the science of today must surely break down. If these taken as a whole are ever to be understood, it will be in the future, when research has penetrated far deeper into the riddle of the properties of matter. Nevertheless an explanation cognate with known laws is conceivable, and in the light of experience it would be folly to think it impossible or even improbable. Such an explanation once attained might, however, avail the biologist little; for a further problem, apparently more difficult, remains. How does it come about that each and all of these many unique properties should be favorable to the organic mechanism, should fit the universe for life? And for the answer to this question existing knowledge provides, I believe, no clew." (p. 251)

    "There is, in truth, not one chance in countless millions of millions that the many unique properties of carbon, hydrogen, and oxygen, and especially of their stable compounds water and carbonic acid, which chiefly make up the atmosphere of a new planet, should simultaneously occur in the three elements otherwise than through the operation of a natural law which somehow connects them together. There is no greater probability that these unique properties should be without due cause uniquely favorable to the organic mechanism. These are no mere accidents; an explanation is to seek. It must be admitted, however, that no explanation is at hand." (p. 276)

"There is, however, one scientific conclusion which I wish to put forward as a positive and, I trust, fruitful outcome of the present investigation. The properties of matter and the course of comic evolution are now seen to be intimately related to the structure of the living being and to its activities; they become, therefore, far more important in biology than has been previously suspected. For the whole evolutionary process, both cosmic and organic, is one, and the biologist may now rightly regard the universe in its very essence as biocentric." (p. 312)

The Silent Speech   Element Formation and Element Abundance

One of the most powerful examples of the Silent Speech is the discovery of how the elements were formed. This discovery is based on the fact that nuclear processes follow straightforward logical rules that build up from relatively simple principles of formation.

The number of protons in the nucleus determines the element. The number of neutrons determines the isotopes of the element.  All elements heavier than hydrogen require at least one neutron in the nucleus (the so-called "di-proton" is extremely unstable and decomposes into deuterium).

Essentially all nuclear reactions are the result of binary collisions -- the high energy collision between two particles, for the geometric reason that  the simultaneous collision of three or more particles is exceedingly unlikely. Given this, only the following interactions are at all likely:

type
particle/element
 element
formula
comment

neutrinos & anti-neutrinos


These do not interact with matter or with each other to any appreciable extent except under conditions of extremely high flux in a supernova.
primordial
p
n
p + n -> deuterium + energy
Requires a free neutron. Rare interaction after the primordial synthesis since free neutrons have a half-life of about 15 minutes.
fusion
p
x
p + x -> element x+1
For an interaction to occur the kinetic energy of the proton and of x has to overcome the charge barrier posed by the nucleus of x. This barrier is increasingly formidable as the atomic number of x increases.
fusion
n
x
n + x -> isotope of x
The neutrons must come from a recent prior collision because of the neutron  half-life. Neutron interactions are relatively easy because there is no charge barrier to overcome.
fusion
x nucleus
y nucleus
x + y ->
element x+y
The charge barrier is increasingly formidable as the atomic numbers of x and y increase.
radioactive beta minus decay
n -> e + p + anti-neutrino
x
element x+1
occurs if the element has an excess of neutrons
radioactive beta plus decay p + energy -> n + positron + neutrino x
element x-1 occurs if the element has a deficiency of neutrons
radioactive electron capture
p + e -> n +  neutrino
x
element x-1
An electron is captured from the element's own shell (K-capture for the K shell). Occurs with extreme gravitational collapse.
alpha decay
x -> x-2 + He

element x-2




Black Holes?  The Schwarzschild radius for a black hole is R = 2gm/c2 where m is the mass of the black hole. The Compton wavelength is λ=h/mc where h is the Planck constant. If the Compton wavelength exceeds the Schwarzschild radius then no black hole is possible. The crossover is the Planck mass, about 2x10-11 g.  For comparison, a proton has a mass of 1.67262158 × 10-24 g -- all of the elementary particles are far too small to become black holes. According to Hawking's theory, micro black holes "evaporate away" over time so that any primordial black holes still around today would have to have masses around 1015 grams.

The intriguing question is whether black holes might have been among the "clumps" produced in the very early universe. Could these account for the missing mass in the universe? Could they have been the "seeds" for the eventual formation of the early galaxies?


There is no lower limit on the size of mass m, but of course the radius becomes very small.



Binary Interactions

Most of the nuclear reactions occur as binary interactions.

Pair Production. In pair production a high energy gamma ray produces a particle and its antiparticle. The energy of the gamma ray must exceed the combined mass-energy of the particles. Thus for electron pair production the energy must exceed 2x0.511 MeV (about 10 Billion °K).
Pair Annhilation.  Pair annhilation occurs when matter collides with the corresponding antimatter particle. The result is the production of two gamma rays of approximately equal energy corresponding to the particle mass-energy. Unlike pair production, pair annhilation can occur at any temperature.


Note that the combination of pair production and annhilation does not exactly restore the original state because one original photon becomes two photons. It is not possible for two photons to combine for form a single photon (or to engage in pair production). Thus the combination increases entropy. Of course pair production is in equilibrium with pair annhilation if the ambient temperture is sufficiently high.

Proton-Neutron Conversion #1. A proton combines with an anti-neutrino to form a neutron and positron. Q: WHEN DOES THIS OCCUR???

Proton-Neutron Conversion #2. A neutron is produced by a proton-electron collision under extremely high energy conditions, such as in K-orbit electron capture by a nuclear proton as the iron core of a dying star collapses. The ambient temperature supplies the difference in mass-energy (0.782 MeV) between the neutron and the combined proton + electron mass, and the energy equivalent of the neutrino.


Note that neutrinos and antineutrinos can be very long-lived particles. They are neutral point particles, so that there is hardly any circumstance when they would naturally collide (unlike electron-positrons which are attracted to each other by electrical forces). So when neutrinos and antineutrinos are produced in stellar nucleosynthesis, the vast majority escape into space and never interact with themselves or with other matter. The Neutron-Proton Conversion #1 occurs in the extremely high antineutrino flux conditions of a supernova explosion.

Neutron-Proton conversion. This is the standard neutron beta-decay. Free neutrons are unstable (with a half-life of 15 minutes) and decay into protons and electrons.







Stable Elements
Most stable/most abundant Isotope
    Element isotopes are formed by adding neutrons. Each isotope has its own atomic mass. The mass per nucleon indicates the binding energy of the isotope. The most stable isotope of a given element is the one with the highest binding energy per nucleon. For example, here are the results for helium:

Helium -- 2 protons
#n
mass (amu)
Binding Energy
per nucleon (MeV)
1
3.01603
2.2315
2
4.00260
6.8142 *Maximum* -- He-4
3
5.01222
5.2739
4
6.01889
4.7033
5
7.02802
3.9687
6
8.03392 3.7938
7
9.04395
3.2306


Carbon -- 6 protons
#n
mass (amu)
Binding Energy
per nucleon (MeV)
2
8.037670
2.7150
3
9.031036
3.9954
4
10.01685
5.7228
5
11.01143
6.3942
6
12.00000 7.4200 *Maximum* C-12
7
13.00335
7.2295
8
14.00324
7.2963
9
15.01060
6.8907
10
16.0147
6.7253


Oxygen - 8 protons
#n
mass (amu)
Binding Energy
per nucleon (MeV)
4
1.00286
4.5367
5
1.00191
5.4949
6
1.00061 6.7567
7
1.00020
7.1870
8
0.99968 7.7160 *Maximum* O-16
9
0.99995 7.5054
10
0.99995
7.5348
11
1.00019
7.3460
12
1.00020
7.3588


Neutrons cannot be added above the Neutron Drip Line. This is the point at which neutrons leak out of the nucleus because the effective binding energy of the added neutron drops below zero. Similarly the Proton Drip Line is the point at which the proton's effective separation energy is zero.




Processes involved in Stellar Nucleosynthesis
As described in
B2FH
   
"Gravitation is a "built-in" mechanism in stars which leads to the development of high temperature in the ashes of exhausted nuclear fuel. Gravitation takes over whenever nuclear generation stops; it raises the temperature to the point where the ashes of the previous processes begin to burn." [p. 567]


Process
T °K
Density gm/cc
Products
Description
H burning 13.6x106
He4
Quantum tunnelling. The process of the main sequence stars.
He burning 100x106 to ~108 ~105 C12, O16, Ne20
density  g/cc.
a process ~109
Mg24,  SI28, S32, A36, Ca40, Ca44, Ti48
Alpha Capture. The source of the a particles is different in the a process than in helium burning. Timescale 102 to 104 years.
e process 4x109
Va, Cr, Mn, Fe, Co, Ni
Equilibrium Process. Timescale seconds to minutes.
r process
neutron density ~1024 n/cc
many isotopes
Rapid Neutron Capture. 0.01-10 s. beta-decay processes. Timescale 10-100 s.
s process

many isotopes
Slow Neutron Capture.  Time scale 100 y to 100,000 y.
p process


proton capture.
x process


D, Li, Be, Bo
unstable at star interiors. Produced in regions of low density and temperature.

Stellar Nucleosynthesis



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FOOTNOTES

* The Background is the galaxy m51 called the Whirlpool Galaxy (Figure ??). It is included in the first catalog of deep sky objects (nebulae, star clusters, galaxies, etc.) published in 1774 by Charles Messier. In 2005 a supernova occurred in this galaxy, denoted SN2005cs, located out of view just above the top center of the figure.

Galaxy m51
Figure ??
Galaxy m51
The Whirlpool Galaxy
distance 31 million light-years

^n01 See for example the straightforward calculations summarized in Equilibrium and Change: The Physics Behind Big Bang Nucleosynthesis. Many references and popular expositions of the primordial synthesis show how to calculate the abundance of primordial helium. It is a half-page calculation involving little more than the relative mass-energy of hydrogen and helium.

Here's a crude illustration of the calculations. Under "equilibrium" or "symmetry" all particles tend to show up in inverse proportion to their energy (mass) content. He++:H+ mass ratio is slightly under 4:1 because He++ has slightly less mass than 4 H+. Thus Hydrogen is slightly over 4x as abundant as helium.  Similarly, p:n mass ratio is slightly under 1.0, so there are slightly more protons than neutrons. When free neutrons decay, more H+ is formed, so the ratio of He++/H+ lowers slightly as the neutrons decay. More precise details depend on the decay rate of neutrons, the presence of H and He isotopes, and of Li. But these are second order effects. It's (almost) that simple!

^n02 The sun's plasma surface is not smooth, but is frequently subject to huge electromagnetic storms. One can imagine that such storms will be frequent in the plasma of the early universe, so the fact that it is neutral at most scales, does not mean that it will be tranquil!

^n03 A precisely uniform universe will remain uniform because the forces of gravity are exactly balanced. But even the smallest non-uniformities will cause centers of gravitational attraction to form, and these will become more pronounced with time. The catch is, that the gravitational centers must exist but they must not include too much mass or too little mass, or else they might collapse into super-massive black holes on the one hand, or on the other hand, expand to a vaporous expanse that is incapable of forming galaxies. This amounts to yet another Goldilocks paradox: not too large, not too small; just right.

From a physicist's viewpoint, the evolution of the universe -- expanding or contracting, forming stars and galaxies -- depends remarkably on certain parameters taking on very precise values. In other words, the universe is not robust: it is peculiarly sensitive to these values. Parameters that come to mind are: (1) the density of the early universe; (2) the minute fluctuations in the density distrbution of the early universe; (3) the mass-excess of neutrons over protons; (4) the instability of elements with atomic weights 5 and 8.

Through history, the success of physics and the ability of mathematical reasoning to describe the universe has depended on the existence of stable and robust ways to model the behavior of physical objects. For the most part, this kind of reasoning has been remarkably -- astoundingly -- successful. In the face of this fact, it is particularly remarkable and strange that the very existence of a universe that allows humans to exist depends at its very foundations on such inherently unstable parameters.

^n04  For comparison, the Sun's surface temperature is about 5,800°K, an ionized plasma. The Rydberg Constant (13.6 eV = 157,760 °K) is the binding energy (ionization energy) of the electron in the hydrogen atom. In order to have a stable hydrogen atom, the ambient temperature should be under a  few percent of this value. At 380,000 years after the BB, the ambient temperature (4,000 °K) was about 2.5% of the hydrogen ionization energy. The Planck Radiation Formula gives the energy distribution corresponding to a give ambient temperature.

^n05 David Medved, Hidden Light: Science Secrets of the Bible  (2008) suggested that God's command "Let there be Light" in the Genesis Creation account (Gen. 1:3) refers to this time when the sky became transparent. My own inclination is to equate this command to the creation of radiant energy in the BB itself. See my review of the book and remarks in Chapter 3.

^n06 This radiation, which is (nearly) uniform blackbody radiation in all directions -- said to be the most perfect example of blackbody radiation in nature -- was discovered in 1964 by Bell Telephone Laboratory scientists Arno Penzias and Robert Wilson. It had earlier been predicted in 1948 by George Gamow, Ralph Alpher, and Robert Herman, and almost immediately upon the discovery in 1964, the connection with the earlier prediction was made. Fine-structure measurements of the cosmic background radiation were made by the NASA Cosmic Background Explorer satellite (COBE) satellite, and its successor, the Wilkinson Microwave Anisotropy Probe.

A Cal Tech movie shows the evolution of the density fluctuations of the universe from the WMAP distribution to the present. See also Thomas Jarrett, Large Scale Structure in the Local Universe and the Wikipedia article, Large-Scale Structure of the Cosmos.

This cosmic background radiation again illustrates the basic simplicity of the mathematical calculations needed to find deep truths about the universe -- limited to: (1) the expansion of the universe since roughly 600,000 years after the BB; (2) the radiation distribution (essentially Planck blackbody radiation); (3) The distribution of times that the radiation started out (a simple function of time (temperature) of the expanding universe at 350,000-850,000 years after the BB). Even the fact that the critical expansion occurred over 13 billion years ago, over a mere 500,000 year timewindow, means that the accuracy in determining the age of the universe can be achieved to better than 1% accuracy.

^n07 Our Sun and the Orion constellation, including the Orion nebula, are both located in the Orion Spur, a branch off of one of the main spirals of the Milky Way, at distances ranging from 250 to 1,6 00 ly. See Chapter 5 for more information.

^n08 This image is a false color composite where light detected at wavelengths of 0.43, 0.50, and 0.53 microns is blue. Light at wavelengths of 0.6, 0.65, and 0.91 microns is green. Light at 3.6 microns is orange, and 8.0 microns is red. Image credit: NASA/JPL-Caltech/STScI (11/7/2006).

^n09  Ejnar Hertzsprung and Henry Norris Russell first developed this diagram 1910-1912 in their work at classifying star types (a lifetime pursuit of Ejnar Hertzsprung. The physical basis for the diagram was not understood until the 1950s. For remarks about the discovery of the spectrum and Auguste Comte's negative appraisal about starlight, see Chapter 1, note 21.

^n10 William Thomson (knighted in 1866 as Lord Kelvin) was one of the first to formulate the first and second laws of thermodynamics, and was also a pioneer (in collaboration with James Prescott Joule) in the kinetic theory of gasses, formally known as statistical mechanics, in which heat is modelled as the rapid motion of many discrete atoms.

In the 19th century there were two particular puzzles in thermodynamics that could not be explained by the science of the day. According to
19th century science  both the earth's interior and the sun heat should have cooled in a period of time far less than geology indicated for the age of the earth. Of course the answer is the heat of nuclear fission in the case of the Earth's interior, and the heat of nuclear fusion in the case of the Sun, neither of which were known to 19th century scientists. The Earth maintains its mild temperatures because of the radioactive decay of uranium and other heavy metals. The heat of the Sun is the result of nuclear fusion, primarily of Hydrogen fusing to form helium.

To appreciate the dilemma as known at the start of the 20th Century, consider the following remarks by 19th Century scientists. Most of the relevant papers of
Sir William Thomson (Lord Kelvin), are available online at Writings of Lord Kelvin; in particular On the Age of the Sun's Heat (1862) (Macmillan's Magazine vol.5 (March 5, 1862) 388-393) and On the Secular Cooling of the Earth (Transactions of the Royal Society of Edinburgh, XXIII, pp. 167-169, (read 1862, published 1864).

The Geologist Sir J. William Dawson gave the following picturesque summary in 1893:

Sir J. William Dawson, Some Salient Points in the Science of the Earth. (1893), p. 416 "The well-known estimate of Lord Kelvin gave one hundred millions of years as the probable time necessary for the change of the earth from the condition of a molten mass to that which we now see. On this estimate we might fairly have assumed fifty millions of years as covering the time from the Laurentian age to the modern period. The great physicist has, however, after allowing us thus much credit in the bank of time, 'suddenly put up the shutters and declared a dividend of less than four shillings in the pound.' In other words, he has reduced the time at our disposal to twenty millions of years." [Note: Actual age from a molten state to the present is about 5 billion years -- dcb]

Other geologists of the era made similar remarks: James D. Dana, Manual of Geology (1896) p. 1025; Karl Alfred von Zittel, History of Geology and Palæontology to the End of the Nineteenth Century (1901) p. 169
; Sir Archibald Geikie, Text-Book of Geology (1902) p. 109-111. Geikie concluded (p. 111): "There can be no doubt that the demands of the earlier geologists for an unlimited duration of past time, for the accomplishment of geological history, were extravagant and unnecessary. But it may be questioned how far the recent limitation of time proposed from physical considerations are really founded on well-established facts. The argument from the geological record in favor of a much longer period than physicists are disposed to concede is so strong that one is inclined to believe that these writers have overstated their case. The evidence from the nature of the sedimentary rocks, and from the succession of organic remains in these rocks, appears to me to demand an amount of time not far short of the hundred millions of years originally granted by Lord Kelvin."

All of these remarks were made prior to Albert Einstein's publication of the Special Theory of Relativity (1905), and the physical explanation of the experiments of the Curies on radioactivity, which opened the door for the correct understanding of the underlying physics. A hint of this can be found in a footnote to John Theodore Merz, History of European Thought in the Nineteenth Century  Vol. III, p. 582 published in 1912:
"It may be well to remark here that the discovery of radium by M. and Mme. Curie in 1898, and the remarkable phenomena of radioactivity, may very considerably change our ideas as to the sources of heat and the gradual cooling of the sun."

^n11 Geoffrey Burbidge, Margaret Burbidge, William Fowler and Fred Hoyle, Synthesis of the Elements in Stars, Reviews of Modern Physics 29 (1957) p547-650 (B2FH - pronounced "B-squared F H"). See the Wikipedia article. See also a brief preceeding article by the Burbidges (1956). For a Forty year update see: G. Wallerstein, Synthesis of the elements in stars: forty years of progress (1997).

An excellent presentation of the remarkable fine-tuning involved in the production of the elements is found in the Reasonable Faith presentations:  Big Bang Theory and the Incredibly Precise Design of the Universe   and Big Bang and Beyond. The latter presentation includes notes on the "stellar mystery" of helium fusion, Hoyle's "Wild Guess" and the problem of achieving a balance between carbon and oxygen production (slides 26-33).

^n12 3,500° K is considered "soft white", 4,500° is blue-white and 5,500° K is "hard-white".

^n13 Note the following timescale for Nucleosynthesis in the stars. Only H-burning has durations of a billion (109) years or more. Helium burning, the next stage in nucleosynthesis, takes about 10 million years, and formation of heavier elements is much less than that -- ranging down to seconds for the heaviest elements.

Timescale
Creation of the Elements in Stars
   
Starburning Timescale
Figure 4
Timescale for Nucleosynthesis in stars
Source: B2FH p. 558

Note: The various processes in this diagram are discussed here.


The life cycle of the Sun is shown in Figure 5. Eventually it will become a red giant and engulf the earth.

Solar Life Cycle
Figure 5
Life Cycle of the Sun (from Wikipedia)

^n14 F. Hoyle, D. N. F. Dunbar, W. A. Wenzel, and W. Whaling, Phys. Rev. 92, 1095 (1953).

^n15 Resonance 

^n16 Bradley S. Meyer et al., Nucleosynthesis and Chemical evolution of Oxygen (2005)

^n17 See the discussion of these resonances in Barrow and Tipler's The Anthropic Cosmological Principle:
"The 7.6549 MeV level in C12 lies just above the energy of Be8 plus He4 (= 7.3667 MeV) and the aquisition of thermal energy by the C12 nucleus within a stellar interior allows a resonance to occur. ... The O16 nucleus has an energy level at 7.1187 MeV that lies just below the total energy of C12 + He4 at 7.1616 MeV. Since Kinetic energies are always positive, resonance cannot occur in the 7.1187 MeV state. Had the O16 level lain just below that of C12 + He4, carbon would have been rapidly removed via the alpha capture: C12 + He4 -> O16 [+ 7.161824 MeV -- dcb]. ... Hoyle realized that this remarkable chain of coincidences -- the unusual stability of beryllium, the existence of an advantageous resonance level in C12 and the non-existence of a disadvantageous level in O16 -- were necessary, and remarkably fine-tuned conditions for our own existence and indeed the existence of any carbon-based life in the Universe."  p. 252-253.

The time may come (but probably not soon) when it is possible to compute these resonance levels from basic facts of nuclear physics. When [if] that happens, then these providential resonances may be shown to be related to more fundamental physical parameters. One wonders, in that case, how much precision in these basic parameters (likely quite high) would be required to achieve these remarkable results without which there would be no life, and indeed the entire makeup of the Universe would not only be hostile to life, but be composed of a very different mix of elements.

Sharp Point
Fred Hoyle on the Laws of Nuclear Physics.
"The genesis [of about half of the elements] depends on the oddest array of apparently random quirks you could possibly imagine.

   "I will try to explain what I mean in terms of an analogy....We would scarcely expect to find Government policy depending in a really crucial way on the fact that the Prime Minister possesses a moustache while the Foreign Secretary does not. These are my random quirks. And if we should find that Government policy depended in a really vital respect on the Minister of Works possessing a mole beneath his left ear, then manifestly we should be justified in supposing that new and hitherto unsuspected connexions existed within the field of political affairs.

   "Yet this is just the case for the building of many complex atoms inside stars. The building of carbon depends on a moustache, the building of oxygen on a mole, and if you prefer a less well known case, the building of the atom dysprosium depends on a slight scar over the right eye.

   "If this were a purely scientific question and not one that touched on the religious problem, I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars. If this is so, then my apparently random quirks become part of a deep laid scheme. If not, then we are back again to a monstrous sequence of accidents." Fred Hoyle, Lecture in Mervyn Stockwood, ed. Religion and the Scientists SCM 1959, p.64.

"A common sense interpretation of the facts suggests that a super intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."
Fred Hoyle, Steady-State Cosmology Revisited, Cardiff Press, 1980. Cited in: Fred Hoyle,  The Universe: Past and Present Reflections (1981); Annual Review of Astronomy and Astrophysics, 20 (1982), p4; Michael J. Denton, Nature’s Destiny: How the Laws of Biology Reveal Purpose in the Universe, Free Press, 1998, p12 .

^n18  Figure from The Stellar Origin of Copper by Ken Croswell (2007).

^n19 See, for example, the description of the nucleosynthesis processes in Lang's Astrophysical Formulae 3rd Edition, Volume I Chapter 4 "High Energy Astrophysics". Figure 4.6 notes the nuclear processes, which are listed on p. 406. The second edition of this reference (which I prefer) includes a comprehensive table of the processes (Table 38 p. 335-372, cf. p. 420) which is missing in the third edition.

^n20 The modern description of the way that the stars form the elements was first given in the famous B2FH paper. For almost a century prior to this paper, some scientists had speculated that the elements were formed in the stars, such as Lawrence Henderson (See the quote at the head of this chapter).

^n21 See B&T p. 3 "For there to be enough time to construct the constituents of living beings, the Universe must be at least ten billion years old and therefore, as a consequence of its expansion, at least ten billion light years in extent...The universe needs to be as big as it is in order to evove just a single carbon-based life-form."

See also the Supplementary Note on the Direct Measurement of Astronomical Distances, where we note that there exist direct measurements of distances on the order of billions of light years.


The Silent Speech          Direct Measurement of Astronomical Distances
Direct measurements of distance rely on the use of geometry.

Parallax. Until recently, the direct measurement of the distances to stars and other astronomical bodies has been limited to a few stars that are a few hundred or thousand light years away, using parallax[FOOTNOTE. Parallax methods have been in use since antiquity.  The first parallax measurement to a star was by Bessel in 1838.] measurements.

The nearest "star"  is Alpha Centauri, actually a system of three stars that appears in the Southern Hemisphere as a single star, near to the Southern Cross. Of the three, the nearest star is Proxima Centauri, and the other two form a binary system that are separated by a distance about equal to the distance between the planet Uranus and the Sun. The nearest star is 4.22 light years away, and the binary pair is 4.35 light years away. If the precise location of these stars is measured when the earth is on opposite sides of its orbit, the difference in the angle (about 1.5 seconds of arc) determines the distance.  [The formula is: tan(p) = 1/d (AU units where 1 AU is the distance of the Earth to the Sun)]. This direct method can measure distances up to a few thousand light years - between 1989 and 1993 the satellite Hipparcos measured the parallax of about 120,000 stars in this direct way.

Radio astronomy measures emissions at very low frequencies, with wavelengths on the order of 10 km (AM radio wavelengths are on the order of 10 to 100 km). The detection of these emissions requires very long baseline arrays (VLBAs). There are two remarkable examples of direct distance measurements in radio astronomy. In 1999 radio astronomers reported a direct measurement of 23.5 million light-years to a galaxy (NGC 4258 = Messier 106) in the Big Bear constellation[FOOTNOTE Radio Astronomers Set New Standard for Accurate Cosmic Distance Measurement Press Release June 1, 1999 by the National Radio Astronomy Observatory using the Very Long Baseline Array (VLBA). This is a system of 10 radio antennas that are placed between Hawaii and St. Croix, a distance of about 5,000 miles and controlled by an operations center in Socorro, NM. This array had the greatest resolving power of any astronomical telescope in operation at the time.]. The radio emitters were masers which orbit a black hole in the center of this galaxy. ??The baseline for parallax measurement in this case is the diameter of the masers' orbits -- about 2 light years. The black hole has a mass equal to 39 million suns.

Here is a summary of triangulation methods.by Dr. David H. Rogstad of Reasons Organization.

Gravitational lensing. A quasar is a distant object that emits radio waves that vary slowly and randomly in time -- perhaps a few percent change in a month. 

In 1979 Astronomers first discovered a double quasar - Q0957+561. The double quasar seemed to come from a single source -- the radio signals of the two quasars matched if one was delayed by 417 ± 3 days. It appears that some massive object (perhaps a black hole) between earth and the quasar bends the signal path so that two signals arrive with a 6 arc second separation. This bending is called gravitational lensing. It is something predicted by Einstein's general theory of relativity.

A straightforward geometry calculation shows that the distance to the source of the quasar(s) must be at least D = 2.7 billion light years away (actual distance 9.1 billion light years)[FOOTNOTE Walsh, Dennis, Carswell, Robert F., and Weymann, Raymond J. 1979, Nature, 279, 381.  They used the Kitt Peak National Observatory 2.1 meter telescope in Arizona. ]. These double quasars are very rare - about 20 have been found so far.
 
Gravitational Lensing Geometry
Figure ?
Gravitational Lensing Calculation of minimum distance to Quasar Q0957+561


Gravitational lensing is a direct prediction of Einstein's Theory of General Relativity. The discovery of this double quasar was the first positive evidence of gravitational lensing. Since that time a number of other instances have been discovered. Most of these involve the light from distant galaxies that are lensed by a massive object in or near to the line of sight to the galaxy. If the lens is compact (a massive black hole, for example) and directly in line of sight then an Einstein ring may result. The first Einstein ring (B1938+666) was discovered in 1998 by a radio telescope array. The diameter of the ring was 0.8 arcseconds.


I DON'T THINK THE FOLLOWING YIELD A DISTANCE MEASUREMENT. NEED TIME DELAY.
If the gravitational lense is exactly in line of sight then the lensed object appears as a ring called the Einstein Ring. The first Einstein Ring (B1938+666) was discovered by an array of radio telescopes in 1998. The diameter of the ring is 0.8 arcsec leading to a minimum distance of ???. The actual distance is ???.  In 2005 the Einstein Ring FORJ0332-3557 was discovered with a 270° arc and radius of 1.75 arcsec. The lense is reported as 7BY and the distant object is 11 BY away based on a redshift of 3.77.

Double Einstein Ring A double Einstein Ring (SDSSJ0946+1006) was observed in 2007 by the Hubble telescope. The inner ring is from a galaxy  7 billion light years distant and the outer ring is from a galaxy 11 Billion light years distant. The lens is 3 billion light years away.


^n22 B&T p. 2 "Many a philosopher has argued against the ultimate importance of life in the Universe by pointing out how little life there appears to be compared with the enormity of space and the multitude of distant galaxies. But the Big Bang cosmological picture shows this up as too simplistic a judgement."

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REFERENCES

[B&T] Barrow, John D. and Tipler, Frank J., The Anthropic Cosmological Principle (1986)

[Coyne] George V. Coyne and Michael Heller, A Comprehensible Universe: The Interplay of Science and Theology, Springer, 2008 (Searchable). This book might have been an extended commentary on the Silent Voice.

Michael J. Denton, Nature’s Destiny: How the Laws of Biology Reveal Purpose in the Universe, Free Press, 1998

F. Hoyle, D. N. F. Dunbar, W. A. Wenzel, and W. Whaling, Phys. Rev. 92, 1095 (1953).

[B2FH] Geoffrey Burbidge, Margaret Burbidge, William Fowler and Fred Hoyle, Synthesis of the Elements in Stars, Reviews of Modern Physics 29 (1957) p547-650. See Wikipedia article.

Heinz Oberhummer, Attila Csótó and Helmut Schattl, Fine-Tuning Carbon-Based Life in the Universe by the Triple-Alpha Process in Red Giants. Published in The Future of the Universe and the Future of our Civilization: Proceedings. Edited by V. Burdyuzha and G.S. Khozin. Singapore, World Scientific, 2000. p. 197.       Abstract: Stellar model calculations for a low-mass, intermediate-mass and massive star using the different triple-alpha reaction rates obtained with different strengths of the N-N interaction have been performed. Even with a change of 0.4% in the strength of N-N force, carbon-based life appears to be impossible, since all the stars then would produce either almost solely carbon or oxygen, but could not produce both elements.

Fred Hoyle, The Universe: Past and Present Reflections (1981)
Simon Mitton, Conflict in the Cosmos: Fred Hoyle, A Life in Science (2005):
An excellent presentation of the remarkable fine-tuning involved in the production of the elements is found in the  Reasonable Faith presentations:  Big Bang Theory and the Incredibly Precise Design of the Universe   and Big Bang and Beyond. The latter presentation includes notes on the "stellar mystery" of helium fusion, Hoyle's "Wild Guess" and the problem of achieving a balance between carbon and oxygen production (slides 26-33).


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Revised February, 2011