The following two pages are reproduced from the autobiographical "Home is Where the Wind Blows" by Fred Hoyle, with kind permission from University Science Books.
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Chapter18
An Unknown Level in Carbon-12
THE PREDICTION in early 1953 of the existence of a hitherto unknown level at an excitation of about 7.65 million electron volts (7.65 MeV) in the nucleus of the common isotope of carbon, carbon-12 (commonly written 12C), has achieved some notice in recent years on account of its being an early application of what is known nowadays as the anthropic principle. Indeed, it is sometimes referred to as the only, predictive application yet made of the anthropic principle. In this chapter, I will explain how, as an outcome of another lucky chain of accidents, the prediction came about.
The anthropic principle is a curious notion that appears to be clear to some people but not to others, as often is the case with concepts to which the word principle is applied. No one can quarrel with the statement that the physical properties of the universe must be consistent with our own existence, a statement so obvious as hardly to justify the term principle, one might think. Nevertheless, this trite observation can be made to do some work, as the 12C story showed. Application of it to cosmology has some predictive possibilities. Thus, in evolving cosmologies, human life could not have existed in earlier times, when the temperature everywhere was too high, nor will it exist in later times, when all dwarf stars, such as the Sun, will have burned out. These two requirements set the epoch of our existence as between about 10 million years and 30 billion years after the Universe started in a big bang. If one believes in the big bang, this is not a negligible deduction. In other forms of cosmology not of the big-bang type, galaxies can be of variable ages - some old, some young.
The anthropic principle requires us to live in a galaxy that is old enough for the evolution of life to have led to our existence. Should this require us to live in an exceptionally old galaxy, then that is where we must be, regardless of the comparative rarity of exceptionally old galaxies. Probabilities do not arise in such a case, as they would for a randomly chosen observer.
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More subtle issues appear when the existence of life is seen to depend crucially on a fine tuning of the laws of physics themselves, in the sense that it is not hard to imagine minor changes in the laws that would have made life impossible. Thus, we are faced with several alternatives. Either our existence is a freakish accident, or the laws of physics are not invariant. Either the Universe is more complex than we think, in that variations of the laws are realized (in which case we happen to pick out the particular choices that are suited to our existence), or the Universe is teleological, with the laws deliberately arranged by some agent to permit our existence. The latter view is, of course, common to most religions, but it were better for a scientist to have a millstone hung around his neck than that he should admit to such a belief - yea, verily. If he does so, his papers will be rejected, he will receive no financial assistance in his work, the publishers of his books will receive threatening letters, and his children will be waylaid on their way home from school. As well might he seek to pass through the eye of a needle, for to hold such a view is the greatest possible scientific heresy. On the other hand, it is possible to hold the inverse view (and even to win plaudits by doing so) - namely, that it is our existence that requires the laws to be the way they are. Stated this way round, you have what is called the strong anthropic principle. Our existence dictates how the Universe shall be, a fine ego-boosting point of view on which you may travel, fare paid, to conferences all over the world.
A balanced person will be surprised to hear that a respectable argument can be given in support of this seemingly outrageous point of view. It concerns the phenomenon of the condensation of the wave function in quantum mechanics. It is possible to set up a physical either/or kind of experiment without difficulty. A radioactive atom either decays in a specified time or it does not. If it does, the decay products are used to trigger a camera, and a picture is taken of the House of Commons in session. If it does not, the absence of decay products triggers a different camera, and a picture is taken of St. Paul’s Cathedral on Easter Sunday. So, inevitably, some picture is taken, and the question is, How do we discover if it is the House of Commons or St. Paul's? Not by calculation - absolutely not.
Any attempt to fiddle the calculations to yield a definite prediction results in abysmal contradictions. Calculation can only assign relative probabilities to the two possible results of the experiment. The widely accepted answer to the problem, given in my youth by what was called the Copenhagen school of quantum mechanics, associated particularly with Niels Bohr and Werner Heisenberg, was that decision is made in the matter by the experimental equipment, the circumstances of the triggers, the electronic storage devices, and the cameras. Schrödinger differed, however, arguing (in what came to be called the "Schrödinger cat experiment")
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Binding Energy
28Nickel62 has the highest binding energy per nucleon. 26iron56 has the lowest mass per nucleon and is the most efficiently bound. 26iron56 and 28nickel58, having an even number of protons and neutrons, are more favoured during nucleosynthesis than 27cobalt59, the third classical ferromagnetic element, with its odd number of protons. Cobalt is at the peak of binding energy per nucleon for elements with an odd number of protons.
It is perhaps not surprising that there is a peak in the binding energy per nucleon curve. In many systems where there are number of competing forces there will be position where these will balance each other. The question I would like an answer to is why iron and nickel are at the peak. Many models, not necessarily mutually exclusive, have been proposed for the structure of the nucleus, but I do not think we have a sufficient understanding yet to answer this question.
Ferromagnetism
The phenomenon is fairly well understood and explained by the way the electrons are arranged in their orbits. There are other ferromagnetic elements than iron, nickel and cobalt. A ferromagnetic alloy can be made from non-ferromagnetic elements e.g. Heusler alloys from manganese and copper.
The first set of transition elements, scandium to zinc, is made by filling the 3d electron orbitals. The orderly filling of the shell is disrupted at chromium and copper, sandwiching manganese, iron, cobalt and nickel in-between. I am not sure if anyone can fully and rigorously explain this behavior. It is interesting that Heusler alloys are made with the two "outside" elements of the iron,cobalt and nickel sandwich.
The transition metals are listed in order: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper and zinc.
Lagrange Points L4 and L5
Created by Neil J. Cornish for WMAP Education and Outreach 1998
The stability analysis around L4 and L5 yields something of a surprise. While these points correspond to local maxima of the generalised potential - which usually implies a state of unstable equilibrium - they are in fact stable. Their stability is due to the coriolis force. Initially a mass situated near L4 or L5 will tend to slide down the potential, but as it does so it picks up speed and the coriolis force kicks in, sending it into an orbit around the Lagrange point. The effect is analogous to how a hurricane forms on the surface of the earth: as air rushes into a low pressure system it begins to rotate because of the coriolis force and a stable vortex is formed.
182Hafnium/182Tungsten decay
The decay chain is 182Hafniun --> 182Tantalum --> 182Tungsten --> 178Hafnium. The half-life of the first decay reaction is ~9x106 years, that of the second is ~14 days and that of the third is ~8x1018 years. So the ratio 182Hafnium/182Tungsten provides a means of determining the likely ages of meteorites and Earth material.
Conclusion
Here we have two phenomena relating to atomic structure - one concerned with the arrangement of protons and neutrons in the nucleus and the other with the arrangement of electrons in their orbitals. I propose that we do not have sufficient knowledge of the atom and its component parts to rule out the possibility that that the structure of the nucleus could influence the arrangement of electrons in their orbits, or vice versa. Regardless, the net result is the production of the most abundant metal in the cosmos with properties that help to provide an environment where life can form and endure.