(atoms minus their electrons) collide, pretty much simultaneously. A helium nucleus comprises two protons and two neutrons. So three of them combined must yield a nucleus with six protons and six neutrons. This is carbon.
In the dense environment of a red giant star, nuclei collide relatively often. But it’s not terribly likely that just as two of them come together, a third joins the party. So the process has to happen in two stages. First, two helium nuclei collide and fuse, making beryllium. Then another helium nucleus fuses with that. Unfortunately for this theory, the form of beryllium involved falls apart after one tenth of one quadrillionth of a second. The chance that a helium nucleus can hit such a rapidly vanishing target is much too small.
Hoyle knew this, and he also knew that there is a loophole. If the combined energies of beryllium and helium just happen to be very close to an energy level of carbon, then the nuclei can fuse much faster and the sums work out fine. Such a near-coincidence of energies is called a resonance. No suitable resonance was then known, but Hoyle insisted that it had to be there. Otherwise Hoyle wouldn’t be there, being made from quite a lot of carbon. That led him to predict an unknown energy level of carbon around 7.7 MeV (million electronvolts, a convenient unit of energy for nuclear reactions). By the mid-1960s the experimentalist William Fowler had found such a resonance at 7.65 MeV, within 1% of Hoyle’s prediction. Hoyle presented this discovery as a triumph of ‘anthropic’ reasoning: deducing something about the universe from the existence of humans. Without that finely tuned resonance, we wouldn’t be here.
It sounds impressive, and it is when told that way. But already we see a tendency to exaggerate. For a start, the link to humans is unnecessary and irrelevant. What matters is the amount of carbon in the universe, not what it can make. We do not need to appeal to our own existence to know how much carbon there is. In The Fallacy of Fine-Tuning, Victor Stenger refers to an investigation of the history of Hoyle’s prediction by the philosopher Helge Kragh. Hoyle did not initially link the resonance to the existence of life, let alone human life. The anthropic connection was not made for nearly thirty years. ‘It is misleading to label the prediction of the 7.65 MeV state [as] anthropic, or to use it as an example of the predictive power of the anthropic principle,’ Kragh wrote. Pan narrans has been at work again, and the human love of narrativium has rewritten the historical story.
Next: it’s simply not true that ‘without that finely tuned resonance, we wouldn’t be here.’ The 7.65 MeV figure for the energy of the resonance is not what’s required for carbon-based life to exist. It is the energy needed to produce the amount of carbon actually observed. Change the energy, and carbon would still be produced … but in different quantities. Not as different as you might think: Mario Livio and co-workers calculate that any value between 7.596 MeV and 7.716 MeV would generate much the same amount of carbon. Anything up to 7.933 MeV would generate enough carbon for carbon-based life to exist. Moreover, if the energy level dropped below 7.596 MeV, more carbon would be produced, not less. The lowest energy that would produce enough carbon for life is the ground state of the carbon atom, the lowest possible energy it can have, which is 7.337 MeV. A finely tuned resonance is not necessary.
In any case, resonances are ten a penny, because atomic nuclei have lots of energy levels. Finding one in the appropriate range isn’t really very surprising.
A more serious objection arises from the calculation itself. When factors that Hoyle neglected are taken into account, the combined energies of helium and beryllium turn out to be significantly higher than the figure he used. What happens to this ‘extra’ energy?
It helps to keep the red giant burning.
The star burns at precisely the temperature required to compensate for the energy difference. This looks like an even more impressive coincidence. Forget carbon: something far deeper is going on. If the basic constants of the universe were different, then the precisely fine-tuned resonance would disappear, the red giant would fizzle out and there wouldn’t be enough carbon to make Fred Hoyle, Adam and Eve, you or the cat.
However, this argument, too, is fallacious. Changing the fundamental constants affects the red giant star as well