Fine-tuning fallacies

In Fiddling with “fine-tuning” I discussed the way theologians and philosophers of religion have used claims of fine-tuning of the cosmological constant erroneously. That they have taken the fact that the value of the measured cosmological constant is 120 orders of magnitude different to the value of vacuum energy used to explain it. This has been described as the “worst calculation in physics history.” But never mind, these apologists have just utilised the huge mistake to claim that the cosmological constant is fine-tuned to 1 part in 10¹²⁰! So there god must be responsible.

This is what happens when you use scientific knowledge opportunistically. Like a drunk uses a lamppost – more for support than illumination. Because the problem with the theological approach is that there is no interest in understanding the world around us – just in using science to support any argument they can drag up to “prove” the existence of their particular god.

Mind you, some non-theists also find the fine tuning concept beguiling. And they can also uncritically accept some of the fine-tuning claims that circulate. The idea that many of the physical and cosmological constants in our universe are extremely delicately balanced to values necessary for life to exist. The so-called anthropic principle.

So, Victor Stenger’s new book The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us will be very useful for anyone attempting to check out these arguments by actually considering the science. He describes the physical and cosmological background to the constants, or parameters as he prefers to call them, usually used in fine-tuning arguments. And then he considers, one by one, just how valid – or invalid – the fine-tuning arguments are.

Here I will just deal with two “fine-tuned” constants – the “Hoyle resonance” for carbon nuclei and the “nuclear efficiency.” I think they illustrate two common mistakes made in estimating the degree of fine-tuning.

Hoyle resonance

This refers to the 1953 prediction of astronomer Fred Hoyle that the reactions necessary for the nucleosynthesis of carbon in stars would “not occur with sufficient probability unless that probability was boosted by the presence of an excited nuclear state of C¹² at a very specific energy. Hoyle proposed that this previously unknown state must exist at about 7.7 MeV. The existence of such a state was quickly confirmed experimentally.”

Although Hoyle did not connect this resonance with the existence of life (and therefore an example of the anthropic principle) it has often been quoted by theists as a miraculous example of fine-tuning. And they like to quote Hoyle himself:

“A commonsense interpretation of the facts suggests that a superintellect 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.”

But Stenger points out that many physicists question how fine-tuned this excited resonance state of carbon really is. He demonstrates this in the following figure from his book.

Here (a) shows two energy levels: (1) the amount by which the total rest energy of Be⁸ + He⁴ exceeds that of the C¹² nucleus, which is 7.3367 MeV; (2) the excited state of C¹² predicted by Hoyle and observed at 7.656 MeV. On this scale, the ground state of C¹² is zero.

And (b) shows the range of values this excited state could assume and still produce that same amount of carbon in the universe. That is 7.596 – 7.716 Mev. So this excited state is not as fine-tuned as often claimed. The “miracle” is disappearing.

But the fine-tuning really evaporates when we acknowledge that while the existence of life like ours requires the presence of carbon, it does not necessarily require the exact amount of carbon that exists in our universe.  As (c) shows, an excited state anywhere from 7.933 Mev down to near the minimum energy would produce adequate carbon!

In this case the fine-tuning argument has been fallacious because recent work of the required values has been ignored. And it has been unnecessarily assumed that life requires exactly the same amount of carbon as present in the current universe.

Nuclear efficiency

Martin Rees describes “nuclear efficiency” in his book Just Six Numbers: The Deep Forces That Shape The Universe. It refers to the fact that in the synthesis of helium from protons and neutron in stars the mass of the original particles and final nuclear differs – 0.007 of the mass is converted into energy. He defines this as the “nuclear efficiency,” Є, and the value of this depends on the forces holding nuclei together determines how long stars can exist. Rees concludes that “any universe with complex chemistry requires Є to be in
the range 0.006-0.008.”

“If the nuclear ‘glue’ were weaker, so that Є were 0.006 rather than 0.007, a proton could not be bonded to a neutron and deuterium would not be stable. Then the path to helium formation would be closed off. We would have a simple universe composed of hydrogen, whose atom consists of one
proton orbited by a single electron, and no  chemistry. Stars could still form in such a universe (if everything else were kept unchanged) but they would have no nuclear fuel. They would deflate and cool, ending up as dead remnants. There would be no explosions to spray the debris back into space so
that new stars could form from it, and no elements would exist that could ever form rocky planets.”

“But we couldn’t have existed if Є had been more than 0.008, because no hydrogen would have survived from the Big Bang. In our actual universe, two protons repel each other so strongly that the nuclear ‘strong interaction’ force can’t bind them together without the aid of one or two neutrons (which add to the nuclear ‘glue’, but, being uncharged, exert no extra electrical repulsion). If Є were to have been 0.008, then two protons would have been able to bind directly together. This would
have happened readily in the early universe, so that no hydrogen would remain to provide the fuel in ordinary stars, and water could never have existed.”

But these estimates assume that other physical constant remain constant. Stenger argues that this is unrealistic because if the value of one parameter could be randomly selected during formation of a universe, so could the values of others.

In particular he considers the effect of just varying one other constant – the electromagnetic strength α. The figure below demonstrates the situation.

If α remains fixed at its current value of 1/137 then Є must take a value between 0.006 and 0.008. Higher and all hydrogen would be converted to helium. Lower and no nuclei would form. But as shown in the figure – if  α varies between 1/191 and 1/107 then Є can vary between 0.004 and >0.01.

So, in this case the fine-tuning fallacy has relied on the unwarranted assumption that the value of only one parameter is varied at a time in the calculations,. In reality this is unlikely.

This particular fallacy will be common to most of the physical and cosmological constants that are usually quoted as examples of fine-tuning by religious apologists.

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