Wednesday, May 11, 2011

Calculating the Hoyle state of carbon-12, from first principles
Calculation of the "Hoyle nucleus" of Carbon
The Hoyle nucleus is that state of the carbon nucleus with very similar energy to three helium nuclei. The similarity allows fusion in stars to create carbon readily, and from there, the rest of the larger atomic nuclei up to iron. (Nuclei bigger than iron only get formed when stars explode.)
Sir Fred Hoyle considered the similarity to be an example of cosmic fine tuning when he first predicted it in 1954, without which we would not exist. As this article points out, this was pretty much an assertion for the last 50 years, but now we are in a position to actually calculate whether it does depend sensitively on other physical constants, and if so, what they are and over what range.
Several years ago, I asked an astrophysicist if the resonance was necessary or just helpful. In our normal model of stellar evolution, as the star ages and uses up hydrogen in the core, it starts fusing helium nuclei. Two He-4 nuclei form an unstable Beryllium-8, but if another He-4 comes along they can form a stable C-12. Everyone agrees the process proceeds faster because of the resonance. My question was - if the resonance didn't exist, would a similar amount of carbon be formed, just later, when the core had reached a higher temperature?
If you do have to wait, that by itself would knock down the total amount of carbon in the universe, since some smaller stars would never reach that temperature without the help of fusing larger and larger nuclei. Their fusion process would stall, and they would evolve towards red dwarfdom, as small stars do in the real physics of our universe. But we are the result of large stars blowing up, so I discount this effect in deciding whether there would be enough carbon for life.
On the other hand, you can't just tinker with the resonance without explaining why it would be different than it is. Changing whatever underlies the resonance of C-12 and 3 He-4 would necessarily change other things as well, perhaps in the direction of producing Carbon by a different route through a new or strengthened alernative resonance. This is of course never considered by fine tuning enthusiasts. Now we are starting to put the tools together to test these ideas
The main article is available for free at the above address.
The money quote, at least for Hoyle worshipers:

          We note the 17 MeV reduction in the ground state binding energy and 12 MeV reduction for the Hoyle state while less than half as much binding correction for the spin-2 state. This degree of freedom in the energy spectrum suggests that at least some fine-tuning of parameters is needed to set the Hoyle state energy near the 8Be-alpha threshold. It would be very interesting to understand which fundamental parameters in nature control this fine-tuning. At the most fundamental level there are only a few such parameters, one of the most interesting being the masses of the up and down quarks.
Emboldenation by mois.

OK, I hope you don't think I'm being a dick about this for going on for so long, but I think this is important.
Why? Because of Hoyle's approach and use of anthropic reasoning, and the subsequent uptake by fine tuning anti-science folk, that's why. Besides, this is damn hard for me to understand, and I'd like to make sure I do understand it.
So, Hoyle says this resonance _must_ exist because we exist, and further, this shows that the universe has been mightily fine tuned.
So what is this amazing fine tuning?
Look at table 1 in the paper.
Be-8 + He-4 = -84.8 MeV
C-12 = -92.16 MeV
Difference? 8%
As a result of which, 4 out of 10,000 Be-8 and He-4 collisions go on to become C-12.
I gotta say, I'm way disappointed. I thought I was going to hear that the difference was only 0.000000...8%, not 8%, and that C-12 production was 9,000 out of 10,000, not 4.
What is Hoyle saying? If it was 8.00001%, then the successful collision rate would crash to 4 in a billion? If it was 7.9999999% the rate would shoot up to 4 out of 10? That in one case no star could synthesize carbon, and in the other the universe would be awash in carbon? I've never heard a numerical guess like that attributed to him, just that the existence of the resonance convinced him a deity exists.
The paper does speculate that the resonance depends on the ratio of the mass of the up and down quarks. Cool, that is a step towards understanding it. But if we imagine the fine tuning in these terms, changing this ratio will also change the energy levels of Be-8 and He-4. A resonance at one energy level might disappear, while one at another level will be created. Hoyle didn't work all that out, did he? No, he just asserted that changing some unknown parameter by any amount would wreck the known resonance, and nothing would replace it.
That is not science.

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