The anthropic diproton

When it comes to particle physics, anthropic arguments usually take the form of “if the laws of nature were any different, we wouldn’t be here”. Here are a couple of references to this argument as far as the strong nuclear force is concerned. The strong force is what holds nuclei together despite the fact that they have lots of protons in them which, all having the same electric charge, naturally repel one another. What if the strong force had a different strength?

Of the nuclei with two nucleons in them, proton plus neutron is the nucleus of deuterium, or heavy hydrogen. Deuterium is stable. There isn’t much of it around because it isn’t made in stars (or rather, if made, it is rapidly cooked up into something else) so all the deuterium we have is left over from the Big Bang.

A proton plus a proton makes a diproton. Or rather, it doesn’t, because the electric repulsion between the protons is stronger than the strong force, so when two protons come close together they sheer away from each other instead of sticking.

(A neutron plus a neutron makes a dineutron. Dineutrons don’t exist either, because the strong force isn’t enough to hold them together so they tend to drift apart. I shan’t say anything more about them because they only add complications to the story without changing its shape).

If the strong force were stronger than it is, it would hold the protons in a diproton together despite their electrical repulsion. How much stronger? Barrow and Tipler (1988) say that an increase of 3.4% is enough. MacDonald and Mullan, quote Barrow in an earlier paper as saying 13%.

What if the strong force were that much stronger? What would the consequences be? Barrow and Tipler say, and they have been quoted endlessly in scientific papers, that the result would be that during the Big Bang all the protons would collide and stick together to form diprotons, which are, chemically, nuclei of helium-2. There would therefore be no hydrogen left. Water is made of hydrogen and oxygen and organic chemistry needs carbon and hydrogen. Stars are made of hydrogen: if a star were made of helium it would be hot and very short-lived. So, as Barrow and Tipler put it (p.322), ‘If the di-proton existed we would not!’.

There is one snag. None of this is true. Just because the diproton is stable doesn’t mean that it gets made, or, having been made, survives.

R.A.W. Bradford, in The Effect of Hypothetical Diproton Stability on the Universe (J. Astrophys. Astr. (2009) 30, 119–131), analyses what would actually happen in the Big Bang. It turns out that the hypothetical reaction ‘proton + proton = diproton’ is very slow, so that before it has time to happen the universe has expanded and cooled down so that there isn’t enough energy for the proton-proton reaction to happen. The reaction is frozen out before it can get going.

Moreover, in the first second of the Big Bang, when the universe is hot enough for a proton-proton reaction, there is so much heat and light around that it instantly frazzles any diprotons that may have formed and blasts them to bits.

The conclusion is that Barrow and TIpler’s vision of everything turning into diprotons is wrong. Even if diprotons are stable, the Big Bang will not make them.

The Big Bang is not the only place where nuclear reactions happen. The other is the interiors of stars. Unlike the Big Bang, stars last rather longer than a second. They are hot and they are dense and they are made of hydrogen – that is, they are full of protons. And it turns out that if the diproton were to exist, it would be made. At the temperatures and pressures inside a star, the reaction would be efficient and inevitable, all the hydrogen would be consumed, and the heat produced would blow the star apart.

Yet even this catastrophe is not all it seems. A stronger strong force would mean that a star as hot and dense as the Sun could not live long; but it would also mean that slightly cooler and less dense stars would have an extra source of heat to keep them hot and keep them from collapsing in on themselves. Simulating a star is beyond our capacity to do in any detail, but Bradford does broad calculations, checking, for instance, that a star of the right density and temperature would not produce more heat than can escape it, and so would not get hotter and hotter without limit. He is careful not to claim too much – merely that with a stronger strong force stable, long lived stars are not necessarily impossible. Of course the world would be different from ours (there’d be more deuterium, for a start) but the differences would not be such as to exclude the possibility of life.

In the arXiv paper Big Bang Nucleosynthesis: The Strong Nuclear Force meets the Weak Anthropic Principle, J. MacDonald and D.J. Mullan present detailed calculations showing how the synthesis of various nuclei in the Big Bang would be affected by a strong force 10%, 20%, 30%,… stronger than the one we have. Their conclusion is ‘Our main result is that the existence of bound diproton and dineutron nuclei does not necessarily lead to com- plete conversion of hydrogen to helium in the big bang. Instead there are parameter ranges for which significant amounts of hydrogen remain… [T]he final hydrogen abundance is greater than 50% of the standard BBN [Big Bang nucleosynthesis] value for increases in the strong force coupling constant less than about 50%. Anthropic limits on the strong force strength from BBN are indeed weak. ‘