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GOD: new evidence

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The mass of the proton and the neutron as an example of fine tuning for life

The difference between the mass of the proton and the mass of the neutron has to be fine tuned for life to be possible. If the mass of a neutron was a seventh of a percent more than it is, stars like most of those we can see would not exist. If the neutron mass was 0.085% less than it is, the Universe would be full of neutrons and nothing else. There is no reason why protons and neutrons should have the masses they do.

1. Background science

Measuring mass

Nuclear scientists measure the mass of protons and electrons in units of millions of electron volts (MeV). If this is unfamiliar, it’s important not to be distracted by it. MeV are convenient units. We could just as well use any other units – kilogrammes, say, or even ounces. It doesn’t matter. The argument would be just the same. Strictly speaking, an electron volt is a unit of energy, but as Einstein famously showed, mass and energy are equivalent, through E = mc2, so it is not a problem to use energy units to measure mass (or vice versa if you are so inclined).

Basic textbooks sometimes say that protons and neutrons have the same mass. This is almost true – but not quite, and the difference is important:

So the difference between them is small: a neutron is about 1.29 MeV heavier than a proton. There is no obvious reason why protons and neutrons should have just these masses, but if they were even slightly different, we wouldn’t be here.

The number of protons and neutrons in the Universe was more or less settled in the first few minutes of the Big Bang.  A hundred protons were created for every sixteen  neutrons.

Because of this, there is now more hydrogen than helium – about three times as much by mass, or twelve times as much if you count atoms. This is important for at least a couple of reasons:

‘There would be no hydrogen available for key biological solvents like water and carbonic acid, and all the stars would be helium-burning and hence short-lived. Almost certainly, helium stars would not have the long-lived nuclear burning phase necessary to encourage the gradual evolution of biological life-forms in planetary systems.’ (Barrow & Tipler 1986:399)

2. If the neutron had a bit more mas there would be no hydrogen burning in stars

The key reaction by which hydrogen ‘burns’ in stars involves two protons colliding, and producing a deuteron -  a particle made of a proton and a neutron. This reaction produces 1.42 MeV of energy. If the mass of a neutron was one seven hundredth more than it is (that is, a seventh of a percent), this reaction would need energy poured into it, rather than producing energy. This means that stars would not be able to burn hydrogen. Stars like most of those we can see today would not exist.

what happens when protons collide

What happens when protons collide inside stars

The first step in forming helium in stars involves two protons combining together. One of the protons changes into a neutron, forming a deuteron. A positron, a neutrino, and a small amount of energy (0.42 MeV) are also released in this reaction.  The positron collides with an electron, annihilating each other in a flash of gamma rays, freeing up another 1.0 MeV of energy. So the total amount of energy released in this reaction is 1.42 MeV.

When a proton and neutron combine like this, they have what is called ‘binding energy.’  Because of this, the mass of a proton and neutron together is different from the masses of the proton and neutron separately.

It may sound a bit strange, but this binding energy is negative. (You have to put some energy into the system to separate them.) So a proton-neutron combination (a deuteron) has less energy than the proton and neutron separately.

If the neutron’s mass was 1.42 MeV more than it is (0.15 %), this reaction wouldn’t happen at all – it would need energy to make it go, rather than producing energy. Deuterons are a key step in burning hydrogen to helium. Without them, hydrogen would not burn, and there would be no long-lived stars.

‘This process can occur because the deuteron is less massive than two protons, even though the neutron itself is more massive. The reason is that the binding energy of the strong force between proton and neutron in the deuteron is approximately 2.2 MeV, thus overcompensating by about 1 MeV for the greater mass of the neutron.’ (Collins)

3. If the neutron had a bit less mass the universe would be full of black holes and neutron stars

If the neutron mass was 0.8 MeV less than it is, all the protons would have been converted to neutrons in the Big Bang. The Universe would be full of neutrons and nothing else.  We would not be here.

Barrow and Tipler say that a small decrease in the mass of the neutron would make life impossible. If the difference between the neutron and proton masses was less than the mass of the electron, all the protons in the Universe would have been converted to neutrons.  Such a Universe wouldn’t have any chemistry: it would just have neutron stars and black holes:*

‘Without electrostatic forces to support them, solid bodies would collapse rapidly into neutron stars (if smaller than about 3 [solar masses]) or black holes. Thus, the coincidence that allows protons to partake in nuclear reactions in the early universe also prevents them decaying by weak interactions. It also, of course, prevents the 75% of the Universe which emerges from nucelosynthesis in the form of protons from simply decaying away into neutrons. If that were to happen no atoms would ever have formed and we would not be here to know it.’ (Barrow and Tipler 1986:400)

4. In between

If the decrease was a bit less than 0.8 MeV (Collins says around 0.5 to 0.7 MeV), roughly equal numbers of protons and neutrons would have been formed in the Big Bang.  All the protons and neutrons would have combined into helium, leaving no hydrogen.  As described above, this makes complicated life highly unlikely.

5. Conclusion

The mass of the neutron is fine tuned with respect to the mass of the proton, to within a seventh of a percent, or perhaps less.

If the difference between the mass of the proton and the neutron was a tiny bit more or less than it actually is, the Universe would be very different, and it would not support any kind of life.

We don’t (yet) know of any reason why the neutron should have just the mass it does. It’s possible that in future we will discover some fundamental reason for this. That will not alter the fact that its mass has to be remarkably tuned if people like us are to exist in the universe.

* Robin Collins is not convinced that a lower neutron mass is fatal. He points out that it is possible for two neutrons to convert into a deuteron (a proton and a neutron) and an electron.

‘Since these sorts of conversions appear to be allowed,  the only effects we can immediately deduce that a moderate decrease of the neutron mass would have are that stars would burn very differently and that stable nuclei, including hydrogen, would shift towards having a higher proportion of neutrons than we presently find. I know of no current well-developed argument, however, that these effects would inhibit the existence of intelligent life. This is an area that needs further exploration.’

However, this does not alter the basic argument, because of the need for what Collins calls ‘one-sided’ fine tuning for the mass of the neutron.

David Couchman MA, M.Sc, M.Min, May 2011


Barrow, J D and Tipler, F J, 1986, Oxford: Oxford University Press, ‘The Anthropic Cosmological Principle.’

Collins, R, ‘Evidence for fine tuning’ undated. http://home.messiah.edu/~rcollins/Fine-tuning/The%20Evidence%20for%20Fine-tuning.rtf

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‘If the rate of expansion one second after the Big Bang had been smaller by even one part in a hundred thousand million million, the Universe would have recollapsed before it ever reached its present state.’ - Professor Stephen Hawking