The proton - neutron mass difference & fine-tuning

The proton - neutron mass difference & fine-tuning 1

The neutron is slightly heavier than the proton by about 1.293 MeV If the mass of the neutron were increased by another 1.4 MeV—that is, by one part in 700 of its actual mass of about 938 MeV—then one of the key steps by which stars burn their hydrogen to helium could not occur. The main process by which hydrogen is burnt to helium in stars is a proton-proton collision, in which two protons form a coupled system, the diproton while flashing past each other. During that time, the two-proton system can undergo a decay via the weak force to form a deuteron, which is a nucleus containing one proton and one neutron. The conversion takes place by the emission of a positron and an electron neutrino:

p+p → deuteron+positron+electron neutrino+0.42 MeV of energy.

About 1.0 MeV more energy is then released by positron/electron annihilation, making a total energy release of 1.42 MeV. 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 the proton and neutron in the deuteron is approximately 2.2 MeV, thus overcompensating by about 1 MeV for the greater mass of the neutron. If the neutron’s mass were increased by around 1.42 MeV, however, then neither this reaction nor any other reaction leading to deuterium could proceed, because those reactions would become endothermic instead of exothermic (that is, they would absorb energy instead of producing it). Since it is only via the production of deuterium that hydrogen can be burnt to helium, it follows that, if the mass of the neutron were increased beyond 1.4 MeV, stars could not exist. On the other hand, a small decrease in the neutron mass of around 0.5 to 0.7 MeV would result in nearly equal numbers of protons and neutrons in the early stages of the Big Bang, since neutrons would move from being energetically disfavored to being energetically favored. The protons and neutrons would then combine to form deuterium and tritium, which would in turn fuse via the strong force to form 4He, resulting in an almost all-helium universe. This would have severe life-inhibiting consequences, since helium stars have a lifetime of at most 300 million years and are much less stable than hydrogen-burning stars, thus providing much less time and stability for the evolution of beings of comparable intelligence to ourselves.

A decrease in the neutron mass beyond 0.8 MeV, however, would result in neutrons becoming energetically favored, along with free protons being converted to neutrons, and hence an initially all-neutron universe. Contrary to what Barrow and Tipler argue, however, it is unclear to what extent, if any, this would have life-inhibiting effects. So the above argument establishes a one-sided fine-tuning of the neutron/ proton mass difference. Since the maximum life-permitting mass difference is 1. 4 MeV, and the mass of the neutron is in the order of 1,000 MeV, by the formula presented in note 5 the degree of one-sided fine-tuning relative to the neutron mass is at least one part in 700, or less, given that the lower bound of the total theoretically possible range of variation in the neutron mass, R, is in the order of the neutron mass itself—that is, 1,000 MeV. Another plausible lower bound of the theoretically possible range R is given by the range of quark masses. According to the Standard Model of particle physics, the proton is composed of two up quarks and one down quark (uud), whereas the neutron is composed of one up quark and two down quarks (udd). Thus we could define the neutron and proton in terms of their quark constituents. The reason the neutron is heavier than the proton is that the down quark has a mass of l0MeV, which is 4 MeV more than the mass of the up quark. This overcompensates by about 1.3 MeV for the 2.7 MeV contribution of the electric charge of the proton to its mass. (Most of the mass of the proton and neutron, however, is due to gluon exchange between the quarks (Hogan 1999: section IIIA).) The quark masses range from 6 MeV for the up quark to 180,000 MeV for the top quark. Thus a 1.42 MeV increase in the neutron mass —which would correspond to a 1.42 MeV increase in the down quark mass—is only a mere one part in 126,000 of the total range of quark masses, resulting in a lower bound for one-sided fine-tuning of about one part in 126,000 of the range of quark masses. Furthermore, since the down quark mass must be greater than zero, its total life-permitting range is 0 to 11.4 MeV, providing a total two-sided fine-tuning of about one part in 18,000 of the range of quark masses.

The atom itself is a bundle of numerous very fortunate "coincidences".  Within the atom, the neutron is just slightly more massive than the proton, which means that free neutrons can decay and turn into protons. A free neutron is unstable and will decay into a proton in about 10 minutes - if not within a nucleus. If the proton were larger and had a tendency to decay rather than the neutron, the very structure of the universe would be impossible. A free proton has a half-life of ~10^33  years. 2

1. GOD AND DESIGN The teleological argument and modern science, page 186
2. http://www.detectingdesign.com/detectingdesign.html

The Stability of the Proton

https://reasonandscience.catsboard.com/t2537-the-proton-neutron-mass-difference-fine-tuning#6513

Not all types of particles are stable; many of them “decay” or disintegrate after a while into other types of particles. The “half-life” tells how long this typically takes. For example, neutrons have a half-life of about ten minutes. Neutrons usually disintegrate into a proton, an electron, and an anti-neutrino. Fortunately, protons are stable. (At least, it is known that they last much longer than the age of the universe.) That is fortunate because the nucleus of ordinary hydrogen (hydrogen 1) consists of just a proton, and if that were unstable, there would be no ordinary hydrogen in the world. And without hydrogen, there would be no water, no organic molecules, no hydrogen-burning stars like the Sun—in short no possibility of life as we know it. Why isn’t the instability of the neutron equally disastrous, considering that all nuclei except hydrogen 1 contain neutrons? And, for that matter, how can it be that there are neutrons in all those nuclei, like carbon 12 and oxygen 16, if neutrons do last only ten minutes or so? The answer is that whereas an isolated neutron is unstable, a neutron can be quite stable if it is inside an atomic nucleus with other neutrons and protons. The reason for this has to do with a subtle quantum effect called “Fermi energy.” The fact that isolated neutrons are unstable does not matter very much, since isolated neutrons, having no electric charge, do not bind together with electrons to form atoms.
The interesting question is how the universe avoids the disaster—not for it but for us—of protons being unstable. Why is the proton stable and the neutron unstable? The key is that the neutron is a tiny bit heavier than the proton. The mass of a neutron is 939.565 MeV, while the mass of a proton is 938.272 MeV— a difference of only a seventh of a percent. Relativity theory tells us that mass is the same thing as energy, so this is the same as saying that a neutron has a little bit more energy packed inside it than a proton does. Because of that, a neutron can decay into a proton plus some other particles, and release energy in the process. But a proton cannot decay into a neutron because it does not have enough energy to do so. Because a neutron has a little more energy inside it than a proton, extra energy would have to be supplied to a proton to get it to turn into a neutron. If things were the other way, if the proton’s mass were even a fraction of a percent larger than the neutron’s, then neutrons would be stable and protons would be unstable, which means that there would be no hydrogen 1, and we would not be here.
The reason for the happy fact that protons are slightly lighter than neutrons has to do with the properties of the quarks out of which protons and neutrons are made. The u quark is slightly lighter than the d quark, and a proton has a preponderance of u quarks in it, while the neutron has a preponderance of d quarks. However, nobody yet knows why u quarks are lighter than d quarks rather than the other way around.
God, Luck, or a multiverse. There is no question - God is the best answer.

1. Modern Physics and Ancient Faith STEPHEN M. BARR page 124