Rick's Critique of the Cosmic Coincidences: Chapter 10

Constraints On Particle Masses Arising From Nuclear And Atomic Stability

In Chapter 9 we considered the constraints on the strength of the nuclear and electrostatic forces arising from the requirement that the nuclei of atoms should be stable. In this Chapter we shall consider what constraints apply to the masses of the nucleons and the electron for nuclei to be stable, and for solids composed of atoms to display rigidity. We shall also consider whether the stability of atoms places any further constraint on the strength of the electrostatic force.

We shall see why the instability of the neutron, and the fact that the neutron mass exceeds that of the proton, are essential in a complex universe. This is because Mn > Mp + me is required to avoid all atoms being unstable to electron capture. This same condition ensures that free neutrons are unstable in a universe with weak interactions.

In this universe, the small size of the mass deficit, Mn - (Mp + me) = 0.782 MeV, compared with the typical binding energy difference between nuclei with Z differing by 1, allows neutrons to become stabilised within a nucleus. The neutron is in a nuclear potential well too deep for it to climb out of by decaying.

To avoid instability of all atoms to electrons capture, but to ensure the stability of key elements against beta decay (or sufficiently long half-lives), the mass deficit is required to lie between zero and approximately 15 times its value in this universe. Choosing to vary the neutron mass and hold the proton and electron masses fixed, we find that there is a strong Type B coincidence. The neutron mass is required to lie between 0.999167 times and ~1.012 times its value in this universe.

The stability of the electron orbital structure of atoms, which is responsible for their chemical properties, follows from the precepts of basic physical theory (quantum mechanics). Thus, in contrast to the stability of nuclei, the stability of the atomic electron structure does not depend upon any universal constants taking special values.

The phenomenon of rigidity in solids is sometimes claimed in the literature to require that the electron mass is small compared with the nucleon mass. We derive an expression for the quantum uncertainty of the position of an atom in a solid in terms of the atomic number, Z, the atomic mass, A, and the electron and proton masses, me and Mp. Assuming equality of the electron and proton masses, me = Mp, we find that for sodium and beyond (Z > 10), the uncertainty in the atom's position is less than 0.3 as a fraction of the atomic size. We believe that this may be sufficiently small to give rise to rigidity in solids. We conclude that the oft-claimed requirement that me/Mp << 1 in order to permit rigidity appears to have been over-stated.

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Water Discovered in Moon Shadow: In November 2009 the LCROSS mission crashed a large impactor into a permanently shadowed crater near the Moon's South Pole. A plume of dust rose that was visible to the satellite, although hard to discern from Earth. The plume is shown above in visible light. The results of a preliminary chemical analysis gave a clear indication that the dust plume contained water. Such water is of importance not only for understanding the history of the Moon, but as a possible reservoir for future astronauts trying to live on the Moon for long periods. The source of the lunar water is now a topic of debate. Possible origins include many small meteorites, a comet, or primordial moon soil. [Credit: LCROSS,NASA]