ELECTRON-NEUTRON MASS RATIO

The mass of the electron is 1/1837th the mass of a neutron. Big deal, right? Actually it IS a big deal.

Suppose we call the difference between the two, which is (1837)^-1, B, and the fine structure constant, A, which equals to e^2~(137)^-1. Quoting from Barrow and Tipler's THE COSMIC ANTHROPIC PRINCIPLE.

"Although the Exclusion Orinciple provides for the overall stability of solid bodies it is not responsible for the comparitively fixed properties of ions within solids. Consider a lattice of ions; it is more realistic to think of the electrons moving through it as a sea amid the islands of fixed irons within solids. Every iron behaves as an independent harmonic oscillater with mass =~mN(mass of Neutron) and vibrates with a frequency (designated as W). If an iron is displaced a distance X from its equilibrium position that it will gain a potential energy ~0.5mN W^2 X^2 which must become AaO^-1 when x is of order aO since the bonds then break. For these ionic oscillations the mean-square velocity is ~2W^2 X^2 and so the mean-square momentum is ~AmN(AmE)^3

"The Uncertainty Principle ensures that the momentum resisting localization is ~^-1 and the uncertainty of the electron's position, (which we'll call U) will be of order aO so the relative fluctuation in the ion location relative to that of the passing electrons in the lattice is

( The square root of (/U^2) ) ~B^1/4 << 1

"and so the nuclei are accurately and rigidly located in the solid. The uncertainy in the position of the atom is ~B^1/4 of the inter-atomic seperation. If ions tried to move further afield than this they would push the electrons into such a small region that their momentum would grow to resist localization and force them back. The dependence in the above formula reveals the key role that B(the difference between the mass of the electron and the neutron) plays in Nature. It ensures that nuclei have well-defined, relatively invariant, locations. When a substance is heated, the positional uncertainty of the irons rises. If atoms stray ~aO from their locations their materials will melt or, if molecules stray, disassociate. If one tried to build up ordered materials built upon the strong nuclear force one would not have this important property since neutrons and protons have similar masses so neither are located with precision in nuclei and from the outside nuclei appear fairly spherically symmetric. It appears that well-ordered structures rely heavily on the small volume of B. The specific application to DNA replicative fidelity was highlighted in..."

And then Barrow and Tipler quote another work...

"It might as well be that a whole set of perfectly reasonable S-matrices exist for any choice of these mE(Mass of the electron)/mN(Mass of the Neutron) parameters, all of them yielding rather weird, self-consistent universes, all but one of them existing only in the sense of Plato. Our universe would be determined by the fact that only the choice mN/mE=1837 guarentees that there are large chain molecules of the right size and kinds to make biological phenomena possible. It could be for instance that the slightest variation in these parameters would change critically the size and lenth of the rings in the DNA helix as to invalidate its typical way of replicating itself. In this sense we could say that mN/mE=1837 just because we are here. Other universe do exist as well but nobody is around to see them. I am describing this somewhat paradoxical mechanism just in order to warn that we may expect quite exotic criteria to come into play when fixing the fundamental constants." Regge, ATTI DEL COVERGNO MENDELEEVIANO, Acad. del Sci. de Torino, p. 398.

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