- On the Fine?]Structure Spectrum of Hydrogen (1991) [Updated 6 years ago]
- An Essay on Discrete Foundations for Physics (1989) [Updated 6 years ago]

- On the Fine?]Structure Spectrum of Hydrogen
(1991) [Updated 6 years ago]
Using our discrete relativistic combinatorial bit?]string theory of physics in the context of the hydrogen spectrum, we calculate our first two approximations for the fine?]structure constant as ??(1) = 1/137 and ??(2) = [1 − 1/(30 ?~ 127)]/137 = 1/137.035 967 4 ?c ; we can then derive the Sommerfeld formula.

- An Essay on Discrete Foundations for Physics (1989) [Updated 6 years ago]
*We*ordering operator^{ }base our theory of physics and cosmology on the five^{ }principles of finiteness, discreteness, finite computability, absolute nonuniqueness, and strict^{ }construction. Our modeling methodology starts from the current practice of^{ }physics, constructs a self-consistent representation based on the^{ }calculus*and provides rules of correspondence that allow us to*^{ }test the theory by experiment. We use program universe to^{ }construct a growing collection of bit strings whose initial portions^{ }(labels) provide the quantum numbers that are conserved in the^{ }events defined by the construction. The labels are followed by^{ }content strings,*which are used to construct event-based finite aned*^{ }discrete coordinates. On general grounds such a theory has a^{ }limiting velocity, and positions and velocities do not commute. We^{ }therefore reconcile quantum mechanics with relativity at an appropriately fundamental^{ }stage in the construction. We show that 1) events in^{ }different coordinate systems are connected by the appropriate finite and^{ }discrete version of the Lorentz transformation, 2) three-momentum is conserved^{ }in events, and 3) this conservation law is the same^{ }as the requirement that different paths can ?interfere? only when^{ }they differ by an integral number of de Broglie wavelengths.^{ }The labels are organized into the four levels of the^{ }combinatorial hierarchy*characterized by the cumulative cardinals 3, 10, 137, 2*c/e^{127}+ 136 1.7 ? 10^{38}. We justify^{ }the identification of the last two cardinals as a first^{ }approximation to^{2}*and*c/Gm = (M_{planck}/m_{p})^{2}*respectively. We show that the*1/ = 137.035 967 4 ?.^{ }quantum numbers associated with the first three levels can be^{ }rigorously identified with the quantum numbers of the first generation^{ }of the standard model of quarks and leptons, with color^{ }confinement and a first approximation to weak-electromagnetic unification. Our cosmology^{ }provides an event horizon, a zero-velocity frame for the background^{ }radiation, a fireball time of about 3.5 ? 10^{6}years,^{ }about the right amount of visible matter, and 12.7 times^{ }as much dark matter. A preliminary calculation of the fine^{ }structure spectrum of hydrogen gives the Sommerfeld formula and a^{ }correction to our first approximation for the fine structure constant,^{ }which leads to*We can now justify the earlier*m^{ }results_{p}/m_{e}= 1836.151 497 ?*and*m_{}/m_{e}= 274.*Our estimate of the weak angle*^{ }is*s**i**n*^{2}_{Weak}= 1/4*and of the fermi constant*G_{F}? m = 1 / (256)^{2}.*Our finite*. Eteris paribus, caveat lector^{ }particle number rela- tivistic scattering theory should allow us to^{ }systematically extend these results