*An Essay on Discrete Foundations for Physics*

Scientific Paper | |
---|---|

Title | An Essay on Discrete Foundations for Physics |

Author(s) | H Pierre Noyes |

Keywords | finite, discrete foundations: relativity, elementary quantum particles, cosmology, dark matter |

Published | 1989 |

Journal | Physics Essays |

Volume | 2 |

Number | 1 |

No. of pages | 25 |

Pages | 76-99 |

## Abstract

*We ^{ }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* ordering operator

^{ }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*<img border="0" align="bottom" alt="[barred aitch]" src="http://physicsessays.aip.org/stockgif3/barh.gif" />c/e

^{127}+ 136 <img border="0" align="bottom" alt="~=" src="http://physicsessays.aip.org/stockgif3/sime.gif" /> 1.7 ? 10^{38}. We justify^{ }the identification of the last two cardinals as a first^{ }approximation to^{2}

*and*<img border="0" align="bottom" alt="[barred aitch]" src="http://physicsessays.aip.org/stockgif3/barh.gif" />c/Gm<img border="0" align="middle" alt="

_{p}

^{2}" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A0%3A28&t=a&d=a" /> = (M

_{planck}/m

_{p})

^{2}

*respectively. We show that the*1/<img border="0" align="bottom" alt="alpha" src="http://physicsessays.aip.org/stockgif3/agr.gif" /> = 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

_{<img border="0" align="bottom" alt="pi" src="http://physicsessays.aip.org/stockgif3/pgr-script.gif" />}/m

_{e}<img border="0" align="bottom" alt="<~" src="http://physicsessays.aip.org/stockgif3/lsim.gif" /> = 274.

*Our estimate of the weak angle*

^{ }is*s'*

**i'**n^{2}<img border="0" align="bottom" alt="theta" src="http://physicsessays.aip.org/stockgif3/thgr.gif" />

_{Weak}= 1/4

*and of the fermi constant*G

_{F}? m<img border="0" align="middle" alt="

_{p}

^{2}" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A0%3A28&t=a&d=a" /> = 1 / <img border="0" align="middle" alt="sqrt(2)" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A1%3A28&t=a&d=a" />(256)

^{2}.

*Our finite*. Eteris paribus, caveat lector

^{ }particle number rela- tivistic scattering theory should allow us to^{ }systematically extend these results