View source for An Essay on Discrete Foundations for Physics

{{Infobox paper
| title = An Essay on Discrete Foundations for Physics
| author = [[H Pierre Noyes]]
| keywords = [[finite]], [[discrete foundations: relativity]], [[elementary quantum particles]], [[cosmology]], [[dark matter]]
| published = 1989
| journal = [[Physics Essays]]
| volume = [[2]]
| number = [[1]]
| num_pages = 25
| pages = 76-99
}}

==Abstract==

<em>We<sup><span style="font-size: x-small;">&nbsp;</span></sup>base our theory of physics and cosmology on the five<sup><span style="font-size: x-small;">&nbsp;</span></sup>principles of finiteness, discreteness, finite computability, absolute nonuniqueness, and strict<sup><span style="font-size: x-small;">&nbsp;</span></sup>construction. Our modeling methodology starts from the current practice of<sup><span style="font-size: x-small;">&nbsp;</span></sup>physics, constructs a self-consistent representation based on the</em> ordering operator<sup><span style="font-size: x-small;">&nbsp;</span></sup>calculus ''and provides rules of correspondence that allow us to<sup><span style="font-size: x-small;">&nbsp;</span></sup>test the theory by experiment. We use <span style="font-size: smaller;"><span style="font-size: x-small;">program universe</span></span> to<sup><span style="font-size: x-small;">&nbsp;</span></sup>construct a growing collection of bit strings whose initial portions<sup><span style="font-size: x-small;">&nbsp;</span></sup>(labels) provide the quantum numbers that are conserved in the<sup><span style="font-size: x-small;">&nbsp;</span></sup>events defined by the construction. The labels are followed by''<sup><span style="font-size: x-small;">&nbsp;</span></sup>content strings, ''which are used to construct event-based finite aned<sup><span style="font-size: x-small;">&nbsp;</span></sup>discrete coordinates. On general grounds such a theory has a<sup><span style="font-size: x-small;">&nbsp;</span></sup>limiting velocity, and positions and velocities do not commute. We<sup><span style="font-size: x-small;">&nbsp;</span></sup>therefore reconcile quantum mechanics with relativity at an appropriately fundamental<sup><span style="font-size: x-small;">&nbsp;</span></sup>stage in the construction. We show that 1) events in<sup><span style="font-size: x-small;">&nbsp;</span></sup>different coordinate systems are connected by the appropriate finite and<sup><span style="font-size: x-small;">&nbsp;</span></sup>discrete version of the Lorentz transformation, 2) three-momentum is conserved<sup><span style="font-size: x-small;">&nbsp;</span></sup>in events, and 3) this conservation law is the same<sup><span style="font-size: x-small;">&nbsp;</span></sup>as the requirement that different paths can ?interfere? only when<sup><span style="font-size: x-small;">&nbsp;</span></sup>they differ by an integral number of de Broglie wavelengths.<sup><span style="font-size: x-small;">&nbsp;</span></sup>The labels are organized into the four levels of the''<sup><span style="font-size: x-small;">&nbsp;</span></sup>combinatorial hierarchy ''characterized by the cumulative cardinals 3, 10, 137, 2<sup><span style="font-size: x-small;">127</span></sup> + 136 <img border="0" align="bottom" alt="~=" src="http://physicsessays.aip.org/stockgif3/sime.gif" /> 1.7 ? 10<sup><span style="font-size: x-small;">38</span></sup>. We justify<sup><span style="font-size: x-small;">&nbsp;</span></sup>the identification of the last two cardinals as a first<sup><span style="font-size: x-small;">&nbsp;</span></sup>approximation to'' <img border="0" align="bottom" alt="[barred aitch]" src="http://physicsessays.aip.org/stockgif3/barh.gif" />c/e<sup><span style="font-size: x-small;">2</span></sup> ''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="<sub>p</sub><sup>2</sup>" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /> = (M<sub><span style="font-size: x-small;">planck</span></sub>/m<sub><span style="font-size: x-small;">p</span></sub>)<sup><span style="font-size: x-small;">2</span></sup> ''respectively. We show that the<sup><span style="font-size: x-small;">&nbsp;</span></sup>quantum numbers associated with the first three levels can be<sup><span style="font-size: x-small;">&nbsp;</span></sup>rigorously identified with the quantum numbers of the first generation<sup><span style="font-size: x-small;">&nbsp;</span></sup>of the standard model of quarks and leptons, with color<sup><span style="font-size: x-small;">&nbsp;</span></sup>confinement and a first approximation to weak-electromagnetic unification. Our cosmology<sup><span style="font-size: x-small;">&nbsp;</span></sup>provides an event horizon, a zero-velocity frame for the background<sup><span style="font-size: x-small;">&nbsp;</span></sup>radiation, a fireball time of about 3.5 ? 10<sup><span style="font-size: x-small;">6</span></sup> years,<sup><span style="font-size: x-small;">&nbsp;</span></sup>about the right amount of visible matter, and 12.7 times<sup><span style="font-size: x-small;">&nbsp;</span></sup>as much dark matter. A preliminary calculation of the fine<sup><span style="font-size: x-small;">&nbsp;</span></sup>structure spectrum of hydrogen gives the Sommerfeld formula and a<sup><span style="font-size: x-small;">&nbsp;</span></sup>correction to our first approximation for the fine structure constant,<sup><span style="font-size: x-small;">&nbsp;</span></sup>which leads to'' 1/<img border="0" align="bottom" alt="alpha" src="http://physicsessays.aip.org/stockgif3/agr.gif" /> = 137.035 967 4 ?. ''We can now justify the earlier<sup><span style="font-size: x-small;">&nbsp;</span></sup>results'' m<sub><span style="font-size: x-small;">p</span></sub>/m<sub><span style="font-size: x-small;">e</span></sub> = 1836.151 497 ? ''and'' m<sub><img border="0" align="bottom" alt="pi" src="http://physicsessays.aip.org/stockgif3/pgr-script.gif" /></sub>/m<sub><span style="font-size: x-small;">e</span></sub> <img border="0" align="bottom" alt="<~" src="http://physicsessays.aip.org/stockgif3/lsim.gif" /> = 274. ''Our estimate of the weak angle<sup><span style="font-size: x-small;">&nbsp;</span></sup>is'' ''s''''i''''n''<sup><span style="font-size: x-small;">2</span></sup> <img border="0" align="bottom" alt="theta" src="http://physicsessays.aip.org/stockgif3/thgr.gif" /><sub><span style="font-size: x-small;">Weak</span></sub> = 1/4 ''and of the fermi constant'' G<sub><span style="font-size: x-small;">F</span></sub> ? m<img border="0" align="middle" alt="<sub>p</sub><sup>2</sup>" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A0%3A28&amp;t=a&amp;d=a" /> = 1 / <img border="0" align="middle" alt="sqrt(2)" src="http://physicsessays.aip.org/servlet/GetImg?key=PHESEM000002000001000076000001%3A0%3A1%3A28&amp;t=a&amp;d=a" />(256)<sup><span style="font-size: x-small;">2</span></sup>. ''Our finite<sup><span style="font-size: x-small;">&nbsp;</span></sup>particle number rela- tivistic scattering theory should allow us to<sup><span style="font-size: x-small;">&nbsp;</span></sup>systematically extend these results''. Eteris paribus, caveat lector

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