Toward the Unification of Physics and Number Theory

K. Irwin
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引用次数: 6

Abstract

This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure. A geometric analogue to the primality test is introduced: when [Formula: see text] is prime, it divides [Formula: see text] for all [Formula: see text]. The geometric form provokes a novel hypothesis about the distribution of prime-simplexes that, if solved, may lead to a proof of the Riemann hypothesis. Specifically, if a geometric algorithm predicting the number of prime simplexes within any bound [Formula: see text]-simplex or associated [Formula: see text] lattice is discovered, a deep understanding of the error factor of the prime number theorem would be realized — the error factor corresponding to the distribution of the non-trivial zeta zeros, which might be the mysterious link between physics and the Riemann hypothesis [D. Schumayer and D. A. W. Hutchinson, Colloquium: Physics of the Riemann hypothesis, Rev. Mod. Phys. 83 (2011) 307]. It suggests how quantum gravity and particle physicists might benefit from a simplex-integer-based quasicrystal code formalism. An argument is put forth that the unifying idea between number theory and physics is code theory, where reality is information theoretic and 3-simplex integers form physically realistic aperiodic dynamic patterns from which space, time and particles emerge from the evolution of the code syntax.
走向物理学和数论的统一
本文介绍了单纯整数的概念,并说明了相对于数字,它们是隐式表达整数及其集合论子结构信息的最强大的数字符号。引入了一个几何上类似于素数检验的方法:当[公式:见文]是素数时,它将[公式:见文]除以所有[公式:见文]。这种几何形式引发了一个关于素数单形分布的新假设,如果这个假设得到解决,可能会导致黎曼假设的证明。具体地说,如果发现了一种几何算法,可以预测任何边界[公式:见文]-单纯形或相关的[公式:见文]格内的素数单纯形的数量,那么将实现对素数定理的误差因子的深刻理解-与非平凡zeta零的分布相对应的误差因子,这可能是物理学与黎曼假设之间的神秘联系[D]。舒迈和d.a.w . Hutchinson, Riemann假设的物理讨论,物理学报,83(2011)307。它表明量子引力和粒子物理学家如何从基于简单整数的准晶体编码形式中获益。提出了数论与物理学的统一思想是码理论,其中实在性是信息论,三单纯形整数形成物理上实在的非周期动态模式,空间、时间和粒子从码语法的演化中产生。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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18
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