物理学中隐藏的一条数学公理

A Mathematical Axiom Hiding In Physics

本文首先介绍了Gdel的不完全性定理和不可判定的概念。其次指出在二阶的标准分析模型M中,普遍存在不可判定的积分公式,如A_6:integral from n=0 to =∞sintdt=1等。第三,本文介绍了物理学Coulomb散射中的通用的数学公式(3,1):integral from ((d^3x/|x|)e^(-iq·x)=4π/|q|~2并证明了A_6和(3,1)的等价性。第四,根据Gdel的不完全性定理和不可判定的概念,本文认为(3,1),或等价地数学公式A_6可以作为物理学中使用的局部的数学公理。

Ⅰ、The paper introduces the notion of undecidability and incompleteness theorem of Godel. Ⅱ, The paper points out that there are almost everywhere undecidable integral formulae in the second-order model M of standard analysis,for example the fomula . Ⅲ、The paper introduces a mathematical formula(3,1) : ,which is commonly used in the Coulomb settering in physics,and proves that A6is equivalent to(3,1). Ⅳ ,According to Godel's incompleteness theorem and the notion of undecidability,the paper claims that the formula(3,1) ,or equivalently ,the formula A6 may be undertaken to be a local mathematical axiom in physics.