一种超越新修订 SI 的基本单位新二元系统
综合物理
2019-08-06 v1 高能物理 - 唯象学
摘要
我们提出了一种基本单位的新系统,它包含并超越了当前 SI 的重新定义,其通过同时选取 c = ℏ = 1 c=\hbar=1 c = ℏ = 1 实现。通过固定 c = c ∘ c=c_\circ c = c ∘ m/s = 1、ℏ = ℏ ∘ \hbar=\hbar_\circ ℏ = ℏ ∘ Js = 1 以及 μ ∘ ‾ = μ ∘ \underline{\mu_\circ}=\mu_\circ μ ∘ = μ ∘ N/A2 ^2 2 = 1,它允许我们将米、焦耳和安培分别定义为等于 (1/299 792 458) s、( 1 / ℏ ∘ = .948... × 10 34 ) s − 1 (1/\hbar_\circ = .948 ... \times \ 10^{34})\ {\rm s}^{-1} ( 1/ ℏ ∘ = .948... × 1 0 34 ) s − 1 和 μ ∘ N = μ ∘ c ∘ / ℏ ∘ s − 1 = 1.890... × 10 18 s − 1 \sqrt{\mu_\circ \rm N}= \sqrt{\mu_\circ c_\circ / \hbar_\circ}\ {\rm s}^{-1}= 1.890...\times 10^{18}\ {\rm s}^{-1} μ ∘ N = μ ∘ c ∘ / ℏ ∘ s − 1 = 1.890... × 1 0 18 s − 1 。该系统同时呈现出 ℏ = c = μ ∘ ‾ = ϵ ∘ ‾ = k = N A = 1 \hbar = c = \underline{\mu_\circ} = \underline{\epsilon_\circ } = k = N_A = 1\, ℏ = c = μ ∘ = ϵ ∘ = k = N A = 1 系统的优势与优雅,其中真空磁导率、介电常数与阻抗均等于 1。所有单位均由自然单位重新标度并正比于 s、s− 1 ^{-1} − 1 、s− 2 ^{-2} − 2 、……或仅为 1,如库仑、欧姆与韦伯,现在为无量纲。库仑等于 μ ∘ c ∘ / ℏ ∘ = 1.890... × 10 18 \sqrt{\mu_\circ c_\circ / \hbar_\circ}= 1.890... \times 10^{18} μ ∘ c ∘ / ℏ ∘ = 1.890... × 1 0 18 ,基本电荷为 e = 1.602... × 10 − 19 C = 4 π α = .3028... e=1.602...\times 10^{-19} {\rm C} = \sqrt{4\pi\alpha}=.3028... e = 1.602... × 1 0 − 19 C = 4 π α = .3028... 。欧姆等于 1 / μ ∘ c ∘ 1/\mu_\circ c_\circ 1/ μ ∘ c ∘ ,从而真空阻抗为 Z ∘ = 376.730... Ω = 1 Z_\circ = 376.730... \Omega =1 Z ∘ = 376.730...Ω = 1 。伏特为 1 / μ ∘ c ∘ ℏ ∘ s − 1 = 5.017... × 10 15 s − 1 1/ \sqrt{{\mu_\circ c_\circ \hbar_\circ}}\ {\rm s}^{-1} = 5.017... \times\ 10^{15}\ {\rm s}^{-1} 1/ μ ∘ c ∘ ℏ ∘ s − 1 = 5.017... × 1 0 15 s − 1 ,特斯拉为 c ∘ c_\circ c ∘ V/m = c ∘ 3 / μ ∘ ℏ ∘ s − 2 = 4.509... × 10 32 s − 2 \sqrt{{c_\circ^3}/{\mu_\circ\hbar_\circ}}\ {\rm s}^{-2} = 4.509... \times 10^{32}\ {\rm s}^{-2} c ∘ 3 / μ ∘ ℏ ∘ s − 2 = 4.509... × 1 0 32 s − 2 。韦伯为 1 / μ ∘ c ∘ ℏ ∘ = 5.017... × 10 15 1/ \sqrt{{\mu_\circ c_\circ \hbar_\circ}} = 5.017... \times 10^{15} 1/ μ ∘ c ∘ ℏ ∘ = 5.017... × 1 0 15 。 K J = 483 597. \ K_J =483\,597. \ K J = 483 597. ... GHz/V = e / π = = e/\pi = = e / π = .09639...,且 R K = 25 812. . . . Ω = 1 / 2 α ≃ 68.518 R_K = 25\,812.\ ...\ \Omega =1/2\alpha\simeq 68.518 R K = 25 812. ... Ω = 1/2 α ≃ 68.518 。也可固定 e e e = 1.602 176 634 × 10 − 19 \times 10^{-19} × 1 0 − 19 C,代价是用 μ ∘ = 4 π × 10 − 7 η 2 \mu_\circ=4\pi\times 10^{-7}\eta^2 μ ∘ = 4 π × 1 0 − 7 η 2 调整库仑与所有电学单位,其中 η 2 , ∝ α \eta^2, \propto \alpha η 2 , ∝ α ,非常接近于 1。
引用
@article{arxiv.1908.01584,
title = {A New Dual System For The Fundamental Units, including and going beyond the newly revised SI},
author = {Pierre Fayet},
journal= {arXiv preprint arXiv:1908.01584},
year = {2019}
}
备注
26 pages, 2 tables